Multiple Crack Analysis in Finite Plates

Abstract

In this study, interactions of multiple cracks in finite rectangular plates are analyzed. A finite plate is treated as a polygon-shaped plate which can be created by contiguous crack segments embedded in an infinite plate forming an enclosed region so there are no true crack tips remaining around the plate. The problem is formulated in terms of integral equations expressed by edge dislocation distributions representing opening displacement profiles for the cracks with both normal and tangential components. To solve this boundary value problem we employ the superposition approach based on the dislocation distributions requiring the determination of crack opening displacement profiles that satisfy the traction- free condition on interior crack faces and the given boundary tractions on four exterior cracks defining the rectangular plate. Applying the method with a new point allocation scheme reducing the number of evaluation points leads to a set of linear algebraic equations in terms of unknown weighting coefficients of opening displacement profiles. These opening displacement profile components are categorized in terms of polynomial terms which are integers and wedge terms which are rational numbers approximated from irrational wedge eigenvalues to evaluate integrals in closed forms. Once the coefficients of opening displacement profile components are obtained, stress and displacement fields on the entire body, as well as stress intensity factors at the crack tips and kinks are calculated. After the accuracy of the method is shown by comparing the results for different sample problems, the strong interactions of multiple cracks in a rectangular plate under various loading conditions are demonstrated with figures and tables.