Dislocation-based model of plasticity and roughness-induced crack closure

Along with external forces and the macro-geometry of cracked bodies, the local stress intensity factors Δk and kmax at fatigue crack fronts are also determined by internal stress fields and the crack front microgeometry (extrinsic shielding). This means that a description of the crack-tip stress field by two external (remote) parameters ΔK (Kmax) and ΔT (Tmax) is not sufficient. The paper presents a discrete dislocation model of contact shielding effects in the case of small-scale yielding under plane-strain conditions. The model is physically transparent and, unlike continuum-based models for plane stress, it enables us to directly assess the magnitude of both plasticity and roughness-induced components of crack closure. Moreover, it reflects an influence of microstructure on the roughness-induced term. The closure components can be simply extracted from experimentally measured values of the remote ΔK using standard data on mechanical properties and microstructure. Thus, the effective threshold ΔKeff,th can be obtained as nearly independent of microstructure coarseness and applied cyclic ratio as shown for several important engineering materials.