A Study of Interface Crack Branching in Dissimilar Anisotropic Bimaterial Composites Including Thermal

Abstract

The interface crack branching phenomena, including thermal effects, has been investigated by using complex variable method and Stroh's dislocation theory, extended to thermo-elasticity in matrix notation. As one of the most catastrophic failure modes in structures like laminated and sandwich composites in aerospace and marine construction, thin film in electronic packaging, rotators in high speed engine of aircraft and reactor in nuclear power station, the study of interface crack branching has become a topic not only having theoretical importance, but also having practical significance. A unified approach is presented to address the thermoelastic interface crack problems in dissimilar anisotropic bimaterial composites, and a compact closed form solution is formulated by analytical continuation principle of complex analysis. Employing the contour integral method, an explicit solution to the interaction between the dislocations and the interface crack is obtained. By modeling the branched portion as a continuous distribution of the dislocations, the thermoelastic interface crack branching problem is then converted to a set of semi-coupled singular integral equations and solved by Gauss-Jacobi integration schemes. The influence of material property mismatches between the two constituents and the thermal loading effects on the interface crack branching are demonstrated by extensive numerical simulation. Some useful criteria for predicting the interface crack branching growth and guidance for optimal composites design are suggested. Further, a contact model to eliminate the overlapping between the two surfaces of an interface crack is also proposed and some new parameters which could influence the interpenetrating phenomena are also discovered. The technique to extend the current method to three dimensional problems is also outlined. Furthermore, the C++ source code has been implemented to manipulate the complicated complex operations for numerically solving the singular integral equations in complex matrix form.