Some applications of singular fields in the solution of crack problems

This paper reviews some recent developments in superposition methods for calculating linear elastic stress intensity factors and eigenvalues for cracks and notches, presents some new results for pairs of edge cracks and provides new insights into the nature of the errors in these processes. The procedure requires a numerical solution to the full cracked problem and a second solution on the same mesh using the known form of the singularity in an in nite region. This is equivalent to the well-known Subtraction of Singularity (SST) method. The advantages of this procedure over conventional SST are: (1) no modi cations need to be made to a standard computer program; (2) multiple crack tips may be analysed without the di culty of unknown rigid body displacements at the crack tips; (3) solutions with di erent boundary conditions on the same mesh may be obtained simply in one step by re-using one singular eld solution; The singular crack tip eld may also be studied independently leading to estimates of the eigenvalues and some insight into mesh-induced errors. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be re-used with a new right-hand side. Numerical experiments using the boundary element method demonstrate the accuracy and simplicity of the superposition approach for notches, simple cracks, mixed-mode cracks, two edge cracks of di erent lengths and eigenvalues under various boundary conditions.