The Propagation and Arrest of an Edge Crack in an Elastic Half-Space Under Conditions of Anti-Plane Shear: Analytical and Numerical Results

Citation

O'Sullivan, Timothy Christopher (1983) The Propagation and Arrest of an Edge Crack in an Elastic Half-Space Under Conditions of Anti-Plane Shear: Analytical and Numerical Results. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jb3j-5460. https://resolver.caltech.edu/CaltechETD:etd-09052006-082841

Abstract

The motion of an edge crack extending non-uniformly in an elastic half-space under conditions of anti-plane shear is analyzed. An expression for the stress intensity factor at the crack tip is obtained, and an energy balance crack propagation criterion is used to find the equation of motion of the tip. On solving this equation numerically, it is found that crack arrest occurs before the second reflected wave from the boundary reaches the tip.

In the second half of this investigation, a numerical procedure for studying anti-plane shear crack propagation problems using finite differences is developed. To approximate the elastodynamic field as accurately as possible near the moving crack tip, where singular stresses occur, the local asymptotic displacement field near the tip is incorporated into the finite difference scheme. The numerical procedure is applied to the edge crack problem analyzed in the first part of this study, and the numerical and exact results are compared.

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