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.

开发了一个有限元框架，以通过位错连续分布理论和实验晶粒尺度观察补充的线性弹性来解决因应用变形而固有地产生的不相容变形的晶内场。离散晶粒平均晶格应变，通过 X 射线衍射显微镜表征晶粒取向，使高保真连续解锚定到测量响应并满足有限元模型内的边界条件、机械平衡和应变兼容性。镍基高温合金中应变场的连续分布，在 R = 0 循环加载期间定期评估，暴露了多晶响应中的基本异质性，这会产生高应力梯度的位置和潜在的故障位置。不相容性被证明是驱动应力空间集中的有效措施，特别是在双晶和大角度晶界处。此外，通过具体示例和统计数据表明，不相容变形主要在弹性恢复时得以保留，从而提高了我们对残余应力历史依赖性的理解。揭示了残余应力和不相容变形与材料响应的饱和或响应循环载荷的稳定之间的正相关性。讨论了在多个长度尺度上进行实验的框架的可扩展性。不相容性被证明是驱动应力空间集中的有效措施，特别是在双晶和大角度晶界处。此外，通过具体示例和统计数据表明，不相容变形主要在弹性恢复时得以保留，从而提高了我们对残余应力历史依赖性的理解。揭示了残余应力和不相容变形与材料响应的饱和或响应循环载荷的稳定之间的正相关性。讨论了在多个长度尺度上进行实验的框架的可扩展性。不相容性被证明是驱动应力空间集中的有效措施，特别是在双晶和大角度晶界处。此外，通过具体示例和统计数据表明，不相容变形主要在弹性恢复时得以保留，从而提高了我们对残余应力历史依赖性的理解。揭示了残余应力和不相容变形与材料响应的饱和或响应循环载荷的稳定之间的正相关性。讨论了在多个长度尺度上进行实验的框架的可扩展性。通过具体的例子和统计数据，主要保留在弹性恢复上，以提高我们对残余应力历史依赖性的理解。揭示了残余应力和不相容变形与材料响应的饱和或响应循环载荷的稳定之间的正相关性。讨论了在多个长度尺度上进行实验的框架的可扩展性。通过具体的例子和统计数据，主要保留在弹性恢复上，以提高我们对残余应力历史依赖性的理解。揭示了残余应力和不相容变形与材料响应的饱和或响应循环载荷的稳定之间的正相关性。讨论了在多个长度尺度上进行实验的框架的可扩展性。