Finite-element solutions of crack growth in incompressible elastic-plastic solids with various yielding extents and loadings: Detailed comparisons with analytical solutions

Abstract

We have conducted numerical finite element studies of plane strain quasistatic crack growth in elastic-plastic material for a wide range of applied loading conditions and yielding extents, especially general yielding. To facilitate precise comparisons with previous analytical results, we have employed a fully incompressible, nonhardening material model. A reduced/selected integration procedure is successfully used to enforce material incompressibility. For crack growth under bending-dominant conditions, we employ an experimentally-measured applied load versus crack length history for a compact tension specimen that experiences crack growth from small-scale yielding through general yielding conditions. A constant crack tip opening angle crack growth criterion is employed to investigate crack growth under tension-dominant loadings in the same geometry. We have also conducted a small-scale yielding crack growth simulation employing a highly refined mesh, and several additional general yielding stationary crack solutions to further explore the effects of different far-field loading combinations. Detailed comparisons of the finite element results with Drugan and Chen's [1] ‘m-family’ of asymptotic analytical solutions are made in an effort to assess the latter's accuracy and range of applicability, and to identify their asymptotically indeterminate parameters m and R as functions of crack growth history. Among several interesting results, we find that Drugan and Chen's near-tip characterizing parameter has a nearly constant value of m ≈ 1.23 for the entire crack growth process from small-scale yielding through general yielding conditions under bending-dominant loading when specimens have traction-free sides. However, we find m to vary significantly from that value as general yielding conditions are approached in tension-dominant loading situations, and whenever specimen sides are subjected to uniform applied loading. The numerical solutions confirm that Chen and Drugan's [2] global approximate analytical solutions for general yielding crack growth are remarkably accurate to substantial distances from the crack tip under a wide variety of loading conditions. The fully incompressible material model employed also facilitates great physical insight into the global stress and deformation fields accompanying general yielding crack growth: numerous figures display the slip lines (which are characteristics for both the stress and velocity fields) throughout the plastically deforming regions.