On the design of polycrystalline materials with an integration of multiscale modeling and statistical learning

A sophisticated though efficient and accurate multiscale stochastic framework for uncertainty quantification has been developed to investigate the mechanical property variability of polycrystalline materials due to diverse sources of uncertainties. Crystal plasticity constitutive model is employed as the point simulator to capture the mechanical response of polycrystalline microstructures under deformation in the mesoscale. Homogenization techniques are introduced to link the mesoand macro-scales. Stochastic partial differential equations are solved via an adaptive sparse grid collocation method with the assistance of model reduction techniques for the input space. The probabilistic distribution of the macroscale properties/responses of the material subjected to a specific process induced by the uncertainty in initial microstructure is studied based on the current framework. A statistical learning approach is also developed for the design of polycrystalline materials. Support vector machine and x-means clustering are introduced as the classifier of microstructural features. Sensitivity-based optimization method is utilized for the design of processes. 1. Motivation and work summary. The effect of diverse sources of uncertainties and the intrinsically multiscale nature of physical systems poses a considerable challenge in their analysis. Such phenomena are particularly critical in material systems where the microstructural variability and randomness at different scales have a significant impact on the macroscopic behavior of the system. Our goal is to develop a novel, high-fidelity multiscale stochastic framework to study mechanical response/properties variability of materials/structures due to uncertainties in microstructual features, processing parameters, etc. The design of processes which can produce desired microstructure and properties is also of interest. Mathematical tools for both simulating material deformation and probabilistic learning are developed. The major achievements are listed below: • Development of crystal plasticity constitutive model to evaluate mechanical responses of polycrystalline microstructures subjected to deformation. • Development of multiscaling strategy linking mesoscale features to macroscale properties through homogenization techniques. • Development of a non-linear model reduction strategy to construct stochastic input models of mesoscale topology variations based on limited data (emphasis on polycrystalline materials). • Development of an adaptive hierarchical sparse grid collocation algorithm for solving stochastic partial differential equations. • Development of stochastic paradigms to investigate mechanical properties/response of polycrystalline microstructures due to uncertainties in microstructural features. • Development of a stochastic multiscale paradigm to address simultaneously the effects of randomness and multiscale nature of physical systems. • Development of a stochastic optimization technique for robust design of deformation processes of polycrystalline metals based on statistical learning. 2. Crystal plasticity constitutive model. Plastic deformation of FCC crystals is primarily controlled by slips of atoms constrained on certain slip systems. In order to study mechanical behavior of crystalline materials subjected to deformation, continuum slip theory is taken into the constitutive model. A total Lagrangian scheme developed in [1] is implemented with Newton-Raphson linearization of the principle of virtual work to solve the governing equations due to the non-linear nature of the large deformation problem. The complete procedure is detailed in [1,2]. In recent work, we extended the single phase FCC constitutive model to two-phase (γ and γ’ phase) nickel-based superalloys. The large size primary γ’ phase is explicitly modeled as individual grains distributed among homogenized γ grains which contain small secondary and tertiary γ’ precipitates. Comparing with our original single-phase model, two main changes are made. First, two separate constitutive models are explicitly programmed. Distinct material parameters are calibrated for γ’ grain and homogenized γ matrix. Secondly, cube slip systems NSF GRANT # 0757824 NSF PROGRAM NAME: CMMI MATERIALS DESIGN & SURFACE ENG