Statistical analysis of cleavage fracture ahead of sharp cracks and rounded notches

Mechanisms of initiation and unstable propagation of transgranular cleavage cracks are compared for brittle fracture ahead of sharp cracks and rounded notches, e.g. for fatigue pre-cracks and Charpy V-notches, respectively, in standard toughness specimens. The comparison is made over a range of temperatures, from the lower shelf into the ductile/brittle transition region, for a single phase material containing a known distribution of particles where weakest link statistics can be used to model the onset of catastrophic failure. Using linear and nonlinear elastic solutions for the stress distribution ahead of a sharp crack, and slip-line field solutions, modified for a power hardening material, for the rounded notch, statistical modelling is employed to define the critical dimensions ahead of the crack or notch tip where initial cracking events are most probable. The analysis provides an interpretation of the role of stress gradient in governing microscopic fracture behavior. Predictions are evaluated by comparison with experimental results on the low temperature flow, Charpy V-notch and plane strain fracture toughness behavior of a low carbon mild steel with simple ferrite/grain boundary carbide microstructures.