Semi-Elliptical Surface Crack Problem: Detailed Numerical Solutions for Complete Elastic Stress Fields

摘要

The p-version of the finite element method together with carefully designed meshes are used to obtain accurate numerical solutions for complete elastic stress fields in a linearly elastic plate containing a semi-elliptical surface crack for two materials having a Poisson ratio of 0.3 and 0.499, respectively. Prior known convergence properties are used to estimate bounds for the error in the numerical solutions. The calculated displacements are accurate at all points located not closer than 0.001a, a being the crack size, from the crack front. It is demonstrated that pointwise values for the traditional edge stress intensity factors are readily obtained with very high accuracy even when using a very simple mesh and a modest computational effort. Socalled vertex and vertex-edge intensity factors are derived which together with numerically determined eigenfunctions fully characterize the complete solution in the vicinity of the vertex where the crack front intersects with the stress free surface. For the nearly incompressible material the second order vertex intensity factor strongly influences the solution close to the vertex. The first order vertex intensity factor may, under different boundary conditions, be of negligible importance (except for extremely small distances from the vertex). The size of the domain where the vertex singularity strongly influences the solution is of the order 0.02a.