A novel eigenfunction expansion solution for three-dimensional crack problems

Abstract

A novel eigenfunction expansion method is developed to obtain three-dimensional asymptotic stress fields in the vicinity of the front of a semi-infinite crack. The present method is relatively easy to implement, and is also computationally more efficient in the sense that it does not need to resort to either iterative schemes or more complicated analytical techniques such as the (Luré Al. Three dimension problems of the theory of elasticity. New York: Interscience, 1964.) symbolic method to solve the system of three coupled partial differential equations of three-dimensional elasticity theory. Explicit expressions for singular stress fields in the neighborhood of the front of a semi-infinite crack are derived in the paper. The order of stress singularity thus computed is compared with counterparts developed by earlier investigators. The primary goal of this study is to settle the controversy that has existed during the last quarter of a century as regards the order of stress singularity at the three-dimensional crack front. Additionally, the relationship between the strain–energy release rate and the stress–intensity factor is investigated from a three-dimensional standpoint Furthermore, numerical results pertaining to development of plastic yield zone ahead of the front of a semi-infinite crack are also obtained.