Machine Learning-Aided Parametrically-Homogenized Crystal Plasticity Models (PHCPM) for Micromechanical and Structural Analysis for Single Crystal Ni-Based Superalloys

This paper establishes a comprehensive multiscale modeling framework for developing the parametrically-homogenized crystal plasticity model (PHCPM) for single crystal Ni-based superalloys. Single crystals of these materials are characterized by an underlying gamma −gamma′ microstructure with a dispersion of gamma ′ precipitates. The PHCPMs explicitly incorporate the relevant statistics of lower scale gamma −gamma ′ descriptors in the single crystal plasticity relations. This enables highly efficient and accurate image-based polycrystalline microstructural simulations without the need for exorbitant simulations of complex gamma −gamma ′ microstructures. An additional advantage of the PHCPMs is that they can be readily used for representing spatial variations in the gamma −gamma ′ morphology in the polycrystalline microstructures. The single crystal PHCPM development process involves a sequence of computational methods, with explicit use of machine learning. These include: (i) construction of SERVEs for intragranular gamma −gamma ′ microstructures of single crystals, (ii) image-based simulations of SERVEs with experimentally calibrated dislocation-density crystal plasticity models, (iii) identification of representative aggregated microstructural parameters (RAMPs) for the gamma −gamma ′ microstructure-response mapping, (iv) selection of a PHCPM constitutive framework, and (v) performing self-consistent homogenization using a multiscale domain to establish functional expressions of PHCPM constitutive coefficients in terms of RAMPs. Novel integration of machine learning tools are explored at every development phase for establishing relations, while overcoming major computational bottlenecks. For constitutive parameter calibration of the CPFE model, rapid minimization of calibration error in a high-dimensional input space is enabled by the use of SVR model emulation in a genetic algorithm framework. For global sensitivity analysis-based identification of RAMPs, an artificial neural network provides a means of sampling high-dimensional conditional distributions constructed from relatively scarce and expensive data. For self-consistent homogenization, k-means minimizes the PHCPM material parameter search optimization to only a few iterations of reduced order computations. For generating the RAMP to PHCPM constitutive coefficient mapping, symbolic regression yields a simple and accurate representation of the relationship that bridges the material behavior across length scales. The combination of these unique machine learning tools with a structured approach to multiscale modeling enables rigorous upscaling for image-based microstructural modeling. The single crystal PHCPM exhibits orders of magnitude speedup over its explicit microstructure counterpart. This capability permits location-specific analysis of gamma −gamma ′ intragranular microstructures within polycrystalline ensembles. In summary, the PHCPM development process demonstrates the seamless integration of physics-based models and data-driven methods to create significantly computational advantageous models for material response in the ICME paradigm.