Constitutive modelling of stress-relaxation behaviour of tempered martensitic P91 steel using sine hyperbolic rate law

A constitutive model describing stress-relaxation behaviour of P91 steel at 873 K has been presented. In the model, the equations defining the evolution of internal stress and relaxation stress with time have been coupled with the sine hyperbolic rate law to predict the relaxation stress as a function of hold time as well as the stress dependence of inelastic strain rate. The evolution of internal stress with time has been derived from the power law dependence of internal stress on relaxation stress. The predicted evolution of internal and effective stresses with time exhibited an initial rapid decrease followed by stress plateaus at longer durations. The applicability of the model has been demonstrated for two different strain holds of 1.3 and 2.5% in P91 steel. It has been shown that the present model can be used to predict the evolution of inter-barrier spacing and activation volume with time for both the strain holds at 873 K. Further, the observed increase in activation volume and inter-barrier spacing with hold time in P91 steel has been presented.