Endochronic description for viscoplastic behavior of materials under multiaxial loading

A new formulation of the rate-sensitivity function of the intrinsic time measure is presented in this paper. The endochronic theory is extended to simulate the viscoplastic behavior of material under multiaxial loading. The rate-sensitivity function proposed by Wu and Yip [Wu, H. C. and Yip, M. C. (1980). Strain-rate and strain-rate history effects on the dynamic behavior of metallic materials. Int. J. Solids Struct.16, 515–536] is shown to be identical to the new formulation of the rate-sensitivity function under uniaxial loading. The first-order ordinary differential constitutive equations of endochronic theory, as derived by Valanis [Valanis, K. C. (1979). Endochronic theory with proper loop closure properties. System Science and Software Report SSS-R-80-4182 (1984). Continuum foundations of plasticity. ASME J. Engng Mater. Technol.106, 367–375], are used in this study. Constitutive equations for combined axial-torsional and biaxial strain-paths are derived. Experimental data found in literature of OHFC copper for rate-independent behavior and 304 stainless steel for viscoplastic response are used for comparison. It is shown that most of the viscoplastic behaviors of materials can be adequately described by the theory.