Rigorous formulation of crack path in two-dimensional elastic body

A rigorous formulation is proposed for the prediction of a path along which a crack propagates smoothly in a two-dimensional elastic body. In this formulation, the curvature and length of a small crack extension are determined when an increment of external load is given. The major features of the proposed formulation are to clarify conditions for the change in the displacement due to the crack growth and to explicitly pose a boundary-value problem for the change in the displacement. It is proved that the effects of the crack growth on the field variables are equivalent to a pair of concentrated forces acting at the crack tip. The change in the displacement yields an explicit expression for the change in the stress intensity factors in terms of the curvature and length of the extension, and these geometrical parameters can be determined from the assumed fracture criteria. This differentiates the analysis based on the proposed formulation from a conventional analysis which takes a trial-and-error approach to determine the crack extension path. The validity of the present formulation is examined by studying crack problems which have analytic solutions. The present formulation is applied to a problem of arbitrary plural cracks which grow smoothly while interacting with each other. (C) 1997 Elsevier Science Ltd.