Modelling Microstructure-Property Relationships in Polycrystalline Metals using New Fast Fourier Transform-Based Crystal Plasticity Frameworks
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The present thesis develops several new full-field, fast Fourier transform (FFT)-based crystal plasticity modelling tools for microstructure engineering. These tools are used to explore elasto-viscoplastic deformation, localized deformation, 3D grain morphology, microstructure evolution, dynamic recrystallization and their effects on formability of polycrystalline metals with particular attention paid to sheet alloys of aluminum and magnesium. The new FFT-based crystal plasticity models developed in this work overcome several inherent problems present in the well-known crystal plasticity finite element method (CP-FEM) and elasto-viscoplastic fast Fourier transform method (EVP-FFT) in solving representative volume element (RVE)-based problems. The new models have demonstrated significant fidelity in simulating various deformation phenomena in polycrystalline metals and prove to be faster and accurate alternatives for obtaining full-field solutions of micromechanical fields in aluminum and magnesium sheet alloys. In particular to the aluminum alloys, which are currently replacing heavier steel parts in the automotive industry, the sheet aluminum alloys have significantly improved corrosion resistance and strength-to-weight properties in comparison to steel. However, aluminum alloys are still outperformed by steel in terms of formability. To improve the formability of an aluminum sheet, one method is to develop physics-based predictive computational tools, which can accurately and efficiently predict the behavior of aluminum alloys and thus allow designing the microstructure with desired properties. Accordingly, in first part of this thesis, a novel numerical framework for modelling large deformation in aluminum alloys is developed. The developed framework incorporates the rate-dependent crystal plasticity theory into the fast Fourier transform (FFT)-based formulation, and this is named as rate tangent crystal plasticity-based fast Fourier transform (i.e., RTCP-FFT) framework. This framework is used as a predictive tool for obtaining stress-strain response and texture evolution in new strain-paths with minimal calibration for aluminum alloys. The RTCP-FFT framework is benchmarked against an existing FFT-based model at small strains and finite element-based model at large strains, respectively, for the case of an artificial Face Centered Cubic (FCC) polycrystal. The predictive capability as well as the computational efficiency of the developed framework are then demonstrated for aluminum alloy (AA) 5754. In the second part of this thesis, the RTCP-FFT framework, developed earlier, is coupled with the Marciniak and Kuczynski (MK) approach to establish a new full-field framework for generating forming limit diagrams (FLDs) of aluminum sheet alloys, e.g., AA3003 and AA5754. The new coupled framework is able to investigate the complex effects of grain morphology, local deformation, local texture and grain interactions on the predictions of forming limit strains. This study reveals that among the various microstructural features, the grain morphology has the strongest effect on the predicted FLDs for aluminum alloys. Furthermore, this study also suggests that the FLD predictions can be significantly improved if the actual grain structure of the material is properly accounted for in the crystal plasticity models. In addition to aluminum alloys, magnesium alloys are getting significant attention by the automotive industry due to their light weight and high specific strength. However, the automotive industry has not been able to take full advantage of the lightweight characteristic of magnesium alloys because of their poor formability at room temperature. Therefore, to enhance the workability and restore their ductility, the magnesium alloys are formed at elevated temperature. High temperature forming of magnesium alloys is often accompanied by dynamic recrystallization (DRX), which allows the final microstructure, as well as the properties of the material (e.g., initial grain size, initial texture, etc.), to be controlled. Therefore, DRX coupled with a full-field crystal plasticity FLD framework can be used as a tool to design microstructure of a material. Since it would be beneficial to be able to redesign the material properties of magnesium alloys using physics-based computational tools than using physical experiments, this work takes a step ahead towards such an outcome by presenting a new framework that predicts DRX and models its effects on the formability of magnesium alloys. Accordingly, in the third part of this thesis, a new full-field, efficient and mesh-free numerical framework, to model microstructure evolution, dynamic recrystallization (DRX) and formability in hexagonal closed-packed (HCP) metals such as magnesium alloys at warm temperatures, is developed. This coupled framework combines three new FFT-based approaches, namely: (a) crystal plasticity modelling of HCP alloys, (b) DRX model, and (c) MK model. First, a rate tangent-fast Fourier transform-based elasto-viscoplastic crystal plasticity constitutive model for HCP metals (RTCP-FFT-HCP) is developed. Then, it is coupled with a probabilistic cellular automata (CA) approach to model DRX. Furthermore, this new model is coupled with the Marciniak-Kuczynski (M-K) approach to model formability of magnesium alloys at elevated temperatures. The RTCP-FFT-HCP model computes macro stress-strain response, twinning volume fraction, micromechanical fields, texture evolution and local dislocation density. Nucleation of new grains and their subsequent growth is modeled using the cellular automata approach with probabilistic state switching rule. This framework is validated at each level of the coupling for magnesium sheet alloy, AZ31. First, the RTCP-FFT-HCP model is validated by comparing the simulated macro stress-strain responses under uniaxial tension and compression with experimental measurements at room temperature. Furthermore, the texture evolution predicted with the new model is compared with experiments. The predictions show a good agreement with experiments with high degree of accuracy. Next, the forming limit diagrams (FLDs) are simulated at 100 C, 200 C and 300 C, respectively, for AZ31 sheet alloy considering the effects of DRX. The predicted FLDs show very good agreement with the experimental measurements. The study reveals that the DRX strongly affects the deformed grain structure, grain size and texture evolution and also highlights the importance accounting for DRX during FLD simulations at high temperatures.
Cite this version of the work
Jaspreet Singh Nagra (2019). Modelling Microstructure-Property Relationships in Polycrystalline Metals using New Fast Fourier Transform-Based Crystal Plasticity Frameworks. UWSpace. http://hdl.handle.net/10012/14457