Initializing intragranular residual stresses within statistically equivalent microstructures for crystal plasticity simulations

We propose a mechanics framework to compute intragranular or type III residual stress within a polycrystalline aggregate for which experimental characterization of residual stress is unknown. The framework is built upon the inter-relationship between intragranular misorientation (IGM), geometrically necessary dislocation (GND), and long-range internal stress. Given a spatial distribution of IGM, we first calculate the spatial distribution of GND density; subsequently, we calculate the internal stress and strain fields due to the GND distribution. For demonstration, we consider a synthetic microstructure of a hexagonal close-packed material, namely Ti-7Al, wherein the grain size and orientation distributions are statistically equivalent to the distributions obtained via experimental characterization. We refer to this microstructure as a statistically equivalent microstructure (SEM). In an SEM, each grain is usually treated as a pristine crystal and therefore, the SEM contains no IGM. We propose a technique to introduce IGM within the SEM and, subsequently, calculate the GND density and residual stress distributions in a consistent manner. In the process, we ensure that statistical distributions of the IGM and residual strain within the SEM are statistically equivalent to the same obtained from the experimental characterization of Ti-7Al. While establishing statistically equivalent residual stress, the thermal effects during processing of Ti-7Al are implicitly taken into account. Next, we perform crystal plasticity finite element simulations to demonstrate the implications of the initialization of IGM and type III residual stress. Although the IGM and residual stress are related, the results suggest that the type III residual stress initialization has a much more pronounced effect on microplasticity-driven damage mechanisms, such as high cycle fatigue, even within a well-annealed material such as Ti-7Al, thereby emphasizing the need for its initialization for microstructure-sensitive fatigue analysis. Finally, we demonstrate that initializing thermally induced residual stress within Ti-7Al SEM through a cooling simulation, accounting for the anisotropic nature of the coefficient of thermal expansion, yields a grain-averaged residual stress distribution statistically similar to that obtained from our framework and is a special case of the type II residual stress implementation.