A homologous ductile failure criterion for generalized stress states

Abstract

The Hancock-Mackenzie failure criterion is here expressed in homologous form and is thereby shown to apply to a range of ductile materials. The method is easily implemented in a finite element code such as DYNA2D/3D, using only a normalizing strain as input. The method is illustrated for the standard “uniaxial” tensile test of a smooth bar; fracture initiates in a region where the stress state is highly triaxial. By DYNA2D simulations of the test, and from the measured fracture strain, the normalizing strain of the homologous criterion is determined. It is also shown that the stress-strain curve derived from experimental data alone does not adequately describe behavior beyond necking, because of the radial variation of stress. An analytical approach, using trial-and-error, is used to obtain the true stress-strain curve.