A continuum model for the creep of single crystal nickel-base superalloys

In this paper, we develop a constitutive theory within a thermodynamic setting to describe the creep of single crystal superalloys that gainfully exploits the fact that the configuration that the body would attain on the removal of the external stimuli, referred to as the "natural configuration", evolves, with the response of the body being elastic from these evolving natural configurations. The evolution of the natural configurations is determined by the tendency of the body to undergo a process that maximizes the rate of dissipation. Here, the elastic response is assumed to be linearly elastic with cubic symmetry associated with the body which remains the same as the configuration evolves. A form for the inelastic stored energy (the energy that is 'trapped' within dislocation networks) is utilized based on simple ideas related to the motion of the dislocations. The rate of dissipation is assumed to be proportional to the density of mobile dislocations and another term that takes into account the damage accumulation due to creep. The model developed herein is used to simulate uniaxial creep of (0 0 1) oriented single crystal nickel-base superalloys. The predictions of the theory agree well with the available experimental data for CMSX-4.