A note on the propagation behavior of a crack nucleated by a dislocation pileup

Abstract

When an operating slip band encounters a microstructural obstacle, nucleation of tensile microcracking can occur by several mechanisms. Linear elastic fracture mechanics is used to analyze one such semibrittle cracking mechanism involving a dislocation pile‐up. After crack nucleation, the dislocations move in and coalesce at one end of the wedge crack. Under overall compressive loading, the wedge crack propagation is stable and arrest occurs at an equilibrium length. Analytic estimates of the equilibrium length and crack orientation are obtained, and are compared with experimental observations of a peridotite and a quartzite. The critical driving shear stress (i.e. the resolved shear stress minus the lattice “friction”) for wedge crack nucleation is relatively small in comparison with the macroscopic yield stress, implying that a significant portion of the applied deviatoric stress is used to overcome the shear resistance due to the lattice “friction” or Peierls stress. The equilibrium wedge crack length depends sensitively on the confining stress, and also depends on the differential stress and the Peierls stress.