An official website of the United States government
Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain boundaries play an essential role in defining the effective properties of materials across multiple scales. In this paper we derive a Fokker–Planck model for the evolution of the planar grain boundary network. The proposed model considers anisotropic grain boundary energy which depends on lattice misorientation and takes into account mobility of the triple junctions, as well as independent dynamics of the misorientations. We establish long time asymptotics of the Fokker–Planck solution, namely the joint probability density function of misorientations and triple junctions, and closely related the marginal probability density of misorientations. Moreover, for an equilibrium configuration of a boundary network, we derive explicit local algebraic relations, a generalized Herring Condition formula, as well as formula that connects grain boundary energy density with the geometry of the grain boundaries that share a triple junction. Although the stochastic model neglects the explicit interactions and correlations among triple junctions, the considered specific form of the noise, under the fluctuation–dissipation assumption, provides partial information about evolution of a grain boundary network, and is consistent with presented results of extensive grain growth simulations.
more »
« less
An experimentally informed continuum grain boundary model
A continuum grain boundary model is developed, which uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a one-dimensional (1D) grain array. The model uses a continuum representation of the misorientation in terms of spatial gradients of the orientation as a fundamental field. The grain boundary energy density employed is non-convex in this orientation gradient, based on physical grounds. Simple gradient descent dynamics of the energy are utilized for idealized microstructure evolution, which requires higher-order regularization of the energy density for the model to be well set; the regularization is physically justified. Microstructure evolution is presented using two plausible energy density functions, both defined from the same experimental data: a “smooth” and a “cusp” energy density. Results of grain boundary equilibria and microstructure evolution representing grain reorientation in 1D are presented. The different shapes of the energy density functions representing a common data set are shown to result in different overall microstructural evolution of the system. Mathematically, the constructed energy functional formally is of the Aviles–Giga/Cross–Newell type but with unequal well depths, resulting in a difference in the structural feature of solutions that can be identified with grain boundaries, as well as in the approach to equilibria from identical initial conditions. This study also investigates the metastability of grain boundaries. It supports the general thermodynamics belief that they persist for extended periods before eventually vanishing due to the lowest energy configuration favored by fluctuations over infinite time.
more »
« less
- Award ID(s):
- 2021019
- PAR ID:
- 10548665
- Publisher / Repository:
- Sage
- Date Published:
- Journal Name:
- Mathematics and Mechanics of Solids
- Volume:
- 29
- Issue:
- 8
- ISSN:
- 1081-2865
- Page Range / eLocation ID:
- 1591 to 1616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract 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.more » « less
-
The complexity of shear-induced grain boundary dynamics has been historically difficult to view at the atomic scale. Meanwhile, two-dimensional (2D) colloidal crystals have gained prominence as model systems to easily explore grain boundary dynamics at single-particle resolution but have fallen short at exploring these dynamics under shear. Here, we demonstrate how an inherent interfacial shear in 2D colloidal crystals drives microstructural evolution. By assembling paramagnetic particles into polycrystalline sheets using a rotating magnetic field, we generate a particle circulation at the interface of particle-free voids. This circulation shears the crystalline bulk, operating as both a source and sink for grain boundaries. Furthermore, we show that the Read-Shockley theory for hard-condensed matter predicts the misorientation angle and energy of shear-induced low-angle grain boundaries based on their regular defect spacing. Model systems containing shear provide an ideal platform to elucidate shear-induced grain boundary dynamics for use in engineering improved/advanced materials.more » « less
-
Abstract Traditional approaches to control the microstructure of materials, such as annealing, require high temperature treatment for long periods of time. In this study, we present a room temperature microstructure manipulation method by using the mechanical momentum of electrical current pulses. In particular, a short burst of high-density current pulses with low duty cycle is applied to an annealed FeCrAl alloy, and the corresponding response of microstructure is captured by using Electron Backscattered Diffraction (EBSD) analysis. We show evidence of controllable changes in grain orientation at specimen temperature around 28 °C. To demonstrate such microstructural control, we apply the current pulses in two perpendicular directions and observe the corresponding grain rotation. Up to 18° of grain rotation was observed, which could be reversed by varying the electropulsing direction. Detailed analysis at the grain level reveals that electropulsing in a specific direction induces clockwise rotation from their pristine state, while subsequent cross-perpendicular electropulsing results in an anticlockwise rotation. In addition, our proposed room temperature processing yields notable grain refinement, while the average misorientation and density of low-angle grain boundaries (LAGBs) remain unaltered. The findings of this study highlight the potentials of ‘convective diffusion’ in electrical current based materials processing science towards microstructural control at room temperature.more » « less
-
316L and 304L stainless steels and a compositional gradient of both are fabricated using the same processing parameters via laser directed energy deposition additive manufacturing. In those alloys, the increase in chromium-to-nickel ratio is accompanied with grain refinement and formation of a high density of twin boundaries, i.e. sigma3 boundaries. By means of electron microscopy, crystallographic and thermodynamic calculations, we demonstrate that two mechanisms arising from the ferrite-to-austenite solidification mode are at the origin of twin boundary formation and grain refinement: 1) inter-variant boundaries emerging from the encounter of pairs of austenite grains formed from a common ferrite orientation with Kurdjumov-Sachs orientation relationship; 2) icosahedral short-range-ordering-induced (ISRO) nucleation of twin-related grains directly from the solidifying liquid. These findings define new routes to achieve grain boundary engineering in a single step in FeCrNi alloys, by tailoring the solidification pathway during the AM process, enabling the design of functionally graded materials with site-specific properties.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/10812865231223921
