Post-yield fracture mechanics theory and its application to pressure vessels

Abstract

A post-yield fracture mechanics theory is presented based on Bilby, Cottrell and Swinden-Dugdale model solutions for cracks in bodies of finite width and subject to stress gradients. The model solutions are in good agreement with computed elastic-plastic values of the path independent integral J up to loads of 0·8 of the collapse load in the case of a cracked plate subject to bending. As an example, the model is applied to a thermal transient in a pressure vessel. The possibility of cracking and failure of a nozzle was considered. It is shown that a semi-circular crack will grow into an extended defect. Therefore, in the main analyses, axial symmetry and infinitely long longitudinal and fully circumferential cracks were considered. The post-yield fracture mechanics solutions are presented in the form of elastic-plastic stress intensity factors. Within the geometric approximations it is shown that longitudinal cracks are more dangerous than circumferential ones and can result in general yielding across, and full penetration of, the pressure vessel wall. In addition, linear elastic fracture mechanics under-estimates the danger of deep cracks and in some circumstances can considerably overestimate the critical size of small cracks. It is shown that the addition of a residual pressure stress considerably reduces the predicted critical defect sizes.