Effects of root radius, stress, crack growth and rate on fracture instability

Abstract

Of various criteria for fracture at the root of a notch, the energy, local stress, and displacement criteria have limited validity. More appropriate is the history of both stress and strain over a small region ahead of the crack, as required for fracture by the coalescence of holes. Expressions are given for crack initiation, growth, and subsequent instability in anti-plane strain of a non-hardening material. Instability is shown to depend primarily on those strain increments arising from crack growth at constant load rather than on those from increasing load at constant crack length. Thus final instability conditions are similar for single and double-ended cracks, round notches, and cracks cut under constant load. Round notches may give instability, restabilization, and final instability. The growth and coalescence of holes in front of a crack in a linearly viscous material is studied for both tensile and anti-plane-strain cracks. The absence of residual strain eliminates instability, but the crack continually accelerates.