Elastic-plastic J-Tz dominance in bending and tension loadings

Purpose Crack tip stresses are used to relate the ability of structures to perform under the influence of cracks and defects. One of the methods to determine three-dimensional crack tip stresses is through the J-Tz method. The J-Tz method has been used extensively to characterize the stresses of cracked geometries that demonstrate positive T-stress but limited in characterizing negative T-stresses. The purpose of this paper is to apply the J-Tz method to characterize a three-dimensional crack tip stress field in a changing crack length from positive to negative T-stress geometries. Design/methodology/approach Elastic-plastic crack border fields of deep and shallow cracks in tension and bending loads were investigated through a series of three-dimensional finite element (FE) and analytical J-Tz solutions for a range of crack lengths ranging from 0.1⩽a/W⩽0.5 for two thickness extremes of B/(W − a)=1 and 0.05. Findings Both the FE and the J-Tz approaches showed that the combined in-plane and the out-of-plane constraint loss were differently affected by the T-stress and the out-of-plane size effects when the crack length changed from deep to shallow cracks. The conditions of the J-Tz dominance on the three-dimensional crack front tip were shown to be limited to positive T-stress geometries, and the J-Tz-Q2D approach can extend the crack border dominance of the three-dimensional deep and shallow bend models along the crack front tip until perturbed by an elastic-plastic corner field. Practical implications The paper reports the limitation of the J-Tz approach, which is used to calculate the state of three-dimensional crack tip stresses in power law hardening materials. The results from this paper suggest that the characterization of the three-dimensional crack tip stress in power law hardening materials is still an open issue and requires other suitable solutions to solve the problem. Originality/value This paper demonstrates a thorough analysis of a three-dimensional elastic-plastic crack tip fields for geometries that are initially either fully constrained (positive T-stress) or unconstrained (negative T-stress) crack tip fields but, subsequently, the T-stress sign changes due to crack length reduction and specimen thickness increase. The J-Tz stress-based method has been tested and its dominance over the crack tip field is shown to be affected by the combined in-plane and the out-of-plane constraints and the corner field effects.