Constraint effects on the ductile-brittle transition in small scale yielding

The effect of constraint on the ductile-brittle transition is investigated numerically under small scale yielding conditions in plane strain. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence.

Two populations of second phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses.

Cleavage is modeled in terms of attaining a temperature and strain rate-independent critical value of the maximum principal stress over a specified material region. A characteristic length is associated with each failure mechanism; the large inclusion spacing for ductile failure and size of the cleavage region for brittle failure.

The crack growth predictions are consequences of the constitutive characterization of the material, so that the present study is free fromad hoc assumptions regarding appropriate crack growth criteria. The numerical results show that the extent of cleavage fracture relative to ductile fracture is strongly controlled by temperature and constraint.

Fracture resistance curves are obtained for a range of conditions.