A unified and integrated numerical-analytical approach for evaluation of Jk-integrals of an interfacial crack in orthotropic and isotropic bimaterials

A new unified and integrated method for the numerical-analytical calculation of Jk-integrals of an in-plane traction free interfacial crack in homogeneous orthotropic and isotropic bimaterials is presented. The numerical algorithm, based on the boundary element crack shape sensitivities, is generic and flexible. It applies to both straight and curved interfacial cracks in anisotropic and/or isotropic bimaterials. The shape functions of semi-discontinuous quadratic quarter point crack tip elements are correctly scaled to adapt the singular oscillatory near tip field of tractions. The length of crack is designated as the design variable to compute the strain energy release rate precisely. Although an analytical equation relating J1 and stress intensity factors (SIFs) exists, a similar relation for J2 in debonded anisotropic solids for decoupling SIFs is not available. An analytical expression was recently derived by this author for J2 in aligned orthotropic/orthotropic bimaterials with a straight interface crack. Using this new relation and the present computed Jk values, the SIFs can be decoupled without the need for an auxiliary equation. Here, the aforementioned analytical relation is reconstructed for cubic symmetry/isotropic bimaterials and used with the present numerical algorithm. An example with known analytical SIFs is presented. The numerical and analytical magnitudes of Jk for an interface crack in orthotropic/orthotropic and cubic symmetry/isotropic bimaterials show an excellent agreement.