A comparison between the elastic strain energy and the plastic work at the crack tip

For ductile fractures it becomes progressively imperative to include the plastic components of the quantities defining each particular fracture criterion, in order to derive a relationship, which not only fits the experimental data but also satisfies some appropriate physical principle. In this paper the plastic components of stresses entering in the experessions for the specific plastic work were derived from the plastic singular solution described by the HRR stress field. In order to ascertain the accuracy of such approximate solutions for criteria based on energy balance, a comparison between the components of elastic strain energy density, and its total value, with the specific plastic work (W_p) was undertaken, in order to derive certain conclusions about the importance of the contribution of energy component and the specific plastic work. The analysis was based on the typical case of a transverse internal crack in plate under plane-stress conditions, which is submitted to a mode I deformation. While the dilatational (T_v) and the distortional (T_D) components of elastic SED were calculated for impending plasticity the specific plastic work (W_p) was evaluated by assuming ssy conditions and the theory of HRR field using the plastic singular solution for mode I. It was shown that the contributions of T_v, T_D, T_e (T_e = t_v + T_D) and W_P for different strain hardening exponents were varying with ductile materials, presenting a strong influence of W_p. The conclusion was that for highly strain-hardened materials the contribution of the elastic SED and particularly of T_v is important to the mode of fracture of the plate.