Mechanical analysis of the interaction between a semi-infinite Griffith crack and its coplanar plastic zone

This paper presents the complete analytical solution of the equilibrium conditions between a dislocation pile-up and a loaded crack. Contrary to previous models, the image distributions (forces) are included in this calculation. Their influence on the effective stress intensity factor, on the dislocation nucleation conditions and on the criteria for crack propagation are underlined. In semi-brittle materials the size of the dislocation free zone is controlled by material characteristics, as expected from the literature. However, in ductile materials its size is controlled by a mathematical limitation resulting from introduction of image forces. If plastic deformation takes place, the Griffith criteria must be modified by adding additional work required to separate dislocations from their images to the surface energy and the plastic work done to develop the plastic zone. A detailed analysis of the stress distribution inside and outside the pile-up is presented. Within the plastic zone the total stress is not constant while outside and close to the limits a square root variation with distance is noticed.

Automated summary

This paper presents the analytical solution for the equilibrium conditions between a dislocation pile-up and a loaded crack, taking into account the influence of image distributions. The study highlights the effects of image forces on the stress intensity factor, dislocation nucleation conditions, and criteria for crack propagation. It also discusses the control of dislocation free zone size in semi-brittle and ductile materials, as well as the modification of Griffith criteria in the presence of plastic deformation.