Dislocation Emission from Surface Crack/Notch under Mode I Loading and its Size Dependence

Abstract

Fatigue and fracture of structures often originate from the surface notch or crack. In this contribution, a Peierls type continuum model developed by Rice (1992, Dislocation Nucleation From a Crack Tip: An Analysis Based on the Peierls Concept, Journal of the Mechanics and Physics of Solids, 40: 239—271) is employed to analyze the critical stress of dislocation emission from the surface notch/crack in the plane strain state in a unified manner. Both the stress field in a notched/cracked half-plane under mode I loading and the stress field induced by an edge dislocation are obtained in closed forms using the Muskhelishvili method. Calculations are carried out to study the effects of the notch/crack depth and the root curvature radius on the dislocation emission. Results show that the critical stress for dislocation emission depends greatly on both of them. The shallower the surface notch/crack is, the higher the critical stress is. This depth dependence of the critical stress for the surface notch is more significant than that for the surface crack. Similarly, the dependence of the critical stress on the slip plane orientation angle for the surface notch is relatively stronger than that for the surface crack. Within a certain range of the slip orientation angle, the critical dislocation emission stress for the surface notch with small root curvature radius is even less than that for the surface crack at the same depth. These results are helpful for us to understand the ductile—brittle fracture behavior of materials with surface notches or cracks.