Studies of the Line-Spring Model for Nonlinear Crack Problems

Abstract

This paper presents an investigation of the line-spring model (LSM) of Rice and Levy as applied to nonlinear crack problems. A J 2 deformation theory of plasticity formulation of a LSM for obtaining the fully plastic crack solutions is first described in the framework of a shell finite element method. Results are obtained for 2-D axial and circumferential cracks in cylinders and are compared against those developed by detailed finite element crack tip analyses. Discrepancies are found in the case of axially cracked cylinders under internal pressure. To overcome this problem a modified approach, termed the continuum-LSM, is presented, and its finite element implementation is described in some detail. It is shown that in contrast to the shell-LSM, the results obtained by the continuum-LSM for internally pressurized axially cracked cylinders are in close agreement with detailed finite element crack-tip calculations. Lastly, a discussion on the fully plastic analysis of surface cracks by the LSM is also given.