Tensile instability and necking in materials with strain hardening and strain-rate hardening

Abstract An in-depth examination of tensile instability and necking in materials with strain hardening and strain-rate hardening has been made to clear up some recent controversies on this subject. A simplified analytical model presented here reveals that a preexisting geometric imperfection can grow from the outset of deformation (i.e. its growth-rate is always positive), even while the load rises. The growth-rate is initially low and rises later on, its kinetics being strongly influenced by the strain hardening exponent, n = ( ∂lnσ ∂lnϵ ) , the strain-rate hardening exponent, m = ( ∂lnσ ∂lnge ) , and the imperfection size, f. Even though the imperfection cross-section is always unstable, when m > 0.6 its profile gradient can actually shrink for a while, leading to its temporary disappearance. In this work, the regimes of stable, quasistable (diffusely unstable) and unstable deformation have been redefined and results are given for specific values of the various parameters. An analysis of imperfections produced by mechanical damages is also given in the Appendix.