Steady-state quasi-static growth of a crack in the anti-plane shear mode through an elastic-plastic material is analyzed. The material is non-hardening and small-scale yielding conditions are assumed. The essential feature of the model is that the active plastic-zone is assumed to be a pair of discrete lines emanating from the crack tip out of the crack plane on which a suitable yield condition is satisfied. An exact solution is obtained for the plastic strain left in the wake of this active line plastic-zone. The extent of the plastic zone from the tip is determined to be 0.071 ( k τ0)2where k and τ0are the remote elastic stress intensity factor and the shear flow stress, respectively, and it is found that 36% of the elastic energy flowing into the crack-tip region during growth is dissipated through plastic work and 64% is trapped as residual elastic energy in the plastic-zone wake. © 1980.
Freund, L. B., & Sills, L. B. (1980). A line plastic-zone model for steady mode III crack growth in an elastic-plastic material. Journal of the Mechanics and Physics of Solids, 28(1), 49–57. https://doi.org/10.1016/0022-5096(80)90011-3