T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modeling

摘要

The non-singular T-stress provides a first-order estimate of geometry and loading mode, e.g. tension vs. bending, effects on elastic-plastic, crack-front fields under mode I conditions. The T-stress has a pronounced effect on measured crack growth resistance curves for ductile metals - trends most computational models confirm using a two-dimensional setting. This work examines T-stress effects on three-dimensional (3D), elastic-plastic fields surrounding a steadily advancing crack for a moderately hardening material in the framework of a 3D, small-scale yielding boundary-layer model. A fiat, straight crack front advances at a constant quasi-static rate under near invariant local and global mode 1 loading. The boundary-layer model has thickness B that defines the only geometric length-scale. The material flow properties and (local) toughness combine to limit the in-plane plastic-zone size during steady growth to at most a few multiples of the thickness (conditions obtainable, for example, in large, thin aluminum components). The computational model requires no crack growth criterion; rather, the crack front extends steadily at constant values of the plane-stress displacements imposed on the remote boundary for the specified far-field stress intensity factor and T-stress. The specific numerical results presented demonstrate similarity scaling of the 3D near-front stresses in terms of two non-dimensional loading parameters. The analyses reveal a strong effect of T-stress on key stress and strain quantities for low loading levels and less effect for higher loading levels, where much of the plastic zone experiences plane-stress conditions. To understand the combined effects of T-stress on stresses and plastic strain levels, normalized values from a simple void-growth model, computed over the crack plane for low loading, clearly reveal the tendency for crack-front tunneling, shear-lip formation near the outside surfaces, and a minimum steady-state fracture toughness for T= 0 loading.