SYMPOSIA PAPER Published: 01 January 1990

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


The p-version of the finite-element method together with carefully designed meshes is 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's ratio of 0.3 and 0.499, respectively. A priori known convergence properties are used to estimate bounds for the error in the numerical solutions. The calculated displacements are believed to be 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 KI are readily obtained with very high accuracy even when a very simple mesh and a modest computational effort are used. So-called 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. In fact, the first-order vertex intensity factor, under different boundary conditions, may 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.

Author Information

Blom, AF
The Aeronautical Research Institute of Sweden, Bromma, Sweden
Andersson, B
The Aeronautical Research Institute of Sweden, Bromma, Sweden
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Developed by Committee: E08
Pages: 77–98
DOI: 10.1520/STP23428S
ISBN-EB: 978-0-8031-5121-5
ISBN-13: 978-0-8031-1284-1