Simulation of corrosion damage, stress concentration, and fatigue crack growth

Transcription

1 28 th ICAF Symposium Helsinki, 3 5 June 2015 Simulation of corrosion damage, stress concentration, and fatigue crack growth Sharon Mellings 1, John Baynham 1, Andres Peratta 1 1 CM BEASY, Ashurst Lodge, Ashurst, Southampton UK sharon@beasy.com Abstract: Airframe structures regularly operate in environments that allow high levels of corrosion damage, and this damage leads to stress concentrations within the structure and potential development of cracks. Even when only a thin film of electrolyte is present on the structure, this can still lead to an electrical field that causes surface damage. Computation of this electrical field can be used to identify areas in the airframe structure that are most susceptible to corrosion damage and which, after possible fatigue crack initiation, may lead to structural failure. Corrosion simulation can be used to take account of the properties of the electrolyte as well as the structural materials, to determine the rate of material loss from the structure. Having removed material from the surface (corresponding to corrosion occurring over a given exposure time) the stress concentrations can be evaluated and, if required, cracks can be initiated in each potential problem area, to identify vulnerability to fatigue failure. Different corrosion damage could arise when different electrolytes are present, for example airframes operating at or near the sea will be subjected to salt water spray, and the electrolyte properties may vary with operational temperatures. Electrolytes produced by condensation, overflows and spillage may be of significant depth inside the aircraft, and may not be pure water. External surfaces may be subject to de-icing chemicals. All-metal airframes are vulnerable to general corrosion, and depending on construction, crevice corrosion and pitting may also occur. Composite airframes which combine aluminium alloy and carbon fibre are at greater risk of galvanic corrosion because of the significant difference between the positions of aluminium and carbon in the electrochemical series. These properties, as well as the effects of surface coatings, all need to be included in the corrosion simulation. Simulation of the galvanic effects leading to corrosion has been successfully used for many years to assist design of cathodic protection systems for marine vessels and offshore structures, and has more recently been applied to aircraft structures. This paper will firstly use simulation to investigate the influence of parameters, including electrolyte thickness and conductivity, on the rate of corrosion for a galvanic cell caused by a metallic sample in contact with a more noble material. The two materials will be exposed to differing environmental conditions, including immersion in a deep layer of electrolyte, exposure to thick layers of electrolyte at junctions between the different materials, and to thinner layers of electrolyte which might be caused by condensation. The paper will reach conclusions regarding the type of environment that is likely to produce higher penetration rates for the assumed geometry and materials and where these higher rates are likely to occur The paper will determine the damage caused by corrosion mass loss over a given operational time, and investigate the effect of such geometry change on the electrical fields in the electrolyte and the resulting rate of corrosion. The geometry change caused by corrosion mass loss will be used to perform stress analysis of the same structure, to determine the stress concentration in the component at the corresponding time in the life of the aircraft. It will then be assumed that cracks initiate, and the subsequent crack growth will be simulated. This crack growth will take into account the corrosion damage and will inherently include local stress concentration due to the damaged surface. In the crack growth simulation, the full crack path and direction will be determined along with the fatigue life. This paper describes a methodology that can be used by design engineers, to identify potential problems in an airframe structure during initial design, giving scope for design changes to reduce potential failures and in-service repair costs. This methodology identifies areas of the

2 2 Sharon Mellings, John Baynham, Andres Peratta structure that have the greatest risk of damage - which may not be obvious without combined corrosion and fracture simulation; and so provides more informed targeting of locations where what if fracture mechanics should be applied. INTRODUCTION Airframe structures regularly operate in environments that allow high levels of corrosion damage, and this damage leads to stress concentrations within the structure and potential development of cracks. Even a thin film of electrolyte on the structure can lead to an electrical field that causes surface damage. Computation of this electrical field can be used to identify areas in the airframe structure that are most susceptible to corrosion damage and which, after possible fatigue crack initiation, may lead to structural failure. Corrosion simulation can be used to take account of the properties of the electrolyte as well as the structural materials, to determine the rate of material loss from the structure. Having removed material from the surface (corresponding to corrosion occurring over a given exposure time) the stress concentrations can be evaluated and, if required, cracks can be initiated in each potential problem area, to identify vulnerability to fatigue failure. Different corrosion damage could arise when different electrolytes are present, for example airframes operating at or near the sea will be subjected to salt water spray, and the electrolyte properties may vary with operational temperatures. Electrolytes produced by condensation, overflows and spillage may be of significant depth inside the aircraft, and may not be pure water. External surfaces may be subject to de-icing chemicals. "All-metal" airframes are vulnerable to general corrosion, and depending on construction, crevice corrosion and pitting may also occur. Composite airframes which combine aluminium alloy and carbon fibre are at greater risk of galvanic corrosion because of the significant difference between the positions of aluminium and carbon in the electrochemical series. These properties, as well as the effects of surface coatings, all need to be included in the corrosion simulation. Simulation of the galvanic effects leading to corrosion has been successfully used for many years to assist design of cathodic protection systems for marine vessels and offshore structures, and has more recently been applied to aircraft structures. The surface damage resulting from corrosion creates stress concentrations in the structure which will increase the chances of cracks initiating in the part. This damage will also affect the crack growth rate and direction. This paper is focused on the modelling of a test specimen exposed to a corrosive environment and subject to cyclic fatigue load, which can lead to the initiation and propagation of cracks. This paper is in two parts. Firstly, the galvanic corrosion modelling of a test specimen exposed to thin and deep layers of electrolyte is presented and discussed. Secondly, the corrosion damaged specimen, after initiation of cracks, is subjected to a fatigue load, with corresponding crack propagation presented. CORROSION MODELLING Introduction The BEASY software has been used to predict the rate of corrosion on a test specimen consisting of a stretch part in contact with two clamps as shown in Figure 1, where the stretch part is aluminium AA2024 and the clamps are carbon fibre reinforced polymer (CFRP). 2

3 Simulation of corrosion damage, stress concentration, and fatigue crack growth 3 Figure 1. Test specimen used for corrosion modelling. The stretch part is considered to be perfectly connected to both clamps with zero electrical resistance. In addition, the internal electrical resistance of CFRP and AA2024 are considered negligible. Because of the dissimilar electrochemical nature of the materials involved, a corrosion cell between the aluminium and the CFRP clamps will be established whenever the specimen is exposed to an electrolyte. CFRP is more noble than AA2024; therefore the stretch part will corrode rather than the clamps. In other words, the stretch part will behave anodically, the CFRP clamps cathodically, and an ionic current driven by the different polarisation properties of the coupled materials, will flow through the electrolyte. The corrosion damage occurs on the anodic region (AA2024) and the distribution of normal current density flowing from the anodic surface to the electrolyte becomes a direct measurement of the corrosion damage, as prescribed by equation (1) based on Faraday s law: jn CR B1 EW, (1) where: CR = Corrosion rate, expressed in mm/year. j n = Corrosion current density, expressed in A/m 2 = Mass density, in kg/m 3 EW = Equivalent weight of the corroding sample B 1 = Constant involving Faraday s constant and unit conversion factors such that the result appears in mm per year. The value of B 1 is mm kg/(a m yr) The specific mass loss rate (S R ) is related to j n by the expression S B R 2 j n EW where B 2 is a constant involving Faraday s constant and unit conversion factors, K2 = mg/(a day), so that S R is expressed in mg/(day m 2 ). Similarly, the mass loss rate for a component can be expressed as: M R B 2 I EW, (2) where I is the total anodic current for the component, and M R is expressed in mg/day The equivalent weight for an alloy can be calculated as follows: EW i 1 n i W i i, (3) where: Φi = mass fraction of the i-th element in the alloy

4 4 Sharon Mellings, John Baynham, Andres Peratta Wi = atomic weight of the i-th element in the alloy expressed in grams per mol ni = the number of electrons involved in the oxidation process of the i-th element in the alloy Using the above expression, the equivalent weight for AA2024 is calculated to be The form of the electric field in the electrolyte is affected by the geometry of the polarising surface, the polarisation curves, the geometry of the electrolyte and electrical properties of the electrolyte. The following sections provide some theoretical background, describe main features of the test specimen under study, and report the modelling results of corrosion damage obtained under the following exposure conditions: Specimen fully immersed in deep electrolyte Specimen covered by a thin layer of electrolyte Theoretical background Simulation involves solution of the 3D Poisson equation for the electrolyte potential with non-linear boundary conditions imposed by the polarisation curves on the active electrodes. The physical and mathematical background for the corrosion modelling in deep electrolyte can be followed from references [1], [2] and [3] and references therein. In the case of thin film electrolyte modelling, the basic formulation is similar to the deep electrolyte case, except that the electrolyte is treated as a two dimensional object warped in three-dimensional space to adopt to the geometry of the specimen. The electrolyte is regarded as a thin sheet that covers the specimen. Referring to Figure 2, we make the following assumptions: the electrolyte thickness (w) and conductivity ( ) are functions of the two-dimensional coordinates X and Y; for the model to be regarded as thin the condition w L must be satisfied; the electric field ( ) in the bulk of the electrolyte is mostly oriented in the X-Y direction, parallel to the underlying surface (i.e. E Z is negligible compared to E x and E y ). Figure 2. Schematic showing current flow between cathodic and anodic regions. Under the above mentioned assumptions, the equation for solution is: w Due jn 2D 2 (4) Where represents the two dimensional gradient operator acting on x and y coordinates, ue is the electrolyte potential, w is the electrolyte thickness, and j n is the current density coming from the active electrodes, or zero if the surface underneath the thin film electrolyte is perfectly coated and acts as an insulator. The difference between potential in the electrolyte above the metal surface and potential of the metal surface is referred to as polarisation potential, and the polarisation curve dictates the way in which u e u m (where m j n varies with u is the metal potential). This is a non-linear polarization curve of the electrode and the electrolyte, which can be experimentally determined. Further details on the theoretical background for thin film modelling and the corresponding theoretical validation can be found in reference [4] and [5] and references therein. 4

5 Simulation of corrosion damage, stress concentration, and fatigue crack growth 5 Modelling Assumptions Figure 3 shows the specimen dimensions. The stretch part is 2mm thick, and the fasteners are considered to be perfectly insulated. Figure 3. Specimen dimensions (in millimetres). Unless specified otherwise, in all cases the electrolyte is a saline solution NaCl 0.3M with conductivity 0.5 S/m. The polarisation properties of CFRP (cathodic branch) and AA2024 (anodic branch) used in this study are shown in Figure 4. Figure 4. Polarisation curves. Unless otherwise indicated, potentials are in Volts relative to a saturated Ag/AgCl reference electrode; currents are expressed in Amperes, and current density in Amperes per square metre. Case 1: Deep electrolyte In this case, the specimen immersed at the centre of a large (2m x 2m x 2m) tank of electrolyte. The tank surfaces are perfectly insulating. Because the dimensions of the tank are big compared to the specimen, the

6 6 Sharon Mellings, John Baynham, Andres Peratta solution obtained is representative of a sample submerged in an infinitely large tank (i.e. the results do not change with increased tank size.). The distribution of polarisation potential on the cathodic and anodic regions is shown in Figure 5. The polarisation potential ranges approximately from about V to V (22 mv difference). Figure 5. Contours of polarisation potential (u) in Volts on anodic and cathodic surfaces. Figure 6 shows the distribution of normal current density on the stretch part and bottom clamp. The stretch part behaves entirely anodically and the current density ranges from approximately 0.07 A/m 2 to A/m 2. The highest value of anodic current density occurs on the side of the stretch part between the two clamps, while the minimum occurs on the most distant areas from the clamps. The cathodic current density (on the clamp) is comparatively more uniformly distributed and averages to approximately 0.12 A/m 2. Figure 6. Contours of normal current density (j n ) in A/m 2 on anodic and cathodic surfaces (positive current density indicates anodic behaviour). The current flowing between the stretch part and the clamps is about 0.81 ma, which corresponds to 6.8 mg/day mass loss rate 6

7 Simulation of corrosion damage, stress concentration, and fatigue crack growth 7 Case 2: Thin film electrolyte Figure 7 shows the distribution of polarisation potential caused by exposure to a uniform electrolyte film of thickness 100 m covering the clamps and stretch part. The polarisation potential ranges from V to V (311 mv difference). Figure 7. Contours of polarisation potential (u) in Volts on the surfaces of the specimen exposed to thin film. Figure 8 shows the corresponding distribution of normal current density using two different scales, one for the cathodic currents on the clamps (with negative values), and the other for the stretch part (with positive values). The highest anodic current density (approximately 3.4 A/m 2 ) occurs at the edges of the stretch part in contact with the clamps, and it rapidly decays to nearly zero in all regions of the aluminium more distant than 20mm from the clamps.

8 8 Sharon Mellings, John Baynham, Andres Peratta Figure 8. Contours of normal current density (j n ) in A/m 2 on the surfaces of the specimen exposed to thin film electrolyte (Electrolyte thickness = 100 m). Figure 9 shows the distribution of corrosion rate in the region of the stretch part with highest damage, and vectors showing the electric field. Figure 9. Showing contours of corrosion rate expressed in millimetres per year zoomed-in on the area of the stretch part with highest damage. The arrows represent electric field in the electrolyte. 8

9 Simulation of corrosion damage, stress concentration, and fatigue crack growth 9 The current flowing between the stretch part and the clamps when exposed to a 100 m thick electrolyte is about 0.2mA, which corresponds to 1.73 mg/day mass loss rate. Figure 10 shows how the mass loss rate changes with the electrolyte thickness. The results were obtained by performing simulations with electrolyte thickness ranging from 100m to 1000 m. Figure 10. Variation of total mass loss in the stretch part as a function of electrolyte thickness. The mass loss due to anodic dissolution implies material removal from the stretch part. Without considering any change of properties as mass is lost, the geometry of the specimen damaged by corrosion will eventually take the form shown in Figure 11. The mesh representing the damaged specimen shown in the figure has been obtained by iteratively modifying the position of each mesh point, with a translation proportional to the corrosion penetration rate and directed along the normal to the sample surface, then re-solving for new corrosion rates. Figure 11. Showing geometry changes in the specimen due to corrosion damage.

10 10 Sharon Mellings, John Baynham, Andres Peratta STRESS CONCENTRATIONS AND CRACK GROWTH RESULTING FROM CORROSION DAMAGE As discussed earlier, corrosion results in loss of material from an affected structure. This leads to localised stress concentrations, which can accelerate development and growth of cracks and fatigue failure of the part. Using the corrosion simulation results, a prediction of material loss after a given time has been determined and used to modify the geometry of the part prior to computation of the stress concentrations. By identifying the areas of highest stress concentration, cracks were initiated in the component using an automatic crack modelling tool. Crack growth simulation was then performed, growing these cracks automatically using fatigue crack growth, under a defined cyclic loading. Since the geometry includes corrosion damage in the "un-cracked" model, the crack growth simulation inherently computes the growth including the corrosion damage. This incorporates stress concentrations due to the material loss directly within the crack growth simulation, rather than requiring any numerical correction in the computed fatigue results. Stress concentration due to the corrosion damage The corrosion simulation showed that the greatest susceptibility to corrosion damage is at the interface between the carbon fibre and the aluminium. The crack growth shown here assumes that there is a line of damage across the part, with a damage depth of 0.15mm. Since the surface damage is a surface feature, the use of boundary element modelling for the stress analysis of the damaged part is ideal. In this example, a line of material has been removed from the stretch part near the intersection with the carbon fibre tie beam (as shown in Figure 12); however it would be possible to simulate any damage that is predicted by the corrosion simulation. Figure 12. Damaged stretch component. 10

11 Simulation of corrosion damage, stress concentration, and fatigue crack growth 11 The stress has been computed in the stretch part by applying a uniform load through the axis of the stretch component with a nominal 1N/mm 2 load applied to one of the bolt holes and a clamp restraint applied to the other bolt hole. In addition normal restraint was applied to the central section where the carbon fibre tie-bar will restrict out of plane deformation of the stretch part. The load applied to the part is 50.2N. Resulting stresses are shown in Figure 13 and Figure 14 Figure 13. Stresses in damaged stretch component. Figure 14. Localised stresses in damaged stretch component.

12 12 Sharon Mellings, John Baynham, Andres Peratta The results show stress concentration factor of 2.52 caused by the corrosion damage to the surface of the part. The peak stress occurs along a line at the bottom of the corrosion damage, and this indicates a likely location for an initial crack. Crack analysis with a single edge crack Whilst cracks could initiate anywhere, in this example, the stress concentration results in a localised area where there is increased chance of crack initiation. The highest stress value occurred at the bottom of the corrosion damage, a short distance from the corner of the part. In addition to increasing the chance of cracks initiating in the part, the damaged shape of the structure may also affect the crack growth rate and direction. Therefore it is preferable to simulate the crack growth in the damaged part. The damaged model as shown in Figure 12 has been used for crack growth simulation, using an initial surface edge crack, of radius 0.1mm, initiated at the point where the highest stress concentration has been computed in the "damaged" model. Figure 15. Stresses around the initial edge crack. The stresses are computed using the Dual Boundary Element Methods [6-9] and the stresses around the crack are shown in Figure 15, with the resultant SIF values, for the applied uniaxial load, shown in Figure

13 Simulation of corrosion damage, stress concentration, and fatigue crack growth Stress Intensity Factor Mode 1 SIF Mode 2 SIF Mode 3 SIF Position along crack front Figure 16. SIF values along the crack front. Fatigue crack growth of a single edge crack The stress intensity factors obtained, using an applied load of around 50N, are not sufficiently high to cause the crack to start growing. However the SIF values have been computed using a nominal crack loading and different load scenarios can be investigated. This could include combined multi-axial loading or complex loading histories. In this example, we assumed that the crack is subject to a fatigue load cycling between 0 and 7530N. This gives a load factor of 150 and, since the stretch part has been analysed using a linear analysis, this allows the SIF values to be computed simply by scaling up the results from the "nominal" load. If the simulation required multiple load cases, this can be achieved by combining the SIF values from each of the load cases. Using this load regime in conjunction with a set of NASGRO 3.0 fatigue properties for an aluminium material, the crack has been grown automatically, re-computing the SIF values periodically during the crack growth. After a number of growth increments, the edge crack reaches the corner of the structure, after which the crack growth automatically continues as a corner crack.

14 14 Sharon Mellings, John Baynham, Andres Peratta Figure 17. Stress plot after crack grows around the corner. The crack growth simulation proceeds, with the stresses and SIFs re-computed at every stage. After a number of additional growth steps the crack grows through the thickness of the stretch part and transitions to a through crack as shown in Figure 18. The life of the crack is shown in Figure

15 Simulation of corrosion damage, stress concentration, and fatigue crack growth 15 Figure 18. Crack transitions to a through crack Transition to through crack 1.4 Crack Size (mm) Transition to corner crack Fatigue Load Cycles Figure 19. Fatigue results for the growth of the single crack.

16 16 Sharon Mellings, John Baynham, Andres Peratta Stress intensity factor calculations for multiple cracks The fatigue crack growth simulation shown above assumed that a single surface crack had initiated, in the damaged area of the part where the stresses are highest. However, the stress concentrations, shown in Figure 14, indicate there is a line of high stress values across the part in the damaged region. Cracks are more likely to initiate along this a line than elsewhere in the part, so it is possible for multiple cracks to initiate in this region. In this second example of fatigue simulation, two cracks have been initiated along the line where the stress concentration is the highest, with both of the cracks close to the corner of the part. The first crack is, as in the previous simulation, a thumbnail edge crack, with radius 0.1mm and located 0.45mm from the corner, whilst the second crack is a corner crack, also with a radius of 0.1mm. In this simulation both cracks are added to the part and a new mesh is created to incorporate both cracks (as shown in Figure 20), before the stresses are re-computed. This process results in inherent modelling of any load interaction between the two cracks, with no numerical correction required. Figure 21 shows the model stress intensity factors computed from this model. Figure 20. Two cracks modelled in the stretch part. Comparison of the SIF results on the edge crack in this example (Figure 21) with those given earlier for the single edge crack (Figure 16) shows that the presence of the additional crack has raised the computed SIF values by around 10% but, for these initial cracks, there does not appear to be any significant distortion of the shape of the graph of K 1 for crack 1 in Figure

17 Simulation of corrosion damage, stress concentration, and fatigue crack growth Corner crack (top face) 1.25 Stress Intensity Factor Corner crack (through thickness) Crack 1 Mode 1 Crack 2 Mode 1 Edge crack (near corner) Position along crack front Figure 21. Mode 1 stress intensity factor results for the two cracks. The simulation was continued using automatic growth of these two cracks; remeshing and recomputing the stress field at each growth increment. After a number of growth steps the cracks appear to interfere, as shown in Figures 22 and 23. The SIF plots in Figure 23 show greatly increased SIF at the nearby ends of the two cracks. Figure 22. Stress plots after a number of crack growth steps.

18 18 Sharon Mellings, John Baynham, Andres Peratta 1.7 Corner crack (top face) Edge crack (nearest corner) Stress Intensity Factor Crack 1 Crack Corner crack (through thickness) Local position along crack front Figure 23. Mode 1 stress intensity factor results for two cracks after a number of crack growth steps. The simulation could be continued by creating a coalesced crack. The coalesced crack would then grow in a similar way to the previous example, growing through the thickness to transition into a through crack. Such further growth simulation has not been presented here, but would continue automatically. SUMMARY The damage caused by galvanic corrosion and subsequent mechanical loading of a specimen consisting of two dissimilar materials exposed to different types of electrolyte has been quantified using a computational modelling approach based on the BEASY software. The corrosion simulation can predict mass loss rate, corrosion penetration rate, current density, electric fields and polarisation potentials on the specimen exposed to different types of electrolytes. With fatigue loading of the corrosion the damaged part, the future simulation can grow an initial crack through to failure, determining the fatigue life from any given time. An example of an aluminium stretch part in between two CFRP clamps has been solved for different environmental conditions. The corrosion damage resulting from anodic dissolution induced a geometry change in the aluminium, which affected the initial distribution of mechanical stress and subsequent crack propagation. Although the example shown assumed no charges at polarisation property with mass removal, it is possible that loss of surface films could lead to locally changed properties, and accelerated corrosion such as pitting. The example shown is for specific materials (CFRP and AA2024) Nevertheless, the results support the following general observations: and specific geometry and electrolyte. 18

19 Simulation of corrosion damage, stress concentration, and fatigue crack growth 19 The galvanic effects observed with exposure to a thin film of electrolyte are much higher than in the case of deep electrolyte. The distribution of anodic current density (and therefore corrosion damage) becomes significantly more localised as the thickness of the electrolyte decreases. In general, when the sample is exposed to thin films, the corrosion damage tends to accumulate at the edges near the junctions between dissimilar materials, whereas for bulk electrolytes, the damage becomes more uniformly distributed, extending to farther regions. Assuming no changes of the concentration of oxygen in the electrolyte, or of the polarisation curves of the materials involved, the overall mass loss rate in the case of fully immersed samples is always bigger than in the case of exposure to a thin film. This is because the electrical resistance through by the electrolyte is increased when the electrolyte thickness decreases. Although it may depend on details of geometry, it is clear that the penetration rate can be much higher with a thin film of electrolyte than with deep electrolyte. The overall mass loss rate, obtained with a thin film of electrolyte, tends as the film thickness increases to the value obtained for the sample in a large tank of electrolyte. Figure 24 shows how the mass loss rate calculated for increasing values of electrolyte thickness using case 2 conditions tend to the limiting value found in case 1. Figure 24. Showing simulation results for mass loss rate as a function of electrolyte thickness. Line (A), indicating mass loss rate = 6.8 mg/day, corresponds to the result obtained in case 1 for the specimen immersed in a large pool of electrolyte. REFERENCES [1] Adey, R. and Niku, S. (1988). In: Galvanic Corrosion, ASTM Committee G-1 on Corrosion of Metals, Hack, H. (Ed.), ASTM International. [2] Roberge, P. (2008). Corrosion Engineering. Principles and Practice. McGraw-Hill. [3] Peratta A, Hack, T., Adey, R., Baynham J., Lohner, H. (2009). Galvanic Corrosion Modelling for Aircraft Environments. Eurocorr, Nice. [4] Peratta A. and Adey R (2013). Modeling Galvanic Corrosion in Multi-Material Aircraft Structures, NACE Corrosion. [5] Palani S, Hack T., Peratta A., Adey R., Baynham J and Lohner H. (2010). Validation Of A Galvanic Corrosion Model For AA2024 And CFRP with Localised Coating Damage. Eurocorr [6] Portela, A.; Aliabadi M.H; Rooke, D.P., The Dual Boundary Element Method: Efficient Implementation for Cracked Problems, International Journal for Numerical Methods in Engineering, Vol. 32, pp , (1992).

20 20 Sharon Mellings, John Baynham, Andres Peratta [7] Mi Y; Aliabadi M.H., Three-dimensional crack growth simulation using 6EM, Computers & Structures, Vol. 52, No. 5, pp , (1994). [8] Mellings, S., Baynham, J., Adey, R.A., Advances in crack growth modelling of 3D Aircraft Structures, International Committee on Aeronautical Fatigue, Rotterdam, Netherlands, May [9] Rigby R.; Aliabadi M.H; Decomposition of the mixed-mode J-integral revisited ; International Journal of Solids and Structures, Volume 35, Issue 17, June 1998, Pages