Multi-scale statistical analysis of the deformation processes and residual stresses in nickel-base superalloys
Keywords: synchrotron x-ray diffraction
residual stress
strain statistics
crystal plasticity finite element method
nickel-base superalloy

The deformation of polycrystalline metallic materials is highly heterogeneous, originating from the anisotropic elastic and plastic properties of individual grains. Plastic deformation is often localized into slip bands or sub-grain shear bands. Recent advances in experimental measurements and numerical simulations, such as focused ion beam-digital image correlation (FIB-DIC), synchrotron X-ray diffraction (XRD), and crystal plasticity finite element modelling (CPFEM) contribute to shifting the research focus in solid mechanics from macroscopic scale toward the assessment and analysis of the strains and stresses within individual grain or grain groups. Nevertheless, very few research studies report precise, quantitative and reliable evaluation of the relationship between the microscopic (Type II+III) strains and stresses, and the apparent macro-scale (Type I) stresses and the overall mechanical behaviour.
The principal objective of the present study is to evaluate the multi-scale distributions of internal strains and stresses in aerospace nickel-base superalloys subjected to thermal and mechanical loading. The report begins with the numerical investigation of the deformation process in polycrystals using statistical distributions. To this end, the carefully calibrated CPFEM simulations of stresses and strains at different scales were conducted, and statistical distributions were extracted. A specially constructed series of numerical experiments was performed to investigate the effect of discretization methods in CPFEM.
As the nature of stress and strain inhomogeneities at different scales were revealed, it was found that the dispersion of local stress and strain distributions is much larger than the those of the macroscopic average. Notably, it is argued based on theoretical analysis and observations that the elastic strain accumulation represents an additive process, whereas the plastic strain accumulation is a multiplicative process. Hence, the statistical distributions of these quantities differ and are normal and lognormal, respectively.
Another important achievement presented in this Thesis connects the macroscopic stress-strain behaviour to the Yield Volume Fraction (YVF) function using lognormal distribution and extreme value (Gumbel) distribution. The incorporation of statistical information in the simulation of complex deformation histories improves the reliability and robustness of predictions.
Finally, the effect of the microstructure and micro-scale properties on the macroscopic deformation resistance was investigated. Two case studies devoted to the quantitative evaluation of the deformation and stresses at the micro-scale using FIB-DIC and synchrotron XRD were conducted for welded and pre-crept samples, respectively. The experimental findings validate and further extend the applicability of the simulation framework that incorporates the modelling of complex thermomechanical processes. Experimental studies in combination with microstructure-based simulations capture the grain interaction scenarios during deformation for polycrystalline (super)alloys and allow the development of improved predictive design methods for enhanced structural integrity.