An integral-equation solution for a bounded elastic body containing a crack: Mode I deformation

• Published in: International journal of fracture Vol. 14; no. 5; pp. 527 - 541
• Main Authors: Rudolphi, T. J., Ashbaugh, N. E.
• Format: Journal Article
• Language: English
• Published: 01-10-1978
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/BF01390473

An integral-equation solution is developed for the two-dimensional problem of a traction-free crack in a bounded, linearly elastic, isotropic medium subjected to in-plane forces which give rise to Mode I type deformations. A set of coupled integral equations involving integrals over the outer boundary and the crack line is derived by superimposing the quadrature-form solution of a crack problem in an unbounded medium upon the boundary integral solution of a problem in the unflawed medium. Since the character of the stress-field singularity is provided by the perturbed problem solution, prior knowledge of the singularity is not required. The stress intensity factors at the crack tips are incorporated directly into the formulation. A procedure for the numerical solution of the coupled equations for regions of fairly general shape and boundary conditions is described. The numerical procedure is applied to several examples in which the stress intensity factors are accurately known.