Perturbation mapping method for sensitivity analysis of three-dimensional cracks near a free surface Original Research Article

A perturbation mapping method and a computational procedure are presented for evaluating the sensitivity coefficients of the stress intensity factors for three-dimensional planar cracks near a free surface. The boundary integral equations for evaluating the sensitivity coefficient are solved by using the boundary element method. Each of the geometric parameters that affect the stress intensity factor (such as, crack orientation, distance from the free surface, and crack shape parameters) is given a perturbation which defines a mapping between the original and perturbed coordinate systems, from which the sensitivity coefficients are derived. The sensitivity coefficients obtained by the perturbation mapping method are validated by comparing them with those obtained by the finite difference method. Numerical results for penny-shaped and elliptical cracks are presented showing the variation of the sensitivity coefficients with various geometric and material parameters.