Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

Detailed finite element (FE) analyses are performed to study the effect of crack depth on crack-tip constraint at full yielding for pure bending of plane strain single-edge-cracked specimens. Analyses are based on small-strain formulations and perfect plasticity. The crack depth a/W ranges from 0.1 to 0.7, and the deformation is applied up to the limiting state of full plasticity where crack-tip stresses reach steady-state limiting values. At load levels smaller than the limit load (contained yielding), the crack-tip constraint (stress triaxiality) gradually decreases as a/W decreases, but, at load levels close to the limit load (or at the limit load), it decreases very sharply. In terms of a/W, tractable closed-form approximations for fully plastic crack-tip stress and strain fields are proposed, and fully plastic values of crack-tip stresses are re-phrased in terms of the Q-parameter [1,2]. The role of crack-tip strains on fracture of shallow-cracked bending specimens is briefly discussed.