ISOTROPIC VISCOPLASTICITY THEORY-BASED ON OVERSTRESS (VBO) - THE INFLUENCE OF THE DIRECTION OF THE DYNAMIC RECOVERY TERM IN THE GROWTH LAW OF THE EQUILIBRIUM STRESS

Two versions of the isotropic, small strain theory of viscoplasticity based on overstress (VBO) are given. They differ only in the dynamic r ecovery term of the growth law for the equilibrium stress. In the Yao formulation, this term is in the direction of the difference between t he equilibrium and the kinematic stress deviators, two state variables of the theory. The inelastic strain rate determines the direction of this term in the Lee formulation. The predictions of the two formulati ons are compared in numerical experiments simulating proportional and nonproportional cyclic and monotonic loading. The two versions have th e same material constants. They give identical results in uniaxial and proportional monotonic and cyclic loadings for a 6061 T6 aluminum all oy. They differ considerably when nonproportional loading is involved. In a strain controlled corner path the stress component corresponding to the strain that is held constant almost reaches zero at large stra ins in the Yao formulation. In the Lee formulation the stress is very different from zero. Also, the effective stress-strain diagram for the rectangular path ultimately joins the stress-strain diagram obtained in monotonic loading for the Yao model. A permanent difference remains for the Lee formulation. In cyclic 90 degrees out-of-phase loading th e hysteresis loops generated by the Lee model are much narrower than t he ones predicted by the Yao version. The predictions of the Yao formu lation are in good agreement with the results of biaxial experiments o n the aluminum alloy. An analysis of the equations shows that differen ces between the predictions of the two formulations must be expected w henever unloadings are involved. The agreement in cyclic proportional loadings for the aluminum alloy is apparently due to the special mater ial properties of this alloy. When material properties close to that o f stainless steel are used a transient difference between the two form ulations is found in cyclic proportional loadings. This experience sug gests that models that predict the same behavior in monotonic loading may have vastly different responses in other loadings. Biaxial, nonpro portional experiments and their numerical simulations are needed for t he development of a reliable constitutive equation. Copyright (C) 1996 Elsevier Science Ltd