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1. Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density

   https://doi.org/10.1088/1361-651X/ad38d1  

   Huang, Guanglong ; Mensah, Alexander ; Chlupsa, Marcel ; Croft, Zachary ; Qi, Liang ; Shahani, Ashwin J. ; Thornton, Katsuyo ( April 2024 , Modelling and Simulation in Materials Science and Engineering)

   We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.

    

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2. 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 stabilized 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. 

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

   https://doi.org/10.1016/j.actamat.2023.118996  

   Babaei, H ; Pratoori, R ; Levitas, V.I. ( May 2023 , Acta Materialia)

   Scale-free phase-field approach and corresponding finite element method simulations for multivariant martensitic phase transformation 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 transformation, which produce essential challenges for computations. 3D polycrystals with 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. 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 phase transformation and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries. This leads to increasing stress during transformation. The developed methodology can be used for studying similar phase transformations with large transformation strains and for further development by including plastic strain and strain-induced transformations. 

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4. 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 crack growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large. 

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5. Deformation Behavior of Grains Near Defects in Direct Metal Laser Sintered Inconel 718 During Indentation

   https://doi.org/10.1115/MSEC2020-8442  

   Rifat, Mustafa ; Basu, Saurabh ( September 2020 , Proceedings of the ASME 2020 15th International Manufacturing Science and Engineering Conference MSEC2020)

   The present work utilizes Orientation Imaging Microscopy and Finite Element Modelling to analyse microstructure evolution in grains near defects during plane strain indentation of direct metal laser sintered Inconel 718. Defects are inevitably produced during printing of metals and they degrade the mechanical behaviour of parent components. Understanding microstructure evolution of grains present near defects can help create better predictive models of mechanical behaviour of components resulting from additive manufacturing. In this work, an ex-situ study of microstructure evolution during plane strain indentation of DMLS Inconel 718 specimens is performed. Regions that lie near volumetric porosity defects were studied. Grain Orientation Spread was utilized as a metric to quantify intra-granular deformation. It was seen that microstructure evolution of grains near defects is enhanced due to strain concentrations whereby they exhibit larger orientation spread after plastic deformation. Finite Element Analysis was used to simulate the plane strain indentation test on the specimen in which, porosity defects and roughness textures similar to those seen in the as-received specimen were programmed using the python scripting interface of Abaqus. Results from finite element analysis were compared with insights from microstructure analysis to describe evolution of microstructure during deformation near defects.

    

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