FINITE-ELEMENT SOLUTIONS FOR PROPAGATING INTERFACE CRACKS WITH SINGULARITY ELEMENTS

A finite element procedure has been developed to provide solutions for the state of stress, displacement and stress intensity factors for a propagating crack at the interface of two dissimilar anisotropic materials. In the finite element mesh the crack-tip is embedded in a singular element and the near-field state of stress and displacement described in our paper in Engng Fracture Mech. 36, 93-103 are used. The remainder of the body is filled with regular finite elements. The singular element formulation provides for the direct solution of the time-dependent stress intensity factors. The procedure for the finite element formulation including the development of the singular element matrices is presented. The element matrices are derived from a variational principle involving a modified functional for elastodynamic problems. The resulting discretized dynamic equations of motion are solved by an implicit method of time integration using Newmark-beta formulas. Local asymmetries in the matrices which arise due to crack propagation are dealt with by modifying the finite difference formulation and by the use of an iterative procedure for convergence of the solution. Crack propagation is accomplished by moving the crack-tip inside the singular element according to a prescribed crack-tip position history. A local redefinition of the finite element mesh is required when the crack-tip reaches an extreme position inside the singular element. When the local mesh redefinition takes place, an extra node is created. This is accomplished using a double-noding technique. The accuracy of the finite element formulation is evaluated by solving problems for which analytical and numerical solutions are available. The solutions are found to compare well with solutions in the literature. The solution to some problems involving propagating and stationary cracks at the interface of two dissimilar orthotropic materials, for which there are no known solutions, are presented.