Fatigue crack propagation analysis of ship hull welded components

Transcription

1 Fatigue crack propagation analysis of ship hull welded components M. Faculty of Offshore Engineering and Ship Technology, Technical University of Gdansk, Poland ^ Polish Register of Ships, Gdansk, Poland m.bogdaniuk@prs.gda.pl Abstract Examples of fatigue lives calculations of typical ship hull structures welded elements such as transverse butt weld connection of the plating and cruciform joint with fillet welds are presented in this paper. The calculations were performed applying S-N curves and fatigue crack propagation analysis. Long term dynamic stresses distribution in form of Weibull distribution, S-N classification recommended in literature and available parametric formulae for calculating stress intensity factors were applied. Some conclusions and recommendations to apply the fatigue crack propagation analysis method successfully to ship structures are given. Symbols #0 - initial depth of crack; D - fatigue damage; K - stress intensity factor; Z,, LSN - fatigue life (in years); LO - scantling length of ship; N - number of cycles to failure; NL - number of cycles for the expected ship's life; # = A"n,in / K^M - stress intensity factor ratio;

2 580 Marine Technology T - thickness of plate; a, - static normal stress; a Y - yield point of steel; Aa, A<JO - stress range. 1 Introduction Fatigue crack propagation analysis method is usually applied for calculation of remaining life of structures where cracks or crack - life imperfections have been found, as it is recommended by Almar-Naess*, DEN" and IIW^. S-N curves approach is typical for many building codes for fatigue design, given by Almar-Naess', DEN" and IIW^ and PRS\ This approach is so popular that attempts are known to replace fatigue crack propagation method by S-N approach, with specially constructed S-N curve, as it is proposed by Xu and Bea^. Scatter of welded joints fatigue tests results is observed. So, the S-N curves applied in the building codes are usually of mean minus two standard deviation type. In the crack propagation analysis the initial shape and dimensions of the imperfections have to be assumed. Elliptical or half-elliptical approximation of crack-like imperfections is recommended by Almar-Naess*, DEN", IIW^ and Dovers & Madhawa?. If fatigue crack propagation analysis method was applied instead of classical S-N approach for the cases with considerable value of fatigue life, the following questions would have to be answered: what are the initial dimensions of assumed elliptical or half-elliptical crack to obtain the same fatigue life value as by applying S-N approach? do the initial dimensions of the cracks depend considerably on long term distribution of dynamic stresses (Weibull distribution, Aa = const, etc.)? do the differences between results obtained by the two methods (crack propagation analysis and S-N approach) depend considerably on the value of R coefficient, thickness of plates and fillet welds, etc.? Some calculations were performed to answer these questions. Two simple welded joints typical for ship structures were analysed. The results are described in Ch. 2 andch Butt weld plate connection Fatigue life of the butt weld joint shown in Fig. 1 was calculated. The joint shown in Fig. 1 can be applied to assess fatigue life of ship deck plating welded connections. The fatigue life can be shorter than expected ship's life in cases where higher tensile steel is applied, for example a^ = 390 MPa. In such cases, according to the requirements of PRS* for general strength of the ship, the nominal stress range Aa values in strength deck of the ships caused by wave

3 Marine Technology 581 bending moments and exceeded with probability 10", can reach the level of 330 MPa. a) butt weld b) butt weld ground flush to plate Aa Fig. 1 Butt weld joint At stress concentration zones Aa values even two times greater than 330 MPa can be expected. According to PRS^ long-term distribution of Aa can be approximated by Weibull distribution: where: Pr(Aa > Aag)- probability that Aa > Aa@ ; E, - Weibull parameter dependent on ship length and ship type ; a - (1) Aa# - value of Aa exceeded with probability N R (A^ -a number, for example N^ =10 ). Taking into account the above given remarks on possible values of Aa, two Weibull distributions were considered with the parameters calculated ace. to for rather large ship (L$ «250 m): A. Aa# =330MPa, A^=10*, -0,95, A^/ =5 10^ (for 20 years of ship's exploitation); B. Aa^ = = 660MPa, 7V^,, A^/ - as above. Fatigue lives of the joints shown in Fig. 1 were calculated for the above Weibull distributions of Aa, applying S-N curves recommended by IIW^. FAT class 100 curve was used for the joint in Fig. la and FAT class 125 curve - for the joint in Fig. Ib. However, ace. to the IIW^ stress concentration factor equal to 1,3 was assummed for these S-N curves, to take into account realistic value of mis. It was decided to consider also the case of ideal of plating by increasing FAT class values by 30%. Miner - Palmgren formula for calculating fatigue damage parameter D was applied. Fatigue life L^, in years, was calculated from the formula:

4 582 Marine Technology 20 D (2) where: D - fatigue damage calculated for TV/ cycles corresponding to 20 years of ship's exploitation. According to DEN", IIW^ and PRS^ S-N curves can be corrected to take into account the influence of compressive stresses or thickness of the plating. In the calculations reported here the correction was not applied because tensile stresses were assumed and the thickness was rather small. Results of the calculations are given in Table 1. Table 1 Fatigue lives for joints shown in Fig. 1 calculated applying S-N curves Joint Fig. la Fig. Ib Fig. laideal Fig. lbideal FAT class ,5 Weib. distr. "A" 45,36 110,58 130,27 344,40 LSN b^ars] Weib. distr. "B" 4,06 8,45 9,64 20,98 For the calculations according to fatigue crack propagation analysis method the following assumptions were applied: crack initiation phase was neglected; initial half-elliptical long surface crack was assumed according to recommendations given by IIW^ and Dovers & Madhawa''. Value a I c - 0,1 was assumed (a, c - see Fig. 2); Paris' equation was applied to calculate the increase of "a" value as function of Ao and number of cycles, with no account of interaction between succeeding stress ranges; at the beginning of propagation value "a" was increased until a = c. After this circular shape of crack was assumed - according to recommendations given by Dovers & Madhawa^. 2c Fig. 2 Half- elliptical surface crack Paris' equation for crack propagation was applied:

5 Marine Technology 583 -^ = CAT" for AK>AK,,, (3) dn where values of parameters recommended by IIW^ were used (units in MPa V/H andw): C = 9,5-10~'-, /w = 3, A/^ =6,0-4,567? but not lower than 2,0. Hybrid method recommended by Almar-Naess* was applied to calculate A/f at point A of the crack, as shown in Fig. 2: s -F^-F^ F^ F^ (4) where: Aa - nominal stress range, normal to the crack surface; F$ - front face factor; FT - finite thickness factor; Fg - basic crack shape factor; PG - stress gradient factor; PW - finite width factor (F^ = 1,0 was applied). Values of F - coefficients were calculated applying parametric formulae and plots given by Almar-Naess. For example, F^ was calculated from the formula: r (5) where: q = log(l 1,584-0,0588*) / log(200) ; a, T- see Fig. 2; ( ) - see Fig. 1. < > = 160 was applied in the calculations. It was checked owever, that changing <j> around 1 60 shows insignificant effect on the results. The calculations were performed for two values of AK,/, : AA^ = 6,0 (for R = 0 ) and AA^ = 2,0 which is the threshold value. Both the values correspond with R>0 and they are consistent with the assumptions applied at the calculations with S-N curves which were not corrected for compressive stresses influence. In the calculations for the defined above "A" and "B" Weibull distributions of Aa, the range < 0,2 ay > was divided into 200 pieces with assumed constant values of Aa and all of Aa were used in eqn. (3) in increasing order, at least 20 times before crack depth a = T. Such a method gave satisfactory accuracy. Lack of the mis was not taken into account. The calculations for T = 10 mm and T = 20 mm (see Fig. 2) were done. Values of L were calculated as functions of initial crack depth a = a$ and compared to L = L^ which were calculated by S-N approach (their values are given in Table 1). Typical plots L I L^ as function of a$ I T are shown in Fig. 3.

6 584 Marine Technology Aa ace. to "A" T = 20 mm Aa ace. to "B" T = 20 mm 2-- 0,01 0,01 0, S-N curve FAT class S-N curve FAT class 130 (ideal ) Fig. 3 LI LM as function of a$ I T In Table 2 values of a$ IT at which L = L^v are given. The Weibull distributions "A" and "B" and two values Aa = const (100 MPa and 200 MPa) were considered. a) Joint Fig. la Fig. Ib Fig. laideal Fig. Ibideal Table 2 Values a$ I T giving L = Load A 7=10 7=10 r = 20 7 = 20 7=10 Af,*=2 AAT,,=6 A^,,=2 A^,A "6 Af,A=2 0,030 0,064 0,015 0,040 0,037 0,015 0,045 0,008 0,025 0,016 0,008 0,040 0,003 0,018 0,009 0,007 0,030 0,004 0,017 0,006 7=10 MT,, =6 0,050 0,028 0,023 0,018 LoadB 7 = 20 Af,*=2 0,023 0,009 0,004 0,003 7 = 20 AK,/, =6 0,030 0,015 0,010 0,009 b) Joint Fig. la Fig. Ib Fig. laideal Fig. lbideal 7=10mm 0,044 0,015 0,013 Aa =100 MPa T = 20 mm 0,028 0,010 0,005 7=10mm 0,022 0,017 0,007 0,005 Aa = 200 MPa T = 20 mm 0,030 0,010 0,005 0,003

7 Marine Technology 585 The symbol " " in Table 2b means that t±k < 2,0 for a = a$ and the crack will not propagate ace. to eqn. (3) while, according to the S-N curve, the fatigue life (number N) is limited. Some remarks and conclusions are given in Ch Cruciform joint Fatigue life of the joint shown in Fig. 4 was analysed. Fig. 4 Cruciform joint with fillet welds The joint in Fig. 4 can be considered as a connection of double bottom floor plates to the central girder of a bulk carrier of unrestricted service, designed also to sail across Great Lakes in North America (DWT « t, length between perpendiculars: 216,6 m, breadth: 23,13 m). The ship has 7 holds and can be loaded alternately with holds Nos. 2, 4 and 6 empty. It was assumed for the purpose of the calculations that the ship is all the time loaded alternately. Static and dynamic stress components at upper edge of the floor, in the middle of empty hold No 2, were calculated according to the requirements of PRS^'. Weibull distribution of Aa was assummed ace. to the requirements of PRS^ - see eqn. (1). The results are as follows: - static stress a^ = 95,0 MPa (tensiled); - Ao\ = 165,6 MPa - value of Aa (see Fig. 4) exceeded with probability 10"*; - 5 = 0,97; N L = 4,7 10* for 20 years of ship's exploitation. Fatigue life of the joint was calculated for long term distribution of Aa as above applying FAT class 45 S-N curve, for Aa'= Aa- 7Y2/, (see Fig. 4) which corresponds to nominal stresses in the fillet welds. The same method of the calculations as in Ch. 2 was applied. Calculated values of fatigue life L = L^ are as follows:

8 586 Marine Technology - for /, = 3,5 mm : L^ = 3,92 years; - for t, = 5,0mm : L^ = 12,82 years. In the calculations according to Paris' equation (3) the following parametric formula for A/C recommended by Almar-Naess* and IIW^ was applied: 1 + T where: Aa, Ay, T- see Fig. 4; a - half of the distance between the tips of the crack, measured along direction perpendicular to Aa. At the beginning a = \ T was assummed; 1 s+-, X, =0, ,287 T ^ Zil +i3j22 ^ -7,7551^1 +1,783 rj I TV lr' ' The equation (6) is valid for a/w<0,7. It was checked, however, that for a/w close to 0,7 rapid increase of daldn calculated ace. to eqn. (3) is observed and remaining fatigue life is negligible. Ace. to IIW* the stress concentration factor SCF = 1,45 is taken into account for FAT class 45 S-N curve. Therefore, it was decided to perform the calculations ace. to equations (3) and (6) for Aa^ = 165,6 MPa (the same as applied in S-N approach) and Aa# = 1,45-165,6 = 240,1 MPa. The method of calculations was the same as described in Ch. 2. In the calculations the three values of AA:,, were considered: a,-'aa - AA:,, = 6,0-4,567? (AA:,, > 2), where R = ^ ; (7) a\+- Aa - AK, =2,0; - A*. =6,0. Calculated values of L compared to LSN are given in Table 3. (6)

9 Marine Technology 587 Aa, [MPa] 165,6 240,1 Table 3 Value of I/Asw for cruciform joint ^ = 3,5 mm f, = 5,0 mm A^, 6,0-4,567? 2,0 6,0 6,0-4,567? 2,0 6,0 L/LSM 1,63 1,61 4,81 0,48 0,48 0,82 Af,A 6,0-4,567? 2,0 6,0 6,0-4,567? 2,0 6,0 6/Aw 1,24 1,21 4,55 0,37 0,37 0,69 Some remarks and conclusions are given in Ch Final remarks and conclusions Results of the calculations given in Table 2 (for butt weld joint) suggest that there is no rule for indicating such values ofao/t which ensure the same fatigue life value calculated applying S-N approach and Paris' equation (3), in cases where fatigue life is of the order of expected ship's exploitation period or even greater. Values of a^/t depend on thickness T of plating and type of load (Aa = const and Weibull distributions were considered). However, the most important parameter is the value of AA^ which depends on 7? coefficient. In design codes based on S-N approach values 7? > 0 formally have not influence on calculated value of L while in the case of crack propagation analysis method the situation is completely different (AA^ = 6,0-4,567?, AA^ > 2). Allowable value of a<jtequal to 0,025 for FAT class 100 (joint in Fig. la), given by IIW\ is not confirmed by the results of the calculations. Applying a,, / T - 0,025 would give, in general, too conservative results (see Table 2). In the case of cruciform joint (Fig. 4) the results given in Table 3 show it clearly that values of LILsN depend significantly on t. and AA^. The results in Table 3 do not confirm the assumed value of SCF = 1,45, ace. to IIW\ for FAT class 100 S-N curve. The value of SCF should be smaller than 1,45 to obtain LI L^ *1. The general conclusion is that, in case of rather long fatigue life, the both considered methods (S-N approach and crack propagation analysis) can give quite different results. S-N curves, which are very simple in form, are a kind of lower bound of experimental results and they do not precisely take into account the influence of many important parameters such as thickness of plating or asymmetry of cycles of Aa, for example. Application of Paris' equation (3) formally allows to take directly into account some important parameters but this

10 588 Marine Technology formally allows to take directly into account some important parameters but this approach is also approximate. Such a method should be applied for remaining fatigue life calculations of structural elements with detected S-N cracks or imperfections, approach seems to be a reasonable tool for design codes for steel structures where considerable value of fatigue life is required. Acknowledgement The author would like to acknowledge the support of National Research Committee (KBN) which financed the research project 7T07B04813 ^Application of fatigue crack propagation criterion to assessment of fatigue lives of ship hulls" - the reported research was performed as a part of it. References 1. Almar - Naess, A. Fatigue Handbook, Tapir, Department of Energy, Proposed Revisions to Fatigue Guidance, August International Institute of Welding, Recommendations on Fatigue of Welded Components, IIW document XIII /XV , March Polski Rejestr Statkow, Rules of Classification and Construction of Seagoing ships, Part II, Hull, Gdansk, Polski Rejestr Statkow, Fatigue Strength Analysis of Steel Ship Hull Structures, (in polish), Publication 45/P, Gdansk, Xu, T. & Bea, R. G. Fatigue of Ship Critical Structural Details, Transactions of ASME, vol. 119, pp , May Dovers, W. D & Madhawa, A. G. (editors) Fatigue in Offshore Structures, Polski Rejestr Statkow, Zone Strength Analysis of bulk carriers, Publication 18/P, Gdansk, 1995.