Analysis of a crack at a weak interface

The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.