Boundary element method analysis of interface cracks between orthotropic layers

Abstract

The boundary element method (BEM) with quadratic quarter-point crack-tip element is employed to obtain the stress intensity factors, K1 and K2, the phase angle ψ, as well as the strain energy release rates G of the crack-tip occurring in either completely isotropic materials or bimaterial interfaces. Several sample modelings are presented to show the accuracy of the boundary element method software ‘bie2s.exe’ used in this project, as well as to validate the way of modeling the crack problems using the software. The orthotropic layers considered in this project are the bilayer double cantilever beam (DCB) and end-loaded-split (ELS) specimens. The 2 layers of either specimen are made of same material, same layer thickness and transversely isotropic. The top layer of either specimen is in the plane of transverse isotropy. 4 parameters, namely, the aspect ratio of the bilayer beam L/2H, the crack length to half-beam thickness ratio a/H, and the 2 purely imaginary roots of the characteristic equation of orthotropic materials η1 and η2, are varied to investigate their effects on the strain energy release rate and the phase angle at the interface crack-tip. The results show that for both the DCB and ELS specimens, the normalized strain energy release rate and the phase angle reach their asymptotic values as a/H → ∞. Also it is observed that the aspect ratio of the beam, does not affect the values of the normalized strain energy release rate and the phase angle significantly for a given set of orthotropic material parameters and the crack length to layer thickness for both DCB and ELS specimens.