Insensitivity of the reciprocal work contour integral method to higher order eigenvectors

Abstract

The Reciprocal Work Contour Integral Method (RWCIM) is a computationally advantageous method of calculating stress intensities and higher order eigenvector coefficients for a general opening crack in a single or bi-material configuration. It involves integrating functions of analytical solutions and finite element results along an inner and outer contour. Except for the case of a zero opening crack in a single material, there can be computational difficulties with the method in calculating higher order eigenvector coefficients. For those cases, predicted lower ordered coefficients are insensitive to higher order eigenvectors only for a small inner contour radius. However, for a small inner contour radius, coefficient prediction with the RWCIM can become very sensitive to the value assumed for that radius. A numerical algorithm is presented for determining if an inner contour radius is adequate to have the algorithm insensitive to both higher order eigenvectors and the value assumed for the inner contour radius. An example is presented emphasizing salient points.