Interpretation of intragranular strain fields in high-energy synchrotron X-ray experiments via finite element simulations and analysis of incompatible deformation

Highlights

• A finite element framework resolves intragranular strains from experimentally obtained grain-averaged lattice strains considering stress equilibrium.

• The resulting state of incompatible distortion reveals the heterogeneous response within the microstructure upon macroscopic loading.

• History dependence of the residual state of the material is highlighted and the elastic nature of unloading/loading is studied for a nickel superalloy.

• The framework can be used to initialize the heterogeneous intragranular strains at any load state for models or used to validate the results of a model.

Abstract

A finite element framework is developed to resolve the intragranular fields of incompatible deformation generated intrinsically in response to applied deformation, through linear elasticity complemented by the theory of continuous distribution of dislocations and experimental grain-scale observations. Discrete grain-averaged lattice strains, characterized along with grain orientations via X-ray diffraction microscopy, enable high fidelity continuous solutions anchored to measured response and satisfy boundary conditions, mechanical equilibrium, and strain compatibility within a finite element model. A continuous distribution of strain fields in a nickel-based superalloy, evaluated periodically during R = 0 cyclic loading, exposes the fundamental heterogeneity in polycrystalline response which creates locations of high stress gradients and potential sites of failure. Incompatibility is shown to be an effective measure driving the spatial concentration of stress with loading, particularly at twin and high angle grain boundaries. Furthermore, incompatible deformation is shown, through both specific examples and statistically, to be predominantly preserved upon elastic recovery improving our understanding of the history dependence of residual stresses. Positive correlation between residual stress & incompatible deformation and saturation of material response or shakedown in response to cyclic loading is revealed. The scalability of the framework with experiments at multiple length scales are discussed.