A critical evaluation of superposition methods for cracks in grossly plastic gradient fields

Abstract

This paper presents a critical assessment of three analytical methods in determining the crack-tip plastic deformation under large scale and gross-section yielding conditions. These theoretical approaches include two stress-based cohesive zone models and a strain-intensity factor approach, all developed on the basis of the principle of superposition. In the two stress-based cohesive zone models, the prospective stresses along the crack path are taken to be the elastic–plastic solution and the nominal elastic solution, respectively. The problem of an edge crack subjected to grossly plastic strain fields with a constant strain gradient is analysed using the finite element method. The plastic zone size and the crack-tip opening displacement determined by the finite element analysis are then compared with the analytical predictions, showing that these theoretical approaches are unable to capture the influence of gross plasticity on the plastic deformation at the crack tip. The present results highlight the deficiencies in existing stress-based superposition approaches.