Microstructure-based 3D finite element modelling of lattice misfit and long-range internal stresses in creep-deformed nickel-base superalloy single crystals

In the present paper, residual stresses and direction-dependent lattice parameters and lattice misfits in the γ′-hardened, tensile creep-deformed monocrystalline nickel-base superalloy SRR 99 have been studied by three-dimensional finite element modelling based on a “simplified creep process”. The main results are as follows. (i) After creep and cooling to room temperature, the internal strains and stresses in both phases γ and γ and γ′ in the directions [001]/[010] are different. From these, differences between the lattice parameters and lattice misfits in the [001] and the [100]/[010] directions follow. During cooling to room temperature after creep, the change in thermal stresses can cause plastic back flow of the γ-phase. The internal stress state is relaxed accordingly. (ii) During the subsequent heating (after creep and cooling to room temperature), the differences of the lattice parameters in the 〈100〉 directions decrease with increasing temperature. (iii) During final cooling from a stress-free state at 105 °C, the lattice misfit and the internal stresses between the [001] and the [100]/[010] directions increase with decreasing temperature. The influences of the creep-induced dislocation networks at the γ/γ′ interfaces, of the coherency stresses and of thermal stresses on the lattice misfit and internal stresses are discussed in detail. The differences between the values of the lattice misfit measured by TEM and by X-ray diffraction are reconciled. The differences between two- and three-dimensional finite element modelling are also discussed. The results are in reasonable agreement with the experimentally measured data.