The unified constitutive equations for Rene´ 80 developed by Bhattachar and Stouffer (1992) are used to predict the thermomechanical fatigue (TMF) response of a Nickel base superalloy Rene´ 80 between 649°C and 1093°C. Predictions using these equations suggest that temperature history effects are significant during TMF, and that the TMF response of Rene´ 80 cannot be predicted completely using only isothermal parameters. It is postulated without metallurgical observations that the two deformation mechanisms in Rene´ 80, planar slip at low temperatures and dislocation climb at high temperatures, produce characteristic microstructures which interact under nonisothermal conditions to produce extra hardening that is not present during isothermal deformation. A state variable approach has been used to model this interaction. The nonisothermal model with temperature history effects could successfully predict the initial and saturated TMF response, and block isothermal response of Rene´ 80 from several tests between 649°C and 1093°C.
Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design
