Closed form line spring yield surfaces for deep and shallow cracks: formulation and numerical performance

The line-spring finite element is a versatile numerical tool for performing engineering fracture mechanics analysis of surface cracked shells. The accuracy of the line-spring finite element solution for deep/medium-sized cracks has shown to be higher than the accuracy for the shallow-sized ones. Proper treatment of shallow cracks is important because they are the ones most frequently encountered in engineering practice. Accurate yield surfaces of plane-strain single edge-cracked specimens having shallow, as well as deep, cracks are developed here in order to improve the overall performance of the line-spring element. The yield surface is represented by equations that automatically satisfy the convexity requirement and that fit the result of limit load analyses. The present study addresses, furthermore, the performance of the backward Euler return algorithm for one of the accurate yield surface formulated here, by means of iso-error maps.