روش نقشه برداری اختلال برای تجزیه و تحلیل حساسیت ترک های سه بعدی در نزدیکی سطح آزاد

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.

Due to the importance of stress intensity factors in determining the fatigue life of materials, considerable attention has been devoted to their accurate determination [1], [2], [3], [4], [5] and [6]. The problem of an arbitrary-shaped crack in an infinite or semi-infinite linear elastic solid can be generally formulated in the form of traction-boundary integral equations [7] and [8]. Efficient boundary integral equations and finite element methods have been developed for the solution of these equations [9] and [10]. Despite the progress made to date, the use of numerical fracture mechanics calculations in automated optimum design of structures requires efficient techniques for calculating the sensitivity of the stress intensity factors to variations in crack geometry and material parameters. The sensitivity coefficients (derivatives of the stress intensity factors with respect to geometric and material parameters) can be used to: 1. Assess the effects of uncertainties in the material and geometric parameters on the accuracy of the calculated stress intensity factors. 2. Predict the changes in the stress intensity factors due to changes in the parameters. Although a number of techniques have been developed for evaluating the sensitivity coefficients of the response quantities of structures, to the authors' knowledge no application of these techniques to the boundary integral equation formulation of fracture mechanics has been reported. The techniques developed for sensitivity analysis can be grouped into three categories: analytical direct differentiation methods, semi-analytical or quasi-analytical methods, and finite difference methods [11], [12] and [13]. The present study focuses on the sensitivity analysis of crack problems. Specifically, this paper presents a perturbation mapping method and a computational procedure for evaluating the sensitivity coefficients of the stress intensity factors for three-dimensional planar cracks near a free surface. The boundary integral equations are solved by using the boundary element method. To fix ideas, only three-dimensional cracks under mode I loading (opening mode) are considered.