Three dimensional analysis of dynamic ductile crack growth in a thin plate

Abstract

A three dimensional analysis of dynamic ductile crack growth in an edge cracked plate is carried out, using a data parallel implementation in a transient three dimensional finite element program. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating owing to plastic dissipation and the resulting thermal softening are accounted for in the analyses. The crack speed and the crack path are based on the ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. A convected coordinate Lagrangian formulation is employed and the discretization is based on twenty-node brick elements with 2 × 2 × 2 Gauss points. The equations of motion are integrated numerically by an explicit integration procedure using a lumped mass matrix. Crack growth occurs by tunneling in the central part of the plate and shear lip formation at the free surface. The effect of various material parameters and of plate thickness on this process is studied. For comparison purposes, a calculation with overall plane strain boundary conditions is carried out.