A thermodynamically-based viscoelastic-viscoplastic model for the high temperature cyclic behaviour of 9-12% Cr steels

Improving the understanding of the long term rate dependent behaviour of materials is of critical importance in many engineering applications. Without this understanding, it is potentially difficult to ensure safe and effective plant operation while simultaneously satisfying requirements for sustainability and responsible resource management. In the present work, a thermodynamically-based constitutive model is proposed to capture the rate sensitivity, the stress relaxation and the accelerated cyclic softening observed during cyclic deformation of a P91 steel at an elevated temperature (600 degrees C). The model is developed within the framework of Thermodynamics of Irreversible Processes and Generalized Standard Materials formalism, thereby offering a thermodynamically grounded coupling of both viscoelasticity (semi-recoverable strain accumulation at vastly different time scales) and viscoplasticity (irreversible strain observed above the stress threshold). The later part combines a hyperbolic sine-power flow rule with non-linear isothermal cyclic evolution of isotropic and kinematic hardening. The applicability of the model to various mechanical loadings (e.g., cyclic tensile-compression tests, fatigue relaxation tests, anhysteretic tests) is validated by designing a heuristic optimisation program based on a nonlinear least-squares function coupled with the Levenberg-Marquardt algorithm. The optimisation procedure is informed (through the estimation of initial material parameter estimates and objective function evaluation) by anhysteretic type experiential data only (wherein long term load hold periods are introduced at various points in the waveform). Rate dependency is determined and validated by considering experimental waveforms with different loading (strain) rates (0.1%.s(-1) 0.01%.s(-1) and 0.001%.s(-1)) and ranges (0.25%, 0.4% and 0.5%) to highlight most of the deformation mechanisms involved during the fatigue and relaxation processes. By comparing predicted and experimentally observed material responses, it is demonstrated in the present work that the viscoelastic-viscoplastic strain decomposition has the ability to capture the accelerated cyclic softening and the uncoupled stress relaxation behaviour (below and above yielding) for a P91 steel at elevated temperatures.