Necking of Creep‐Cavitating Bars

Abstract

This paper is a finite element study of the nonuniform (necking) deformation of creep‐cavitating bars under constant load or constant load with superimposed hydrostatic pressure. The multiaxial constitutive model used in the analysis is a finite strain generalization of a physically based model that incorporates Dyson's micromechanical mechanism of constrained cavity growth. The mechanism governs the phenomenon of coupled grain boundary cavitation and creep in polycrystalline metals at elevated temperatures and within the low‐to‐moderate stress regime. The finite element study, which is based on the principle of virtual work and constitutive model in the convected Lagrangian view, includes calculations of elongation, area, stress, and damage histories. Comparisons of elongation history as well as necked profiles of various cases are carried out. The results predict (1) Transitional behavior of catastrophic necking and brittle fracture to the tendency for diffuse necking and ductile rupture under a constant load with increasing superimposed hydrostatic pressure; (2) the effects of imperfections on the fracture time; (3) the locations of failure initiation; and (4) the sensitivity of necking behavior to geometrical imperfection (varying radius) and material imperfection (varying Monkman‐Grant constant).