A microstructural rafting state-based constitutive model for single crystal Ni-based superalloys at elevated temperature

Single crystal (SC) Ni-based superalloys undergo microstructural degradations such as rafting and coarsening due to the extremely harsh service environment, which consequently introduce the challenge in inelastic behaviours prediction when considering the time-varying microstructural state. Within this content, a thermodynamically microstructural state-based constitutive model for SC Ni-based superalloys is proposed at elevated temperature. A rafting state variable satisfying the positive dissipation is determined and then is introduced into the crystal plasticity framework to depict the inelastic deformation of SC Ni-based superalloys with different rafting microstructures. The interconnection between rafting and constitutive law is achieved by altering the internal state variables (ISVs) through a series of micromechanical mechanisms rather than through continuum damage mechanics. Specially, a novel microstructure-based back stress model is proposed considering the morphology and size variation of the gamma'/gamma structure on the basis of dislocation wall theory. The capability of the model is validated by the stress-strain responses and the microstructural rafting behaviours by coupling the thermodynamic rafting model. Finally, an application case of a centre-hole component made by a SC Ni-based superalloy is provided to highlight the capability of the model for the analysis of inelastic deformation combined with inhomogeneous microstructural rafting for engineering components. The proposed framework not only gives inherent understanding on the interaction between microstructural rafting and constitutive law by means of microphysical mechanisms, but also provides a powerful tool for analysing rafting and inelastic deformation of complex structures.