Dynamic effects in mode III crack bifurcation

Abstract

Transient elastodynamic nonplanar self-similar Mode III crack growth in brittle materials is examined. The dynamic similarity and Chaplygin's transformation reduce the class of problems considered to the solution of Laplace's equation in a semi-infinite strip. The Schwarz-Christoffel transformation is subsequently employed to map the semi-infinite strip on a half-plane. The theory of analytic functions can then be used. Elastodynamic influences in the vicinity of a rapidly moving tip after branching are examined in a rather general fashion.To reveal the sensitivity of one branch's crack tip elastodynamic stress intensity factor to the relative velocity and orientation of the other, the problem of asymmetric crack bifurcation under stress wave loading is chosen for study. The development of specific analytical solutions requires the solutions to the symmetric bifurcation problem subjected to loading that induces either antisymmetrical or symmetrical deformations, respectively, about the original crack plane. For asymmetric geometries the solution required the numerical evaluation of several integrals in the final stages. It is ultimately shown that the stress intensity factor of one branch is significantly altered by changes in the velocity and orientation of the other and by the angle of stress wave incidence.