Cavity formation from inclusions in ductile fracture

The previously proposed conditions for cavity formation from equiaxed inclusions in ductile fracture have been examined. Critical local elastic energy conditions are found to be necessary but not sufficient for cavity formation. The interfacial strength must also be reached on part of the boundary. For inclusions larger than about 100Å the energy condition is always satisfied when the interfacial strength is reached and cavities form by a critical interfacial stress condition. For smaller cavities the stored elastic energy is insufficient to open up interfacial cavities spontaneously. Approximate continuum analyses for extreme idealizations of matrix behavior furnish relatively close limits for the interfacial stress concentration for strain hardening matrices flowing around rigid non-yielding equiaxed inclusions. Such analyses give that in pure shear loading the maximum interfacial stress is very nearly equal to the equivalent flow stress in tension for the given state of plastic strain. Previously proposed models based on a local dissipation of deformation incompatibilities by the punching of dislocation loops lead to rather similar results for interfacial stress concentration when local plastic relaxation is allowed inside the loops. At very small volume fractions of second phase the inclusions do not interact for very substantial amounts of plastic strain. In this regime the interfacial stress is independent of inclusion size. At larger volume fractions of second phase, inclusions begin to interact after moderate amounts of plastic strain, and the interfacial stress concentration becomes dependent on second phase volume fraction. Some of the many reported instances of inclusion size effect in cavity formation can thus be satisfactorily explained by variations of volume fraction of second phase from point to point.