Un Método Computacional para Cálculos Fractomecánicos en Tres Dimensiones

Abstract

The solution to three-dimensional crack problems can be obtained by such techniques us the finite element method (FEM) and the boundary element method (BEM). When the basic assumption of linear elastic fracture mechanics is adopted, the stress intensity factors can be evaluated by a variety of techniques, such us the extrapolation of displacements or stresses, the virtual crack extension method, the subtraction of singularity technique, and the J-integral methods. The J-integral methods have been addressed by a number of authors, and different schemes based on the evaluation of either a domain integral or the combination of path and area integrals have been proposed. Volume integrals exhibit the drawback that the computed value corresponds to an average of the fracture parameter over certain portion of the crack front. On the other hand, the combined use of path and surface integrals results cumbersome to implement.
It is presented in this work a new methodology for the computation of the J-integral that involves the evaluation of an area integral only. The methodology is an extension of the Energy Domain Integral (ED!) approach, which makes use of an auxiliary function q that can be regarded as a virtual crack extension. The proposed methodology is implemented using the BEM, since the required stresses, strains and derivatives of displacements at internal points can be directly obtained from their boundary integral representations.