An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity

Three type 304 stainless steel specimens of the same geometry were subjected to complex, cyclic axial-torsional histories characterized by varying degrees of non-proportionality of straining. All tests were at room-temperature. The data from cyclically stable hysteresis loops were reduced and the direction of the plastic strain rate vector, variation of plastic hardening modulus, and direction of translation of a rate and time-independent yield surface were studied. It is shown that the independent variables in a Mroz-type formulation map the experimental results with a higher degree of uniqueness than other popular formulations studied for both the hardening modulus and direction of yield surface translation. Also, the plastic strain rate is not, in general, in the direction of the deviatoric stress or stress rate.

An Experimental Investigation Into the Plastic Flow and Strain Hardening of Mild Steel Under Proportional and Abruptly Changing Deformation Paths at a Controlled Rate

Tension-torsion tests are reported on thin-walled tubes up to strains of the order of five percent. Attention was given to the question of whether, as has been suggested, in the continued loading after a sudden direction change in the deformation path, the behavior of the material quickly approaches that predicted by a von Mises plastic potential and isotropic hardening. The results show a slower approach of the deviatoric stress vector direction to the plastic strain-rate vector direction than had been expected, as well as considerable variations in the von Mises equivalent stress versus equivalent plastic strain curves.

A Simplified Theory of the Constitutive Equations of Metal Plasticity at Finite Deformation

Derivation of the constitutive equations of elastic-plastic and elastic-viscoplastic solids at finite deformations is discussed. The deformation is uncoupled by using the Lee-Freund three-configuration deformation model. By assuming elastic properties to be independent of plastic deformation, the elastic and plastic (or viscoplastic) constitutive equations are essentially uncoupled. The normality condition of the plastic strain-rate vector to the yield surface in stress space is obtained by incorporating the concept of internal variables in the energy equation.