Finite element analysis of propagating interface cracks in composites

Abstract

A complex variable formulation has been developed to describe the near-field state of stresses and displacements for a propagating crack along the interface of two dissimilar anisotropic materials. It is shown that the formulation is general and can be reduced to all the other subordinate cases. The crack can be propagating or stationary and each of the materials on the sides of the crack can be anisotropic, orthotropic or isotropic. The near-field stresses contain the regular square root singularity and the oscillatory behavior in case of dissimilar materials on the sides of the crack.A new definition for the stress intensity factors is proposed. It is proportional to the coefficient of the lowest order term of the near-field state of stresses and reduces to all the subordinate cases to within a multiplicative factor.A detailed description of the development of the near-field state of stresses and displacements is presented. A finite element procedure has been developed to provide solution. The finite element procedure utilizes a singular element which gives the direct solution of the time-dependent stress intensity factors. The procedure for the finite element formulation including a detailed description of the development of the singular element 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 temporal integration using Nemark-(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 using a method of double noding technique.The accuracy of the finite element formulation is evaluated by solving problems for which analytical and numerical solutions are available. Finally, recommendations are made for further development of the finite element procedure. (Abstract shortened with permission of author.)