Phase-field Modeling of Microstructure Evolution coupled with Plasticity, Interfacial Sliding and Coherency Loss - Poster
Poster Presented by NETL at MS&T 2019, 09/19
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Poster Presented by NETL at MS&T 2019, 09/19
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TMS 2022, Virtual, February 27–March 3, 2022
TMS 2022, Virtual, February 27–March 3, 2022
23rd International Conference on Solid State Ionics (SSI-23), Boston, MA, July 17-22, 2022
For presentation at the Gordon Research Conference of High Temperature Corrosion, New London, NH, July 17-20, 2023.
Modeling nuclear materials is a multi-scale, multi-physics endeavor. Researchers are currently investigating how bulk material properties are affected by the evolution of microscopic material structures, i.e. microstructures. Development of tools that can mechanistically predict the effects of processes like diffusion and grain growth on properties like thermal conductivity will transform nuclear material design, manufacturing, and use. Intermediate-scale, i.e. mesoscale, modeling is among the most promising tools available for this task. Expedited development of mesoscale models, however, will require structured collaboration between modelers and experimentalists. Coupling these fields promises to improve both model accuracy and experiment design. With these ideas in mind, a mesoscale model of the U-Pu-Zr system is being developed. Its development will accompany a series of experiments involving irradiation of metallic fuel samples.
This interim report presents progress towards the development of meso-scale models of magnetic behavior that incorporate microstructural information. Modeling magnetic signatures in irradiated materials with complex microstructures (such as structural steels) is a significant challenge. The complexity is addressed incrementally, using the monocrystalline Fe (i.e., ferrite) film as model systems to develop and validate initial models, followed by polycrystalline Fe films, and by more complicated and representative alloys. In addition, the modeling incrementally addresses inclusion of other major phases (e.g., martensite, austenite), minor magnetic phases (e.g., carbides, FeCr precipitates), and minor nonmagnetic phases (e.g., Cu precipitates, voids). The focus of the magnetic modeling is on phase-field models. The models are based on the numerical solution to the Landau-Lifshitz-Gilbert equation. From the computational standpoint, phase-field modeling allows the simulation of large enough systems that relevant defect structures and their effects on functional properties like magnetism can be simulated. To date, two phase-field models have been generated in support of this work. First, a bulk iron model with periodic boundary conditions was generated as a proof-of-concept to investigate major loop effects of single versus polycrystalline bulk iron and effects of single non-magnetic defects. More recently, to support the experimental program herein using iron thin films, a new model was generated that uses finite boundary conditions representing surfaces and edges. This model has provided key insights into the domain structures observed in magnetic force microscopy (MFM) measurements. Simulation results for single crystal thin-film iron indicate the feasibility of the model for determining magnetic domain wall thickness and mobility in an externally applied field. Because the phase-field model dimensions are limited relative to the size of most specimens used in experiments, special experimental methods were devised to create similar boundary conditions in the iron films. Preliminary MFM studies conducted on single and polycrystalline iron films with small sub-areas created with focused ion beam have correlated quite well qualitatively with phase-field simulations. However, phase-field model dimensions are still small relative to experiments thus far. We are in the process of increasing the size of the models and decreasing specimen size so both have identical dimensions. Ongoing research is focused on validation of the phase-field model. Validation is being accomplished through comparison with experimentally obtained MFM images (in progress), and planned measurements of major hysteresis loops and first order reversal curves. Extrapolation of simulation sizes to represent a more stochastic bulk-like system will require sampling of various simulations (i.e., with single non-magnetic defect, single magnetic defect, single grain boundary, single dislocation, etc.) with distributions of input parameters. These outputs can then be compared to laboratory magnetic measurements and ultimately to simulate magnetic Barkhausen noise signals.
In this work, new non-orthogonal computational grids are implemented into a phase field model called Phase Field Dislocation Dynamics (PFDD). We demonstrate that the new non-orthogonal grid can accommodate multiple slip planes in either the face centered cubic (FCC) or body centered cubic (BCC) crystallographic systems. Here, we show that they avoid numerical errors induced when modeling glide on inclined slip planes in an orthogonal grid. The Gibbs effect that arises in the orthogonal or rotated orthogonal grids is substantially diminished when a non-orthogonal grid is employed. A few test cases demonstrate the effectiveness of using non-orthogonal grids in solving systems with multiple non-planar slip systems.
Prediction of microstructure evolution and properties of ultrafine-grained materials is one of the most significant, current problems in materials science. Several advanced methods of analysis can be applied for this issue: vertex models, phase field models, Monte Carlo Potts, finite element method (FEM) discrete element method (DEM) and finally cellular automata (CA). The main asset of the CA is ability for a close correlation of the microstructure with the mechanical properties in micro- and meso-scale simulation. Joining CA with the DEM undoubtedly improves accuracy of modeling of coupled phenomena during the innovative forming processes in both micro- and macro-scale. Deformation in micro-scale shows anisotropy, which connected with that the polycrystalline material contains grains with different crystallographic orientation, and grain deformation is depended from configuration of directions of main stresses and axis of grain. Then, CA and DEM must be joint solutions of crystal plasticity theory. In the present model, deformation in macro-scale is transferred to meso-sale, where a block contains several, score or hundreds grains, and then is applied in micro-scale to each grain. Creation of low-angle boundaries and their development into high-angle boundaries are simulated by the cellular automata on the base of calculations using finite element method and crystal plasticity theory. The idea proposed in this study and particular solutions are discussed for the case of ultrafine-grained low-carbon steel.
This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.
To improve the economics of light water reactors for commercial nuclear energy generation, utility operators are seeking to obtain regulatory approval to run UO2 fuel to higher levels of burnup. One potential impediment to obtaining this approval is the phenomenon of fuel fragmentation, relocation, and dispersal (FFRD). FFRD can result when fuel experiences a rapid temperature transient, such as that occurring during a Loss Of Coolant Accident (LOCA). FFRD has historically been most associated with the rim region in UO2 fuel pellets, where the phenomenon of fragmentation is also referred to as pulverization due to the small size of the fragments. More recent evidence suggests that the so-called “dark zone” (due to its appearance in micrographs) that can be observed in the mid-radial regions of high burnup fuel is also susceptible to FFRD. Although empirical fuel performance models have been developed that can adequately predict pulverization in the rim region under typical LWR conditions, a scientific understanding of what underlies fuel restructuring and subsequent FFRD is lacking even in the rim region, and no models are currently available for the behavior the dark zone. To address these challenges, the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has employed a multi-scale modeling approach to improve scientific understanding and develop new fuel performance models. In this talk, I will focus on meso-scale efforts, which form a crucial link between atomic-scale and engineering-scale models. Phase-field modeling combined with cluster dynamics is used to predict the restructuring process in the rim region. Phase-field fracture modeling, informed by atomistic simulations, is used to predict the onset of pulverization in the rim region. Combining these techniques together allows the extent of rim pulverization to be predicted. The formation and evolution of the dark zone has also been simulated with the phase-field method, using an improved approach to vacancy source term parameterization. The work shows the important impact of microstructure on fuel performance.
The phase-field dislocation dynamics (PFDD) model is extended to simulate cross-slip in body-centered cubic materials. The model makes use of a non-orthogonal, body-centered cubic numerical grid such that all calculable points lie on dislocation glide planes. We demonstrate that the advanced PFDD model predicts a low-energy, non-planar core for screw dislocations and a planar core for edge dislocations. These core differences result in screw-edge character dependence in the critical stress to initiate glide and dislocation drag coefficients. Finally, we show that this model can be used to study the propensity of screw dislocations to cross-slip around or transmit through a coherent, crystallographic obstacle, depending on obstacle strength.
Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.