Most of the literature about fracture mechanics considers cracks having an elliptical shape with a flaw aspect ratio a/l lower or equal to 0.5 where ‘a’ is the crack depth and ‘l’ the total length of the crack. This is also case in the ASME XI Appendix A where Stress Intensity Factors KI formulations are given for a large range of crack depths and for a flaw aspect ratio a/l between 0 and 0.5. The limitation to 0.5 corresponds to a semi-circular shape for surface cracks and to a circular shape for subsurface cracks. This limitation does not seem to be inspired by a theoretical limitation nor by a computational limit. Moreover, it appears that limiting the ratio a/l to 0.5 may generate in some cases some unnecessary conservatism in flaw analysis. The present article specifically deals with the more unusual narrow cracks having a/l >0.5, in the case of surface cracks in infinite flat plates. Several Finite-Elements calculations are performed to compute KI for a large range of crack depths and for 4 typical load cases (uniform, linear, quadratic and cubic). The results can be presented with the same formalism as in the ASME XI Appendix A, such that the work can provide an extension of the ASME coefficients in table A-3320-1&2. By doing the study, one had the opportunity to compare the results obtained by two different Finite-Elements softwares (Systus and Ansys), each one with a different cracked mesh. In addition, a comparison has been made for some cases with results obtained by a XFEM approach (eXtended Finite-Element Method), where the crack does not need to be meshed in the same way as in classical Finite-Elements. The results indicate how the KI can be reduced when considering the real flaw aspect ratio instead of the conventional semi-circular flaw shape. They also show that, for specific theoretical stress distributions, it is not always possible to reduce the analysis of KI to only 2 points, namely the crack surface point and the crack deepest point. The crack growth evaluation of such unusual crack shape should still be investigated to verify whether simple rules can be established to estimate the evolution of the crack front.
Stress-Intensity Factors at Internal Crack Tips for Longitudinal Shear Problems
