Analysis of Fatigue Life in Two Weld Class Systems

Transcription

1 Analysis of Fatigue Life in Two Weld Class Systems Master Thesis in Solid Mechanics Niklas Karlsson, Per-Henrik Lenander LITH-IKP-EX--5/3--SE November 5 i

2 Master Thesis in Solid Mechanics Niklas Karlsson, Per-Henrik Lenander Analysis of Fatigue Life in Two Weld Class Systems LITH-IKP-EX--5/3--SE Department of Mechanical Engineering Linköping University SE Linköping, Sweden Printed in Sweden by UniTryck, Linköping, 5 ii

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5 Abstract In current welding standards, there is a lack of connection between acceptance limits and fatigue life. In an ideal standard there should be a clear and consistent connection, assuring that a certain welding class always implies a certain fatigue life of the welded joint. Volvo Construction Equipment is currently involved in reworking the company welding standard STD55,5, aiming at introducing such a fatigue connection in the standard. The objective of this thesis work is to provide the basic data for reworking the standard, i.e. to calculate fatigue lives for the defect types in the current welding standard. To extend the study, the corresponding ISO standard ISO587 is studied as well. For the fatigue life calculations, FEM (finite element method) and LEFM (linear elastic fracture mechanics) are used. A few other methods are briefly described and quantitatively compared. The results show a very scattered acceptance limit dependence for the fatigue lives in the different defect cases. This implies that the acceptance limits in most cases need to be revised. Furthermore, some cases should be removed from the standard and some cases from the ISO standard could be included in the Volvo standard. v

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7 Preface This thesis has been performed as the final assignment for the examination as Master of Science at Linköping University. The thesis work was initiated by and carried out at Volvo Articulated Haulers in Braås, Sweden, between June and November of 5. The intention is to provide a foundation for further work on reviewing the company s welding standard. Finite element modelling and calculation of the fatigue lives of all applicable defect types included in the Volvo standard, as well as in the corresponding ISO standard, has been performed. Applied theories and methods are thoroughly described in theory chapters, but the reader is assumed to have basic knowledge in solid mechanics. We would like to thank the following people at Volvo Articulated Haulers in Braås, who have all contributed to our thesis work: Our supervisor M.Sc. Bertil Jonsson, for invaluable support; weld auditor Stefan Stålberg, for hands-on experience on the shop-floor; Quality engineer Stig Malmqvist, for sharing his expertise on welding standards; everybody at Helfordonsgruppen, for a memorable time. We would also like to thank our examiner Prof. Tore Dahlberg at the Division of Solid Mechanics, Department of Mechanical Engineering, Linköping University, for reading and commenting the entire thesis, and our opponents Mr Mats Andersson and Mr Mattias Danielsson for their valuable opinions. Braås in November 5 Niklas Karlsson Per-Henrik Lenander vii

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9 Notations The following constants, functions and variables are used in this thesis. The constants, functions and variables not listed here are explained in the text. Throughout the thesis variables are written in italic and constants in plain text. Variables, functions and symbols A Acceptance limit (in STD55,5) a Crack length C Material parameter C FAT-value in the (Swedish BSK) c Crack length f rk Stress range (in the Swedish BSK) h Acceptance limit (in ISO587) K I Stress intensity factor in mode I K Ic Fracture toughness in mode I K eff Effective stress intensity factor K Stress concentration factor t K I Δ Stress intensity range in mode I Δ K th Threshold value m Slope N n n t t R W z α φ ϕ Q ϕ t Number of Material parameter Number of (in the Swedish BSK) Sheet thickness Radius Sheet width Utilization factor (in the Swedish BSK) Angle Angle Probability factor (in IIW) Thickness factor ν Poisson s ratio σ Stress σ Nominal stress nom σ Geometrical stress geo σ hs Hot spot stress σ Notch stress notch σ Ultimate strength UTS σ FL Fatigue limit σ Y Yield limit Δ σ Stress range τ Shear stress ix

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11 Contents Abstract... v Preface...vii Notations... ix Contents... xi Introduction.... The company.... Background....3 Objectives....4 Procedure Restrictions....5 Outlines of the report... Fatigue life calculation Basic theory on LEFM Loading of cracks Stress intensity factor Paris law Requirements Plane stress versus plane strain Other methods Type of fracture S-N curves The Swedish standard The nominal stress method Example of the nominal stress method..... Comparison with the Swedish standard Problems with interpreting the standard The Hot spot method Example of the Hot spot method..... The effective notch method Example of the notch method Linear Elastic Fracture Mechanics....3 Comparison of methods Advantages with LEFM Disadvantages with LEFM... 3 Procedure and methods Modelling Basic modelling Boundary conditions Influence of boundary conditions Meshing Achieving a meshable model Elements The crack tip The box The centre lines Remaining parts of the model Meshing problems... 3 xi

12 3..8 Convergence Macros Postprocessing How stress intensity factors are calculated in ANSYS Numeric integration Verification of integration method Approximation with upper and lower summations Spline values integrated in Excel Analytical case for an internal crack Crack growth rate Algorithm Discussion about integration limits Comparison with AFGROW Weld auditing Overall on weld auditing Review of previous weld audits Weld audit on a rear frame Profile projector measuring of silicone impressions Comments Compilation of STD55, About the standard Modelling Results... 5 Compilation of ISO About the standard Modelling Results Study of sheet thickness dependence Introduction Studied geometry - STD55,5 Case Requirements Modelling Dimensions Influence of sheet length Results Comments on the results The thickness effect Effect of absolute acceptance limits Sheet length The bending case Conclusions Theory and calculations on the thickness effect Conclusions and discussion Conclusions General discussion Proposals for revising the standards Primary proposal for guidlines Secondary proposal for guidelines Other proposals for STD55, Other proposals for ISO xii

13 8.4 Discussion for STD55, Cases which could be added or removed from STD55, Recommendations for achieving proposals for STD55, Discussion for ISO Cases which could be added or removed from ISO Recommendations for achieving proposals for ISO Recommendations for further studies References Appendix A Appendix B diagrams for STD55, Appendix C diagrams for ISO xiii

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15 Introduction Introduction. The company The thesis work was carried out at Volvo Articulated Haulers in Braås, 3 kilometres northeast of Växjö in southern Sweden. It has recently been merged with Volvo Wheel Loaders into Volvo HLBL (Hauler Loader Business Line), which is a part of Volvo Construction Equipment. In the Braås factory articulated haulers are designed and manufactured. An articulated hauler is most commonly used to transport gravel and rocks in rough terrain during road and building construction, but also other applications are available. Volvo CE markets articulated haulers in a payload range of 5 to 4 tons. In Braås the 5 employees currently produce over machines yearly. There is also a factory situated in Pederneiras, Brazil. Volvo CE has approximately 4% of the world market for articulated haulers.. Background The background of this thesis is the ongoing efforts to review the Volvo company welding standard, STD55,5 []. An important objective of this is to achieve a clear and consistent connection between the acceptance limits in the standard and the fatigue lives of the welded structures. The welding standard contains descriptions of a number of possible weld defects, with limits for the accepted dimensions of the defects for each welding class. In the Volvo standard, four welding classes, A to D, can be used for assigning suitable requirements when designing a weld joint. They also contain additional designations, for example U for fatigue loaded welds. Reworking the welding standard requires a large amount of quantitative data on current fatigue lives to be calculated. This thesis was initiated to produce all this data as well as additional knowledge on fatigue life issues for weld joints..3 Objectives The main objective of the thesis work is to provide life calculations for all interesting defect types, in all welding classes, both for the Volvo standard STD55,5 and for the corresponding ISO standard ISO587 []. The ISO standard is studied in order to take advantage of possibly useful features. The fatigue life data is presented in tables and diagrams, and also thoroughly commented in the text. As an effect of the extensive work on modelling and calculating all cases, a lot of knowledge of various factors affecting the fatigue life has been achieved and will be presented in the report. The influence of sheet thickness and bending loads will be separately investigated. It is the authors objective to provide general recommendations for how the standards could be revised; primarily for the Volvo standard, but since ISO587 has also been thoroughly reviewed, it will be discussed as well..4 Procedure A specified set of interesting defect cases in the two standards are being investigated. For each case the geometry is modelled, stress intensity factors are obtained, and finally the fatigue life is calculated. Previously STD55,5 was called 5.5E. It is now also known as STD8-. Throughout this work the Volvo CE weld standard will be referred to as STD55,5

16 Analysis of Fatigue Life in Two Weld Class Systems For a normal type of defect (a few exceptions exist), the weld joint geometry with a defect of the current type and an initial crack is modelled in the FE programme ANSYS. A macro is then used to let propagate in certain steps into the model. For every crack length the FE problem is solved and the stress intensity factors are calculated. The results are used to determine the stress intensity factor as function of crack length for the particular case. Then this function is used when calculating the fatigue life by use of fracture mechanics (integration of Paris law). The life is assumed to be finished when the crack reaches half the sheet thickness. All steps of the procedure are described thoroughly in the following chapters. In a few cases, especially for some internal defects, special methods for estimating the crack propagation have to be applied. This is further discussed in theory chapters and case descriptions..4. Restrictions It should be emphasised that all results in this report are theoretical, based on the exact conditions that are given in the description of each case. In reality, for example, geometries are never perfect, material quality varies and loading conditions can be very complex. All geometries have been modelled in -D. Thus, the depth direction is not considered, except in the analytical case used for internal cracks. An important restriction is that an initial crack length of. mm is assumed. This means that no life during the crack initiation phase is taken into account. All calculations are performed on mm thick sheets. Applying the results to other thicknesses can not be done without consideration. This is investigated and discussed in Chapter 7. Occasionally it is commented in the report that some issue is not fully investigated (normally due to lack of time or due to the problem lying outside the scope of this work). In these cases conclusions are based on reasonable assumptions, given in the text..5 Outlines of the report In Chapter, basic theory on methods for fatigue life calculation is presented. The focus lies on LEFM (linear elastic fracture mechanics), which is used in this thesis. This is followed by a brief description of a few other methods for fatigue calculations and a comparison of all the methods for two particular cases. The procedure of work used in the thesis is thoroughly described in Chapter 3; modelling, FE analysis and integration of Paris law. An analytical solution method used for internal cracks is also described. An introduction to weld auditing is given in Chapter 4. Chapters 5 and contain the results, descriptions and comments for all cases that have been calculated, for Volvo STD55,5 and for ISO587 respectively. For each of the standards a short introduction is followed by a compilation of the results. Detailed information on each defect type is then presented in a commentary page followed by one data sheet per welding class for the defect. Chapter 7 describes a special study of the sheet thickness effect on the fatigue life, investigating the applicability of the results on different sheet thicknesses.

17 Introduction 3 Conclusions and discussion are presented in Chapter 8. The authors give their recommendations for how the standards could be reworked to obtain a better connection between welding class and fatigue life. A few other important observations and conclusions are also provided, as well as suggestions for further research in the area. Appendix A contains the MATLAB program for calculating stress intensity factors for the analytical case with an elliptical inner crack. In Appendices B and C, tables and diagrams of results for STD55,5 and ISO587 can be found respectively.

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19 Fatigue life calculation 5 Fatigue life calculation This chapter contains theory on LEFM as well as other methods for predicting the fatigue life of a structure subjected to cyclic loading. There is also a comparison between the four methods brought up in this chapter.. Basic theory on LEFM In order to calculate the number of to fracture, Linear Elastic Fracture Mechanics (LEFM) is used. When using LEFM one assumes that the stresses at the crack tip tend to infinity. The theory in this chapter is taken from the reference Failure, Fracture, Fatigue An Introduction [3]... Loading of cracks A crack can be loaded in three different ways, see Figure.. Mode I Mode II Mode III Figure.. Three different modes can be loaded in. In Mode I the crack is opened. Mode I is the most dangerous way to load the crack because this loading case generates the greatest stress intensity of all loading cases. In Mode II and III the crack is sheared in two different planes... Stress intensity factor The stress intensity factor is defined as K I = σ nom f where σ is the nominal stress, a the crack length, and f is a function of geometry and loading. Numerous analytical cases have been derived giving the f-function. Some of them can be found in, for example, Formelsamling i hållfasthetslära, reference [4]. The range of the stress intensity factor can be calculated as Δ K I = K Imax πa K Imin

20 Analysis of Fatigue Life in Two Weld Class Systems where Δ K I = K Imax if K Imin Δ K = K K if K I Imax Imin I min > ΔK I = if K Imax The stress intensity range ΔK I is used in Paris law when calculating the number of to failure, see Equation (.). Stress intensity factors in the same mode can be added by superposition, i.e., K = K K K total A B C I I + I + I + If is loaded in several modes at the same time an effective stress intensity factor, can be calculated as where = + + K eff K I K II κ + 4 K... III κ = 3 4ν for plane strain K eff, 3 ν κ = for plane stress + ν and ν is Poisson s ratio. There are also other suggestions for calculating the effective stress intensity factor...3 Paris law When plotting the logarithm of the crack propagation rate versus the logarithm of the range of the stress intensity factor, the following graph is achieved (Figure.). d log a dn log Δ K I log Δ K th log K Ic Figure.. The crack propagation rate versus the stress intensity range.

21 Fatigue life calculation 7 For Δ K I < ΔK th the crack is so short or the load so small that the crack will not propagate. This implies that Δ K th is a threshold value for crack growth. When K I = K Ic the length of the crack or the nominal stress is so large that fracture will occur momentarily at plain strain. Therefore K Ic is the critical value for crack growth. The linear part of the curve in Figure., between Δ K th and K Ic, is described by Paris law and it is used when calculating the number of to failure for a component. Paris law describes the increment of the crack growth for every cycle, i.e. the crack propagation rate or the increment in length per cycle. The crack propagation rate is a function of the stress intensity range, Δ K I. One has da = C( ΔK ) n I (.) dn where a is the length of the crack, N is the number of, and C and n are material constants. When calculating the life, one has to integrate Paris law, which is a separable differential equation. Since Δ K I is a function of the above mentioned f-function and the f-function usually is very difficult to integrate analytically, a numerical integration technique is normally preferred...4 Requirements The following requirements must be fulfilled in order to use LEFM at plane strain for the final fracture. afinal K Ic.5 t σ Y W a final If these requirements are not fulfilled, a non-linear model or a linearized non-linear model must be used, for example the Irwin approach or the Dugdale model...5 Plane stress versus plane strain In this thesis, plane stress conditions are assumed. This was given as one of the basic conditions for the work. In reality, plane stress or plane strain is determined by the dimensions of the structure. Assuming plane stress conditions gives a more conservative result. The reason why plane stress ( σ zz = ) is used instead of plane strain ( ε zz = ), is that plane stress gives a larger affected zone around the crack, i.e. plane stress is the worst case. It would be correct to assume plane strain conditions since the material is considered to have an infinite depth. Plane stress is present at thin structures.. Other methods Four different methods for calculating the life of welded structures are investigated. The methods are the nominal stress method, the hot spot method, the effective notch method, and

22 8 Analysis of Fatigue Life in Two Weld Class Systems linear elastic fracture mechanics (LEFM). Theory on all methods except LEFM are taken from the reference Svetsutvärdering med FEM [5] All methods in this chapter use data from the International Institute of Welding (IIW) [] for calculating the life of the weld. Data from IIW are based on real welded structures which have been exposed to cyclic loading. Values from these tests have been plotted in an S-N-diagram and a FAT value (FATigue) of the stress for sustaining million has been calculated. This FAT value gives a failure probability of.3% for the weld. Two examples are used when describing the methods. Both are taken from IIW s Fatigue designs for welded joints and components []. The first example is a transverse butt weld, Case 3 (see Figure.3) and the second example is a cruciform joint, Case 43 (see Figure.4). t crack R w Figure.3. Case 3, transverse butt weld. t crack t R.5t h w Figure.4. Case 43, cruciform joint. Both cases are modelled with a transition radius R = mm. This is the smallest radius which can be expected for a normal weld without any subsequent machining [5]. A comparison with the Swedish standard is performed.

23 Fatigue life calculation 9.. Type of fracture In Case 43, with the cruciform joint, could propagate both from the weld toe and from the root. All calculation will be made on cracks propagating from the toe. A toe crack is advantageous because it can more easily be detected with the eye and steps to repair the weld can be taken before fracture. To detect a root crack some kind of instrument, for example ultrasound, must be used. This is a much more time consuming process and a toe crack is therefore favourable... S-N curves In an S-N curve, also known as a Wöhler curve, the logarithm of the stress is plotted versus the logarithm of the number of (see Figure.5). log Δσ log σ UTS slope m Constant amplitude fatigue limit log σ FL slope for varying amplitude log N Figure.5. S-N curve. August Wöhler found that the stress amplitude described the fatigue life better than the maximum stress. The stress amplitude is defined as The stress range is defined as σ a σ max σ = min Δ σ = σ max σ min For welds it is a more appropriate approach to use the stress range for fatigue analysis. For stresses above the ultimate strength, σ, the component fractures immediately while for stresses below the fatigue limit, amplitude loading. σ FL UTS, the component has a theoretical infinite life at constant

24 Analysis of Fatigue Life in Two Weld Class Systems Δ σ is used instead of σ a for welds. The reason for this is that residual stresses close to the yield limit σ Y can be expected in both tension and compression when the metal cools in the weld. This means that if, for example, compressive stresses are applied to a weld where the residual stress is near the yield limit in tension, the weld will endure a positive stress range even though weld is loaded in compression. The root for fillet welds often have negative residual stresses while toe cracks have positive residual stresses, but this may vary. A conservative approach when calculating the fatigue life of welds, is thus to use the stress range Δ σ. When the residual stresses are known, correction factors for compensating the worst case scenario can be found in, for example, []. The correction factors are functions of the stress ratio, which is defined as σmin R = σ max These correction factors are greater than one and are multiplied with the FAT-value in order to receive a longer fatigue life. This may be used for the ground material and to some extent on simple welds. The correction factors are not used for complex structures. To calculate the number of to failure, the straight line with slope m can be used. The equation log N = mlog Δσ + logc gives the life C N = Δσ m C = Δσ The IIW uses a FAT-value of the stress which has been selected so that a certain component should sustain million before failure. This gives the following equation for calculating the number of to failure for a certain range of the stress: m C = FAT m C = Δσ N FAT m m N = Δσ m N m N (.) FAT = Δσ Equation (.) makes it possible to use the tested cases in the IIW s handbook [] to calculate the life of a component...3 The Swedish standard The Swedish BSK [7], [8] (translated: Regulations for Steel Constructions) standard uses the same methods as the IIW standard. The following equation can be found in [7] / 3 3 C rk = C nt = nt f rk f (.3) When Equation (.3) is compared to (.) one can see that it is the same equation, only the notations differ. N is the same as n t, f rk equals Δ σ and C corresponds to the FAT-value.

25 Fatigue life calculation Fatigue lives for a number of cases, as for the IIW standard, have been tested. The major difference is that the Swedish standard also deals with three different welding classes from A to C, where class A gives the longest life. However the descriptions of the classes are vague, without any actual acceptance limits. This makes it difficult to define which class the component belongs to. Therefore the predicted number of may differ a lot, depending on which class is chosen. The BSK also offers the opportunity to predict the fatigue life for varying stress amplitude with a special equation which takes the new slope of the curve into consideration, see Figure.5. The BSK can only be used to evaluate the fatigue life for nominal stresses, i.e. it does not support the hot spot and effective notch methods...4 The nominal stress method In the nominal stress method the nominal stress, σ nom, is used to calculate the life of the welded structure. This is a simple method which usually can be carried out with only handbook results if the geometry is simple. For more complex structures the nominal stress is often hard to find in an FE model. To be able to use the nominal stress method the current structure must be similar to one of the structures available for the method. Misalignments and defects must lie within the weld classes. The nominal stress is defined as the global stress, for example the stress applied far away from the weld in Case 3 and 43, and is mostly perpendicular to the weld. If the structure is not loaded solely in tension, for example when there is a bending moment present, the nominal stress can be extrapolated to the weld toe, see Figure.. σ σ nom x Figure.. The nominal stress, σ nom, extrapolated from the true stress at the surface.

26 Analysis of Fatigue Life in Two Weld Class Systems For evaluation of fatigue life with nominal stress a large number of cases with associated FAT-values are available from the IIW, []...5 Example of the nominal stress method The following first principal stress curve is achieved for Case 3 and 43 (see Figure.7 and.8). Both cases have a transition radius of mm. 8 Nominal method for Case 3 Start of transistion radius End of transistion radius σ nom st principal stress [MPa] x Figure.7. Nominal method for Case 3 in IIW. 3 5 Nominal method for Case 43 Start of transistion radius End of transistion radius σ nom st principal stress [MPa] x Figure.8. Nominal method Case 43 in IIW. Since there is no bending moment here, the nominal stress is equal to the applied stress, i.e. 4 MPa for Case 3 and 8 MPa for Case 43. The FAT-value is 8 MPa for Case 3 respectively 3 MPa for Case 43 but both these values have been multiplied with a factor of

27 Fatigue life calculation 3.3 ( ϕ Q ) to achieve 5% probability of failure instead of.3% which is the case for the FATvalue. The life for the welded structure can be calculated with the modified Equation (.) as which gives a life of 3 ϕq FAT nom = σ nom N (.4) for both Case 3 and Comparison with the Swedish standard If the Swedish BSK [7], [8] standard is used with welding class B on similar cases the fatigue life (Equation.3 with probability factor as in Equation.4) becomes.4 for Case 3 (Case WB in [7]) and.4 for Case 43 (Case 3 WB in [7]) i.e., the fatigue life is about 3% lower than for the IIW. The BSK standard is in general more conservative than IIW. An interesting notation can be made when predicting the life for Case 3. Two cases are available in the BSK; Case, which is used here, deals with rewelded root, while Case does not. The differences between the welds are might seem small for an untrained eye and if Case is used, with the same welding class, the fatigue life becomes.85 instead of the.4 it was for Case, i.e., more than twice the life. This is quite remarkable and describes the difficulties with predicting fatigue life. The achieved results illustrate the problems with predicting the life of welded structures. Even though almost the same fatigue data have been used, interpretation of the data leads to different results due to different approaches...7 Problems with interpreting the standard There is no straightforward description in the Swedish BSK standard of how the standard should be interpreted. This could cause some problems. As an example the fatigue life for Case 43 will be calculated. The easy way is to use the nominal stress at the edges. Then enter f = 8 MPa ( Δ σ ) in Equation.3. This gives for the life rk.4 for Case 3 WB [7], as mentioned above. Another way to calculate the stress range is described below. This method of solving fatigue problems was developed at Bombardier in Kalmar, Sweden, by Per-Olof Danielsson [9] and Anders Lindström. The first step is to make a free-body diagram of the cruciform joint in Case 43, see Figure.9.

28 4 Analysis of Fatigue Life in Two Weld Class Systems σ nom t a τ σ σ τ τ σ nom τ σ Figure.9. Free-body diagram of the cruciform joint in Case 43. Note that the possible misalignment has been disregarded. The following stresses can be derived : : σ σ = τ = τ σ = nom t a = 8 58 MPa 5 When the stresses, σ ( σ rd ) and τ ( τ rd ) are known, these can be used to calculate the utilization factor for multiaxial stress state, which can be calculated with the following equation Δσ Δτ z = +. Δσ, allowed Δτ, allowed Δσ, allowed = 5 MPa ( f rd ) for Case 3 WB [8] and Δ τ, allowed =. Δσ, allowed ( f rvd ). Both Δ σ, allowed and Δ τ, allowed are multiplied with the factor ϕ Q =. 3 for 5% probability of failure, which gives z = The corresponding uniaxial stress can now be calculated as z.8 f rk = C = 5 MPa.. This stress is considerably higher than the nominal stress, σnom = 8 MPa. Now the fatigue life can be calculated as n 3 3 C 5 t = =.5 f rk

29 Fatigue life calculation 5 which is considerably lower than the.4 achieved by use of nominal stress. This is a very conservative way to calculate the life but enlighten the problems which arises when there are almost no instructions given to the user of the standard. If the probability factor, ϕ Q, is inserted when the number of are calculated instead of in the utilization factor, z, as described below n z = f rk z. = C = ϕqc.3 5 t = =.7 f rk the fatigue life becomes almost three times as high. Again this confirms the difficulties with predicting the life...8 The Hot spot method The Hot spot method was originally designed to be used within the offshore industry using measured strains. This made the method applicable in situations were no stresses had been calculated. Later, FE-analysis have been used to calculate the stresses near the weld and predict the life of a given structure. This method can be used where the local geometry disturbs the nominal stress or where no IIW case describes the particular structure. In practice, only one S-N diagram is needed for most welds regardless of the defects in the geometry. Disadvantages with the hot spot method are that only toe cracks can be evaluated. The stress needs to be almost perpendicular to the weld, the density of the mesh must be fine close to the weld toe, and all geometrical defects near the toe must be modelled. Another disadvantage is that the method is not accurate for thick plates. The Hot spot is the toe of the weld. A Hot spot stress or a geometrical stress is extrapolated from points on the st principal stress curve close to the weld (see Figure.).

30 Analysis of Fatigue Life in Two Weld Class Systems σ Extrapolation points σ hs x.4t.t Figure.. The Hot spot stress, σ, linear extrapolation. hs Different equations are used to extrapolate the stress. The following equation describes linear extrapolation. σ σ (.5) nom=.7σ.4t. 7 where σ.4t is the stress at.4 times the thickness from the toe, etc. The first extrapolation point, σ.4t, has been chosen since the stress here is not affected by the weld toe geometry...9 Example of the Hot spot method The same example as for the nominal stress gives the following graphs for Case 3 and 43 (see Figure. and.)..t

31 Fatigue life calculation 7 st principal stress [MPa] Hot spot method for Case 3 Start of transistion radius End of transistion radius σ hs Extrapolation points x Figure.. The hot spot method for Case Hot spot method for Case 43 Start of transistion radius End of transistion radius σ hs Extrapolation points st principal stress [MPa] x Figure.. The hot spot method for Case 43. According to [] the FAT value for flat butt welds is the same as used for the nominal stress method i.e., 8 MPa, while it should be MPa for fillet welds with crack at toe ground. With these FAT values the equation 3 ϕq FAT hs= σ hs N gives a life of.9 for Case 3 and 9. for Case 43. The reason why the fatigue life for Case 43 is remarkably long is that the FAT value is relatively large compared to the extrapolated hot spot stress.

32 8 Analysis of Fatigue Life in Two Weld Class Systems In both examples the st principal stress has decreased to a value close to the nominal stress at the distance.4t from the toe... The effective notch method In the effective notch method the notch is replaced by a radius of mm more than the real case. For a welded condition all notches are modelled with a radius of mm (see Figure.3) implying that the real radius is zero. radii Figure.3. All notches modelled by a radius. The FE-model or a handbook with the radii gives the stress concentration at the notch and the stress is then used to calculate the life in the same way for the nominal stress method as for the hot spot method. The effective notch method is advantageous if root cracks are to be evaluated or if different geometries are to be compared. Disadvantages are that the method has not been verified for thicknesses less than 5 mm and the stress must be perpendicular to the weld. Since the stress must be perpendicular to the weld, the st principal stress is commonly used in order to simulate the worst case scenario... Example of the notch method The maximum stress at the notch in both Case 3 and 43 is given in Figures.4 and.5 respectively.

33 Fatigue life calculation 9 8 Notch method for Case 3 Start of transistion radius End of transistion radius σ notch st principal stress [MPa] x Figure.4. Effective notch stress, σ notch, for Case 3. Notch method for Case Start of transistion radius End of transistion radius σ notch st principal stress [MPa] x Figure.5. Effective notch stress, σ notch, for Case 43. Note that only the toe notch is considered in Case 43. For the effective notch method only one FAT-value is available in [3] for modelled radii of mm. This single FAT-value, 5 MPa, does not treat possible misalignment. The same equation as in previous examples N 3 ϕq FAT notch= σ notch

34 Analysis of Fatigue Life in Two Weld Class Systems gives the life 5.45 for Case 3 and.97 for Case Linear Elastic Fracture Mechanics Theory about LEFM was given in chapter. (Basic Theory). How LEFM is applied for Case 3 and 43 is given in chapter 3 (Procedure and methods)..3 Comparison of methods All four methods described above are compared qualitatively in Figure.. Accuracy Working effort LEFM Notch method Hot spot method Nominal stress method Complexity Figure.. The diagram describes a qualitative comparison of accuracy and model complexity for the four methods. Figure. is taken from Modelling and Fatigue Life Assessment of Complex Fabricated Structures by Marquis and Samuelsson [] and describes the accuracy in calculated life compared to the complexity of the model for the four above described methods. Example of complexity could be whether or not it is a simple D model of a fillet weld or an advanced 3D model of the rear frame in an articulated hauler. It can be seen in Figure. that LEFM is a very accurate method which also requires a lot of work while the other, simpler methods, are ranked depending on accuracy as the notch, hot spot and nominal stress method. The nominal stress method is the least accurate. The notch method gives relatively good result at a lower working effort. The nominal stress method can not always be used at very complex structures since it requires non disturbed nominal stresses [5]. Results for all four methods are shown in Table. and. below. Table.. Results for Case 3. Nominal Hot spot Effective Fracture Notch Mechanics Life (): % of : % 95% 73% 74%

35 Fatigue life calculation Table.. Results for Case 43. Nominal Hot spot Effective Fracture Notch Mechanics Life (): % of : % 458% 99% 45% As can be seen in the tables, the hot spot method have a life close to the expected million for Case 3 while it divert extremely much for Case 43. This result must be questioned. The reason why the life it is extremely long is that the prescribed FAT value for fillet welds is very high compared to the extrapolated hot spot stress. The effective notch method seems to agree for Case 43 while it diverts a lot for Case 3. This is because the stress concentration is quite small compared to the FAT value, which results in a longer life. Also this result must of course be questioned. Fracture mechanics gives a shorter life than all the other methods. When using fracture mechanics and Paris law the life has been integrated from an initial crack length of. mm. Linear elastic fracture mechanics (LEFM) is not applicable on small cracks, which is a problem since most defects have values below. mm. To be able to use fracture mechanics one has to assume that there is a known crack which is not too small. If one does not want to assume that there is from the beginning other methods must be used during the initial stage of the formation of the crack, before LEFM can be used. However in reality there are always flaws and pores which serves as initial cracks..3. Advantages with LEFM Linear elastic fracture mechanics (LEFM) will be used to evaluate the life of the welded structures in the Volvo CE standard STD55,5 and in the ISO 587 standard. The reason why LEFM is chosen instead of the other methods is that the conditions change from the initial stage as the crack grows down into the material, and LEFM offers a chance to catch these changes. All the other methods look only upon the initial state. This may result in a too simplified picture of reality because all cases in the welding classes have to be compared with only two cases from the IIW. For example, if the stress concentration is the same for an undercut (see Chapter 5, STD55,5 Case ) as for a penetration bead (see Chapter 5, STD55,5 Case ) and the effective notch method is used, both cases will get the same life. This, however, may give a totally wrong picture of the reality since the crack in the case with the undercut may grow 3 mm while the crack in the penetration bead can grow 5 mm before reaching half the thickness of the material. The extra mm which the crack in the penetration bead can grow results in a longer life. However, this will not be seen in the results if, for example, the effective notch method is used..3. Disadvantages with LEFM When LEFM is used several different FE-simulations must be performed in order to have enough points to describe the curve to be integrated in Paris law. When using any of the three other methods to calculate the life, only one FE-simulation has to be performed. Thus, LEFM needs more working effort. Another problem which arises is to mesh the area around the crack. Relatively small elements must be used to get a good result. Small elements results in many elements, which further

36 Analysis of Fatigue Life in Two Weld Class Systems results in larger models and longer simulation times. Another problem is the transition region between relatively small element near the crack tip and larger elements far away, which often contains badly shaped elements that are not desirable. Badly shaped elements are rectangular elements which have a large quotient between the long and short side or contain large blunt or small sharp angles. One further disadvantage with LEFM is that a curve of the achieved results from the FEsimulation must be approximated and later integrated numerically. Errors can occur in both these steps. Though there are some disadvantages with LEFM, especially the many extra simulations and the more time-consuming steps, the advantages of more geometry dependent and accurate results outweigh the disadvantages.

37 3 Procedure and methods 3 3 Procedure and methods This chapter contains description about the overall analytical and FE modelling, which gives the stress intensity factors. There is also information about how the stress intensity factors with corresponding crack length are integrated numerically in order to determine the fatigue life. 3. Modelling In this chapter questions about the modelling of the crack and the rest of the geometry will be discussed. All cases in the Volvo CE standard STD55,5 and the ISO587 are modelled in the FEprogram (Finite Element) ANSYS [], [], except a handful of cases which are solved analytically. 3.. Basic modelling In ANSYS, like in most FE-programs, the geometry is built by use of keypoints, which are placed in space. Lines are drawn between the keypoints and the lines are used to create areas. Areas are the highest order in D simulations. If 3D modelling is performed, the areas are used to build up volumes. To model the crack a small cut in the geometry is performed. This means that there is a relatively small distance between the points at the opening of the crack. In all models (in this study) the growth of the crack is perpendicular to the horizontal sheet. Crack growth is simulated by moving the crack tip keypoint into the material. 3.. Boundary conditions Both for transverse butt welds and for cruciform joints three types of boundary conditions are tested. One way is to apply stress, σ, in both ends see Figure 3.. To prevent the model from performing rigid body motions one point in the middle of the model is locked in both degrees of freedom. To prevent the model from rotation, one more point is locked in the x-direction. σ σ y x Figure 3.. Natural boundary conditions for a butt weld. Another set of boundary conditions was tested, for the left side and the right side respectively. One end of the model was supported in the x-direction and stress was applied at the other end. To prevent the model from rigid body motion, one node on the side where the model is supported in the x-direction is also locked in the y-direction (see Figure 3. and 3.3).

38 4 Analysis of Fatigue Life in Two Weld Class Systems σ y x Figure 3.. Left side of the welded sheet is supported. σ y x Figure 3.3. Right side of the weld is supported. Results for all three types of boundary conditions are given in Table 3.. Table 3.. Results for different boundary conditions. K_eff [MPa (mm)] Crack length : Natural: Left side locked: Right side locked:,,,,,5 9,9 9,8 9,9,5 8,3 7,87 8,3, 39,5 39,48 39,5, 54,83 54,3 54,83,4 74,59 74,55 74,59,8 98,7 98,7 98,7, 5,77,3 5,77,3 58,98 58,77 58,98,4 3,5 4,93 3,5,8 79,48 8, 79,48,5 45, 45,5 45, 5, 8,89 83, 8,89 Max difference: -,9%,%

39 3 Procedure and methods 5 As can be seen in Table 3., the types of boundary conditions do not influence the results very much. The maximum difference compared to the boundary conditions in Figure 3. is around.9%. Henceforth boundary conditions given in Figure 3. will be used. Reaction forces at the supports have been controlled for all types of boundary conditions. For the boundary conditions selected for further use, the reaction forces were negligible both in x- and the y-direction. For the other types of boundary conditions, the total reaction force was the same as the applied force in the x-direction, while it was negligible in the y-direction as expected Influence of boundary conditions The geometry is modelled with a mm long horizontal sheet. Boundary conditions are applied at the ends of this sheet. To study the effects of the boundary conditions and to investigate the influences of bending at the crack, the model has been prolonged mm at one end at the time, see Figure 3.4 and 3.5. The results are presented in Table 3. below. σ Figure 3.4. Left end prolonged. σ Figure 3.5. Right end prolonged.

40 Analysis of Fatigue Life in Two Weld Class Systems Table 3.. Results when one end of the sheet is prolonged. K_eff [MPa (mm)] Crack length : Original: Elongated left: Elongated right:,,,,,5 9,9 9,8 9,9,5 8,3 7,87 8,3, 39,5 39,48 39,5, 54,83 54,3 54,83,4 74,59 74,55 74,59,8 98,7 98,7 98,7, 5,77,3 5,77,3 58,98 58,77 58,97,4 3,5 4,93 3,55,8 79,48 8, 79,48,5 45, 45,5 45, 5, 8,89 83, 8,89 Max difference: -,9%,% As can be seen in Table 3. the boundary conditions in the original model have no decisive effect on the result and can be used further on without complications. The maximum difference according to boundary conditions in Figure 3. is around.9%. 3. Meshing Meshing of the model turned out be one of the largest challenges in this work. How the meshing problems were solved is described in this chapter. 3.. Achieving a meshable model A model with can be difficult to mesh because the elements must be relatively small near the crack tip. In order to get around that problem the total area of the sheet is divided into smaller areas. Since the elements around the crack tip must be relatively small and it is extremely time consuming to use these small elements on the whole model small-size elements are used around the crack and larger elements are used far away from the crack. Problems may occur in the transition area between smaller and larger elements. Badly shaped elements i.e., rectangular elements that have a large ratio between the long and the short side or elements with large blunt or small sharp angles, are often generated. Dividing a complex area into more simple areas makes the model easier to mesh. It also makes it possible to choose a different element size on a specified area. This method is used to create a fine mesh around the crack tip. This is done by creating a box around the crack tip, see Figure 3.., containing small elements.

41 3 Procedure and methods 7 crack opening crack tip Figure 3.. Four areas create a box around the crack tip. There is also an area division from the crack tip vertically through the material, see Figure 3.. This facilitates the meshing. 3.. Elements The elements used when meshing the models are plane stress eight node serendipity elements and six node triangular elements. Each node has two degrees of freedom; one in the x- and one in the y-direction The crack tip When meshing the model, relatively small elements are preferred close to the crack tip. Pie elements are created around the tip (see Figure 3.7 ) crack tip Figure 3.7. Pie elements around the crack tip.

42 8 Analysis of Fatigue Life in Two Weld Class Systems To obtain stresses going to infinity at the crack tip, the side nodes on the triangular pie elements are moved to the quarter point of the element towards the crack tip. Figure 3.8 shows an actual ANSYS plot of the crack tip elements..5 3 mm crack tip Figure 3.8. Screenshot from ANSYS of the crack tip. The first two rows of elements around the crack tip have the length.5 3 mm.

43 3 Procedure and methods The box The box around the crack consists of four areas. The element length is An ANSYS plot over the box can be seen below (Figure 3.9). 3 mm in the box. crack tip Figure 3.9. The mesh in the box around the crack tip. Screenshot from ANSYS. The mesh in the box is of high quality with no badly shaped elements.

44 3 Analysis of Fatigue Life in Two Weld Class Systems 3..5 The centre lines The centre line and the crack surfaces are divided into two lines outside the box. The part of the line nearest to the box receives a gradually decreasing node density while the remaining part of the lines get an element side length of. mm (see Figure 3.). gradually increasing element size. mm Figure 3.. The centre line below the box. The same situation is applied to the two crack surfaces above the box. One could say that the size and number of elements near the crack tip is overkill but for many cases the crack is set to move from. mm down to 5 mm. In order to build a general macro which can take care of the entire crack growth, this solution was regarded as a straightforward method.

45 3 Procedure and methods Remaining parts of the model The remaining lines of the model get an element size of mm. This is shown in Figure 3.. crack tip Figure 3.. The global model is meshed with larger elements Meshing problems Problems with badly shaped elements, i.e. rectangular elements with a large ratio between the long and the short side or elements with large blunt and small sharp angles between the sides, appears in the transition area between the box and the global mesh. Smaller element size and gradually larger elements on the centre lines is one way of solving the problem. Another way is to create more areas around the crack and gradually increase the element size further away from the crack in these areas. This is however time consuming to carry out. The chosen solution, as described above, is a relative fine mesh on the centre lines which moves the problem to the mesh generator. On some geometries so called guiding lines are drawn in the immediate surroundings to the crack. This helps the mesh generator to create good elements. Although large efforts have been made to control the mesh, sometimes some bad elements appear around the box. One example of this is shown in Figure 3., where the light grey elements are badly shaped.

46 3 Analysis of Fatigue Life in Two Weld Class Systems Figure 3.. The light grey elements are badly shaped. When using a smaller element side length on the global areas,. mm instead of mm, the badly shaped elements disappear. The calculation time however is about to times longer and the calculated stress intensity factors improve less than.5%. Since more than geometries are to be calculated the coarser mesh is used to save time Convergence In order to guarantee convergence, the two prior test examples - the transverse butt weld and the cruciform joint (Case 3 and 43) - are calculated with the above mentioned mesh and a mesh that has half the element size on all elements except the crack elements. Results in Table 3.3, for Case 3 and Table 3.4, show that the solution has converged. As mentioned before, lack of time is the main factor for choosing the coarser mesh, because over one hundred geometries are to be calculated. The calculation time increase to times with the finer mesh, and that justifies the decision to use the coarser mesh.

47 3 Procedure and methods 33 Table 3.3. Convergence results for transverse butt weld, Case 3. K_eff [MPa (mm)] Crack length : Coarse mesh: Finer mesh: Deviation:,,,,%,5 9,9 9,77,74%,5 8,3 7,8,97%, 39,5 39,,%, 54,83 54,7,3%,4 74,59 73,99,8%,8 98,7 98,43,5%, 5,77,75,77%,3 58,98 59,85,55%,4 3,5 4,3,37%,8 79,48 79,8,7%,5 45, 45,,% 5, 8,89 83,,% Table 3.4. Convergence results for cruciform joint, Case 43. K_eff [MPa (mm)] Crack length : Coarse mesh: Finer mesh: Deviation:,,,,%,5,3,5,9%,5 37,8 37,43,9%, 5, 5,48,7%, 7,44 7,94,9%,4 98,99 99,73,75%,8 3,58 3,55,74%, 7,5 8,73,73%,3 3,79 5,4,%,4 43,9 45,9,74%,8 33,9 34,7,54%,5 43,45 433,5,48% 5, 947,84 949,44,7% 3..9 Macros After the geometry has been modelled, all of the remaining work - crack growth, area subdivision, meshing, solving and calculation of stress intensity factors - is the same for all models. Therefore generic macros are developed for ANSYS.

48 34 Analysis of Fatigue Life in Two Weld Class Systems When the crack has propagated a small distance into the material, a generic macro looks the same for any geometry. The differences between different geometries occur in the beginning of the crack growth, when geometrical differences like undercuts, transition radii, sharp transitions and flat sheets affect the area subdivision. Therefore all the macros with the above mentioned geometries look basically the same and differ only for the initial state of the crack. The advantage of the macros are that they need only three keypoints as input and then automatically move the crack tip into the geometry, divide it into areas and put the correct mesh size on all lines. After solution, the stress intensity factors are calculated and written to a file containing the results for all the steps during the crack growth. The macros also save the meshed models for each crack depth, making it possible to review the mesh afterwards. 3.3 Postprocessing This chapter deals with how the ANSYS calculates the stress intensity factors and how the results from the ANSYS are treated in order to calculate the fatigue life How stress intensity factors are calculated in ANSYS There are various ways to calculate the effective stress intensity factor for, for example the J-integral, energy release rate, nodal displacement near the crack, etc.. The latter is used to calculate the stress intensity factors in ANSYS. Paris and Sih [3], derived the displacement near for each mode. The equations below describe the total displacements and have been compiled in the ANSYS, Inc Theory Reference [4]. K I Δu = 4G K I Δv = 4G K Δw = G III r π r π II ( κ ) cos cos ( κ + 3) sin + sin + Ο() r II ( κ ) sin sin ( κ + 3) cos + cos + Ο() r r θ sin + Ο π θ θ () r 3θ 3θ K 4G K 4G r π r π θ θ 3θ 3θ where Δ u, Δ v, Δ w are displacements and r, θ are the coordinates in the two local coordinate system given in Figure 3.3 below. (3.:) (3.: ) (3.: 3) Figure 3.3. Local coordinate systems at crack front. Picture taken from ANSYS, Inc Theory Reference [4].

49 3 Procedure and methods 35 Further K I, 3 4ν κ = 3 ν + ν K II and K III are the stress intensity factors for the three different modes, and for plane strain or an axisymmetric case for plane stress G is the shear modulus, i.e. E G = ( + ν ) where E is Young s modulus and ν is Poisson s ratio. Ο ( r) are terms of order r or higher. The stress intensity factors are interesting when r and θ = 8º, therefore the given angle is inserted into equations (3.:-3) and the higher order terms are neglected. It gives K II r ( ) G Δu Δu = + κ K II = π (3. :) G π + κ r K I r G Δv Δv = ( + κ) K I = π (3. : ) G π + κ r K Δ III r w Δw = K III = G π (3. : 3) G π r In all equations (3.:-3) the following limit values must be evaluated Δ lim r r where Δ is either Δ u, Δ v or Δ w. This is done by using the 5 nodes in the path in ANSYS, mentioned above, see Figure 3.7 and 3.4. Figure 3.4. (a) displays the crack tip for a half-crack model, while (b) displays the crack tip for a full crack model, which is used in this study. Picture taken from [4]. The following curve is fitted for Δ v.

50 3 Analysis of Fatigue Life in Two Weld Class Systems ( r) Δv Δ v() r = r ( A + Br) = A + Br (3.3) r The displacement of the crack tip node is said to be zero, while the known displacement in points K and J are used to determine the constants A and B. The limit value becomes ( r) Δv lim r r = lim A r ( + Br) = A (3.4) The same thing is performed for mode II and III, which gives corresponding constants. Combining Equation (3.4) and Equation (3.) finally gives the stress intensity factors below. K K K I II III = = GA I π + κ GA II π + κ = GA III π (3.5 :) (3.5 :) (3.5 :) 3.3. Numeric integration As described above, the macros create a result file with the effective stress intensity factor. The results are transferred to the calculation program MATLAB [5]. In MATLAB the effective stress intensity factor is plotted as a function of the crack length and a curve is approximated with cubic splines []. The advantage of using splines is that the slope of the curve is the same for the incoming and outgoing line of each point. This gives a smoother curve. Efforts were made to fit a curve with different degrees of polynomial functions. Degree 3 gave the best curve fit but the problem was that the curve did not go through the origin. This is very important when calculating the life of a structure (i.e. when performing the numeric integration) since a great deal of the life refers to small crack lengths. Therefore the curve fitted to the points needs to be more exact for small crack lengths. It is not so important when the crack has grown over, say, approximately mm for a mm sheet, since the crack propagates rapidly at this stage and not many percent of the life is left. This is why splines are chosen to approximate the curve; they give a better curve at small crack lengths. One other effort that was made to better describe the curve at small crack lengths was to use a geometrical series for the crack length when calculating the stress intensity factor. This means that many stress intensity factors were calculated for small crack lengths and only a few for longer crack lengths. The series used was m a =, m =,,,, 3,..., i.e., stress intensity factors were calculated for each model. Ten integration points were used below mm and only 3 points above mm. The extra point comes from the stress intensity factor being zero when the crack length is zero. Figure 3.5 displays the stress intensity factor as a function of crack length for Case 3.

51 3 Procedure and methods 37 4 (a) 35 3 [MPa (m)] a Figure 3.5. The stress intensity factor as a function of crack length for Case 3. The lines in Figure 3.5 at. mm and 5 mm mark the integration limits. Numerical integration in MATLAB with Simpson quadrature [] for this case gives a life of.48. The dots in Figure 3.5 mark the crack lengths where the stress intensity factor has been calculated. The splines are based on these points. To rule out the possibility of errors in life due to too few points for longer cracks, a test with one value for each half mm was carried out. This means that 9 integration points instead of 3 are used (see Figure 3.). A comparison of the curves and lives shows that differences in life are negligible.

52 38 Analysis of Fatigue Life in Two Weld Class Systems 4 (a) 35 3 [MPa (m)] a Figure 3.. The difference between many (squares) and fewer (dots) integration points for longer cracks. The dotted curve and the boxes in Figure 3. display the previous results, which were presented in Figure 3.5. The solid curve and the squares in Figure 3. display what happens if more integration points are used for longer crack lengths. Between and 5 mm in crack lengths, the small difference between the two curves gives a difference in life of.% only. 3.4 Verification of integration method The life is calculated using Paris law. This is done numerically by use of the function Δ a. K eff ( ) In order to verify the use of splines to approximate the Δ ( a) K eff -curve and the numerical integration technique, a few different approximations are made in Excel [7]. All data is taken from Case 3 and can be found in Table 3.5 below.

53 3 Procedure and methods 39 Table 3.5. Data from Case 3, ANSYS results a : K eff [MPa (m)]: The values in Table 3.5 are plotted together with the approximated splines in Figure (a) Integration points Curve approximation with splines Curve with straight lines 3 [MPa (m)] a Figure 3.7. Plotted data from Case 3. As can be seen in Figure 3.7, the difference between the spline approximated curve and the straight line curve becomes greater for larger crack depths.

54 4 Analysis of Fatigue Life in Two Weld Class Systems No integration point is available for the crack length. mm, which is used as start defect when integrating with Paris law. However there is a point at a =.8 mm which will be used in the verification of the calculated life. MATLAB gives the life. when Simpson quadrature [] is used to integrate the life over the interval.8 a 5. mm Approximation with upper and lower summations Paris law gives N dn = ac ai C ( ΔK ) The curve f ( a) = is to be integrated numerically in the interval of C( ΔK ( a) ) n I.8 a 5. mm. Since there is not the same distance between any of the integration points, the integration is done with both over and under sums. The fatigue life is then f a is described. approximated with the average of the over and under sums. In Figure 3.8 ( ) f ( a) I n da f ( a) based on spline values f ( a) with straight lines between the integration points upper sum lower sum a i a i a i+ a Figure 3.8. Upper and lower summations. The upper sum becomes and for the lower sum N u n = + i= C I i ( ) ( a ) n i ai ΔK

55 3 Procedure and methods 4 N n l = n i+ i= C( ΔK I ) i+ ( a a ) An approximation of the fatigue life is N u + N N = l This is the same as a Riemann integral. If this is done for integration points.8 a 5. mm, the fatigue life becomes.78 compared to. for the spline approximation. It should be mentioned that this method overestimates the fatigue life since the spline based curve always will have less or equal values than the average line. However it shows that the value calculated with splines in MATLAB is approximately good Spline values integrated in Excel A spline curve for K( a) Δ is created in MATLAB. The distance is. mm in crack length between each point which builds the curve, so from mm to 5. mm it contains more than 5 integration points. The crack length vector and the corresponding stress intensity factor vector is transferred to Excel and integrated as a Riemann integral, according to n N = C a a i+ i n ( ΔK ) i= I i Description of the Riemann integral can be found in Figure 3.9. i f ( a) f ( a) based on splines a i- ai a i+ a Figure 3.9. Approximation with Riemann sums.

56 4 Analysis of Fatigue Life in Two Weld Class Systems The approximation with Riemann sums gives. i.e., the same as with the Simpson quadrature in MATLAB, which means that the integration method is verified. 3.5 Analytical case for an internal crack A few cases in the Volvo STD55,5 standard handle internal defect. These cases are; internal crack (Case 5), lack of fusion (Case ) and lack of penetration (Case 7). When the defect is set to have a maximum length in the depth direction, the analytical case for an elliptical buried flaw in a flat plate from [8] can be used. Descriptions of the case can be found in Figure 3. and 3.. W t c σ a Figure 3.. An internal elliptical crack under tension. Φ t a c Figure 3.. Denotations for the crack. This case, taken from [], is programmed in Matlab [7]. The Matlab program can be found in the Appendix A. The stress intensity factor is calculated as where F can be calculated as K I = σ m F 4 a a F = M + M M 4 gf φ f w + t t i.e., F is a function of the angle φ, which means that K I can be calculated at an arbitrary position along the crack tip. In these cases K I will be calculated for the angle º ( K Ic ) and 9º ( K Ia ), i.e. where the two extreme values of the stress concentration factor K t can be expected. Further πa Q

57 3 Procedure and methods 43 π = t a W c f sec w = c a M = c a M φ + = cos 4. 4 c a t a t a g The following conditions apply depending on in which direction, a or c, the ellipse is larger. For c a : = c a Q 4 / sin cos φ φ + = φ c a f = M For > c a : = a c Q 4 / cos sin φ φ + = φ a c f a c M = 3.5. Crack growth rate The crack growth is not the same in the a-direction as in the c-direction. To calculate the next crack length the following equation is used + = + = + + M d d M d d i i i i N c c c N a a a (3.) where M is a dimensionless constant. Paris law was given in Chapter :

58 44 Analysis of Fatigue Life in Two Weld Class Systems da = C( ΔK ) n Ia (.) dn Paris law (.) can be inserted into (3.:) and the corresponding for (3.:), which gives ai ci + + = a = c i i + C + C ( ΔK Ia ) n ( ΔK ) The next crack lengths which the program uses to calculate the stress intensity factors in the a- and c-directions, depend on the stress intensity factor in the given direction. The constant M determines the resolution i.e., how many integration points that will be used. The greater M is, the fewer integration points. The stress intensity factors and corresponding crack lengths are later integrated with Paris law, in the same way as described in Chapter 3.3., in order to achieve the fatigue life Algorithm The Matlab program is based on the following algorithm:. Start lengths of the crack in the a- and the c-direction ( a i and c i ) are given from the acceptance limits in the weld classes.. a i and c i are used to calculate ( Δ K Ia ) i and ( Δ K Ic ) i. 3. The new crack lengths, a i+ and c i+, are calculated based on ( Δ K Ia ) i and ( Δ K Ic ) i 4. The interruption criterion is checked. In this case the crack is set to grow up to a given length in the a-direction. If the criterion is fulfilled, all necessary stress intensity factors have been calculated and the fatigue life can be integrated, if not, the program starts over from. The interruption criterion is based on the length in the a-direction. The crack grows faster in this direction, and in all other cases in the standard the fatigue life has been integrated from the initial crack length until the crack length is half of the sheet thickness. Therefore the calculations are interrupted when the crack length a is half the sheet thickness. Ic n M M (3.7) Discussion about integration limits It can be discussed whether the crack should be integrated to half of the sheet thickness in the a-direction. The sheet often has a larger depth in the c-direction, implying that lots of the fatigue life is left after the crack has reached the surface in the a-direction. This can be seen if the crack length is plotted versus the number of. For cracks with the same depth as the sheet, the curve tends rapidly towards infinity when half of the sheet is left in the a-direction, implying that the rest of the life is negligible (see Figure 3.).

59 3 Procedure and methods 45 (N) N [-] 8 x 5 Figure 3.. Crack length a(n) for an infinitely deep crack. STD55 Case 7 D. For an internal elliptical crack the same curve goes more slowly towards infinity at the same crack length, basically because the crack can grow a very long distance in the c-direction (see Figure 3.3). (N) N [-] x 5 Figure 3.3. Crack length a(n) for an internal elliptical crack. STD55 Case 7 C. However, in order to be consistent compared to other cases, the fatigue life is integrated to half of the thickness also for this case.

60 4 Analysis of Fatigue Life in Two Weld Class Systems Comparison with AFGROW AFGROW [9] is a freeware program used by the United States Department of Defence and the aircraft industry to validate and predict the fatigue life of new and old structures. The program is developed within the United States Air Force. Many elementary cases are available in the program and one of its strengths is that the fatigue life for a large number of load spectra can be calculated. There are also five different material models to choose between, with lots of material parameters to use. The elliptical internal crack is defined in AFGROW and is here used together with the Walker equation, to confirm the values from the MATLAB program. Comparison with AFGROW for a sheet with thickness t = mm and width W = mm gives the same result for which grows from a = mm and c = 5 mm to a = 4. mm. The fatigue life becomes.4 million. The curves from AFGROW and MATLAB have been plotted in Figure 3.4. (N) N [-] x 5 Figure 3.4. The points from from AFGROW coincide with the curve from MATLAB. As can be seen in Figure 3.4, the data points from AFGROW coincide with the curve generated with the MATLAB program i.e., the values from the MATLAB program are confirmed.

61 4 Weld auditing 47 4 Weld auditing This chapter is an introduction to weld auditing in Volvo CE. Audits are performed to reveal problems in the manufacturing process in order to improve the quality of for example welds. It is also important to discover defects on welds of high criticality in order to prevent disastrous failures. 4. Overall on weld auditing In Volvo CE, welded parts are regularly being audited regarding the requirements in the company welding standard STD55,5. For every audit a record is written, listing all defects that are revealed. Every defect is classified in one of the categories (), () and (3), where () denotes a defect which is against safety requirements, () is a defect that has to be reworked and (3) does not have to be reworked. 4. Review of previous weld audits In order to get a picture of normally occurring defects, a number of weld audit records from February and March were studied. A total of 5 audits were examined, of which the six audited A-stays all together contained only one defect. Results are presented in Table and Figure 4.. Table 4.. Studied audit records. Object No. of objects No. of defects Month A-stay March Body Feb/March Front frame 3 Feb/March Rear frame 5 45 Feb/March

62 48 Analysis of Fatigue Life in Two Weld Class Systems Table 4.. Compilation of occurring defects. Defect A-stay Body Front frame Rear frame Total Lack of fusion 4 Non-filled weld Excessive penetration Hole Leg deviation 5 Throat deviation Sharp transition 7 3 Undercut Weld missing / too short 3 4 Overlap Category (Security) (Re-work) (No re-work) % 5% % 5% % 5% % Lack of fusion Non-filled weld Excessive penetration Hole Leg deviation Throat deviation Sharp transition Undercut Weld missing / too short Overlap Figure 4.. Rate of each defect.

63 4 Weld auditing 49 As seen above, an average object (apart from A-stays) has a number of defects of the order of ten.z The vast majority are of category, i.e. they have to be reworked. Defects against safety requirements (category ), normally referring to joints of higher consequence classes, are luckily not very common. Especially three types of defects are frequent; throat deviation, sharp transition and undercut. The most common defect is the sharp transition. This depends on most welds having the additional designation U, fatigue requirements, where smooth transitions are required. 4.3 Weld audit on a rear frame As a part of this work, the authors had the opportunity to take part in a weld audit of a rear frame. During the audit, discovered imperfections were discussed with the experienced weld auditor, and silicone impressions of listed defects and other interesting features were made. Figure 4.. A sharp transition has been marked for making a silicone impression Profile projector measuring of silicone impressions For measuring the outer geometrical properties of a weld joint, a silicone impression of the weld can be cast. In this study, a two-phase silicone (polyvinylsiloxane) impression material, originally for dental use, was applied. The two phases (base and catalyst) are automatically mixed in the tip of the dispensing device, and the material sets within a few minutes. When the impression has set, a thin slice of it is cut out for further examination in the profile projector. The projector provides a ten times magnification of the profile, which also can be moved in x and y directions on the screen. Measuring scales on the screen make it possible to estimate distances with. mm accuracy. Angles can be measured by turning a screen with indicator lines, while the integrated measuring equipment provides the turned angle with high accuracy. After the weld audit, the authors studied a number of the silicone impressions in the profile projector, as commented below.

64 5 Analysis of Fatigue Life in Two Weld Class Systems 4.3. Comments The profile projector measuring illuminated a few of the difficulties involved in measuring of weld geometries. The legs and throat lengths are quite easy to measure with sufficient accuracy, but when it comes to angles and radii problems arise. The angle between the sheet and the weld surface is easy to measure with the projector equipment the problem is where it should be measured. If the intention is to measure the angle after the transition (as in this study), then the question is where the transition ends. This is in most cases far from obvious. An even more difficult property to estimate is the nature of the transition. Determining whether the transition is sharp or even is a central issue, as even transition is required in welding classes used for fatigue loaded joints. ( Even is the term used in STD55,5. Smooth would be more correct.) Normally, the even transition is interpreted as a mm radius, but as the curve is always more or less jagged, it is often impossible to decide if there is a radius. Furthermore, features as small as this can vary a lot along the weld. If a nearby cross-section is chosen for examination, the results can be completely different. Thus, measuring of weld dimensions demands more than just measuring one cross-section. To obtain reliable figures, several samples have to be examined and the whole weld has to be inspected to make sure that the picked samples are representative.

65 5 Compilation of STD55,5 5 5 Compilation of STD55,5 This chapter contains overall information on the Volvo CE STD55,5 weld standard. Also results and some detailed conclusions and recommendations from all calculated cases in the standard are presented in diagrams, tables and on result sheets. 5. About the standard The STD55,5 [] is the welding standard used in the Volvo CE company. It is not applied in the Volvo Cars company. The standard was developed during the 8s and has its origin in the Swedish steel norm, StBK-N []. The standard contains four different welding classes, from A to D, where A has the highest quality and D the lowest. The welding classes C and D can be assigned an additional designation U (short for the Swedish word Utmattning, fatigue) for structures which are subjected to fatigue loading. Without the designation U, classes C and D are used only for static loading. Designation U is not needed for classes A and B, since they already contain requirements necessary for fatigue loading. However both A and B are rarely used; class B does exist for some parts, for example hydraulic cylinders, but class A is practically never used within Volvo CE. A few other parameters come with the standard and can be seen in Figure 5., below. Dimension referring to weld cross-section Mått som avser svetsens tvärsnitt Number of weld elements Antal delsvetsar Arrow line Hänvisningsslinje a.5 5 x () Spacing Delning 35-D-F [3] Consequence class (see STD 5,3) Konsekvensklass (se STD 5,3) Reference line Referenslinje Elementary symbol Grundsymbol Welding process (see STD 55,5) Svetsmetod (se STD 55,5)

66 5 Analysis of Fatigue Life in Two Weld Class Systems to welds, which at breakdown could lead to immediate stand-still of the vehicle. Finally, class [3] apply to welds, which at failure could lead to loss of performance and require repair, but no immediate stand-still. When a defect is found in a weld of consequence class [] or [] at the weld audit, there are certain routines within Volvo CE to catch the errors and make sure they are not repeated. 5. Modelling All transverse butt welds in the standard with the requirement not permitted for a certain welding class have been modelled as Case A in the STD55,5 standard, i.e., IIW Case 3 but without the transition radius of mm. The corresponding cases for fillet welds have been modelled as IIW Case 43, but with the difference that a 4 mm transition radius has been used for welding class A, a mm transition radius has been used for classes B, CU and DU, and a sharp transition has been used for class C and D. Other comments on modelling are given in Chapter 3, and in the result sheets for all cases (Chapter 5 and ). 5.3 Results Results with pictures and diagrams for each case and welding class can be found on the following pages. All results are also compiled in Figure B.-B.8 and in Table B.-B., in Appendix B. An overview of the results can be found in Figure B.. It shows large scatter in the results. However, patterns can be discerned, for example, some cases have nearly no difference in life between the welding classes, while some show large differences. A rough grouping of the cases can be seen in Table 5.. Table 5.. Influence of acceptance limits on the fatigue life for a certain welding class. Large influence Some influence No influence Butt welds Fillet welds Butt welds Fillet welds Butt welds Fillet welds In Figure B. and B.3 the transverse butt welds and fillet welds have been separated. For the butt welds in Figure B., Case 3, and differ a lot since there are nearly no difference in life between almost all the welding classes. However the lack of differences in Case 3 depends on that no sharp transitions are permitted for the additional designation U. Case 5, and 7 are internal defects and are very hard to compare with the remaining cases for butt welds. Figure B.3, with only fillet welds, show just a little agreement. Case 3 and 4 could be separated from the remaining fillet welds since these cases are guidelines for all fillet welds and not real defects. Case 3 and 4 are modelled with a radius of,, 3 and 4 mm for DU, CU, B and A respectively. This has been done to study the influence of different radii and is not based on the requirements, except for welding class A. Case show only small variations in fatigue life between the different welding classes, while Case and show influence from the acceptance limits on fatigue life.

67 5 Compilation of STD55,5 53 Since welding class A is barely ever used and C and D are meant only for static loading, B, CU and DU could be separated and can be seen in Figure B.4-B.. These figures reflect what has been said above for the overall results in Figure B.-B.3 - the classes used for fatigue loaded joints are not more consistent than other classes when it comes to fatigue life. If the ratio of B and CU and of CU and DU is plotted (Figure B.7) one can see that the ratio of B and CU lies between to for almost all the cases, which shows that there is a little bit of consistency in the standard. But the ratio of CU and DU is very scattered, between and 8, with nearly no pattern. Case 5-7 have been left out due to above mentioned differences. Figure B.8 shows the maximum, minimum, average, and median life for each welding class. Preferably these four values should be equal, but due to the present standard they vary a lot. One can see that for many welding classes there is a factor ten or more between the minimum and maximum value. Welding class D and DU appears the most scattered. There is almost a factor of between maximum and minimum in these classes. It is also possible to see in Figure B.8 that the average life for each class is always longer than the median. This shows that there are a few cases with long fatigue lives, which increase the average life. In other words, if these cases with unreasonably long fatigue lives are reworked the average and median lives coincide. Further, all four values; maximum, minimum, average and median, are lower in welding class C compared to CU and in D compared to DU. This is expected since the additional designation U should give the structure a longer fatigue life. It can also be seen that there is a stair with longer life in A than B, B than C and so on, for all welding classes, something which could also be expected. However if also the additional designation U is regarded, one can see that the trend that welding class DU have longer life for the maximum, average and medium value, than class C. This shows that transition radii and smooth notches in general give longer lives even though the defect (acceptance limit) may be larger, which is usually the case between class DU and C. In Figure B.9-B. the fatigue life in percent of million has been plotted as a function of the acceptance limit, for different sets of cases (mainly, 7, 8, 3, 4, ) and classes. The reason why these cases are chosen are that the acceptance limit has a major impact on the fatigue life, as described above and presented in Table 5.. An exponential trendline has been fitted to the points in all four diagrams. Note that there might be coincident (overlapping) points in the diagram. In Figure B., also an exponential trendline is fitted to the points. One can see that the trendlines fit the scattered points relatively well, except for small acceptance limits i.e., around.5 mm for Figure B.9-B.. Equations for the trendlines can be found in each diagram. The trendline could serve as a tool when setting new acceptance limits. For example, if the desired life in a certain welding class has been decided, the acceptance limit can be read from the curve. Of course this might not give the exact life for the certain case, but it will at least be possible to get a hint of the size of the desired acceptance limit. It is not possible to create an appropriate trendline for all the calculated data, since it is too scattered and many of the acceptance limits for different defects do not have any influence on the fatigue life. In Figure B.3-B.8, results for each welding class can be found. These results also confirm large scatter in the results.

68 54 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 Incomplete root penetration l Requirements and results D C B A A.t, but max. mm. L mm A.t, but max. mm l t but max. 5 mm Not permitted Not permitted. % of.35 8% of.48 4% of.48 4% of With additional designation U:.48 4% of.48 4% of 4% % A B CU DU % 8% % 4% % % C D Modelling and comments All classes have been modelled the same way with growing from the lower surface. The fatigue lives have been integrated from initial cracks which correspond to the acceptance limits. The additional designation U tolerates no sharp transitions and therefore the life of CU and DU is the same as for A and B, where no incomplete root penetration is permitted. The results show that C and D have considerably shorter life than the other classes. This is because the initial crack is longer. Conclusions and recommendations This case shows that most of the life for the structure lies in the growth of the first millimetre of the crack. After a few tenths of a millimetre nearly no life is left and the crack grows rapidly.

69 5 Compilation of STD55,5 55 This case does not supply so much additional information to the standard. Since no sharp transitions are allowed in CU and DU and incomplete root penetration is not permitted for A and B, the acceptance limits cannot be reworked for A and B, because then CU and DU will have a longer life than A and B and this is not wanted. C and D are meant only for static loading. Geometrically Case 3 is the same as Case 8 in the STD55,5 standard but the two cases does not have the same acceptance limits for welding class B. Since the cases are similar and it could be hard for others than experts to see the differences between incomplete root penetration (Case 3) and root concavity (Case 8), it is recommended that these two cases are united into one case. It is not consistent to allow a different acceptance limit, which is the case for welding class B, when the cases are so similar. Further, it should be mentioned that the additional designation U implies a full penetration.

70 5 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 A, B, CU and DU Description: Incomplete root penetration l Requirements and results: Not permitted initial crack =. mm σ nom = 4 MPa N =.48 Nf = 4% of Modelling and boundary conditions: Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

71 5 Compilation of STD55,5 57 STD55,5 Case 3 C Description: Incomplete root penetration l Modelling and boundary conditions: Requirements and results: A. t, but max. mm, l t but max. 5 mm. A = mm, l = mm initial crack =. mm σ nom = 4 MPa N =.35 Nf = 8% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

72 58 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 D Description: Incomplete root penetration l Modelling and boundary conditions: Requirements and results: A. t, but max. mm. L mm A = mm initial crack =. mm σ nom = 4 MPa N =. Nf = % of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 4

73 5 Compilation of STD55,5 59 STD55,5 Case Undercut l Requirements and results D C B A Permitted locally if A.t, but max. Permitted locally if A.t, but max. Permitted locally if A.5 t, but max. Not permitted mm mm.5 mm. l 5 mm. 5% of.37 8% of.74 37% of.58 79% of With additional designation U:.3 % of.4 % of 9% 8% A 7% % 5% 4% B 3% % % C CU D DU % Modelling and comments The undercut has been modelled as a notch with a radius of mm for CU and DU, and as a crack for B, C and D, where the acceptance limit is the same as the initial crack, see details on the following pages. CU and DU have only a little bit longer lives compared to C and D. This suggests that it is not the smooth transition but the amount of material between the crack tip and the centre of the sheet that has the primary influence on the life. Of course the crack initiation stage and the number of until the. mm initial crack has been formed have not been taken into account for classes CU and DU. Therefore, almost the same effective stress intensity factor is achieved for C as for CU and for D as for DU. This leads to almost the same fatigue life for the additional designation U as for C and D (without U). As have been said before, B, C, and D reveal that lots of the life lies within the first tenths of a millimetre for the crack.

74 Analysis of Fatigue Life in Two Weld Class Systems Conclusions and recommendations Undercut has proven to be of great interest when studying defects which may affect the fatigue life of welded joints. There is absolutely no recommendation to delete this case from the standard.

75 5 Compilation of STD55,5 STD55,5 Case A Description: Undercut l Requirements and results: Not permitted initial crack =. mm σ nom = 4 MPa N =.58 Nf = 79% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

76 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case B Description: Undercut l Modelling and boundary conditions: Requirements and results: Permitted locally if A.5 t, but max..5 mm. l 5 mm A =.5 mm initial crack =.5 mm σ = 4 MPa nom N =.73 Nf = 37% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

77 5 Compilation of STD55,5 3 STD55,5 Case C Description: Undercut l Modelling and boundary conditions: Requirements and results: Permitted locally if A. t, but max. mm. A = mm initial crack =. mm σ = 4 MPa nom N =.37 Nf = 8% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

78 4 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case CU Description: Undercut l Requirements and results: Permitted locally if A. t, but max. mm. A = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.4 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

79 5 Compilation of STD55,5 5 STD55,5 Case D Description: Undercut l Modelling and boundary conditions: Requirements and results: Permitted locally if A. t, but max. mm. A = mm initial crack =. mm σ = 4 MPa nom N =. Nf = 5% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 4

80 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case DU Description: Undercut l Requirements and results: Permitted locally if A. t, but max. mm. A = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.3 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

81 5 Compilation of STD55,5 7 STD55,5 Case 7 and 8 Non-filled weld (7) Root concavity (8) Requirements and results D C B A A.t, but max. A.t, but max. A.5t, but max. Not permitted mm. mm.5 mm.. % of.4 % of.9 4% of 3.5 3% of With additional designation U:.3 % of.45 % of 8% % 4% % % 8% % 4% % % A B C CU D DU Modelling and comments Case 7, non-filled weld and Case 8, root concavity, looks almost the same. Therefore they are modelled the same way with growing from a flat metal sheet for B, C and D. For classes CU and DU a notch with radius mm, with a small crack at the bottom, has been modelled. This is almost the same modelling as for Case (undercut), something which is reflected in the results. Therefore, for a discussion about the results, the reader is refered to Case. Conclusions and recommendations Conclusions and recommendations are the same as in to Case.

82 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 7 and 8 A Description: 7. Non-filled weld 8. Root concavity Modelling and boundary conditions: Requirements and results: The weld reinforcement shall be removed and the surface machined to the level of the parent metal initial crack =. mm σ nom = 4 MPa N = 3.5 Nf = 3% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

83 5 Compilation of STD55,5 9 STD55,5 Case 7 and 8 B Description: 7. Non-filled weld 8. Root concavity Modelling and boundary conditions: Requirements and results: A.5 t, but max..5 mm. A =.5 mm initial crack =.5 mm σ = 4 MPa nom N =.9 Nf = 4% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

84 7 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 7 and 8 C Description: 7. Non-filled weld 8. Root concavity Modelling and boundary conditions: Requirements and results: A. t, but max. mm A = mm initial crack =. mm σ nom = 4 MPa N =.4 Nf = % of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

85 5 Compilation of STD55,5 7 STD55,5 Case 7 and 8 CU Description: 7. Non-filled weld 8. Root concavity Requirements and results: A. t, but max. mm A = notch depth + initial crack =.9 +. = mm σ = 4 MPa nom N =.45 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

86 7 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 7 and 8 D Description: 7. Non-filled weld 8. Root concavity Modelling and boundary conditions: Requirements and results: A. t, but max. mm. A = mm initial crack =. mm σ = 4 MPa nom N =. Nf = % of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 4

87 5 Compilation of STD55,5 73 STD55,5 Case 7 and 8 DU Description: 7. Non-filled weld 8. Root concavity Requirements and results: A. t, but max. mm. A = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.3 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

88 74 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case Weld reinforcement b Requirements and results D C B A A.5 +.5b. Overlap is permitted to a small extent A.5 +.b. Overlap is not permitted A.5 +.5b. Overlap is not permitted The weld reinforcement shall be removed and the surface machined to the level of the parent metal.5 78% of.3 8% of.73 8% of 3.5 3% of With additional designation U:.7 85% of.7 88% of 8% % A 4% % % 8% B C CU D DU % 4% % % Modelling and comments Welding classes B, C and D have been modelled with a sharp transition. The results show a decreasing life for case B, C and D. CU and DU have been modelled with a transition radius of mm. This is reflected in the results. One can see that the height of the weld reinforcement does not play a major role. Instead, the transition radius evens out the differences between the models and almost the same life is achieved for CU and DU. Conclusions and recommendations Weld reinforcement is not a big problem for the fatigue life of a transverse butt weld. The results show that the difference from A = 3 mm, for welding class D, down to A = mm, for class B, does not affect the fatigue life noticeable. Therefore it is recommended, from a fagtigue point of view, that this case is deleted from the standard. With the present acceptance limit, this case has no influence on the life.

89 5 Compilation of STD55,5 75 It is not recommended, however, to entirely delete the case from the standard since some kind of limitation of the weld reinforcement could be important for reasons of appearance or for technical reasons (too large weld reinforcements could interfere with other parts etc.). However, it should be clear that the weld reinforcements have no influence on the fatigue properties. Further, the requirement for welding class D Overlap is permitted to a small extent should be replaced by something more concrete with a length in actual figures. Otherwise the requirement could be widely interpreted.

90 7 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case A Description: Weld reinforcement b Requirements and results: The weld reinforcement shall be removed and the surface machined to the level of the parent metal initial crack =. mm σ nom = 4 MPa N = 3.5 Nf = 3% of Modelling and boundary conditions: Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

91 5 Compilation of STD55,5 77 STD55,5 Case B Description: Weld reinforcement b Requirements and results: A b. Overlap is not permitted. A = mm, b = mm initial crack =. mm σ nom = 4 MPa N =.73 Nf = 8% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

92 78 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case C Description: Weld reinforcement b Requirements and results: A b. Overlap is permitted to a small extent. A =.5, b = mm initial crack =. mm σ nom = 4 MPa N =.3 Nf = 8% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

93 5 Compilation of STD55,5 79 STD55,5 Case CU Description: Weld reinforcement b Requirements and results: A.5 +. b. Overlap is not permitted. A =.5 mm, b = mm initial crack =. mm σ nom = 4 MPa N =.7 Nf = 88% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

94 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case D Description: Weld reinforcement b Requirements and results: A b. Overlap is permitted to a small extent. A = 3 mm, b = mm initial crack =. mm σ nom = 4 MPa N =.5 Nf = 78% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

95 5 Compilation of STD55,5 8 STD55,5 Case DU Description: Weld reinforcement b Requirements and results: A b. Overlap is permitted to a small extent. A = 3 mm, b = mm σ nom = 4 MPa initial crack =. mm N =.7 Nf = 85% of Modelling and boundary conditions: Modelling: R A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

96 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case Penetration bead c Requirements and results D C B A A.5 +.3c A.5 +.c A.5 +.c The penetration bead shall be removed and the surface machined to the level of the parent metal.9 84% of.9 84% of.9 85% of.48 4% of With additional designation U:.7 88% of.77 89% of 4% % A % 8% B C CU D DU % 4% % % Modelling and comments The penetration bead is modelled approximately as the weld reinforcement in Case. Comments on the modelling are given in Case. In order to get the right proportions between the weld reinforcement and penetration bead the measure C in the figure, which describes this case, is set to 3 mm (after measuring the proportions in the figure). The results in Case show that the height of the penetration bead plays an even smaller role for the fatigue life than the height of the weld reinforcement in Case. Conclusions and recommendations The penetration bead is not a large problem for the transverse butt weld. The recommendation for the penetration bead is, from a fatigue point of view, to delete the case from the standard. The acceptance limits have no large impact on the fatigue life, even though the acceptance limits vary from A =.4 mm in class D to A =.8 mm in class B.

97 5 Compilation of STD55,5 83 It is not recommended to delete the case from the standard entirely since some kind of limitation of the penetration bead is important for reasons of appearance as well as for technical reasons (too large penetration beads could interfere with other parts etc.). However, it should be clear that the penetration bead has no influence on the fatigue properties.

98 84 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case A Description: Penetration bead c Modelling and boundary conditions: Requirements and results: The penetration bead shall be removed and the surface machined to the level of the parent metal initial crack =. mm σ nom = 4 MPa N =.48 Nf = 4% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

99 5 Compilation of STD55,5 85 STD55,5 Case B Description: Penetration bead c Modelling and boundary conditions: Requirements and results: A.5 +. c A =.8 mm, C = 3 mm σ nom = 4 MPa initial crack =. mm N =.9 Nf = 85% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

100 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case C Description: Penetration bead c Modelling and boundary conditions: Requirements and results: A.5 +. c A =. mm, C = 3 mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = 84% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

101 5 Compilation of STD55,5 87 STD55,5 Case CU Description: Penetration bead c Modelling and boundary conditions: Requirements and results: A.5 +. c A =. mm, C = 3 mm initial crack =. mm σ nom = 4 MPa N =.77 Nf = 89% of Modelling: initial crack R Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

102 88 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case D Description: Penetration bead c Modelling and boundary conditions: Requirements and results: A c A =.4 mm, C = 3 mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = 84% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

103 5 Compilation of STD55,5 89 STD55,5 Case DU Description: Penetration bead c Modelling and boundary conditions: Requirements and results: A c A =.4 mm, C = 3 mm initial crack =. mm σ nom = 4 MPa N =.7 Nf = 88% of Modelling: initial crack R Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

104 9 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 Edge displacement, one side welding Requirements and results D C B A A.5 +.5t, but A.5t, but max. A.t, but max. A.t, but max. max. t or 4 mm 3 mm mm mm.4.9% of.3 % of. 3% of. 3% of With additional designation U:.4.% of.34 7% of 35% 3% 5% A B % 5% % C CU 5% % D DU Modelling and comments The top side of the weld has been modelled with a radius, see Figure 5.. A x r - A r crack Figure 5.. The radius is derived from the known distances A and x. The radius becomes

105 5 Compilation of STD55,5 9 r = x A A + where x is constant and x = mm, i.e. the gap between the sheets before welding. The lower side of the weld has been modelled to resemble the picture in the standard (see the top right side of this result sheet. A line fillet with a radius of mm has been used. A, B, C and D have been modelled with a sharp transition, while CU and DU have been modelled with a transition radius of mm. Class A and B have the same acceptance limits and therefore the same results. As can be seen in the results, CU and DU have only insignificantly longer life than C and D. Boundary conditions Two types of boundary conditions are available for this case, see Figure 5.3 and 5.4. crack Figure 5.3. Boundary conditions for generating the results. The arrow indicates the direction of rotation. crack Figure 5.4. Boundary conditions which gives longer fatigue life. The arrow indicates the direction of rotation. Boundary conditions according to Figure 5.3 causes the sheets to perform a counter-clockwise rotation, which opens the crack. There are both a bending moment and an uniaxial tension which contributes to the crack growth. This results in a considerably lower fatigue life compared to the boundary conditions in Figure 5.4. In Figure 5.4 the tension causes a clockwise rotation on the sheets which results in a bending moment closing the crack. The crack would not grow if the uniaxial tension was not high enough to overcome the bending moment and open the crack.

106 9 Analysis of Fatigue Life in Two Weld Class Systems Placement of the crack As can be seen in Figures , the crack is placed on the top side of the metal sheet. The way the lower side of the weld is modelled would generate a larger stress concentration, since on the lower side there is a steeper angle towards the sheet, probably resulting in shorter fatigue life if boundary conditions according to Figure 5.4 are used. It is, however, hard to tell what the geometry would look like on the lower side of the weld because it depends on the size of the misalignment, how much melt metal will flow down, etc.. Therefore the crack is set to grow from the top side of the weld, although it might seem wrong in this particular case. Conclusions and recommendations The additional designation U does not affect the results significantly for C and D. The life becomes drastically shorter with such a large misalignment as A = 4 mm, which is the case in D. This is probably because A is relatively large compared to the thickness of the metal sheets (t = mm). If the thickness where 5 mm, the influence on the fatigue life would probably be smaller. Of course, the thicker the sheets are, the harder it is to join them without any misalignment and then the tolerance towards misalignment could then be greater, because the misalignment probably has less influence on the life. It should be recommended to increase the thickness dependence for the acceptance limits, in this case, or tightening of the requirements in some other way. If only geometrical issues are dealt with this case could be united with Case 4, since they look almost the same and also generates approximately the same fatigue life for the same acceptance limits. However if full penetration is not assumed, it is not appropriate to unite the two cases. In case of thicker sheets, full penetration might be harder to achieve for Case 3. The standard is, however, not consistent in the way that the requirements are lower in a some of the welding classes for Case 4 and not for all. If it is harder to achieve full penetration in Case 3, the requirements ought to be harder for all the welding classes in this case. Note that the conclusions above only apply to matters of fatigue strength, and not to constructional issues. Limits for dimension deviations must of course be considered as well. There should be a corresponding case for fillet welds (cruciform joints) since this type of defects have a large impact on the fatigue life.

107 5 Compilation of STD55,5 93 STD55,5 Case 3 A and B Description: Edge displacement, one-sided welding Modelling and boundary conditions: Requirements and results: A. t, but max. mm. A = mm initial crack =. mm σ = 4 MPa nom N =. Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

108 94 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 C Description: Edge displacement, one-sided welding Modelling and boundary conditions: Requirements and results: A.5 t, but max. 3 mm. A =.5 mm initial crack =. mm σ nom = 4 MPa N =.3 Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

109 5 Compilation of STD55,5 95 STD55,5 Case 3 CU Description: Edge displacement, one-sided welding Modelling and boundary conditions: Requirements and results: A.5 t, but max. 3 mm. A =.5 mm initial crack =. mm σ nom = 4 MPa N =.34 Nf = 7% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

110 9 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 D Description: Edge displacement, one-sided welding Modelling and boundary conditions: Requirements and results: A t, but max. t or 4 mm. A = 4 mm initial crack =. mm σ nom = 4 MPa N =.4 Nf =.9% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

111 5 Compilation of STD55,5 97 STD55,5 Case 3 DU Description: Edge displacement, one-sided welding Modelling and boundary conditions: Requirements and results: A t, but max. t or 4 mm. A = 4 mm initial crack =. mm σ nom = 4 MPa N =.43 Nf =.% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

112 98 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 Edge displacement, double-sided welding Requirements and results D C B A A.5 +.5t, but A.t, but max. A.5t, but max. A.t, but max. max. t or 5 mm 5 mm 3 mm mm.4.9% of.8 9% of.3 % of. 3% of With additional designation U:.4.% of. % of 35% 3% A 5% % 5% % B C CU 5% D DU % Modelling and comments Both the upper and the lower side of the weld have been modelled with the same radius that is described for STD55,5 Case 3. A, B, C and D have been modelled without a transition radius, while CU and DU have been modelled with a transition radius of mm. For further comments, boundary conditions, etc., the reader is referred to the corresponding part for Case 3. Conclusions and recommendations Conclusions and recommendations are the same as in Case 3. These cases are very similar.

113 5 Compilation of STD55,5 99 STD55,5 Case 4 A Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A. t, but max. mm A = mm initial crack =. mm σ nom = 4 MPa N =. Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

114 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 B Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A.5 t, but max. 3 mm A =.5 mm initial crack =. mm σ = 4 MPa nom N =.3 Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

115 5 Compilation of STD55,5 STD55,5 Case 4 C Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A. t, but max. 5 mm A = mm initial crack =. mm σ nom = 4 MPa N =.8 Nf = 9% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 8 ( ) (N) [MPa (m)] N [-] x 5

116 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 CU Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A. t, but max. 5 mm A = mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = % of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 8 ( ) (N) [MPa (m)] N [-] x 5

117 5 Compilation of STD55,5 3 STD55,5 Case 4 D Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A t, but max. t or 5 mm A = 4 mm initial crack =. mm σ nom = 4 MPa N =.4 Nf =.9% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

118 4 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 DU Description: Edge displacement, double-sided welding Modelling and boundary conditions: Requirements and results: A t, but max. t or 5 mm A = 4 mm initial crack =. mm σ nom = 4 MPa N =.44 Nf =.3% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

119 5 Compilation of STD55,5 5 STD55,5 Case Undercut t Requirements and results D C B A Locally A.t, but max. mm Locally A.t, but max. mm Locally A.5t, but max..5 mm. l 5 mm Not permitted.3 7% of.34 7% of.9 45% of.47 8% of With additional designation U:. % of.54 7% of 8% 7% A % 5% B 4% 3% CU % % C D DU % Modelling and comments In classes B, CU and DU the undercut has been modelled as a notch with a transition radius of mm, while in C and D it has been modelled as (see the following pages). There is a significantly longer life for CU than for C and also the life of DU is noticeably longer than for D. Conclusions and recommendations Undercut has proven to be of great importance when studying defects which may affect the fatigue life of welded joints. Therefore this case is important in the standard.

120 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case B Description: Undercut Requirements and results: Locally A.5 t, but max..5 mm. l 5 mm A = notch depth + initial crack =.4 +. =.5 mm σ 8 MPa nom = N =.9 Nf = 45% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

121 5 Compilation of STD55,5 7 STD55,5 Case C Description: Undercut Modelling and boundary conditions: Requirements and results: Locally A. t, but max. mm. A = mm initial crack =. mm σ 8 MPa nom = N =.34 Nf = 7% of Modelling: A = initial crack z Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

122 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case CU Description: Undercut Requirements and results: Locally A. t, but max. mm. A = notch depth + initial crack =.9 +. = mm σ 8 MPa nom = N =.54 Nf = 7% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

123 5 Compilation of STD55,5 9 STD55,5 Case D Description: Undercut Modelling and boundary conditions: Requirements and results: Locally A. t, but max. mm. A = mm initial crack =. mm σ 8 MPa nom = N =.3 Nf = 7% of Modelling: A = initial crack Crack length as a function of number of : Stress intensity factor as a function of crack length: 4 ( ) (N) [MPa (m)] N [-] x 4

124 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case DU Description: Undercut Requirements and results: Locally A. t, but max. mm. A = notch depth + initial crack =.9 +. = mm σ 8 MPa nom = N =. N f = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 8 ( ) (N) [MPa (m)] N [-] x 5

125 5 Compilation of STD55,5 STD55,5 Case Leg deviation Requirements and results D C B A A +.a A +.a A.5 +.5a A.5 +.5a.7 3% of.7 3% of.9 45% of. 8% of With additional designation U:.89 45% of.89 45% of 9% 8% 7% % 5% 4% 3% % % % A B C CU D DU Modelling and comments In order to achieve the largest stress intensity and the shortest life, the crack has been placed at the end of the shorter leg. Figures of where the crack is placed can be seen in the result sheets for this case. C and D have the same acceptance limits and therefore the results for classes C/D and CU/DU are the same. According to standard, B has been modelled with a transition radius of mm, while A has been modelled with a radius of 4 mm. This, combined with the tight acceptance limits for A, leads to a significantly longer life than for B. Conclusions and recommendations It is remarkable that the difference in life is so small for welding class B and CU/DU (about.8%). A =.5 mm for class B and A = 3 mm for classes CU/DU while the transition radius ( mm) is the same for both classes. The same phenomenon can be seen in STD55,5 Case, the penetration bead, where the size of the defect for this type of geometries does not seem to play a major role for the fatigue life. The phenomenon is discussed in Chapter 8. From a fatigue point of view C and D could have higher acceptance limits than at present CU and DU essentially have the same lives as B. However, at this stage the length of the deviated

126 Analysis of Fatigue Life in Two Weld Class Systems leg does not affect the life of the joint substantially and therefore the leg could be very long and still have sufficient life. Thus the acceptance limits should not be relaxed too much (if at all). The current acceptance limits for C and D might intentionally have been set identically just to avoid too long legs. The present acceptance limits have no influence on the life and therefore, from a fatigue point of view, this case could be removed from the standard. It is not recommended to delete the case from the standard entirely since some kind of limitations for the leg deviation is important for reasons of appearance as well as for technical reasons. However, it should be clear that the leg deviation has no influence of the fatigue properties.

127 5 Compilation of STD55,5 3 STD55,5 Case A Description: Leg deviation Modelling and boundary conditions: Requirements and results: A.5 +,5 a A =.5 mm, a = 5 mm initial crack =. mm σ 8 MPa nom = N =. Nf = 8% of Modelling: R4 initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x

128 4 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case B Description: Leg deviation Modelling and boundary conditions: Requirements and results: A a A =.5 mm, a = 5 mm initial crack =. mm σ nom = 8 MPa N =.9 Nf = 45% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

129 5 Compilation of STD55,5 5 STD55,5 Case C and D Description: Leg deviation Modelling and boundary conditions: Requirements and results: A +. a A = 3 mm, a = 5 mm initial crack =. mm σ 8 MPa nom = N =.7 Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

130 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case CU and DU Description: Leg deviation Modelling and boundary conditions: Requirements and results: A +. a A = 3 mm, a = 5 mm initial crack =. mm σ 8 MPa nom = N =.89 Nf = 45% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

131 5 Compilation of STD55,5 7 STD55,5 Case Throat deviation Requirements and results D C B A Locally -.a Locally -.a Throat must not be Throat must not be less than specified less than specified.45 3% of.59 3% of.9 45% of (from Case 4 DU).47 74% of (from Case 4 A) With additional designation U:.53 % of.9 34% of 8% 7% A % 5% B 4% 3% % C CU D DU % % Modelling and comments C and D have been modelled with a sharp transition, while CU and DU have been modelled with a transition radius of mm. The weld has equally long legs, i.e. both legs have been shortened correspondingly to the throat. In reality, throat deviation often occurs because of one leg being shorter. A and B, which have no deviation, have not been modelled especially for this case, since they are identical to Case 4 A and DU. (Transition radii 4 mm and mm, respectively.) Conclusions and recommendations The acceptance limits for C and D could be more generous. Currently, the lives for these cases are not that much shorter than for the ideal throat in class B. However, the influence on toe/root crack propagation is an important issue, as discussed below. When the throat gets smaller, the risk for a root crack increases. Normally it is favourable to have the crack at the toe side, were it can be detected before failure. A weld joints that is designed to fail at the toe side first might consequently fail from a root crack instead if the

132 8 Analysis of Fatigue Life in Two Weld Class Systems throat becomes too small [5]. This has to be considered when reviewing the acceptance limits for throat deviation. Furthermore, a too small throat should always be handled with precaution. The model used has its crack in the sheet, and the only effect of the deviated throat is a somewhat higher stress intensity around the crack tip. On the other hand, directly in the weld could have serious consequences if the weld is substantially weakened by throat deviation.

133 5 Compilation of STD55,5 9 STD55,5 Case C Description: Throat deviation Modelling and boundary conditions: Requirements and results: Locally -. a a = 5-.5 mm = 4.5 mm initial crack =. mm σ 8 MPa nom = N=.59 Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

134 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case CU Description: Throat deviation Modelling and boundary conditions: Requirements and results: Locally -. a a = 5-.5 mm = 4.5 mm initial crack =. mm σ 8 MPa nom = N =.9 Nf = 34% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

135 5 Compilation of STD55,5 STD55,5 Case D Description: Throat deviation Modelling and boundary conditions: Requirements and results: Locally -. a a = 5- mm = 4 mm initial crack =. mm σ 8 MPa nom = N=.45 Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

136 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case DU Description: Throat deviation Modelling and boundary conditions: Requirements and results: Locally -. a a = 5- mm = 4 mm initial crack =. mm σ 8 MPa nom = N =.53 Nf = % of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

137 5 Compilation of STD55,5 3 STD55,5 Case 3 Connecting radius, fully penetrated T-weld joint r Requirements and results D C B A Even transition r 4 min % of 3. 55% of With additional designation U:.54 7% of.74 37% of 8% % 4% % % 8% % 4% % % A B CU DU Modelling and comments The welding classes contain only the following requirements: B: Even transition A: r 4 mm In order to get more useful results, the following dimensions are used in this study: D: r mm C: r mm B: r 3 mm A: r 4 mm Since the geometries, as specified above, are modelled with even transitions, C and D practically correspond to CU and DU. The initial crack is situated at the point with the highest stress concentration on the transition radius. The geometry is different from all other cruciform joints, since the joint is fully penetrated. This means that there is no slit between the sheets, and it implies that the force can flow straight through the joint. Furthermore, there is no throat except for the material within the connecting radius. This implies an even less deviation of the force flow. This has an obvious

138 4 Analysis of Fatigue Life in Two Weld Class Systems effect on the results. In the normal case with no penetration, the force has to flow around the slit, and then concentrating towards the surfaces (where the initial crack is). Here, the force is more uniformly distributed over the cross section, and that gives a lower stress intensity factor for small crack lengths. Approaching half the thickness, the stress intensity exhibits more normal values, as compared to other cases. The low stress intensity for small cracks results in long life. However, considering the significant geometrical differences, the fatigue lives are difficult to compare with other cases. Conclusions and recommendations The test with the transition radii,, 3 and 4 mm shows very insignificant differences between welding classes. The recommendation for this case is to keep the current acceptance limits, i.e. 4 mm for A and even transition, interpreted as mm, for B. (C and D then, as today, have a 9 degrees sharp transition but can of course be assigned additional designation U when needed.) It would be suitable to clarify in the standard that even transition denotes a certain radius, for example mm. One interesting result from this case is the almost perfectly linear relation between the life and the transition radius. This supports the results in Case 4, where there is a similar relation for fillet welds. Quantitatively, Case 4 is of more importance since it applies to the same geometry as in other cases in this study.

139 5 Compilation of STD55,5 5 STD55,5 Case 3 A Description: Connecting radius. Fully penetrated T- weld joint r Requirements and results: r 4 min initial crack =. mm σ 8 MPa nom = N = 3. Nf = 55% of Modelling and boundary conditions: Modelling: R4 initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x

140 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 B Description: Connecting radius. Fully penetrated T- weld joint Modelling and boundary conditions: r Requirements and results: Even transition r = 3 mm is used initial crack =. mm σ 8 MPa nom = N =.9 Nf = 4% of Modelling: R3 initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x

141 5 Compilation of STD55,5 7 STD55,5 Case 3 CU Description: Connecting radius. Fully penetrated T- weld joint Modelling and boundary conditions: r Requirements and results: No requirements in welding class r = mm is used initial crack =. mm σ 8 MPa nom = N =.74 Nf = 37% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x

142 8 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 3 DU Description: Connecting radius. Fully penetrated T-weld joint r Requirements and results: No requirements in welding class r = mm is used initial crack =. mm N = 3.4 Nf = 57% of Modelling and boundary conditions: Modelling: R A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x

143 5 Compilation of STD55,5 9 STD55,5 Case 4 Connecting radius, fillet weld r Requirements and results D C B A Even transition r 4 min % of.47 74% of With additional designation U:.9 45% of.8 54% of 8% 7% % 5% A B CU DU 4% 3% % % % Modelling and comments The welding classes contain only the following requirements: B: Even transition A: r 4 mm In order to get more useful results, the following transition radii are used in this study: D: r mm C: r mm B: r 3 mm A: r 4 mm This means that an even transition is used only for classes corresponding to the additional designation U. Comments on crack location In order to obtain the "worst case", i.e. the shortest life, for geometries with smooth transition between weld and sheet, the initial crack was placed at the point that had the highest stress concentration when no crack was present. In the original models the crack was placed right above the point where the tangents of the weld and parent material intersect. This was considered a decent approximation.

144 3 Analysis of Fatigue Life in Two Weld Class Systems In most cases this resulted, as expected, in shorter life. In all this cases the initial crack was moved to a higher x-value. However, in Case 4 for welding classes A, B and CU the highest stress concentration, and thus the place for the initial crack, was situated at lower x-coordinate values than in the original models. This resulted, somewhat surprisingly, in longer life. After all, if the crack grows from the point with the highest stress it could be expected to give approximately the shortest life, as in the other cases. But apparently there are some geometrical characteristics that make the stress concentration at the crack tip increase considerably slower for at a lower x - value. Because of this, one can doubt if the x-coordinate for the maximum stress which the FEprogram provides is correct. There is, however, no indication of any error in the FE-model. It can be discussed whether it is correct to use the results from the models with the initial crack at the current locations. They obviously imply longer life than in the worst case. On the other hand, the initial crack is situated at the point where it is most likely to start growing. Despite the results in this case, putting the initial crack at the point with the highest stress concentration still seems to be the best idea for a general procedure. Neither in the cases with better (more probable) results is it known for sure how close they are to the actual minimum life. Conclusions and recommendations As in Case 3, the relation between life and transition radius is very obvious. Increasing the radius by mm prolongs the life with approximately. for these radii. (It should be noticed that this result probably can not be extrapolated towards r =, as it is likely to deviate from linearity for small radii.) The recommendation for this case, as for Case 3, is to keep the current acceptance limits, i.e. 4 mm for A and even transition for B. And again, to clarify in the standard that even transition denotes a certain radius, for example mm. Another opinion is that Cases 3 and 4 maybe should not be defect types in the standard, because they are fundamental requirements of the weld. If they are to be kept in the standard, to be consistent they could be named for example Insufficient connecting radius in stead of just Connecting radius which is a requirement but not a defect. Possibly the whole issue of sharp/even transitions and connecting radii could be dealt with in a separate section of the standard. Finally, the illustration in the standard is somewhat misleading. It looks more like one large connecting radius between the two sheets than connecting radii between sheet and fillet weld.

145 5 Compilation of STD55,5 3 STD55,5 Case 4 A Description: Connecting radius, fillet weld r Requirements and results: r = 4 mm initial crack =. mm σ 8 MPa nom = N =.47 Nf = 74% of Modelling and boundary conditions: Modelling: R4 initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

146 3 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 B Description: Connecting radius, fillet weld r Requirements and results: r = 3 mm initial crack =. mm σ 8 MPa nom = N =.7 Nf = 4% of Modelling and boundary conditions: Modelling: R3 initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

147 5 Compilation of STD55,5 33 STD55,5 Case 4 CU Description: Connecting radius, fillet weld r Requirements and results: r = mm σ 8 MPa nom = initial crack =. mm N =.8 Nf = 54% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 5 [MPa (m)] N [-] x 5

148 34 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 4 DU Description: Connecting radius, fillet weld r Requirements and results: r = mm σ 8 MPa nom = initial crack =. mm N =.9 Nf = 45% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

149 5 Compilation of STD55,5 35 STD55,5 Case 5 Crack Requirements and results D C B A Inner crack with A,t but max. 4 mm, and l t is permitted. Crack which reaches the surface or crack in the heat-affected zone is not permitted Not permitted Not permitted Not permitted l.9 4% of.58 79% of.58 79% of.58 79% of 9% 8% 7% % 5% 4% 3% % % % A B C D Modelling and comments In welding class A, B and C internal cracks are not permitted. Therefore all these classes have been modelled as a transverse butt weld without a transition radius. Comments on modelling of the analytical case for welding class D are given in Chapter 3. The calculated fatigue life do not say much about the real fatigue life in reality since the life is only calculated to half the thickness of the sheet and the crack can in real life continue to grow in the depth direction of the plate after the crack has reached the surface. Conclusions and recommendations It is hard to draw any extensive conclusion when only one case has been calculated with the interior defect. Internal cracks are not wanted since they are hard to detect before they have reached the surface. When the crack has reached the surface it might in some cases be too late to do anything about it.

150 3 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 5 D Description: Crack Modelling and boundary conditions: l Requirements and results: Inner crack with A. t but max. 4 mm, and l t is permitted. Crack which reaches the surface or crack in the heat-affected zone is not permitted. A = mm, l = c = mm σ nom = 4 MPa N=.9 Nf = 4% of Modelling: W Φ t c σ t a a c Analytical case [8] Denotations according to analytical case. Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 [MPa (m)] N [-] x 5

151 5 Compilation of STD55,5 37 STD55,5 Case Lack of fusion l Requirements and results D C B A A,t, but max. 4 mm, and l t is permitted. Lack of fusion must not reach the surface Not permitted Not permitted Not permitted.9 4% of.58 79% of.58 79% of.58 79% of 9% 8% 7% % 5% 4% 3% % % % A B C D Modelling and comments In welding class A, B and C lack of fusion is not permitted. Therefore all these classes have been modelled as a transverse butt weld without a transition radius. Comments on modelling of the analytical case for welding class D are given in Chapter 3. The calculated fatigue life do not say much about the real fatigue life in reality since the life is only calculated to half the thickness of the sheet and the crack can in real life continue to grow in the depth direction of the plate after the crack has reached the surface. Conclusions and recommendations It is hard to draw any extensive conclusion when only one case has been calculated with the interior defect. Internal cracks are not wanted since they are hard to detect before they have reached the surface. When the crack has reached the surface it might in some cases be too late to do anything about it.

152 38 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case D Description: Lack of fusion Modelling and boundary conditions: l Requirements and results: A, t, but max. 4 mm, and l t is permitted. Lack of fusion must not reach the surface. A = mm, l = c = mm σ = 4 MPa nom N =.9 N f = 4% of Modelling: W Φ t c σ t a a c Analytical case [8] Denotations according to analytical case. Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) [MPa (m)] N [-] x 5

153 5 Compilation of STD55,5 39 STD55,5 Case 7 Incomplete root penetration l Requirements and results D C B A A,t, but max. 4 mm. In-complete root penetration must not occur closer than mm to the end of the weld or the crossing points respectively Not permitted A,t, but max. mm. l t, but max. 5 mm. Incomplete root penetration must not occur closer than mm to the end of the weld or the crossing point respectively A, t, but max. mm. l,4 t, but max. mm. Incomplete root penetration must not occur closer than mm to the end of the weld or the crossing point respectively. 3 % of.73 3 % of.95 47% of.58 79% of % 4% B % % 8% A % 4% C D % % Modelling and comments Welding class B and C have been modelled with the analytical case described in Chapter 3. The crack in class D is assumed to have an infinite depth and has therefore been modelled in ANSYS. Since incomplete root penetration is not permitted for welding class A, it has been modelled as a transverse butt weld without any transition radius. Conclusions and recommendations When studying the lives for welding class C and D, which both has the same integration limits in the a-direction (see coming pages for details and pictures), one can draw the conclusion that it does not seem that the extension in the c-direction matters so much for the fatigue life. Welding class C has a limited extension in the depth direction which is mm while D has an infinite depth. However, with a limited extension in the c-direction can continue to grow after the crack has broken the surface in the a-direction. This means that the fatigue life is not finished when the crack has broken the surface but is dependent on the extension of the sheet in the c-direction.

154 4 Analysis of Fatigue Life in Two Weld Class Systems Internal cracks are not favourable since they are hard to detect before they have reached the surface. When the crack has reached the surface it might in some cases be too late do anything about it.

155 5 Compilation of STD55,5 4 STD55,5 Case 7 B Description: Incomplete root penetration Modelling and boundary conditions: l Requirements and results: A, t, but max. mm. l,4 t, but max. mm. Incomplete root penetration must not occur closer than mm to the end of the weld or the crossing point respectively. A = mm, l = 4 mm σ = 4 MPa nom N =.95 Nf = 47% of Modelling: W Φ t c σ t a a c Analytical case [8] Denotations according to analytical case. Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 8 [MPa (m)] N [-] x

156 4 Analysis of Fatigue Life in Two Weld Class Systems STD55,5 Case 7 C Description: Incomplete root penetration Modelling and boundary conditions: l Requirements and results: A, t, but max. mm. l t, but max. 5 mm. Incomplete root penetration must not occur closer than mm to the end of the weld or the crossing point respectively. A = mm, l = mm σ = 4 MPa nom N =.73 Nf = 3% of Modelling: W Φ t c σ t a a c Analytical case [8] Denotations according to analytical case. Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 8 [MPa (m)] N [-] x 5

157 5 Compilation of STD55,5 43 STD55,5 Case 7 D Description: Incomplete root penetration Modelling and boundary conditions: l Requirements and results: A, t, but max. 4 mm. Incomplete root penetration must not occur closer than mm to the end of the weld or the crossing points respectively. A = mm, l = infinite σ = 4 MPa nom N =. Nf = 3% of Modelling: A = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 8 [MPa (m)] N [-] x 5

158 44 Analysis of Fatigue Life in Two Weld Class Systems

159 Compilation of ISO Compilation of ISO587 This chapter contains overall information on the CEN ISO587 weld standard. Also results and some detailed conclusions and recommendations from all calculated cases in the standard are presented in diagrams, tables and on result sheets.. About the standard ISO587 [] is the European standard for fusion welded joints and was adopted in 3 by CEN European Committee for Standardization (French: Comité Européen de Normalisation). The members of CEN are in general the members of the European Union. The ISO587 standard has three different welding classes i.e., B, C and D, where B has the best quality and D the worst. Unlike the Volvo STD55,5 [] standard, the ISO587 does not have any additional designation for fatigue loading. However, in some of the cases smooth transition is required. Compared to the STD55,5 standard, the ISO587 standard is more vague in its descriptions. For example, the designation short imperfections is commonly used but there is no figure on the size of a short imperfection i.e., a short imperfection can vary a lot depending on who is assessing the weld. The same applies to smooth transition and locally permitted. When modelling the cases in the standard smooth transition has been translated to a radius of mm and short imperfections and locally permitted have been modelled as an infinite imperfection, since no numbers are available. This is the worst case scenario. Further, the ISO587 standard contains a few cases which are not available in the STD55,5 standard, for example overlap (also known as cold lap) and angular misalignment.. Modelling All transverse butt welds in the standard with the requirement not permitted have been modelled with Case A in the STD55,5 standard, i.e., Case 3 without the transition radius of mm. Case 3 with the transition radius of mm has been used when smooth transition is required. Corresponding cases for fillet welds with the requirement smooth transition have been modelled with Case 43, while ISO587 Case.B has been used if smooth transition is not prescribed. Further comments on modelling are given in Chapter 3 and in the result sheets for each case and class..3 Results Results with pictures and diagrams for each case and welding class can be found on the following pages. All results are also compiled in Figure C.-C. and in Table C.-C., in Appendix C. An overview of the results can be found in Figure C.. It shows large scatter in the results. However, patterns can be discerned. For example, some cases have nearly no difference in life between the welding classes, while some show large differences. Heavy grouping of the cases can be seen in Table..

160 4 Analysis of Fatigue Life in Two Weld Class Systems Table.. Influence of acceptance limits on the fatigue life for a certain welding class. Large influence Some influence No influence Butt welds Fillet welds Butt welds Fillet welds Butt welds Fillet welds one db As can be seen in Table. especially the acceptance limits for the fillet welds have very little influence on the fatigue life. It can also be seen in Table. and Figure C. that there are only five cases out of 9 calculated where the acceptance limits have a major impact on the fatigue life. This is quite remarkable. In other words, fatigue properties have not been thoroughly evaluated when the standard was written. The same conclusion can easily be drawn when looking at Figure C. and C.3 for transverse butt welds and fillet welds respectively. The poor fatigue properties are most clearly seen in Figure C.3 for fillet welds, where no class show the desired pattern of a gradually decreasing life with a gradually decreasing welding class. In a few cases the undesirable pattern can be explained by the fact that the defect for classes B and C are not permitted. They have therefore been modelled with Case 3 or 43, which give the same lives for both B and C. The ratios between B and C and C and D have been plotted in Figure C.5. Many cases have the ratio one between the classes while a few cases show a different pattern. A ratio of one between the welding classes simply means no difference in fatigue life between the welding classes. The deviant value for Case., lack of fusion, depends on an internal defect where the initial crack is 4 mm. Thus, the crack can only be integrated mm before half the thickness has been reached. This results in the short fatigue life and large ratio between welding class C and D. Case.4,.7 (fillet weld), 3. (one-sided and double sided welding) and 3. can be lifted out from the standard along with Case.7 (fillet and butt weld). The results for these cases are plotted in Figure C.4. Case. and.3 are left out because they are internal defects. The cases presented in Figure C.4 have a connection between the acceptance limits and the fatigue life, something which separates them from the rest. If the ratios between the welding classes are plotted for these cases, see Figure C., one can see that many of the cases have a ratio of.5-.5 between B and C. The ratio between C and D varies more. Half of the cases have a ratio of about to while the other half have a ratio of about.5 to 3.5. It should be said that the same pattern as described above was found in STD55,5. Many cases had a ratio of approximately between B and CU (compared to B and C in ISO587) The ratio between CU and DU varied a lot (compare with C and D in ISO587). In Figure C.7 the maximum, minimum, average and median value for each welding class has been plotted. The results are more less scattered than for the STD55,5 standard i.e., the maximum and the minimum value in each welding class do not differ more than a factor of ten. This is true if the maximum value in welding class D is disregarded. The maximum value

161 Compilation of ISO in welding class D comes from Case.3, overlap (or coldlap), where the defect is a horizontal crack which makes a 9º turn before growing vertically into the material. In welding class B and C, this type of defect is not permitted and Case 3 without the transition radius gives much shorter life than the cold lap. This makes it hard to compare this case with the others and the deviating large maximum value can be disregarded when studying Figure C.7. Further, if the maximum value in welding class D is disregarded, the maximum, minimum, average and median value decreases when moving from welding class B to D, something which is expected, since a higher class ought to give a longer life. Cases.7,.4,.7, 3. and 3. all show influence from the acceptance limits on the fatigue life. The lives of these cases have been plotted versus the acceptance limit in Figure C.8. An exponential trendline has been fitted to the points and the equation for the line is fitted in Figure C.8. The trendline could serve as a tool when setting new acceptance limits. For example, the acceptance limit can be read on the curve if the desired life in a certain welding class has been decided. Of course this might not give the exact life for the certain case, but it will at least be possible to get a notion about in what hundred the desired acceptance limit might be. Similar more extensive data can be found in Figure B.9-B. for the STD55,5. These data can be a great help if new acceptance limits are to be set. It is not possible to create an appropriate trendline for all the calculated data, since they are too scattered and many of the acceptance limits for different defects do not have any influence on the fatigue life. In Figure C.9-C., results for each welding class can be found. These results also confirm large scatter in the results.

162 48 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.7 (fillet weld) Undercut Requirements and results D C B Smooth transition is required. h. t, but max. mm Smooth transition is required. h. t, but max..5 mm Smooth transition is required. h.5 t, but max..5 mm.54 7% of.9 45% of.9 45% of 5% 45% 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments The geometry is, unlike as shown in the figure, modelled with only the undercut in the horizontal sheet. (Even if there were an undercut in the vertical sheet as well, it is uncertain if it would have any significant effect on the stress flow because the joint is solely horizontally loaded.) This means that here the undercut is modelled the same way as the undercut in Volvo STD55,5. An interesting difference from the Volvo standard is that smooth transition is required for all classes. (Note that the ISO standard uses the term smooth instead of even.) The smooth transition is modelled as a mm radius. Welding classes B/C and D are identically the same as B and CU in the Volvo standard. (For thicknesses up to 5 mm B, C and D correspond to B, CU and DU, but for the mm sheet modelled here, the ISO standard limits the undercut depths.) Conclusions and recommendations The maximum depth restrictions make ISO587 less useful when mm sheet is commonly used (in for example articulated haulers). The fatigue life results show that the acceptance limits in the Volvo standard, which are thickness depending up to mm, gives a good relation between lives for the different welding classes. Furthermore the Volvo standard is more flexible, as it is possible to choose additional designation U or not.

163 Compilation of ISO ISO587 Case.7 B and C (fillet weld) Description: Undercut Modelling and boundary conditions: Requirements and results: Smooth transition is required. Class B: h.5 t, but max..5 mm Class C: h. t, but max..5 mm h = notch depth + initial crack =.4 +. =.5 mm σ 8 MPa nom = N =.9 Nf = 45% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

164 5 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.7 D (fillet weld) Description: Undercut Modelling and boundary conditions: Requirements and results: Smooth transition is required. h. t, but max. mm h = notch depth + initial crack =.9 +. = mm σ 8 MPa nom = N =.54 Nf = 7% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

165 Compilation of ISO587 5 ISO587 Case.7 (butt weld) Undercut Requirements and results D C B Smooth transition is Smooth transition is required. required. h. t, but max. h. t, but max..5 mm mm.4 % of.7 3% of Smooth transition is required. h.5 t, but max..5 mm.7 3% of 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments The geometry is, unlike as shown in the figure, here modelled with only one undercut (one of the tow shown in the figure). This means that it is modelled the same way as the undercut in Volvo STD55,5. (A double-sided defect may lead to slightly different results because the stress flow through the geometry will change, but that is not investigated here.) As for the fillet weld undercut, smooth transition is required for all welding classes. This distinguishes the B classes, where the Volvo STD55,5 does not require smooth transition for butt welds. The acceptance limit for welding class B is identical to class B in the Volvo standard. Conclusions and recommendations Like in the undercut case for fillet weld, the Volvo standard provides a more useful scale for classifying the requirements on a certain weld. (See also comments on Case.7 fillet weld.)

166 5 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.7 B and C (butt weld) Description: Undercut Modelling and boundary conditions: Requirements and results: Smooth transition is required. Class B: h.5 t, but max..5 mm Class C: h. t, but max..5 mm h = notch depth + initial crack =.4 +. =.5 mm σ nom = 4 MPa N =.7 Nf = 3% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) [MPa (m)] N [-] x 5

167 Compilation of ISO ISO587 Case.7 D (butt weld) Description: Undercut Modelling and boundary conditions: Requirements and results: Smooth transition is required. h. t, but max. mm h = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.4 Nf = % of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

168 54 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.9 Excess weld metal Requirements and results D C B Smooth transition is required h mm +.5b but max. mm h = 3.5 mm, b = mm Smooth transition is required h mm +.5b but max. 7 mm h =.5 mm, b = Smooth transition is required h mm +.b but max. 5 mm h = mm, b = mm.8 84% of mm.7 88% of.85 9% of % 9% 8% 7% % 5% 4% 3% % % % B D D Modelling and comments This case is identical to the STD55,5 Case, weld reinforcement. The only identical acceptance limits are B (ISO) and CU (Volvo). The slight difference in life between these two classes is probably due to some minor differences in the modelling of the weld reinforcement. The accepted reinforcement heights for B, C and D are,.5, and 3.5 mm for the ISO standard and,.5, and 3 mm for the Volvo standard i.e., they are quite similar. In ISO587 though, smooth transition is required for all classes. Conclusions and recommendations For both standards the results show that even large weld reinforcements (several millimetres) do not shorten the life considerably, implying that the acceptance limits are of no substantial importance. Therefore, from a fatigue point of view, the case could be deleted from the standard. It is not recommended to delete the case from the standard entirely since some kind of limitation of the weld reinforcement is important for reasons of appearance as well as for technical reasons (too large weld reinforcements could interfere with other geometry etc.). However, it should be clear that the weld reinforcement has no influence on the fatigue properties.

169 Compilation of ISO ISO587 Case.9 B Description: Excess weld metal (butt weld) Modelling and boundary conditions: Requirements and results: Smooth transition is required h mm +.b but max. 5 mm h = mm, b = mm initial crack =. mm σ nom = 4 MPa N =.85 Nf = 9% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

170 5 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.9 C Description: Excess weld metal (butt weld) Modelling and boundary conditions: Requirements and results: Smooth transition is required h mm +.5b but max. 7 mm h =.5 mm, b = mm initial crack =. mm σ nom = 4 MPa N =.7 Nf = 88% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

171 Compilation of ISO ISO587 Case.9 D Description: Excess weld metal (butt weld) Modelling and boundary conditions: Requirements and results: Smooth transition is required h mm +.5b but max. mm h = 3.5 mm, b = mm initial crack =. mm σ nom = 4 MPa N =.8 Nf = 84% of Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

172 58 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. Excessive convexity Requirements and results D C B h mm +.5b but max. 5 mm h = 3.5 mm, b = mm h mm +.5b but max. 4 mm h =.5 mm, b = mm h mm +.b but max. 3 mm h = mm, b = mm.5 33% of. 33% of. 33% of 35% 3% 5% % 5% % 5% % B C D Modelling and comments Sharp transition is used between the weld and the sheet metal. This case has no counterpart in the Volvo STD55,5. Interesting in this case is the effect the convexity might have on the angle between the weld and the parent material. A larger convexity implies a higher angle, which makes the joint more exposed to fatigue. However, the required heights of the convexities (the same as for weld reinforcements) do not have any effect on the life. The differences are so small it differs less than between C and D that no reasonable changes of the acceptance limits could give any meaningful results. Conclusions and recommendations From a fatigue point of view the acceptance limits have no influence on the life. Therefore this case could be removed from the standard if only fatigue properties are considered.

173 Compilation of ISO ISO587 Case. B Description: Excessive convexity (fillet weld) Modelling and boundary conditions: Requirements and results: h mm +.b but max. 3 mm h = mm, b = mm initial crack =. mm σ 8 MPa nom = N =. Nf = 33% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

174 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. C Description: Excessive convexity (fillet weld) Modelling and boundary conditions: Requirements and results: h mm +.5b but max. 4 mm h =.5 mm, b = mm initial crack =. mm σ 8 MPa nom = N =. Nf = 33% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

175 Compilation of ISO587 ISO587 Case. D Description: Excessive convexity (fillet weld) Modelling and boundary conditions: Requirements and results: h mm +.5b but max. 5 mm h = 3.5 mm, b = mm initial crack =. mm σ 8 MPa nom = N =.5 Nf = 33% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

176 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. (butt weld) Excess weld metal Requirements and results D C B h mm +.b but max. 5 mm h = 4 mm, b = 3 mm h mm +.b but max. 4 mm h =.8 mm, b = 3 mm h mm +.b but max. 3 mm h =. mm, b = 3 mm.9 85% of.9 85% of.9 85% of 9% 8% 7% % 5% 4% 3% % % % B C D Modelling and comments This case corresponds to STD55,5 Case, penetration bead. It is modelled with a sharp transition. There is practically no difference at all between the classes. Conclusions and recommendations Since the acceptance limits obviously have no influence on the life, this case could be deleted from the standard if only fatigue properties are considered. It is not recommended to delete the case from the standard entirely since some kind of limitation of the penetration bead is important for reasons of appearance as well as for technical reasons (too large penetration beads could interfere with other geometry etc.). However, it should be clear that the penetration bead has no fatigue properties.

177 Compilation of ISO587 3 ISO587 Case. B Description: Excess penetration Modelling and boundary conditions: Requirements and results: h mm +.b but max. 3 mm h =. mm, b = 3 mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = 85% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

178 4 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. C Description: Excess penetration Modelling and boundary conditions: Requirements and results: h mm +.b but max. 4 mm h =.8 mm, b = 3 mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = 85% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

179 Compilation of ISO587 5 ISO587 Case. D Description: Excess penetration Modelling and boundary conditions: Requirements and results: h mm +.b but max. 5 mm h = 4 mm, b = 3 mm initial crack =. mm σ nom = 4 MPa N =.9 Nf = 85% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

180 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. (fillet weld) Incorrect weld toe Requirements and results D C B α 9º α º α º.74 37% of.75 37% of.75 37% of 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments All welding classes have been modelled with a sharp transition. The weld reinforcement has been kept the same but the part in front of the crack opening has been modelled as a. mm straight line with the correct toe angle, α, relative to the sheet (see Figure.). α. mm initial crack Figure.. Modelling of the transition at the weld toe. This case could provide interesting information about the influence of the transition angle on the fatigue life, especially since there is no corresponding case in STD55,5. However, the acceptance limits for this case give no significant differences at all, even though the angle

181 Compilation of ISO587 7 difference of degrees between the classes is a seemingly distinct difference that could have been expected to have a noticeable effect on the results. Conclusions and recommendations Obviously, this kind of angular difference does not affect the life. (This is principally the same result as obtained in case., where the increased angle depends on the convexity.) It was discussed whether the choice of initial crack has any substantial effect on the life. The ANSYS results showed the angle affects the stress intensity factors more for shorter cracks. However, for an initial crack of.5 mm the difference in life will still be only a few percent. As the toe angle is generally considered an important factor for determining the life of the joint, the results in. are remarkable. With the current acceptance limits the case is of no interest and could be removed from the standard. However, that the angle has so little impact on the life is definitely a result must be considered. Possibly the differences would be more significant for smaller angles, even if there are no indications of this in case. neither for butt nor fillet weld. Finally it can be noticed that the name Incorrect weld toe is a bit misleading. This case deals only with the issue of the angle at the transition, and hence should be named something more appropriate.

182 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. B and C Description: Incorrect weld toe fillet weld Requirements and results: α º initial crack =. mm σ 8 MPa nom = N =.75 Nf = 37% of Modelling and boundary conditions: Modelling: initial crack initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

183 Compilation of ISO587 9 ISO587 Case. D Description: Incorrect weld toe fillet weld Requirements and results: α 9º initial crack =. mm σ 8 MPa nom = N =.74 Nf = 37% of Modelling and boundary conditions: Modelling: initial crack initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

184 7 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. (butt weld) Incorrect weld toe Requirements and results D C B α 9º α º α 5º.45 7% of.45 7% of.47 73% of 8% 7% % 5% 4% 3% % % % B C D Modelling and comments All welding classes have been modelled with a sharp transition. The weld reinforcement has been kept the same but the section close to the crack opening has been modelled as a. mm straight line with the correct toe angle, α, relative to the sheet (see Figure.). α. mm initial crack Figure.. Modelling of the transition at the toe. The transition between the weld reinforcement and the sheet metal is a singular point. I.e., the finer the mesh the larger stress is obtained. The stress goes towards infinity at a sharp corner. Therefore there is no need to evaluate any stress concentration at the transition. In real life there will never be a sharp transition but there is always a transition radius. Since the crack initiation phase is not studied, no investigation will be performed on how much longer life there is in this phase. This case could provide interesting information about the influence of the transition angle on the fatigue life, especially since there is no corresponding case in STD55,5. However, the

185 Compilation of ISO587 7 acceptance limits for this case give no significant differences at all, even though the difference in angle between 9 and 5 degrees is seemingly distinct and could have been expected to have noticeable effects on the results. Conclusions and recommendations Obviously, this kind of angular deviation does not affect the life. (This is essentially the same result that is obtained for weld reinforcements and penetration beads.) It was discussed whether the choice of initial crack has any substantial effect on the life. The Ansys results showed the angle affects the stress intensity factors more for shorter cracks. However, for an initial crack of.5 mm the difference in life will still be only a few percent. As the toe angle is generally considered an important factor for determining the life of the joint, the results in. is remarkable. With the current acceptance limits the case is of no interest and could be removed from the standard. However, the angle having so little impact on the life is definitely a result that ought to be further investigated. Possibly the differences would be more significant for lower angles, even if there are no indications on this in case. neither for butt nor fillet weld. Finally it can be noticed that the name Incorrect weld toe is a bit misleading. This case deals only with the issue of the angle at the transition, and hence should be named something more appropriate.

186 7 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. B Description: Incorrect weld toe butt welds Requirements and results: α 5º initial crack =. mm N =.47 Nf = 73% of Modelling and boundary conditions: Modelling: initial crack initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

187 Compilation of ISO ISO587 Case. C Description: Incorrect weld toe butt welds Requirements and results: α º initial crack =. mm N =.45 Nf = 7% of Modelling and boundary conditions: Modelling: initial crack initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

188 74 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. D Description: Incorrect weld toe butt welds Requirements and results: α 9º initial crack =. mm N =.45 Nf = 7% of Modelling and boundary conditions: Modelling: initial crack initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

189 Compilation of ISO ISO587 Case.3 Overlap Requirements and results D C B h.b Not permitted Not permitted h = mm, b = mm.3 3% of.58 79% of.58 79% of 4% D % % 8% % 4% % % B C Modelling and comments Class B and C are the same as IIW Case 3 without a transition. Welding class D is special in the way it has been modelled. An overlap or a cold lap is obtained when melted metal flow over but do not fuse with the sheet. Instead a horizontal crack is created. When the weld is loaded the crack starts to turn vertically down into the material. To model this the equation ϕ 3ΔK II + ΔK I ΔK I + 8ΔK II = arccos (.) ΔK + Δ I 9 K II [] is used. The equation describes the kink angle the crack will grow with. Equation (.) combines the stress intensity factors in mode I and II ( Δ K I and Δ K II ) to calculate the angle. Step Starting condition is that the crack, or the overlap, is horizontal (see Figure.3).

190 7 Analysis of Fatigue Life in Two Weld Class Systems overlap initial crack Figure.3. The horizontal initial crack. First the stress intensity factors are calculated for the initial crack (they become almost equal in mode I and II). The stress intensity factors are then used in Equation (.) to calculate the angle, at which the crack will continue to grow. In this case the angle becomes ϕ = 54 Step. The FE-model is rebuilt and the crack is chosen to become. mm longer in the ϕ = 54 The increment of the crack does not follow any given equation but is chosen freely. The model now looks like in Figure.4. overlap. ϕ = 54 crack tip Figure.4. The crack has turned down into the sheet. The stress intensity factors are once again calculated. Now Δ K I becomes approximately twice the size of Δ K II, because the crack is loaded more in mode I now. If these values are inserted into Equation (.) the angle becomes ϕ = 3. This means that the crack has now

191 Compilation of ISO turned ϕtot = ϕ + ϕ = 54 3 = 9, i.e. it is now moving vertically down. The crack is once again set to grow with an increment of. mm (this time vertically, see Figure.5). Then a general macro can take care of the remaining calculations of the crack growth. The stress intensity factors for mode I and II are calculated and combined using Equation (.). The life is then integrated, but this time the overlap is taken into account when calculation the life. overlap ϕ = 54 ϕ = 3 crack tip Figure.5. The crack has turned 9º and is now propagating vertically. Conclusions and recommendations Results show a longer life for an overlap/coldlap than for classes B and C where no overlap is allowed. This probably depends on the fact that the crack does not grow vertically from the start, and it thus takes longer time for the crack to reach half the thickness. However, overlaps may lead to cracks which are not visible to the human eye. They can only be detected by for example ultrasound or x-ray. It is also difficult to know how much of the overlap that actually lacks fusion. Therefore overlaps are hazardous to deal with and acceptance limits should be restrictive. The safest solution is of course not allowing any overlap at all, but that may be unnecessarily restrictive. Possibly, overlaps could be prohibited for fatigue loaded joints (additional designation U in the Volvo standard). More studies ought to be conducted on the modelling and computation of overlaps. In this case the increment of the crack was set to. mm. For example, the influence of the increment length should be evaluated, but that is not within the scope of this study.

192 78 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.3 D Description: Overlap Modelling and boundary conditions: Requirements and results: h.b h = mm, b = mm h = initial crack = mm σ nom = 4 MPa N =.3 Nf = 3% of Modelling: h = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) 8 (N) [MPa (m)] N [-] x

193 Compilation of ISO ISO587 Case.4 Sagging / Incompletely filled groove Requirements and results D C B Smooth transition required Smooth transition required Smooth transition required h.5t but max. mm h.t but max. mm h.5t but max..5 mm.3 % of.45 % of.98 49% of % 5% 4% 3% % B C % D % Modelling and comments All welding classes have been modelled as a notch, with a transition radius of mm. The same model is used in Case.7. Conclusions and recommendations As can be seen the amount of missing material in the weld has huge impact on the fatigue life. Much of the life lies within the first tenths of one millimetre of the crack growth. This case very well demonstrates influence of the acceptance limits on the fatigue properties.

194 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.4 B Description: Sagging, incomplete filled groove Requirements and results: Smooth transition required h.5t but max..5 mm h = notch depth + initial crack =.4 +. =.5 mm σ nom = 4 MPa N =.98 Nf = 49% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

195 Compilation of ISO587 8 ISO587 Case.4 C Description: Sagging, incomplete filled groove Requirements and results: Smooth transition required h.t but max. mm h = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.45 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

196 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.4 D Description: Sagging, incomplete filled groove Requirements and results: Smooth transition required h.5t but max. mm h = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.3 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

197 Compilation of ISO ISO587 Case. Excessive asymmetry of fillet weld (excessive unequal leg length) Requirements and results D C B h mm +.a h mm +.5a h.5 mm +.5a.7 3% of.7 3% of.7 3% of 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments The crack has in all welding classes been placed at the steepest transition. No class has been modelled with a transition radius, since there is no requirement of a smooth transition. As can be seen there are nearly no differences in the results. There is neither any larger difference between class B and D, welding class B has.5 mm as acceptance limit, while D has 3 mm. Compared to the life of a model with no leg deviation (IIW Case 43 without misalignment), which has a life of 38% of million, the difference is negligible. Conclusions and recommendations The results above compared to the case with correct legs shows that leg deviation does not have a major impact on the fatigue life. From this point of view the case could be removed from the standard.

198 84 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. B Description: Requirements and results: Excessive asymmetric of fillet weld (excessive unequal leg length) h.5 mm +.5a h =.5 mm initial crack =. mm σ 8 MPa nom = N =.7 Nf = 3% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

199 Compilation of ISO ISO587 Case. C Description: Requirements and results: Excessive asymmetric of fillet weld (excessive unequal leg length) h mm +.5a h =.75 mm initial crack =. mm σ 8 MPa nom = N =.7 Nf = 3% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

200 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. D Description: Requirements and results: Excessive asymmetric of fillet weld (excessive unequal leg length) h mm +.a h = 3 mm initial crack =. mm σ 8 MPa nom = N =.7 Nf = 3% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

201 Compilation of ISO ISO587 Case.7 (butt weld) Root concavity Requirements and results D C B Smooth transition is required. Short imperfections: h.t, but max. mm Smooth transition is required. Short imperfections: h.t, but max. mm Smooth transition is required. Short imperfections: h.5t, but max..5 mm.3 % of.45 % of.98 49% of % 5% 4% 3% % B C % D % Modelling and comments All welding classes have been modelled with a notch with a transition radius of mm. The same model is used in Case.4. Conclusions and recommendations As can be seen the amount of missing material in the weld has a huge impact on the fatigue life. Much of the life lies within the first tenths of one millimetres of the crack growth. This case very well demonstrates fatigue properties of the acceptance limits.

202 88 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.7 B Description: Root concavity Requirements and results: Smooth transition is required. Short imperfections: h.5t, but max..5 mm h = notch depth + initial crack =.4 +. =.5 mm N =.98 Nf = 49% of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

203 Compilation of ISO ISO587 Case.7 C Description: Root concavity Requirements and results: Smooth transition is required. Short imperfections: h.t, but max. mm h = notch depth + initial crack =.9 +. = mm σ nom = 4 MPa N =.45 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

204 9 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.7 D Description: Root concavity Requirements and results: Smooth transition is required. Short imperfections: h.t, but max. mm h = notch depth + initial crack =.9 +. = mm N =.3 Nf = % of Modelling and boundary conditions: Modelling: R initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 8 5 [MPa (m)] N [-] x 4

205 Compilation of ISO587 9 ISO587 Case. Insufficient throat thickness Requirements and results D C B Short imperfections: h.3 mm +.a, but max. mm Short imperfections: h.3 mm +.a, but max. mm Not permitted.5 5% of.5 5% of.7 38% of 45% 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments With a throat of 5 mm the acceptance limits for welding class C and D become the same, i.e..8 mm. Class B is the same as IIW Case 43 without any transition radius. Conclusions and recommendations In this case it could be recommended to review the requirements for welding class C and D. The throat has to be more than 7 mm if there should be any difference between the acceptance limit for C and D. Not many applications have throats greater than 7 mm. It is reasonable that there should be a difference between class C and D for sensible throat thicknesses. Other conclusions are essentially the same as for STD55,5 Case ; the limits could be relaxed to some extent, but the risks with a smaller throat should be considered. (See Case for further discussion.)

206 9 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. B Description: Insufficient throat thickness Requirements and results: Not permitted initial crack =. mm N =.7 Nf = 38% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

207 Compilation of ISO ISO587 Case. C and D Description: Insufficient throat thickness Modelling and boundary conditions: Requirements and results: Short imperfections: h.3 mm +.a, but max. mm h =.8 mm initial crack =. mm N =.5 Nf = 5% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

208 94 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. Excessive throat thickness Requirements and results D C B Unlimited. h mm +.a, but max. 4 mm h = mm h mm +.5a, but max. 3 mm h =.75 mm % of.48 74% of 9% 8% 7% % 5% 4% 3% % % % B C Modelling and comments This case is modelled without any transition radii. The throat has been changed to correspond to the acceptance limits. Conclusions and recommendations As expected the life is increased when the throat is increased, since the throat is transmitting the load through the sheet metals. Excessive throat thickness may at first sight appear only positive, but if the throat is increased in one part of the construction, the stress distribution might change and other welds in the structure may fail instead. This could lead to shorter life for the overall construction. For example, it might be favourable that one part of the construction fails first in order to reduce the damages. If there is an excessive throat thickness in that part of the construction, another, more vital, part of the structure may fail first, causing a worse scenario with larger damages. Furthermore, it is not economical to make thicker welds than necessary. Because of this, a general limit for excessive throat thickness ( mm for example) is recommended to be introduced.

209 Compilation of ISO ISO587 Case. B Description: Excessive throat thickness Modelling and boundary conditions: Requirements and results: h mm +.5a, but max. 3 mm h =.75 mm initial crack =. mm σ nom = 8 MPa N =.48 Nf = 74% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

210 9 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case. C Description: Excessive throat thickness Modelling and boundary conditions: Requirements and results: h mm +.a, but max. 4 mm h = mm initial crack =. mm σ nom = 8 MPa N =.59 Nf = 8% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x

211 Compilation of ISO ISO587 Case. Lack of fusion (incomplete fusion) - Lack of side wall fusion Requirements and results D C B Short imperfections Not permitted Not permitted permitted, but not breaking of the surface h.4s, but max. 4 mm h = 4 mm, s = mm. % of.58 79% of.58 79% of 9% 8% 7% % 5% 4% 3% % % % B C D Modelling and comments Classes B and C are the same as IIW Case 3 but without the transition radius since lack of fusion is not permitted. Therefore, classes B and C have been modelled as growing at the transition between the excessive weld and the sheet metal. Class D has been modelled as an internal crack in the material. It has been set to grow equally in both directions for each cycle and the life has been integrated from 4 mm to 5 mm. It is not obvious in the standard how the defect is to be modelled. At first glance it looks like a crack from the surface and deep down into the material. However, the case has been interpreted as an internal crack since breaking of the surface is not permitted. This case is principally the same as for STD55,5 cases 5//7. The crack is placed in the middle of the sheet metal i.e., symmetrically extended around the centre line. However, in the STD55,5 standard many of the cases require a finite depth of the crack. Therefore an analytical case has been used for finite depths. Further, a model with the crack displaced towards one side would probably lead to a worse case, as the crack then reaches the surface much faster. This geometry is also the same as in Case.3, lack of penetration, with the exception of the crack there being placed straight below the weld reinforcement instead of beside it. It is

212 98 Analysis of Fatigue Life in Two Weld Class Systems remarkable that the acceptance limit is 4 mm for Case., while it is only mm for Case.3, when the defects in Case. and.3 (butt weld) are very similar. Conclusions and recommendations The disadvantage with internal cracks is that they cannot be detected with the eye, but instead other methods, for example ultrasound, are needed. There is a great risk of fracture before the crack is detected, and even if detected, it is harder to repair the crack. Cracks from the surface are more easily detected and can be repaired before they lead to fracture. Since internal cracks are not favourable, it is not recommended to set new acceptance limits without further investigation.

213 Compilation of ISO ISO587 Case. D Description: Lack of fusion (incomplete fusion) Modelling and boundary conditions: Requirements and results: Short imperfections permitted, but not breaking of the surface h.4s, but max. 4 mm h = mm, s = mm initial crack = 4 mm σ nom = 4 MPa N =. Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 8 [MPa (m)] N [-] x 5

214 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.3 (fillet weld) Lack of penetration Requirements and results D C B Short imperfections Not permitted Not permitted permitted h.a, but max. mm h = mm.9 4% of.7 3% of.7 3% of 4% 35% 3% 5% % 5% % 5% % B C D Modelling and comments Welding class D has been modelled with a small triangle of lacking material at the root of the weld. Imperfections are not permitted for classes B and C, these classes have been modelled as IIW Case 43 without any transition radius. In this case the crack is set to grow from the root. In welding class D, the initial crack is pointing in vertical direction from the top corner of the small triangle of lacking penetration, see Figure.. In class B and C the crack grows from one end of the slit between the two sheets, which have not been fused.

215 Compilation of ISO587 initial crack slit σ Figure.. Placement of the initial crack in welding class D The crack growth direction is calculated with the equation 3K = arccos + K I K I + 8K K + 9K ϕ II I II II (.) [] which has previously been used in Case.3. However, one problem arises; the Equation (.) can only turn in one direction because K I is always greater than zero in this case. The x reason why K I > is that the crack is never closed and further, arccos 8. The r crack strives to be loaded solely in mode I and the problem is that Equation (.) is unstable if the crack turns too much. For example, if the value ϕ = 5. is received and is rounded down to ϕ =, then K II might grow more than K I, resulting in a greater change of angle for the next step. In the end this leads to an unrealistic result. This proves to be the case when Equation (.) is used for several steps in the crack growth process. After a few steps the crack has turned almost parallel to the horizontal tension. This is unrealistic and therefore the process is stopped. In order to overcome this problem, Equation (.) is used as long as the angle is decreasing with each step. When a calculation results in greater change in angle than the previously calculated angle, the process is stopped, and the crack is assumed to continue growing in the direction of previously calculated angle until half of the throat has been reached. The crack is set to grow with an increment of. mm for the first steps. In the first step the crack makes a turn of about º. In the second step the turning angle has decreased to about - 5º, and in the following step the angle starts to grow again. The process is stopped at the second step, see Figure.7.

216 Analysis of Fatigue Life in Two Weld Class Systems Step Step Path after Step slit Desired path according to Equation (.) σ Figure.7. Step and which lead to the final crack growth direction. As can be seen in Figure.7 the desired crack growth direction from Equation. is unrealistic. Conclusions and recommendations Other ways of modelling this case should be tested before drawing any extensive conclusions. There are other equations for predicting the crack path. Possibly there are equations that can correct the crack path if it is turning too much. Due to lack of time no further investigations will be carried out in this thesis work. Since the fatigue life is less than half in welding class D compared to B/C one can draw the conclusion that lack of penetration have a large impact on the results. The question, whether or not the crack should grow from the root, is once again brought up. As said before, root cracks are not favourable since they are hard to discover before failure.

217 Compilation of ISO587 3 ISO587 Case.3 B and C Description: Lack of penetration Requirements and results: Not permitted initial crack is the slit between the sheets N =.7 Nf = 3% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) 3 (N).5 [MPa (m)] N [-] x 5

218 4 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.3 D Description: Lack of penetration Modelling and boundary conditions: Requirements and results: Short imperfections permitted h.a, but max. mm h = mm initial crack =. mm σ nom = 8 MPa N =.9 Nf = 4% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) 3 (N).5 [MPa (m)] N [-] x 5

219 Compilation of ISO587 5 ISO587 Case.3 (butt weld) Lack of penetration Requirements and results D C B Short imperfections Not permitted Not permitted permitted h.t, but max. mm. 3% of.58 79% of.58 79% of 9% 8% 7% % 5% 4% 3% % % % B C D Modelling and comments Class D has been modelled as an internal crack in the material. It has been set to grow equally in both directions for each cycle and the life has been integrated from mm to 5 mm. Since the lack of penetration is not allowed for welding classes B and C, these cases have been modelled with STD55,5 Case A. This implies a surface crack growing at the transition between the excessive weld and the sheet metal. Conclusions and recommendations In this case the internal crack has considerably shorter life than a surface crack The disadvantage with internal cracks is that they cannot be detected with the eye, but instead need other methods for detection. For example, ultrasound or x-ray could be used. There is a great risk of fracture before detection of the crack, and even if detected, it is harder to repair the crack. Cracks from the surface are more easily detected and can be repaired before they cause fracture. As long as methods to evaluate internal cracks are not frequently used in weld auditing, acceptance limits for internal defects are of little use since they cannot be measured. It is recommended to remove internal defects from the fatigue part of a new standard until they have been investigated more carefully.

220 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case.3 D Description: Lack of penetration Modelling and boundary conditions: Requirements and results: Short imperfections permitted h.t, but max. mm h = initial crack = mm σ nom = 4 MPa N =. Nf = 3% of Modelling: h = initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 3 ( ) (N) 5 8 [MPa (m)] N [-] x 5

221 Compilation of ISO587 7 ISO587 Case 3. Linear misalignment, doublesided welding Requirements and results D C B h.5t, but max. 5 mm h.5t, but max. 4 mm h.t, but max. 3 mm. % of.3 % of. 3% of 35% 3% 5% % 5% B C % 5% D % Modelling and comments Comments on modelling are referred to STD55,5 Case 4. Conclusions and recommendations Conclusions in general are referred to STD55,5 Case 4. A slight difference between the ISO and Volvo standards, is that in ISO587 the acceptance limits for one-sided and double-sided welding are the same for all welding classes. In STD55,5, the limits are tighter for one-sided welding in some classes. Strictly geometrically the cases are principally the same, implying that the acceptance limits ought to be the same in both cases. However there could be other considerations, for example a higher risk of lack of penetration in one-sided welds.

222 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case 3. B Description: Linear misalignment, double-sided welding Modelling and boundary conditions: Requirements and results: h.t, but max. 3 mm h = mm initial crack =. mm σ nom = 4 MPa N =. Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

223 Compilation of ISO587 9 ISO587 Case 3. C Description: Linear misalignment, double-sided welding Modelling and boundary conditions: Requirements and results: h.5t, but max. 4 mm h =.5 mm initial crack =. mm σ nom = 4 MPa N =.3 Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

224 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case 3. D Description: Linear misalignment, double-sided welding Modelling and boundary conditions: Requirements and results: h.5t, but max. 5 mm h =.5 mm initial crack =. mm σ nom = 4 MPa N =. Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 8 ( ) (N) [MPa (m)] N [-] x 4

225 Compilation of ISO587 ISO587 Case 3. Linear misalignment, onesided welding Requirements and results D C B h.5t, but max. 5 mm h.5t, but max. 4 mm h.t, but max. 3 mm. % of.3 % of. 3% of 35% 3% 5% % 5% B C % 5% D % Modelling and comments Comments on modelling are referred to STD55,5 Case 3. Conclusions and recommendations Conclusions in general are referred to STD55,5 Case 3. A slight difference between the ISO and Volvo standards, is that in ISO587 the acceptance limits for one-sided and double-sided welding are the same for all welding classes. In STD55,5, the limits are tighter for one-sided welding in some classes. Strictly geometrically the cases are principally the same, implying that the acceptance limits ought to be the same in both cases. However there could be other considerations, for example a higher risk of lack of penetration in one-sided welds.

226 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case 3. B Description: Linear misalignment, one-sided welding Modelling and boundary conditions: Requirements and results: h.t, but max. 3 mm h = mm initial crack =. mm σ nom = 4 MPa N =. Nf = 3% of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

227 Compilation of ISO587 3 ISO587 Case 3. C Description: Linear misalignment, one-sided welding Modelling and boundary conditions: Requirements and results: h.5t, but max. 4 mm h =.5 mm initial crack =. mm σ nom = 4 MPa N =.3 Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : ( ) (N) 5 5 [MPa (m)] N [-] x 5

228 4 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case 3. D Description: Linear misalignment, one-sided welding Modelling and boundary conditions: Requirements and results: h.5t, but max. 5 mm h =.5 mm initial crack =. mm σ nom = 4 MPa N =. Nf = % of Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 8 ( ) (N) [MPa (m)] N [-] x 4

229 Compilation of ISO587 5 ISO587 Case 3. Angular misalignment Requirements and results D C B β 4º β º β º.5 8% of.83 4% of.3 5% of % 5% 4% B C 3% D % % % Modelling and comments Two different ways of modelling this case have been tested. In the first the initial crack was placed on the right side of the weld reinforcement (Figure.8) and in the second, the crack was placed on the left side (Figure.9). The two different ways of placing the crack was tested for welding class D and gave totally different results. When the crack was placed on the left side.3 was achieved. The crack on the right side resulted in a fatigue life of.5 i.e., less than half of the number of. The reason why there was such a huge difference can be seen in Figure.8 and.9. high bending stress initial crack Figure.8. The initial crack on the right side.

230 Analysis of Fatigue Life in Two Weld Class Systems high bending stress initial crack Figure.9. The initial crack on the left side. The angular misalignment results in bending stresses at the fixed right side of the structure. These bending stresses decline towards the left end of the structure in Figure.8 and.9. This results in higher stresses if the crack is placed on the right side of the weld reinforcement, which further leads to higher stress intensity factors and a shorter life. Neither of the ways of modelling this case is wrong - it depends on the situation in real life. Here, the worst case i.e., the initial crack on the right side is chosen when modelling the rest of the classes. Conclusions and recommendations From a fatigue point of view, the acceptance limits for classes C and D could probably be relaxed to some extent. However, an angular misalignment of 4 degrees (current class D) or even more would be devastating for the overall structure for many designs. This is why fatigue considerations might not be limiting. There are no particular recommendations for this case.

231 Compilation of ISO587 7 ISO587 Case 3. B Description: Angular misalignment Requirements and results: β º initial crack =. mm σ nom = 4 MPa N =.3 Nf = 5% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 4 ( ) (N) [MPa (m)] N [-] x 5

232 8 Analysis of Fatigue Life in Two Weld Class Systems ISO587 Case 3. C Description: Angular misalignment Requirements and results: β º initial crack =. mm σ nom = 4 MPa N =.83 Nf = 4% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

233 Compilation of ISO587 9 ISO587 Case 3. D Description: Angular misalignment Requirements and results: β 4º initial crack =. mm σ nom = 4 MPa N =.5 Nf = 8% of Modelling and boundary conditions: Modelling: initial crack Stress intensity factor as a function of crack length: Crack length as a function of number of : 5 ( ) (N) 4 5 [MPa (m)] N [-] x 5

234 Analysis of Fatigue Life in Two Weld Class Systems

235 7 Study of sheet thickness dependence 7 Study of sheet thickness dependence This chapter contains a study of different sheet thicknesses for undercut on a fillet weld. Since only one sheet thickness has been used in all previous calculations, it was decided to investigate the overall impact of different thicknesses. In order to further extend this study, also the influence of a bending moment was investigated. 7. Introduction The aim of this study is to investigate the effect of the sheet thickness on the fatigue life. The study is performed on a range of thicknesses from 5 to 4 mm for one particular case in STD55,5; Case, undercut (fillet weld). An important objective is to review the applicability of the mm results on other sheet thicknesses. As the thickness mm is used throughout the whole work, it is very important to know to what extent these results are valid for other thicknesses, which factors that affect this, and how they can be considered. Along with variation in thickness, also the throat thickness was varied. This was done so that the ratio between the throat thickness and the sheet thickness was.5, i.e., a t =. 5. The same ratio has previously been used for all cases in both standards investigated. However, this leads to an unrealistic throat thickness for the thicker sheets. For example, the throat is mm for a 4 mm thick sheet. In order to examine how the fatigue life is affected by other loads than tension (worst case), also a bending stress is investigated. 7. Studied geometry - STD55,5 Case The parameter study is conducted on Case in the STD55,5 standard. Case is a cruciform joint with an undercut (see Figure 7.). t notch t σ σ h h Figure 7.. Cruciform joint subjected to tension.

236 Analysis of Fatigue Life in Two Weld Class Systems Two types of load conditions are tested; one with uniaxial tension (see Figure 7.) and one with a bending moment applied on both ends (see Figure 7.). In both cases the same boundary conditions are applied, see Figure 7. and 7.. t notch σ t σ h σ σ h Figure 7.. Cruciform joint subjected to bending. The maximum stress at bending, as well as the stress at pure tension, is the same as the FATvalue for the corresponding Case 43 in IIW [], i.e., σ = 8 MPa. 7.. Requirements According to the STD55,5 standard, the requirements according to Table 7. apply to undercuts for cruciform joints,. Table 7.. Requirements for Case in STD55,5. D C B A Locally A.t, but max. mm Locally A.t, but max. mm Locally A.5t, but max..5 mm. l 5 mm Not permitted Note that the maximum value in classes C, D and B are reached already for a thickness of mm. This means that for t > mm, the relative measure of the acceptance limit decreases with increasing thickness.

237 7 Study of sheet thickness dependence Modelling The undercut is modelled differently depending on the welding class. In Figure 7.3 the notch area in Figure 7. and 7. is described for each welding class. Since undercut is not permitted for welding class A, this class has been modelled with an initial crack of. mm at the transition radius. According to the standard, welding class A should have a transition radius of 4 mm. The initial crack has been inserted at the place where the stress concentration has its maximum. This means that the initial crack has been inserted at different places depending on if the structure is subjected to bending or tension. A B C R4 R A R initial crack initial crack A = initial crack CU D DU R A R R A initial crack A = initial crack initial crack Figure 7.3. Modelling of the undercut for each welding class. Classes B, CU, and DU have been modelled as a notch with the transition radius mm. The depth of the notch is the acceptance limit A minus the initial crack length of. mm. Classes C and D have been modelled the same way, i.e. with an initial crack starting after the end of the transition radius. The accepted measure A has served as the length of the initial crack. The reaction forces at the supports are checked for each model and type of boundary 5 conditions. Results show that the reaction forces are very small, below N, and can therefore be neglected.

238 4 Analysis of Fatigue Life in Two Weld Class Systems The same model is used both during bending and tension Dimensions Six different thicknesses are tested: 5,, 5,, 3 and 4 mm. Each thickness and each welding class has been subjected to both tension and bending, resulting in 7 different simulations. The throat thickness is always half of the sheet thickness. (This is in fact not fully appropriate for thicker plates, where weld preparation is often used resulting in other throat thicknesses.) 7.4 Influence of sheet length The distance h between the edges (see Figure 7. and 7.) is mm for the thicknesses 5,, 5 and mm. For the thicknesses 3 and 4 mm it is not possible to use this distance, since the weld toe ends up close to or outside the edge of the sheet. In these cases the ends of the sheets were prolonged to give a distance of 5 mm from weld toe to the end of the sheet. The models represent only a small section around the weld joint. Since the applied load is uniform over the cross-section at the end of the sheet, the distance between the weld toe and the sheet end may have considerable effect on the results. Therefore it is of interest to investigate how long the horizontal sheets in the model have to be, not to affect the results. I.e., the same stress distribution through the joint should be obtained, as if the load was applied far away from the joint. A special study of this was carried out for the thickness t = 3 mm, welding class DU, for both bending and tension. Sheet lengths giving distances between 5 mm and 5 mm from weld toe to sheet end were tested. The results are plotted in Figure 7.4 and (a) for different distances from edge to weld, for bending 5 mm mm 5 mm 5 mm [MPa (mm)] Crack length, a, Figure 7.4. Stress intensity factor as a function of crack length for different sheet thicknesses (bending).

239 7 Study of sheet thickness dependence 5 The results show that the length of the horizontal sheet has a negligible influence on the stress intensity factors when the distance is 5 mm or more from the weld toe. However, it can be seen that the length of the horizontal sheet has an influence on the stress intensity factors for distances up to around to 5 mm at bending. 5 (a) for different distances from edge to weld, for tension 5 mm mm 5 mm 5 mm [MPa (mm)] Crack length, a, Figure 7.5. Stress intensity factor as a function of crack length for different sheet lengths (tension). The results at tension are similar to the results at bending. The sheet length affects the stress concentration at the crack tip when the distance from weld to end is less than approximately 5 mm. However the differences for small cracks are negligible. Only at depth of about.5 mm significant differences appear. Because of the small differences in stress intensity factor for small cracks, the differences in life are quite modest compared to the bending case. Thus it, would not have any large influence if the sheets were modelled a bit too short. The conclusion of the sheet length study is that the modelled sheet lengths, giving a distance of 5 mm or more between weld toe and sheet end, are sufficient for both bending and tension. (As mentioned above, models with thicknesses 3 and 4 mm have been prolonged to obtain a distance of 5 mm from weld to sheet end. The mm thickness model has a distance of approximately mm from weld to end, and thinner sheets will have even longer distances.) It should be noticed that the case reviewed is welding class DU, which has the largest defect. Thus it is most probably the case that demands the longest sheets to give correct results. Smaller defects may not demand these sheet lengths. Another conclusion is that the modelled sheet length used in the entire report - mm from end to end, giving a distance of 38 mm from weld to end - is by far on the safe side.

240 Analysis of Fatigue Life in Two Weld Class Systems 7.5 Results The results of the parameter study are presented in Table 7.-3 and Figure 7.- below. Table 7.. Fatigue life [ ]; bending. Welding Sheet thickness class A B C CU D DU Table 7.3. Fatigue life [ ]; tension. Welding Sheet thickness class A B C CU D DU

241 7 Study of sheet thickness dependence 7 Fatigue life as a function of thickness - welding class A Bending Tension Number of x [-] Sheet metal thickness Figure 7.. Results for welding class A Fatigue life as a function of thickness - welding class B Bending Tension 3.5 Number of x [-] Sheet metal thickness Figure 7.7. Results for welding class B.

242 8 Analysis of Fatigue Life in Two Weld Class Systems Fatigue life as a function of thickness - welding class C.5 Bending Tension Number of x [-] Sheet metal thickness Figure 7.8. Results for welding class C. Fatigue life as a function of thickness - welding class D..4 Bending Tension Number of x [-] Sheet metal thickness Figure 7.9. Results for welding class D.

243 7 Study of sheet thickness dependence 9 Fatigue life as a function of thickness - welding class CU.5 Bending Tension Number of x [-] Sheet metal thickness Figure 7.. Results for welding class CU. Fatigue life as a function of thickness - welding class DU. Bending Tension.4 Number of x [-] Sheet metal thickness Figure 7.. Results for welding class DU.

244 3 Analysis of Fatigue Life in Two Weld Class Systems 7. Comments on the results This section focuses on the results for tension, as this is the same load case that is used in the rest of the report. The factors affecting the results are discussed below. The results for bending are generally similar to the tension results, but deviate in some aspects. This is discussed at the end of this section. Results for all welding classes are plotted in Figure 7. and 7.3 for the tension and bending cases respectively. 3, Life as function of sheet thickness (tension) Life [e ],5,,5,,5 A B C CU D DU, Thickness Figure 7.. Results for tension, all welding classes. Life as function of sheet thickness (bending) Life [e ] 7,, 5, 4, 3,,, A B C CU D DU, Thickness Figure 7.3. Results for bending, all welding classes.

245 7 Study of sheet thickness dependence The thickness effect The thickness effect, primarily depending on the higher stress gradient in the crack growth direction for thicker sheets, is the reason for the general downward slope of the life curve towards larger thicknesses. (In some classes, especially D/DU, this effect is only vaguely visible.) The effect can be estimated with handbook equations. The thickness effect is particularly apparent in welding class A, with no defect allowed, were the effect can clearly be seen. For the other classes, other factors are superimposed on the thickness effect, making it harder to evaluate. See the last section of this chapter for further theory, calculations, and discussion on the thickness effect. 7.. Effect of absolute acceptance limits In the current case, STD55,5 Case, as in many other cases, there is an absolute maximum value of the defect size. In this case the acceptance limits imply that the defect depth is the same for all sheets with t mm (see Table 7. above). This means that for thicknesses below mm the defect is proportional to the thickness, but for thicknesses of to 4 mm the defect is identical for all, i.e., the defect is relatively smaller for larger thicknesses. As an effect of this, the life curve decreases considerably from 5 to mm due to the thickness effect. It then makes a sharp turn for thicknesses over mm. This phenomenon is visible for classes with large allowable defects. The effect actually overrides the thickness effect, especially for thicknesses to mm, resulting in increasing life for thicker sheets. The reason for this is obvious. In, for example, welding class D, a maximum undercut of mm is allowed. Thus, for a mm thick sheet, the crack has to grow 3 mm - from mm to 5 mm (half the thickness) while it in a 5 or mm thick sheet the crack has to grow 5.5 or 8, mm respectively. This increases the number of for crack growth more than the thickness effect decreases it Sheet length The modelling of the sheets was initially suspected to have substantial effect on the results. However, as described earlier, the sheet lengths have been proven sufficient. For both bending and tension, there has to be a minimum distance of about to 5 mm between the weld toe and the sheet end in order not to affect the results. This is fulfilled for all models. It should be noticed, though, that it is always important to model sufficiently long sheets The bending case Generally, the results for bending and tension are similar. The interaction between the thickness effect and the absolute acceptance limits is the same. The lives are substantially longer for the bending case, since in that case the stress decreases with the depth. An interesting result is that the additional designation U has less effect for bending than for tension. This is due to the different stress distributions. For bending, the effect of the U requirement is almost negligible, while it for thin sheets in tension almost doubles the life.

246 3 Analysis of Fatigue Life in Two Weld Class Systems Another remarkable result is the small difference in life between 5 and mm for class A. Since theses cases could be expected to give results in accordance with the thickness effect, the 5 mm sheet should have considerably longer life. There is no obvious explanation for this. The magnitude of the thickness dependence at bending should be further investigated, but this is not done in this report. However, the thickness effect, judging from the 5 and mm results, seems to be somewhat smaller for bending than for tension. 7.7 Conclusions An important objective of the thickness study was to investigate the applicability of the results from mm sheets on other thicknesses. Since the thickness mm is used throughout the in this work, it is very important to know to what extent these results are valid for other thicknesses. The main conclusion is that it is necessary to be cautious when applying a result to another thickness. The two counteracting effects described above makes the thickness dependence look different from case to case. Under certain circumstances it is possible to quantify the thickness effect. This, however, requires that thicknesses have proportional geometrical properties. For example, if two models with different thicknesses have a defect of the same depth, this will distort the result of the thickness effect. Handbook rules seem to be useful for calculating the thickness effect. Though, before using such, the choice of method and parameter settings should be further investigated. (In this case, t ref = 5 mm and n =.5 in Equation 9. appear to give reliable results for class A.) Due to the absolute acceptance limits for many defect types, it is often difficult to generalize the results to larger thicknesses. As the results in this parameter study show, the life for thicknesses 5 and mm is often longer than that for mm. However, this totally depends on the combination of defect type and acceptance limits, and varies from case to case. 7.8 Theory and calculations on the thickness effect The thickness effect is a combination of three factors a statistic factor, a technological factor and a geometrical factor [5]. The first two are not considered in this study. The statistic effect is due to the higher probability of a defect in a larger volume (i.e. in a thicker sheet). The technological effect depends on thicker sheets having lower strength than sheets of the same material that has been mechanically machined (forged, rolled) to a thinner thickness. Finally, the geometrical effect depends on a higher stress gradient in the crack growth direction for larger thicknesses [5]. In this study, the material in the models is ideal (homogenous and identical for all thicknesses) implying that the first two factors have no effect. The geometrical effect, though, is a natural consequence of the modelled geometry. This effect is one important explanation to the results in the parameter study. When considering the thickness effect in real-life fatigue life calculations, a thickness factor ϕ for the allowed stress range can be used: t ϕ t t = t In Equation 7. t is the thickness, while the parameters t ref (reference thickness) and n are obtained from some suitable handbook. Different standards use the thickness factor ref n (7.)

247 7 Study of sheet thickness dependence 33 differently. For example, in the IIW recommendations it is used only to reduce the allowed stress range for sheet thicknesses larger than t ref, while in BSK 99 [8] it is used in the opposite way, i.e., to increase allowed stress for thinner sheets (t ref = 5 mm in both standards). A thickness factor can also be used for both thinner and thicker plates (see below). It should be noticed that this applies to toe cracks, when the crack propagates through the sheet. For cracks through the weld (root cracks), the thickness effect is less investigated, but it is probably smaller (partly because there is no technological effect) [5]. In [5] is given one example of a method to calculate the thickness factor. It can be used for sheets both thinner and thicker than the reference thickness t ref, which for this method is 5 mm. For fillet welds the exponent n is recommended to be.5 for 4 < t 5 mm and.5 for t > 5 mm. The thickness factor, intended for increasing the allowed stress range, can also be used to calculate a longer life for the original stress range. If the thickness factor ϕ t is multiplied with the allowed stress range, the same life as for the reference thickness is obtained. But the life is inversely proportional to the third power of the stress, and thus (for identical stress) the factor 3 in life is ϕ t. The thickness factors and the life factors (compared to t ref = 5 mm), for the thicknesses used in this parameter study are listed in Table 7.4. Table 7.4. Thickness factor φ t (see Equation 7.) and life factor as the function 3 ϕ t. t n φ t (= φ 3 t ) Life factor 5 mm mm mm.5.. mm mm mm The life factor for each thickness compared to t ref = 5 mm, as obtained from the results in this parameter study, are shown in Table 7.5 for all welding classes. These factors are also plotted in Figure 7.4.

248 34 Analysis of Fatigue Life in Two Weld Class Systems Table 7.5. Normalized life factors computed from the results in the parameter study. Life factor for welding class Theoretical value Thickness A B C CU D DU from Table mm mm mm mm mm mm Fatigue life as function of thickness (tension),5 Normality,5, Thickness A B C CU D DU Theoretical Figure 7.4. Plot of results from table 7.5. As can be seen in Figure 7.4 and Table 7.5, the life factors in a few cases correlate very well to the values obtained by computing backwards from the design recommendations. This is the case especially for thick sheets in welding class A. This is expected, since A is the ideal case without defect and therefore has the expected stress gradient causing the thickness effect. In other cases the defects may modify the stress distribution, possibly affecting the magnitude of the thickness effect. Furthermore, as discussed above, the effect of the absolute acceptance limits for t mm has a very large impact on the lives in some cases. The deviation for thinner sheets in class A suggests that the value of n might be slightly incorrect (or maybe just conservative, in order to be on the safe side). If n =.5 is used also for 4 < t 5 mm, the thickness factors will give life factors that correlate well to the results obtained from the parameter study.

249 7 Study of sheet thickness dependence 35 An interesting observation is that the ratio in life between thicknesses 5 and mm is approximately the same for all welding classes, i.e. for the whole range of defect sizes (-. t). Since the defect is proportional to the thickness for thicknesses 5 and mm, this implies that for the thickness effect calculation to be valid, the whole geometry should be scaled by the same factor as the thickness. It can also be noted that the results correlate well with the handbook rule, despite the fact that the statistical and technological effects, dealing with material properties, are not considered. This may be interpreted as these two factors having little influence, and thus the geometrical factor playing the major role in the thickness effect. However, this limited study does not support any extensive conclusions on this.

250 3 Analysis of Fatigue Life in Two Weld Class Systems

251 8 Conclusions and discussion 37 8 Conclusions and discussion This chapter contains the conclusions of the thesis work, both general and specific for each standard. Proposals for revising the standards are presented as well as detailed recommendations for each standard. The chapter is completed with proposals for further work. 8. Conclusions The main conclusions on the studied welding standards are the following: Today, both STD55,5 and ISO587 show large scatter in the results and there is no general relationship between the acceptance limits and the fatigue life. It would be possible, however not easy, to create a general standard. In addition, a few general conclusions can be drawn: The angle between weld and sheet does not have any significant influence on the fatigue life. Internal defects ought to be excluded from a general standard. Arbitrary denotations, for example locally permitted, smooth transition etc. should be avoided and replaced by numbers. These conclusions are thoroughly discussed in the following section. After this, a few proposals for revising the standards are presented, followed by discussions and recommendations for each standard based on the proposals. 8. General discussion A remarkable discovery was made concerning fatigue life of cracks in corners with a transition angle α between the sheet and the weld, see Figure 8.. α initial crack Figure 8.. The transition angle between weld and sheet. In Case., incorrect weld toe, in the ISO587 standard the acceptance limit is defined as an angle between the sheet and the weld. For transverse butt welds there is almost no difference in fatigue life for angles α (see Figure 8.) between 3º and 9º. For fillet welds the angle can vary between 7º and 9º, and it gives only one percentage point in difference in fatigue life.

252 38 Analysis of Fatigue Life in Two Weld Class Systems This variation in angle is not so large for the fillet weld. In Case. B the transition angle is 45º. If the result for Case. B is comperad to the results in Case., one can see that the transition angle is of no interest of the fatigue life for sharp transitions when the. mm initial crack is present. This is also reflected in many other cases, for example weld reinforcement, penetration bead and leg deviation. This conclusion is confirmed by for example Martinsson in Fatigue Strength of welded cruciform joint with cold laps [3]. In the article, the fatigue life is calculated on different geometries for different initial cracks.. The geometries have different stress concentration factor K t, for no initial crack available. For a. mm initial crack there are nearly no differences in fatigue life. One can see that the longer initial crack is, the less is the impact on the fatigue life. This can be explained by the fact that once the crack is there, the crack propagation is governed by the stress intensity factor at the crack, and the stress concentration due to the transition angle plays a minor role. It is possible that the transition angle has an effect during the crack initiation phase, and that the life is shorter for larger angles during this stage. This should be the case because the stress concentration factor increases with an increasing transition angle, under the condition that there is a transition radius present between weld and sheet, which there always is in real life. If, on the contrary, there is a sharp transition the stresses goes towards infinity for a singular point in the FE-model. The crack initiation phase, which could give a larger difference in life for different angles, is not included in this study. All internal defects are too difficult to deal with. Internal defects should be avoided since they cannot be detected with the human eye, but require some kind of other method for detection, for example ultrasound or x-ray. The internal defects may result in cracks which reach the surface and causes failure before they have been detected and taken care of. Therefore it is the standpoint of this work that the internal defects are excluded from the standard. Another aspect why internal defects are hard to include in a general standard is that it is difficult to predict the life of internal cracks with a limited extension in the length direction of the weld. Once they have reached the surface, they can still grow in the length direction, thus making it hard to find reasonable integration limits. If these defects are included, theory and reality might divert too much from each other and the standard will be useless from that point of view. Possibly, it could be better to have internal defects in a special section in the standard, and then omit fatigue properties. All vague denotations, for example locally permitted, permitted to a small extent, short imperfection, smooth transition etc., must be changed to give real information in the standard. If the standard is to be consistent, important factors influencing for the fatigue life can not be replaced by notations which can be interpreted arbitrarily. 8.3 Proposals for revising the standards The whole idea of setting new acceptance limits is that there should be a clear relation between the fatigue life and the acceptance limits. This is very important both from design and from production aspects. Below a few proposals for guidelines are presented which can be used when modifying the standard. It is meant that only one of the proposals for guidelines is carried out when revising the standard. The proposals could perhaps not always be realized, but they should be the goal for the revised standard.

253 8 Conclusions and discussion Primary proposal for guidlines The primary proposal for a new standard should be that a certain defect for both butt and fillet welds should have the same acceptance limit. This makes it easier when welds are inspected during the manufacturing process. Further, general fatigue lives should be given i.e., all welding classes have a fixed life. Since butt welds and fillet welds have different fatigue properties (fillet welds have shorter lives than butt welds) the fatigue life depend on the stress level at a given acceptance limit. It can be mentioned that the primary guideline could be implemented relatively easy without making too many new FE simulations. The reason is that the acceptance limits for a given defect already today are almost the same for butt welds as for fillet welds. Old FE results can be scaled easily in order find the correct stress level if the acceptance limits are not changed. This is a very cost effective way to alter the standard but it has the disadvantage that very low stress levels will be achieved for certain cases Secondary proposal for guidelines The secondary proposal for a new standard should be that, regardless of case, each welding class has a given fatigue life. No difference should be made between transverse butt welds and cruciform joints. It should be possible for the design engineer or the production engineer, etc. to look into the standard when examining a weld and say this defect will reduce the fatigue life of this component by 34%, which means that it will last for. million at this given stress level, for example. The secondary proposal is much more difficult to achieve than the primary proposal since many new FE simulations must be carried out in order to find the new acceptance limits. Another disadvantage is that the acceptance limit which applies to a certain fatigue life might get a decimal value, for example.73. It would be more convenient to deal with even numbers such as.5,.75 and Other proposals for STD55,5 If the primary and secondary proposals turn out to be too difficult to achieve, it could at least be reasonable to change the standard so that the same ratio between the welding classes designed for fatigue loading is obtained. In for example the STD55,5 standard, class B, CU, and DU, should have the same ratio between B and CU, as between CU and DU. Welding class A is disregarded due to its academic nature since there are nearly no useful numbers available, It could also be possible to have a given fatigue life for welding class B, CU and DU and to disregard the other classes. In this case it might be necessary to separate butt welds and cruciform joints Other proposals for ISO587 If the primary and secondary proposals turn out to be too difficult to achieve, it could at least be reasonable to change the standard so there is the same ratio between the welding classes i.e., there should be the same ratio between B and C as between C and D. 8.4 Discussion for STD55,5 The results show that data on the fatigue life for the welding classes in the STD55,5 is scattered. This makes it hard to draw comprehensive conclusions and to determine a general fatigue life for each welding class. However should be impossible to unite at least the majority of welding classes to a general description of the fatigue life. If this is done,

254 4 Analysis of Fatigue Life in Two Weld Class Systems questions will arise whether or not some of the cases should be deleted from the standard or completely revised. Some of the scattered data depend on only limitations when modelling several cases. This is, for example, because of the additional designation U requiring smooth transitions, that in some cases require completely different modelling of the different classes. In, for example Case 3, incomplete root penetration, welding classes C and D have been modelled with a crack according to the acceptance limits, i.e. mm for C and mm for D. Classes CU and DU however was modelled only with the initial crack length. mm, since it was considered impossible to have an smooth transition in a defect of this type. This resulted in very long lives for classes CU and DU, while C and D got significantly shorter lives. The standard must be revised, or the additional designation must be dropped, for cases like these if conformity is to be reached. The standard is inconsistent in the sense that Case 4 state that cruciform joints should have transition radii for welding class A (r = 4 mm) and B (r = mm), while there is no corresponding requirement for transverse butt welds. This means that butt welds can never be assigned fatigue requirements in a higher welding class than CU! In order to emphasize the transition radius requirements for welding classes A and B it is recommended to move Case 4 from its current position as the last case for cruciform joints and place it either in the beginning of the standard or first among the cruciform joints. Similarly, a new case or some other type of definition ought to be introduced for transverse butt welds Cases which could be added or removed from STD55,5 A few cases in the standard do not have no influence on the fatigue life. This is easy to see when studying Figure B.-B.3. If only fatigue properties are to be considered these cases could be removed from the standard. If these cases are kept in the standard then it should be clear that a higher welding class does not give a noticeable change in fatigue life. Some suggestions of cases that should be added to the standard are now given. Cases which do not exist in the standard Linear misalignments for transverse butt welds are included in the standard, but there are no corresponding cases for fillet welds. As can be seen for Case 3 and 4, misalignment has a major effect on the fatigue life for transverse butt welds. A butt weld without any defect and transition radius, has a fatigue life of.58 million, which corresponds to 79% of million (Case A in STD55,5). For Case 3 and 4 the corresponding fatigue life of welding class A is only 3%. From the fatigue point of view the effect of misalignment would probably be a large threat for fillet welds as well. Another case which does not exist in the standard is angular misalignment obtained when the sheets connected by the weld do not lie in the same plane, see Case 3. in the ISO587 standard, Chapter. Results from Case 3. show that this defect affects the life, since the introduction of bending aggravates the situation for the crack. Therefore it is suggested that angular misalignments for both transverse butt welds and fillet welds are added to the standard. One case that could be considered added to the standard is cold lap or overlap, see Case.3 in the ISO587 standard, Chapter. Even if this case is not fully investigated here. Just one simulation of a horizontal crack turning vertical. Further studies with variations of the turning angle and crack growth length must be conducted before it can be decided whether or not this case should be included.

255 8 Conclusions and discussion 4 It could be difficult to fit cold laps into a general standard, because of the long lives. If included it could be placed among the cases which do not affect the fatigue life. Further, it is worth raising the question whether or not the size of the cold lap matters? Maybe it does not. A cold lap of or mm seems to give the same fatigue life. However further studies have to answer this question. Cases which could be removed Case, weld reinforcement, Case, penetration bead and Case, leg deviation, all deal with an angle between weld and sheet. As has been said above, the angle between the two surfaces does not affect the fatigue life noticeably when there is an initial crack present. These cases could be deleted from the standard if fracture mechanics with a known initial crack of. mm is regarded. However, before deleting these cases, the fatigue life in the crack initiation stage should be further investigated. Note that these three cases have an impact on the fatigue life but it is not the size of the defect but rather the initial crack that reduces the life. Case 3, incomplete root penetration and Case 8, root concavity are very similar. Therefore it is recommended to join these cases into one case i.e., remove either Case 3 or Case 8. Maybe the name should be changed to something that describes the new case better Recommendations for achieving proposals for STD55,5 Many parameters could be changed in order to achieve the stated proposals. This is not as easy as just, for example, changing the depth of a certain acceptance limit in order to get the wanted fatigue life. It is not only the design engineer s wishes that are to be satisfied. In many cases the production engineers have an opinion on whether or not it is possible to produce a weld of a certain quality in a reasonable amount of time. Longer production times will end in economical drawbacks. If any of the proposals below are to be achieved, Case, and must be either deleted from the standard or moved to a section in the standard which does not deal with fatigue properties. Deleting these cases might be disadvantageous from a production technical point of view. From a fatigue point of view the acceptance limits must be changed so much that the defects will be unreasonably large. For example, Case, the penetration bead, which already now has a relatively long life in all welding classes, can vary between.8 mm and.4 mm in the acceptance limits, for B respectively D. If the acceptance limits are to be changed to fulfil the primary proposal, the fatigue life of Case must be reduced dramatically, something which will lead to an unreasonably large penetration bead. The same thing applies to Case, weld reinforcement and Case, leg deviation. Another thing that should be done in order to achieve the goals is to remove Cases 5-7. Their geometries give lives that divert too much from remaining cases. The large differences in life depend on the defects being internal cracks, while in all other cases the crack grows from the surface into the material. Another reason for setting these cases aside is that internal defects are dangerous since they can not be detected with the human eye, but need other detection methods, for example ultrasound. Therefore internal defects should not be compared to surface defects. Below some comprehensive suggestions will be made in order to achieve the proposals above. More detailed descriptions can be found for each case on the pages to come. Primary proposal for guidelines The undercut is the only defect which exists both for butt and fillet welds, and this case has the same acceptance limits i.e., no changes have to be done in order to achieve the same

256 4 Analysis of Fatigue Life in Two Weld Class Systems acceptance limits for butt welds and fillet welds. Of course some acceptance limits might have to be changed if they don t affect the fatigue life as wanted. Achieved results from the FE simulations could easily be scaled in order to achieve the correct stress level for a given fatigue life and acceptance limit. Secondary proposal for guidelines Case 3, incomplete root penetration, needs major reworking for welding classes B, CU and DU, but it has some values which fit with the remaining cases. Further Case, throat deviation, needs extensive rework since the fatigue life is far too long and this case diverts too much from the other cases. Finally, Case 3 and 4, which both deal with the transition radius, are not ordinary cases but rather guidelines to the other cases since they have no real defects. Therefore they should be excluded when working for achieving the primary guideline. All other cases need minor revision. Other proposals for guidelines Since welding classes B, CU, and DU are all meant for fatigue loading, these classes are interesting to study more deeply. When plotting the ratio of fatigue life between B and CU, and between CU and DU (Figure B.7), one can see that the ratio between B and CU lie between and for all cases. It could be relatively easy to modify the acceptance limits to achieve a common ratio for these two classes. The ratio should of course should be greater than, preferably around.5-. It is more difficult to find consistency when studying the ratio between CU and DU. The values are very scattered. If possible, the ratio should be the same or almost the same as the ratio between B and CU. 8.5 Discussion for ISO587 A first glance at the results in Figure C. reveals that in about half of the cases there is no noticeable difference in fatigue life between different welding classes. This is quite remarkable from a fatigue point of view, since one expects that a higher welding class will give a longer life. It seems that no theoretical studies have been carried out when setting the acceptance limits but they have been set empirically or from other points of view, for example production aspects. Below follows a discussion about what could be done in order to achieve better fatigue properties for ISO Cases which could be added or removed from ISO587 Since the acceptance limits in many of the calculated cases have no influence on the fatigue life, these cases could be removed from the standard if only fatigue properties are to be considered. Maybe these cases should be kept in the standard from production aspects, but then it should be clear that a higher welding class does not give a noticeable change of the fatigue life. Maybe some cases should be added to the standard since they may have a considerable influence on the fatigue life. Cases which do not exist in the standard Angular and linear misalignments for transverse butt welds are available in the standard but there are no corresponding cases for fillet welds. As can be seen for Case 3. and 3. both angular and linear misalignment have a major effect on the fatigue life for transverse butt welds. A butt weld without any defect and transition radius have a fatigue life of.58 million

257 8 Conclusions and discussion 43, which is 79% of million (Case A in STD55,5). For Case 3., the life of welding class B is 3% while it is 5% for the same class in Case 3.. The effect of misalignment would probably have a large impact on the fatigue life for fillet welds as well. Cases which could be removed Case.9, excess weld metal (or weld reinforcement) and Case., excess penetration (or penetration bead) have proven - both in the ISO587 and the STD55,5 standard - to be useless from a fatigue point of view. The average life is very long and it does not differ much between the different classes. If a general life for each welding class should be set, the defect would be so large that it would probably not be tolerated from a production point of view. Thus, from a fatigue point of view the defect could be excluded from the standard. Case., excessive convexity, Case., incorrect weld toe and Case., excessive asymmetry of fillet weld (excessive unequal leg length or leg deviation) all deal with an angle between weld and sheet. As stated above (Chapter 8.), the angle does not affect the fatigue life noticeably when there is an initial crack present. This means that these cases could be deleted from the standard if an initial crack of. mm is presumed. However, before deleting these cases the fatigue life in the crack initiation stage should be investigated. Note that these three cases have an impact on the fatigue life but it is not the size of the defect but the initial crack which reduces the life. Case., excessive throat thickness, should not be adopted in the standard since the life becomes longer with a worse welding class. This is impossible to fit with any of the guidelines for a new standard. Case.3, lack of penetration for a transverse butt weld, should be removed from the standard since internal defects are not possible to handle. Internal defects cannot be discovered by the human eye before breaking of the surface. This might lead to unexpected failures. Another undesirable factor is that it is hard to determine the integration limits for an internal crack which do not have an infinite length in the depth directions. The crack could continue growing after breaking the surface. This means that many might remain and this fact makes it hard to determine the fatigue life for a structure with this defect. Uncertain cases Calculations on Case.3, overlap (or coldlap), show that this type of defect gives a longer life than might have been expected. However, this case is not fully investigated after just one simulation of a horizontal crack turning vertical. Further studies with variations of the turning of the crack must be conducted before it can be decided whether or not this case belongs in the standard. Case.3, lack of penetration for a fillet weld, could with changed acceptance limits easily be included in a revised standard. However with internal defects the crack might grow from the root. This is dangerous because such cracks are hard to discover before failure. Therefore, this case should perhaps be brought out into a special section of the standard, and the defect should not be permitted for any welding class Recommendations for achieving proposals for ISO587 Cases recommended to be removed above should be removed in order to make it possible to achieve the recommendations for a new standard. Results for all the cases which remain (after removing also the uncertain cases) can be found in Figure C.4.

258 44 Analysis of Fatigue Life in Two Weld Class Systems Primary proposal for guidelines A part of the primary prosal is already implemented in the ISO587 i.e., the same acceptance limit apply for both butt and fillet welds. Only Case., incorrect weld toe and Case.3, lack of penetration, show some differences but these cases have already been decided to be dropped from the fatigue part of the standard. The acceptance limits in Case. does not have any impact on the fatigue life and Case.3 is an internal defect. Apart from these two cases, new acceptance limits have to be decided. If old acceptance limits are used, it will be easy to scale the results from the FE simulation conducted in this study. This will give the correct stress level for a given fatigue life. Secondary proposal for guideline If the secondary proposal of a clear-cut standard are to be achieved, all the remaining cases, Case.7,.4,.7,., 3., and 3., need some minor revision according to below. Case.7, undercut, in order to create a wider range in fatigue life needs to relaxe the maximum requirement in welding class B and C. Also the acceptance limits need rework. Case.4, sagging or incompletely filled groove and Case.7, root concavity, need minor revision regarding the acceptance limits. Case., insufficient throat thickness, can not have the same acceptance limit in welding class C and D. The only difference is on the maximum deviation. Except from this, only minor revision needs to be done. Case 3., linear misalignment, needs only minor revision regarding the acceptance limits. Case 3., angular misalignment, the acceptance limits can be increased i.e., greater angles can be tolerated in order to reduce the fatigue lives. However, this might be incompatible with production aspects. Other proposals for guidelines The cases mentioned above already have a good ratio between welding class B and C and between C and D. This as can be seen in Figure C.5 and C.. A ratio of depends on badly set acceptance limits. This could easily be adjusted in order to get better ratios. A ratio of.5 to.5 between B and C and between C and D is possible to achieve, with only some minor changes of the acceptance limits. If all cases were included it would be impossible to set acceptance limits which would give the same ratio between all the welding classes In some cases the angle between weld and sheet does not matter for the life. 8. Recommendations for further studies Investigation of the number of needed in the crack initiation phase. This cannot be done with LEFM. As proved in this study. After the. starting crack has been initiated the fatigue life varies only a little for large variations of the angle between the sheet and weld. Cold laps or overlaps ought to be studied more carefully before being added or removed from the standards. Investigation of new cases which could be added, for example linear misalignment and angular misalignment for fillet welds.

259 8 Conclusions and discussion 45 Investigation of internal cracks to determine if it is possible to change the acceptance limits in order to fit them into the standards. This requires that, for example, integration limits in Paris law are investigated. Proposals for a new standard require many simulations before new acceptance limits can be determined. Different sheet thicknesses should be investigated. This is an extensive task that also need input from production engineers.

260 4 Analysis of Fatigue Life in Two Weld Class Systems

261 References 47 References [] Volvo Group Standard (989). 5.5E Welding Manual Design and Analysis (contains the STD55,5 standard also referred to as STD8-). Gothenburg, Sweden: Volvo [] Comité Européen de Normalisation (3). ISO587:3, Welding Fusion-welded joints in steel, nickel, titanium and their alloys (beam welding excluded) Quality levels for imperfections. Brussels, Belgium: CEN [3] Dahlberg T and Ekberg A (). Failure, Fracture, Fatigue an Introduction. Lund, Sweden: Studentlitteratur. ISBN [4] Sundström B et al. (999). Handbok och formelsamling i hållfasthetslära (in Swedish). Stockholm, Sweden: Institutionen för hållfasthetslära KTH. [5] Eriksson Å and Lignell A-M, Olsson C, Spennare H: Svetsutvärdering med FEM (in Swedish). Stockholm, Sweden: Industrilitteratur. ISBN [] Hobbacher A et al. (99). Fatigue design and welded joints components. Cambridge: The International Institute of Welding. ISBN [7] Holm L, Mårtensson A, et al. (987). Bestämmelser för stålkonstruktioner, BSK (in Swedish). Stockholm, Sweden: Statens planverk och AB Svensk Byggtjänst. ISBN [8] Göransson L, Åkerlund S et al. (). Boverkets handbok om Stålkonstruktioner, BSK 99 (in Swedish). Karlskrona, Sweden: Boverket. ISBN [9] Per-Olof Danielsson, Lic. Eng. Volvo CE, previously Bombardier Transportation in Kalmar, Sweden [] Marquis G and Samuelsson J (5). Modelling and Fatigue Life Assessment of Complex Fabricated Structures, Symposium on Structural Durability, in Darmstadt, 9- June 5. Darmstadt, Germany [] ANSYS Version 8.. SAS IP, Inc [] ANSYS Version 9.. SAS IP, Inc [3] Paris P.C. and Sih G.C. (95). Stress Analysis of Cracks. Fracture Toughnesss and Testing and its Applications STP 38: 3-85 [4] ANSYS (995). ANSYS Theory Reference, seventh edition. USA: SAS IP, Inc [5] MATLAB Version (R4) Service Pack. The Mathworks, Inc [] Eldén L and Wittmeyer-Koch L (). Numeriska beräkningar analys och illustrationer med MATLAB. Lund, Sweden: Studentlitteratur. ISBN

262 48 Analysis of Fatigue Life in Two Weld Class Systems [7] EXCEL Version SP-. Microsoft Corporation [8] Newman J.C. and Raju I.S. (98). Stress Intensity Factor Equations for Cracks in Three-Dimensional Bodies Subjected to Tension and Bending Loads. Computational Methods in the Mechanics of Fracture Chapter 9. Hampton, USA: Elsevier Science Publishers B.V. [9] AFGROW Version 4.9e.. access date 5--3 [] von Essen W et al. (98). Byggsvetsnorm utgåva, StBK-N (in Swedish). Stockholm, Sweden: Statens stålbyggnadskommitté. ISBN [] Volvo Corporate Standards (4). STD5- Critical Characteristics for Design Products. Gothenburg, Sweden: Volvo [] Richard H.A. (). In: CD-ROM Proceedings of ICF. Honolulu, USA. [3] Martinsson J. (). Fatigue Strength of welded cruciform joint with cold laps. Proc. Design and Analysis of Welded High Strength Steel Structures, pp. 3-85, in Stockholm June. Stockholm, Sweden: EMAS

263 Appendix A 49 Appendix A %Function which calculates stress intensity factors for analytical case function [a dk_eff c dk_i_c] = invandig_spricka(a_start,a_end,c_start) %=========== Constants =========== W = e99; %Sheet depth t = ; %Sheet thickness t = t/; C = 5e-; n = 3; sigma = 4; %Constant in Paris' law %Constant in Paris' law %Tension [MPa] a = a_start; c = c_start; delta_m = ; fi_ = ; fi_9 = 9; fi_ = (fi_*pi)/8; fi_9 = (fi_9*pi)/8; %Angle in c-direction %Angle in a-direction %Transformation into radians %Transformation into radians i = ; while a(i) <= a_end f_w(,i) = sqrt(sec( ((pi*c(i))/(*w)) * sqrt(a(i)/t) )); if a(i)/c(i) <= else end Q(i,) = +.44*(a(i)/c(i))^.5; M_(i,) = ; f_fi_(i,) = ( (a(i)/c(i))^*cos(fi_)^ + sin(fi_)^ )^(/4); f_fi_9(i,) = ( (a(i)/c(i))^*cos(fi_9)^ + sin(fi_9)^ )^(/4); Q(i,) = +.44*(c(i)/a(i))^.5; M_(i,) = sqrt(c(i)/a(i)); f_fi_ = ( (c(i)/a(i))^*sin(fi_)^ + cos(fi_)^ )^(/4); f_fi_9 = ( (c(i)/a(i))^*sin(fi_9)^ + cos(fi_9)^ )^(/4); M_(i,) =.5/(. + (a(i)/c(i))^(3/) ); M_3(i,) =.9/(.3 + (a(i)/c(i))^(3/) ); ) / g_(i,) = - ( ( (a(i)/t)^4 * sqrt(. - *(a(i)/t)) )*abs(cos(fi_)) ( + 4*(a(i)/c(i)) );

264 5 Analysis of Fatigue Life in Two Weld Class Systems g_9(i,) = - ( ( (a(i)/t)^4 * sqrt(. - *(a(i)/t)) )*abs(cos(fi_9)) ) / ( + 4*(a(i)/c(i)) ); * * F_a(i,) = ( M_(i) + M_(i)*(a(i)/t)^ + M_3(i)*(a(i)/t)^4 ) * g_9(i) f_fi_9(i) * f_w(i); F_c(i,) = ( M_(i) + M_(i)*(a(i)/t)^ + M_3(i)*(a(i)/t)^4 ) * g_(i) f_fi_(i) * f_w(i); dk_i_a(i,) = sigma * sqrt((pi*a(i))/q(i)) * F_a(i); dk_i_c(i,) = sigma * sqrt((pi*a(i))/q(i)) * F_c(i); a(i+) = a(i) + C*dK_I_a(i)^n*delta_M; c(i+) = c(i) + C*dK_I_c(i)^n*delta_M; i = i + ; end dk_i_a = dk_i_a/sqrt(); dk_i_c = dk_i_c/sqrt(); a = a(:end-)'/; c = c(:end-)'/; dk_eff = dk_i_a;

265 Appendix B 5 Appendix B diagrams for STD55,5

266 5 Analysis of Fatigue Life in Two Weld Class Systems

267 Appendix B 53

268 54 Analysis of Fatigue Life in Two Weld Class Systems

269 Appendix B 55

270 5 Analysis of Fatigue Life in Two Weld Class Systems

271 Appendix B 57

272 58 Analysis of Fatigue Life in Two Weld Class Systems

273 Appendix B 59

274 Analysis of Fatigue Life in Two Weld Class Systems

275 Appendix B

276 Analysis of Fatigue Life in Two Weld Class Systems

277 Appendix B 3

278 4 Analysis of Fatigue Life in Two Weld Class Systems

279 Appendix B 5

280 Analysis of Fatigue Life in Two Weld Class Systems

281 Appendix B 7

282 8 Analysis of Fatigue Life in Two Weld Class Systems

283 Appendix B 9

284 7 Analysis of Fatigue Life in Two Weld Class Systems

285 Appendix C 7 Appendix C diagrams for ISO587

286 7 Analysis of Fatigue Life in Two Weld Class Systems

287 Appendix C 73

288 74 Analysis of Fatigue Life in Two Weld Class Systems

289 Appendix C 75