This paper introduces a concurrent multiscale modeling framework for developing parametrically-upscaled crystal plasticity models (PUCPM) for crystalline metals that are characterized by multiple phases in their intragranular microstructure. Specifically, Ni-based superalloys with distributions of ${\gamma }^{\prime }$ precipitates in the $\gamma$ matrix in their sub-grain microstructure are modeled in this study. The interaction of the $\gamma -{\gamma }^{\prime }$ phases with nano-scale dislocation mechanisms determine the elasto-plastic behavior of the material across multiple scales. The PUCPM is designed to explicitly account for the morphological and configurational statistics of these $\gamma -{\gamma }^{\prime }$ intragranular microstructures in its crystal plasticity constitutive coefficients. This approach provides a thermodynamically-consistent foundation to enable microstructure-aware material simulation at the higher scale. Establishing this multiscale characteristic requires an automated toolchain of computational methods to generate and embed heterogeneous, statistically-equivalent representative volume elements (SERVEs) into the concurrent multiscale simulation domains for self-consistent homogenization. The self-consistency condition is enforced through an optimization strategy invoking a series of coupled nonlinear finite element solutions. Supervised and unsupervised machine learning methods are integrated with the physics-based modeling at all stages of model development to overcome computational limitations and to provide the final, connecting map between PUCPM constitutive coefficients and $\gamma -{\gamma }^{\prime }$ microstructural descriptors. The resulting PUCPM benefits from orders of magnitudes of speedup compared to the equivalent explicit representation of the lower scale microstructure. This advantage enables unique model capabilities for the multiscale analysis of deformation and failure in materials and location-specific design.

本文介绍了一个并发多尺度建模框架，用于为晶体金属开发参数放大晶体塑性模型 (PUCPM)，这些晶体金属的特征在于其晶内微观结构中有多个相。具体来说，镍基高温合金的分布为${\gamma }^{\text{'}}$沉淀在$\gamma$在本研究中模拟了其亚晶粒微观结构中的基体。的相互作用$\gamma -{\gamma }^{\text{'}}$具有纳米级位错机制的相决定了材料在多个尺度上的弹塑性行为。PUCPM 旨在明确解释这些的形态和构型统计$\gamma -{\gamma }^{\text{'}}$晶内显微组织的晶体塑性本构系数。这种方法提供了一个热力学一致的基础，以实现更高尺度的微观结构感知材料模拟。建立这种多尺度特征需要计算方法的自动化工具链，以生成异构的、统计等效的代表体积元素(SERVE) 并将其嵌入到并发的多尺度模拟域中，以实现自洽同质化。自洽条件是通过调用一系列耦合非线性有限元解决方案的优化策略来实施的。有监督和无监督机器学习方法在模型开发的所有阶段都与基于物理的建模相结合，以克服计算限制并提供 PUCPM 本构系数和$\gamma -{\gamma }^{\text{'}}$微观结构描述符。与较小尺度微观结构的等效显式表示相比，由此产生的 PUCPM 受益于几个数量级的加速。这一优势为材料和特定位置设计中的变形和失效的多尺度分析提供了独特的模型功能。