Pressure dependency,strength-differential effect,and plastic volume expansion in metals

Within the framework of a purely mechanical rate-type theory of finitely deforming elastic-plastic materials, a special set of constitutive equations is introduced. These equations include a dependence both on mean normal stress and on plastic strain, and involve non-normality of plastic strain-rate. They accommodate both the strength-differential effect and plastic volume expansion. Values of the material coefficients in the constitutive equations are approximately determined with the help of published experimental data for AISI 4330 steel. The plastic strain-rate is shown to have a large non-normal component, resulting in a small plastic volume expansion. The theory is in reasonable agreement with experiment for plastic strains up to about 2% in magnitude. Further experiments are suggested so that the constitutive coefficients can be completely and accurately determined.