A viscoplastic constitutive model for nickel-base superalloy, part 1: kinematic hardening rule of anisotropic dynamic recovery

A series of deformation experiments was conducted on nickel-base polycrystalline superalloy IN738LC at 850 °C. The material showed distinct rate/time-dependent deformation, while cyclic hardening or cyclic softening behavior was relatively small in general. In the case of cyclic deformation with tensile or compressive strain holding time, anomalous inelastic behavior was observed; a stress–strain hysteresis loop continued to shift toward the opposite direction of the strain hold with the increase in the number of cycles. Consequently, the mean stress continued to increase significantly with cycles. Using conventional kinematic hardening rules, the expression capability under the strain hold waveform conditions was discussed through numerical calculations. It seemed that adequate description of the evolutionary behavior of the mean stress was difficult to achieve using the conventional hardening rules because of the characteristics of the dynamic recovery term of back stress. A kinematic hardening rule was proposed within a viscoplasticity framework in order to describe the growth behavior of the mean stress under the strain hold waveform conditions precisely. A new internal variable that had influence on the dynamic recovery property of the back stress was incorporated into the evolutionary equation of the back stress. An evolutionary law of the proposed internal variable was assumed to be a function of the static recovery property of the back stress. Numerical simulations were conducted using the proposed viscoplastic constitutive equations for various inelastic behaviors of the IN738LC at 850 °C, such as monotonic tension, stress relaxation, creep and cyclic deformation with/without the strain holding period. It was demonstrated that the present viscoplastic constitutive model can describe the inelastic behavior of the material with sound accuracy, including the anomalous behavior observed under the cyclic deformation with the strain holding period, i.e. the evolutionary behavior of the mean stress with the increase of cycles.