Modeling phase transformations in single and polycrystalline aggregate and grain growth

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2024-05
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Pratoori, Raghunandan
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Levitas, Valery I
Sheidaei, Azadeh
Bastawros, Ashraf
Xiong, Liming
Lee, Jonghyun
Evans, James
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Engineering Mechanics
Abstract
In this thesis, we present a comprehensive study on the scale-free phase-field approach, augmented by finite element method simulations, to investigate multivariant martensitic phase transformations in crystalline aggregates. Central to our exploration is a model meticulously developed to scrutinize phase transformation behaviors and microstructural evolutions within single crystals under finite strains. This model innovatively diverges from traditional nanoscale phase-field theories through several pivotal modifications: (i) elimination of gradient terms from the interface energy expressions to render the model scale-independent, (ii) abstraction over interfaces between martensitic variants to streamline computational processes at the microscale, (iii) simplification of complex polynomials in order parameters to a linear mixture theory for material properties, and (iv) designation of the total martensite volume fraction as the primary order parameter governing material instability, with the volume fractions of individual variants treated as internal variables. Utilizing this model, we delve into the $\alpha\rightarrow\omega$ phase transformation in single-crystal Zirconium through finite element simulations conducted with the deal.II library, examining how element count and various boundary and initial conditions influence microstructural evolution. Expanding the model to polycrystalline systems, we incorporate grain rotations into our simulations to adapt the phase-field framework to the intricacies of polycrystalline aggregates. This enhanced model, implemented via the finite element method in deal.II, serves to elucidate microstructural evolution in both Zirconium and Silicon. For Silicon, a stress-dependent athermal threshold is introduced to accommodate the observed hysteresis during the Si I to Si II phase transformation. We investigate the microstructural dynamics under diverse loading regimes and grain counts, shedding light on the transformative processes at play. Addressing the enigmatic phenomenon of anomalous grain growth observed in high-pressure phase transformations at room temperature across a variety of materials, including Zirconium, Indium antimonide, Palladium, Bismuth, and Strontium, we propose an analytical, stepwise mechanism for the $\alpha\rightarrow\omega$ phase transformation in powdered Zirconium samples. Collaborative evidence from our partners at HPCAT (Argonne National Lab) supports this proposed mechanism, pinpointing it as a uniquely energetically viable pathway for grain growth, particularly in Zirconium. This groundwork paves the way for future extensions and validations of this mechanism across other materials exhibiting similar grain growth phenomena during phase transformations.
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