Evaluation of Two-Parameter Approaches to Describe Crack-Tip Fields in Engineering Structures

The application of two-parameter approaches to describe crack-tip stress fields has generally focused on Ramberg–Osgood (RO) power law material behavior, which limits the range of applicability of such approaches. In this work we consider the applicability of a $J-Q$ or $J-A2$ approach (the latter is designated here as the $J-A$ approach) to describe the stress fields for RO power law materials and for a material whose tensile behavior is not described by a RO model. The predictions of the two-parameter approaches are compared with full field finite-element predictions. Results are presented for shallow and deep-cracked tension and bend geometries, as these are expected to provide the expected range of constraint conditions in practice. A new approach for evaluating $Q$ is proposed for a RO material, which, for a given geometry, makes $Q$ dependent only on the strain hardening exponent.