A theoretical relation between K IC and basic material properties in ductile metals

Abstract

A model for the ductile fracture process at the tip of an existing crack in a predominantly elastic solid is developed from a theory for ductile fracture by internal necking of cavities. The crack tip displacement and the length of a small elastic-plastic zone at the crack tip are derived from a modification of the Dugdale model for crack tip plastic zones; an approximation to the crack tip stress distribution is derived from Hill's slip-line field solution for a parallel sided crack of finite tip radius. The model provides a relation between the pre-instability strain (or strain hardening exponent), the volume fraction of cavity nucleating second phase particles, the crack tip radius and the critical plane-strain stress intensity factor K IC . Theoretical estimates of K IC for an SAE 4340 steel correlate closely with experimental K IC values for an assumed value of the effective crack tip radius of 0.0005 ins.