Micromechanism-Quantification for Creep Constitutive Equations

A uniaxial constitutive equation-set for commercial precipitation-strengthened alloys, consisting of a hyperbolic sine law kinetic creep equation and several microstructure-evolution (damage-rate) equations, has been described. Only a small number of materials- and heat treatment-specific model parameters are required to predict creep curve shapes in these microstructurally unstable alloys. The sinh-law kinetic creep equation is theoretically-derived and so displays several advantages over the ubiquitous but empirical power-law, including explicit predictions of the effects of microstructure on creep rates. Evolution rate equations for three types of microstructural instability (dislocation, particulate and grain boundary cavitation) are quantified generically and are illustrated throughout the paper with a model parameter-set for the nickel-base superalloy IN738LC. Independently variable creep damage terms within an equation-set is extremely parameter-efficient and enables the synthesis of complex materials responses by suitable permutations. For example, creep behaviour of conventionally-cast IN738LC has been predicted from the directionally-solidified alloy parameter-set by reducing the magnitude of creep ductility and activating the cavitation damage term. Similarly, the equation-set has also been used to predict the experimentally-found reciprocity between minimum creep rate/applied stress data and peak stress/applied straining rate data. The (low) inelastic strain to reach minimum creep rate was identical to that required to achieve the corresponding peak-stress because a common intrinsic microstructural instability operates in each loading mode. Computed stress-strain trajectories at the lower applied strain rates demonstrate the increasing dominance of damage due to particle-coarsening over that due to dislocation-multiplication. An approximate extension of the uniaxial kinetic law to predict the behaviour of polycrystals under multiaxial stressing is also briefly described and contrasted with the different methodology required for multiaxially-loaded single crystals.