Phase Field Modeling of Void Growth Under Creep
TMS 2022, Virtual, February 27–March 3, 2022
Cheng, Tianle↗
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Phase-Field Modeling of Crack Growth and Mitigation in Solid Oxide Cells
23rd International Conference on Solid State Ionics (SSI-23), Boston, MA, July 17-22, 2022
Xue, Fei↗
Phase-Field Modeling of the Thermally-Grown Oxide in High-Temperature Coating Systems
For presentation at the Gordon Research Conference of High Temperature Corrosion, New London, NH, July 17-20, 2023.
Cheng, Tianle↗
Non-orthogonal computational grids for studying dislocation motion in phase field approaches
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.
36 MATERIALS SCIENCE↗
A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction
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.
fracture↗
Meso-scale modeling of UO2 nuclear fuel to high burnup
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.
fracture↗
Phase-field dislocation modeling of cross-slip
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.
36 MATERIALS SCIENCE↗
PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations
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.
Prabhune, Bhagya [Oak Ridge National Laboratory (O↗
A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method
Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.
42 ENGINEERING↗
FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials
This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.
42 ENGINEERING↗
MEUMAPPS (C++ Version)
Many materials, metal alloys in particular, have features on the on micrometer or nanometer scale that have a large impact on the properties of the material. These features are known as the microstructure of the material. Understanding why and how the microstructure forms in a material is of fundamental scientific interest as well as of significant technological interest. The capability to predict microstructure evolution in a material allows the intentional design of microstructures and hence the intentional design of material properties. The phase-field method is one of the leading methods for predicting microstructure evolution. One of the most significant problems for phase-field models is their computational expense. Even limited phase-field simulations can easily require thousands of CPU core-hours to complete, which significantly limits their use. This code provides both a general framework for creating scalable, GPU-accelerated phase-field model applications as well as several applications themselves. The code is capable of using hundreds of GPUs efficiently, which greatly reduces the time required to perform simulations. The code is written with an emphasis on performance portability, that is the ability for the code to run efficiently on a number of different computing architectures without modification of the source code. The performance portability of this code is primarily enabled through the use of two libraries, Kokkos (performance portable data structures and execution patterns) and heFFTe (performance portable distributed 3D fast Fourier transforms). The code consists of a core library, applications, and tests. The core library includes shared functionality between applications. This includes interfaces with fast Fourier transform (FFT) libraries such as heFFTe, data structures based on Kokkos, file input and output capabilities, and a solver for infinitesimal strain mechanical equilibrium problems. Five applications are included in the code. The flagship application is the MEUMAPPS-SS application, which implements the Kim-Kim-Suzuki phase-field model for precipitation for an arbitrary number of phases and components in a metal alloy. Five simpler applications are also included that solve the Eshelby inclusion problem, Allen-Cahn equation, the coupled Allen-Cahn and diffusion equations, and the Cahn-Hilliard equation. The code includes two applications to solve the Cahn-Hilliard equation, one with constant-step-size first-order time integration and the second with adaptive high-order time integration.
DeWitt, Stephen [Oak Ridge National Lab. (ORNL), O↗
Analytical model and dynamical phase-field simulation of terahertz transmission across ferroelectrics
Here, we theoretically investigate the steady-state transmission of continuous terahertz (THz) wave across a freestanding ferroelectric slab. Based on the Landau-Ginzburg-Devonshire theory of ferroelectrics and the coupled equations of motion for polarization and electromagnetic (EM) waves, we derive the analytical expressions of the frequency- and thickness-dependent dielectric susceptibility and transmission coefficient at the thin slab limit in the harmonic excitation regime. When the slab thickness is much smaller than the THz wavelength in the ferroelectric, the analytical predictions agree well with the numerical simulations from a dynamical phase-field model that incorporates the coupled dynamics of strain, polarization, and EM wave in multiphase systems. At larger thicknesses, the transmission is mainly determined by the frequency-dependent attenuation of THz waves in the ferroelectric and the formation of a standing polarization/THz wave. Our results advance the understanding of the interaction between THz wave and ferroelectrics and suggest the potential of exploiting ferroelectrics to achieve low-heat-dissipation, nonvolatile voltage modulation of THz transmission for high-data-rate wireless communication.
36 MATERIALS SCIENCE↗
Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method
Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.
36 MATERIALS SCIENCE↗
Benchmark problems for the Mesoscale Multiphysics Phase Field Simulator (MEMPHIS)
This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported classical phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.
74 ATOMIC AND MOLECULAR PHYSICS↗
A phase-field diffraction model for thermo-hydro-mechanical propagating fractures
This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.
Diffraction systems↗
Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases
Abstract Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.
Zhang, Shuaifang↗
Modeling discontinuous dynamic recrystallization containing second phase particles in magnesium alloys utilizing phase field method
Pre-existing second phase particles can induce particle stimulated nucleation (PSN) and pinning effect on grain boundaries during DRX process of magnesium alloys. The interaction among pinning effect, PSN mechanism and strain-induced grain boundary migration (SIBM) nucleation mechanism imposes challenge in quantitative study of microstructure evolution. A phase field model that describes discontinuous dynamic recrystallization process considering second phase particles (PF-DDRX-SP) which mainly distribute along grain boundaries is developed. The second phase order parameter with diffusion interface is introduced to the free energy function. With considering the pinning effect of second phase particles on grain boundaries, the grain boundary energy couples the interaction between second phase and grains. The effect of second phase on dislocation density evolution is considered in the model, and the PSN and SIBM mechanism are both executed by limiting the nucleation position to the grain boundary and the second phase interface. For the validation, the initial topology consistent with initial microstructure is applied to the simulation of DRX kinetics and flow behavior of AZ80 magnesium alloy, and great reliability and accuracy of developed model is indicated. Furthermore, through the model, the microstructure evolution with different particle size and with different volume fraction of round particle during DRX process were simulated. Finally, the results show that particles with higher dispersion reduce the number of DRX nuclei, which indicate that second phase particles suppress the nucleation at grain boundaries because of the pinning effect. More importantly, the proposed model could also quantitatively predict the relationships between the parameters of second phase particles and DRX behaviors, and enable to optimize the initial second phase structure in a uniform grain structure during thermomechanical process.
36 MATERIALS SCIENCE↗
Multi-scale modeling of the electric field assisted sintering process
The electric field assisted sintering (EFAS) process involves tightly coupled physics that influence microstructural evolution in the particles being compacted. It is also an inherently multi-scale phenomenon, with the microstructure of the compact influencing the subsequent engineering-scale response of the sintering system. To improve understanding of how processing parameters influence microstructural evolution, we have developed a multi-scale modeling approach that couples a continuum-level model of the sintering system with a phase-field model for microstructural evolution of particles within the compact. The phase-field model couples the effect of chemical and electrical driving forces on microstructural evolution and includes the effect of charged defect segregation to surfaces and grain boundaries; this segregation leads to enhanced defect transport and heat generation at these interfaces in response to applied electric field. The effect of enhanced heat generation on particle neck growth and the influence of microstructural evolution on the engineering-scale model are demonstrated.
36 - MATERIALS SCIENCE↗