The Modeling of Unusual Rate Sensitivities Inside and Outside the Dynamic Strain Aging Regime

The viscoplasticity theory based on overstress (VBO) is altered by introducing an augmentation function into the dynamic recovery term of the growth law of the equilibrium stress, which is a tensor valued state variable of the model. It is a measure of the defect structure of metals and alloys. The flow law is unaltered but affected by the equilibrium stress whose growth is modified by the augmentation function. The augmentation function does not affect the initial, quasi-elastic region but exhibits a strong influence on the long-time, asymptotic solution that applies approximately when the flow stress is reached in a laboratory experiment. On the basis of the long-time asymptotic solution positive (stress increases with strain rate), zero (no influence of strain rate) and negative rate sensitivity (stress decreases with an increase in strain rate) can be easily modeled. In the simplest case the augmentation function is a constant and the rate sensitivity remains equal throughout the deformation. The modeling of a change from one kind of rate sensitivity, say negative, to another, say positive can be accomplished by making the augmentation function dependent on the accumulated, effective inelastic strain. The theory is applied to model the varying rate sensitivity of a modified 9Cr-1Mo steel, which changes from negative, to zero and to positive with temperature. The unusual rate sensitivities are modeled well together with relaxation and strain rate change tests.