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1. Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach

   Babaei, Hamed ; Pratoori, Raghunandan ; Levitas, Valery I. ( February 2023 , arXivorg)

   Scale-free phase-field approach (PFA) at large strains and corresponding finite element method (FEM) simulations for multivariant martensitic phase transformation (PT) from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor εt = {0.1753; 0.1753; −0.447} and stress-tensor dependent athermal dissipative threshold for PT, which produce essential challenges for computations. 3D polycrystals with 55 and 910 stochastically oriented grains are subjected to uniaxial strain- and stress-controlled loadings under periodic boundary conditions and zero averaged lateral strains. Coupled evolution of discrete martensitic microstructure, volume fractions of martensitic variants and Si II, stress and transformation strain tensors, and texture are presented and analyzed. Macroscopic variables effectively representing multivariant transformational behavior are introduced. Macroscopic stress-strain and transformational behavior for 55 and 910 grains are close (less than 10% difference). This allows the determination of macroscopic constitutive equations by treating aggregate with a small number of grains. Large transformation strains and grain boundaries lead to huge internal stresses of tens GPa, which affect microstructure evolution and macroscopic behavior. In contrast to a single crystal, the local mechanical instabilities due to PT and negative local tangent modulus are stabilizedmore »at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries and generating the internal back stresses. This leads to increasing stress during PT. The developed methodology can be used for studying similar PTs with large transformation strains and for further development by including plastic strain and strain-induced PTs.« less
2. Influence of Grain Size Distribution on Ductile Intergranular Crack Growth Resistance

   https://doi.org/10.1115/1.4045073  

   Molkeri, Abhilash ; Srivastava, Ankit ; Osovski, Shmuel ; Needleman, Alan ( March 2020 , Journal of Applied Mechanics)

   Abstract The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode I small-scale yielding conditions. The finite element formulation accounts for finite deformations, and the constitutive relation models the loss of stress carrying capacity due to progressive void nucleation, growth, and coalescence. The discrete unit events are characterized by a set of finite element calculations for crack growth at a single-grain boundary junction. A directed graph of the connectivity of grain boundary junctions and the distances between them is used to create a directed graph in J-resistance space. For a specified grain boundary distribution, this enables crack growth resistance curves to be calculated for all possible crack paths. Crack growth resistance curves are calculated based on various path choice criteria and compared with the results of full-field finite element calculations of the initial boundary value problem. The effect of unimodal and bimodal grain size distributions on intergranular crack growth is considered. It is found that a significant increase in crackmore »growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large.« less
3. Physics-embedded graph network for accelerating phase-field simulation of microstructure evolution in additive manufacturing

   https://doi.org/10.1038/s41524-022-00890-9  

   Xue, Tianju ; Gan, Zhengtao ; Liao, Shuheng ; Cao, Jian ( September 2022 , npj Computational Materials)

   The phase-field (PF) method is a physics-based computational approach for simulating interfacial morphology. It has been used to model powder melting, rapid solidification, and grain structure evolution in metal additive manufacturing (AM). However, traditional direct numerical simulation (DNS) of the PF method is computationally expensive due to sufficiently small mesh size. Here, a physics-embedded graph network (PEGN) is proposed to leverage an elegant graph representation of the grain structure and embed the classic PF theory into the graph network. By reformulating the classic PF problem as an unsupervised machine learning task on a graph network, PEGN efficiently solves temperature field, liquid/solid phase fraction, and grain orientation variables to minimize a physics-based loss/energy function. The approach is at least 50 times faster than DNS in both CPU and GPU implementation while still capturing key physical features. Hence, PEGN allows to simulate large-scale multi-layer and multi-track AM build effectively.
4. Effect of the initial microstructure on the pressure-induced phase transition in Zr and microstructure evolution

   Pandey, K. K. ; Levitas, Valery I. ; Park, Changyong ; Shen, Guoyin ( January 2023 , arXivorg)

   The effect of initial microstructure and its evolution across the α→ω phase transformation in commercially pure Zr under hydrostatic compression has been studied using in situ x-ray diffraction measurements. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α→ω initiates at lower pressure for pre-deformed sample, suggesting pre-straining promotes nucleation by producing more defects with stronger stress concentrators. With transformation progress, the promoting effect on nucleation reduces while that on growth is suppressed by producing more obstacles for interface propagation. The crystal domain size reduces and microstrain and dislocation density increase during loading for both α and ω phases in their single-phase regions. For α phase, domain sizes are much smaller for prestrained Zr, while microstrain and dislocation densities are much higher. On the other hand, they do not differ much in ω Zr for both prestrained and annealed samples, implying that microstructure is not inherited during phase transformation. The significant effect of pressure on the microstructural parameters (domain size, microstrain, and dislocation density) demonstrates that their postmortem evaluation does not represent the true conditions during loading. A simple model for the initiation of the phase transformation involving microstrain ismore »suggested, and a possible model for the growth is outlined. The obtained results suggest an extended experimental basis is required for better predictive models for the pressure-induced and combined pressure- and strain-induced phase transformations.« less
5. Impact of the plastic deformation microstructure in metals on the kinetics of recrystallization: A phase-field study

   https://doi.org/doi.org/10.1016/j.actamat.2022.118332  

   Hamed, Ahmed ; Rayaprolu, Sreekar ; Winther, Grethe ; El-Azab, Anter ( January 2022 , Acta materialia)

   The sensitivity of recrystallization kinetics in metals to the heterogeneity of microstructure and deformation history is a widely accepted experimental fact. However, most of the available recrystallization models employ either a mean field approach or use grain-averaged parameters, and thus neglecting the mesoscopic heterogeneity induced by prior deformation. In the present study, we investigate the impact of deformation-induced dislocation (subgrain) structure on the kinetics of recrystallization in metals using the phase-field approach. The primary focus here is upon the role of dislocation cell boundaries. The free energy formulation of the phase-field model accounts for the heterogeneity of the microstructure by assigning localized energy to the resulting dislocation microstructure realizations generated from experimental data. These microstructure realizations are created using the universal scaling laws for the spacing and the misorientation angles of both the geometrically necessary and incidental dislocation boundaries. The resulting free energy is used into an Allen-Cahn based model of recrystallization kinetics, which are solved using the finite element method. The solutions thus obtained shed light on the critical role of the spatial heterogeneity of deformation in the non-smooth growth of recrystallization nuclei and on the final grain structure. The results showed that, in agreement with experiment, the morphologymore »of recrystallization front exhibits protrusions and retrusions. By resolving the subgrain structure, the presented algorithm paves the way for developing predictive kinetic models that fully account for the deformed state of recrystallizing metals.« less