Limits of J-T Characterization of Elastic—Plastic Crack—Tip Fields

Abstract

Plane strain elastic-plastic analyses were performed on a variety of 2-D planar cracked geometries and loading conditions, based on a small strain formulation and de-formation theory plasticity (termed finite boundary (FB) analysis hereafter). For the majority of the cases analyzed, the crack-tip fields in the mechanistically significant region around the crack tip agreed well with those of the corresponding modified boundary layer (MBL) solutions for load levels up to large scale yielding. The crack-tip fields in the MBL solutions were normalized using the elastic-plastic J values and the elastically-scaled T-stress values of the corresponding FB specimens. However, good agreement could be obtained with (J, T) only up to moderate scale yielding for a center-cracked tension (CCT) geometry. At large scale yielding, the MBL solution based on the elastically-scaled T-stress could not capture the effects of crack tip stress and strain redistribution in the CCT. An alternative method was proposed to calculate the T-stress using weight functions and the elastic-plastic remote stress field of the CCT (termed effective T-stress). Incorporating the effective T-stress into the MBL solutions, good agreement in both stress and strain fields was obtained between the MBL solution and the FB CCT solution at load levels up to general yielding. To demonstrate the limits of two-parameter characterizations in accurately describing elastic-plastic cracktip fields, a three-point-bend specimen was analyzed for load levels up to large plasticity. It is shown that although Q-values could be operationally defined at large plasticity, in general, no complete, consistent, two-parameter description was forthcoming to accurately describe the crack-tip stress and strain fields beyond certain limits. The inherent limits of two-parameter characterization of elastic-plastic crack tip fields should be recognized, analogous to those of one-parameter (J) characterization. A locus of two-parameter (J, T) characterization limits is proposed based on the crack-tip stress fields of the geometry and loading configurations analyzed. The J-T based two-parameter approach is shown to greatly extend the validity domain of fracture mechanics analysis for specimens with negative T-stress.