The relation between crack growth resistance and fracture process parameters in elastic-plastic solids

Crack growth initiation and subsequent resistance is computed for an elastic-plastic solid with an idealized traction -separation law specified on the crack plane to characterize the fracture process. The solid is specified by its Young's modulus,E, Poisson's ratio, v, initial tensile yield stress, σ Y ,and strain hardening exponent,N. The primary parameters specifying the traction—separation law of the fracture process are the work of separation per unit area, Γ0, and the peak traction, σ̌gs. Highly refined calculations have been carried out for resistance curves, K R (Δa), for plane strain, mode I growth in small-scale yielding as dependent on the parameters characterizing the elastic-plastic properties of the solid and its fracture process. With K0= [ Eγ0 (1 − v2) ] 1 2 as the intensity needed to advance the crack in the absence of plasticity, KR K0 is presented in terms of its dependence on the two most important parameters, σ ̌ σY and N, with special emphasis on initiation toughness and steady-state toughness. Three applications of the results are made : to predict toughnesss when the fracture process is void growth and coalescence, to predict the role of plasticity on interface toughness for similar materials bonded together, and to illuminate the role of plasticity in enhancing toughness in dual-phase solids. The regime of applicability of the present model to ductile fracture due to void growth and coalescence, wherein multiple voids interact within the fracture process zone, is complementary to the regime of applicability of models describing the interaction between a single void and the crack tip. The two mechanism regimes are delineated and the consequence of a transition between them is discussed.