A phase field – Finite element approach to model the interaction between phase transformations and plasticity in shape memory alloys
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Paranjape, Harshad M.↗
SEARCH · Engineering Papers
Results for “Phase field”
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Understanding and predicting geometrical constraint ferroelectric charged domain walls in a BiFeO 3 island via phase-field simulations
It has been known that ferroelectric charged domain walls (CDWs), which break the polarization continuity, may be electrically active with an elevated conductivity. However, the bound charge at CDWs may render them energetically unstable, and thus, forming CDWs naturally and manipulating them electrically is still challenging. Here, we theoretically utilize phase-field simulations to design spontaneously generated CDWs with center-type quad-domains in a single square-shaped BiFeO 3 nanoisland. It is shown that the stability of the spontaneously emerging head-to-head domain walls with center-convergent quad-domains is mainly determined by three contributions, namely, the geometrical constraint from approximately 45°-tilted bottom edges, the electric boundary condition, and the necessary screening free charges to compensate head-to-head domain walls. It is demonstrated that the center-convergent quad-domains with head-to-head CDWs can be electrically switched to the center-divergent one with tail-to-tail CDWs, providing guidance for achieving ferroelectric domain-wall-based nanodevices with low-power dissipation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Phase Field Sintering Simulations of Tagged UO 2
Isotopic taggants are being considered as an additive for UO 2 manufacturing to improve nuclear security. Before taggants can be adopted, it must be determined whether taggants have any effect on the fuel microstructure or performance. As part of this effort, a grand potential formulation of the phase field method was used to model untagged, Cr-tagged, and Fe-tagged UO 2 . The simulations were compared to determine whether the taggants had any effect on fuel density or grain size. The results suggest that the taggants will not affect the density or grain size, but these findings may not be reliable because of high uncertainty. Causes of the uncertainty were discussed, and future work is proposed to reduce the model uncertainty.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
High-throughput phase-field simulations and machine learning of resistive switching in resistive random-access memory
Metal oxide-based Resistive Random-Access Memory (RRAM) exhibits multiple resistance states, arising from the activation/deactivation of a conductive filament (CF) inside a switching layer. Understanding CF formation kinetics is critical to achieving optimal functionality of RRAM. Here a phase-field model is developed, based on materials properties determined by ab initio calculations, to investigate the role of electrical bias, heat transport and defect-induced Vegard strain in the resistive switching behavior, using MO 2- x systems such as HfO 2- x as a prototypical model system. It successfully captures the CF formation and resultant bipolar resistive switching characteristics. High-throughput simulations are performed for RRAMs with different material parameters to establish a dataset, based on which a compressed-sensing machine learning is conducted to derive interpretable analytical models for device performance (current on/off ratio and switching time) metrics in terms of key material parameters (electrical and thermal conductivities, Vegard strain coefficients). These analytical models reveal that optimal performance (i.e., high current on/off ratio and low switching time) can be achieved in materials with a low Lorenz number, a fundamental material constant. This work provides a fundamental understanding to the resistive switching in RRAM and demonstrates a computational data-driven methodology of materials selection for improved RRAM performance, which can also be applied to other electro-thermo-mechanical systems.
36 MATERIALS SCIENCE↗
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach
In this paper we introduce a new formulation for shape optimization problems in fluids in a diffuse interface setting that can in particular handle topological changes. By adding the Ginzburg–Landau energy as a regularization to the objective functional and relaxing the non-permeability outside the fluid region by introducing a porous medium approach we hence obtain a phase field problem where the existence of a minimizer can be guaranteed. This problem is additionally related to a sharp interface problem, where the permeability of the non-fluid region is zero. In both the sharp and the diffuse interface setting we can derive necessary optimality conditions using only the natural regularity of the minimizers. We also pass to the limit in the first order conditions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Phase-Field Modeling of Thermally-Grown Oxide and the Induced Damage Evolution in Environmental Barrier Coatings
The advent of next-generation hydrogen-based engines necessitates materials capable of withstanding temperatures beyond the reach of current superalloys. SiC-based ceramic matrix composites, augmented with environmental barrier coatings (EBCs), present a promising materials solution. Given the active search for effective and durable EBCs, there is a pressing need for modeling tools to understand and predict damage evolution in these materials to help accelerate their development. This study introduces a phase-field model (PFM) designed to simulate the critical role of thermally grown oxides (TGO) in the degradation and failure of EBCs. The model accounts for the severe volume expansion due to oxidation, alongside phase transformations and microstructural evolution during thermal cycling, offering a comprehensive view of the damage processes. Simulation results are validated against experimental findings reported in the literature, establishing the model's potential as a significant tool for understanding and improving the resilience of EBCs in cyclic oxidative environments.
Cheng, Tianle↗
A Rate-Theory–Phase-Field Model of Irradiation-Induced Recrystallization in UMo Nuclear Fuels
Experiments showed that recrystallization dramatically speeds up the gas bubble swelling kinetics in metallic UMo fuels. In this work a recrystallization model is developed to study the effect of microstructures and radiation conditions on recrystallization kinetics. The model integrates the rate theory of intra-granular gas bubble and interstitial loop evolution and a phase field model of recrystallization zone evolution. A fast passage method is employed to describe one dimensional diffusion of interstitials which have diffusivity several order magnitude larger than that of the fission gas Xe. With the model, the effect of grain sizes on recrystallization kinetics is simulated.
Hu, Shenyang↗
A New Efficient Quantitative Multi-component Phase Field: Lattice Boltzmann Model for Simulating Ti6Al4V Solidified Dendrite Under Forced Flow
Ti6Al4V is a widely used, multi-component alloy in additive manufacturing, during which the fluid flow in the molten pool significantly affects the solidified dendrites. To predict and further control the microstructure, modeling and simulating the microstructure evolution play a critical role. In this study, a newly developed, efficient, quantitative multi-component phase-field (PF) model is coupled with a lattice Boltzmann (LB) model to simulate Ti6Al4V solidified dendrite evolution under fluid flow. The accuracy and convergence behavior of the model is validated by the Gibbs–Thomson relation at the dendrite tip. Single and multiple two-dimensional (2D) equiaxed dendrite evolution cases under forced flow were simulated. Results show that the dendrite pattern is influenced remarkably by the fluid flow. Underlying mechanisms of the asymmetrical evolution are revealed by discussing the interaction among the flow, composition distribution and dendrite morphology, quantitatively. The dendrite kinetics are also derived, which ascertains the relationship between tip velocity and undercooling and inlet velocity and is the foundation for larger-scale simulation. We believe that the coupled quantitative multi-component PF–LB framework employed in this study helps in investigating the solidified dendrite morphology evolution in a deep and quantitate manner.
36 MATERIALS SCIENCE↗
Optimizing Piezoelectric Nanocomposites by High‐Throughput Phase‐Field Simulation and Machine Learning
Abstract Piezoelectric nanocomposites with oxide fillers in a polymer matrix combine the merit of high piezoelectric response of the oxides and flexibility as well as biocompatibility of the polymers. Understanding the role of the choice of materials and the filler‐matrix architecture is critical to achieving desired functionality of a composite towards applications in flexible electronics and energy harvest devices. Herein, a high‐throughput phase‐field simulation is conducted to systematically reveal the influence of morphology and spatial orientation of an oxide filler on the piezoelectric, mechanical, and dielectric properties of the piezoelectric nanocomposites. It is discovered that with a constant filler volume fraction, a composite composed of vertical pillars exhibits superior piezoelectric response and electromechanical coupling coefficient as compared to the other geometric configurations. An analytical regression is established from a linear regression‐based machine learning model, which can be employed to predict the performance of nanocomposites filled with oxides with a given set of piezoelectric coefficient, dielectric permittivity, and stiffness. This work not only sheds light on the fundamental mechanism of piezoelectric nanocomposites, but also offers a promising material design strategy for developing high‐performance polymer/inorganic oxide composite‐based wearable electronics.
42 ENGINEERING↗
Atomistic and phase field simulations of three dimensional interactions of {$10\bar12$} twins with grain boundaries in Mg: twin transmission and dislocation emission
In polycrystals, the interaction of dislocations and twins with grain boundaries (GBs) plays a role in hardening and formability during plastic deformation. While dislocation-GB interactions are relatively well-understood, twin-GB interactions remain mostly unknown. In this work, an approach using molecular dynamics and phase-field simulations is followed to study the forward and lateral interactions between {$10\bar12$} twins and tilt grain boundaries in Mg. Molecular dynamics results show that the resolved shear stress on slip/twinning modes of the neighboring grain, not the geometric alignment, is the dominant factor in determining the outcome of the twin-GB interactions. For some lateral interaction configurations, as the misorientation angle increases, the resolved shear stress on the same {$10\bar12$} twin variant of the neighboring grain reduces while it increases for slip or I 2 stacking fault emissions or other twin modes such as {$11\bar12$} and {$10\bar11$}, explaining why twin transmission is not seen at high misorientation angles. Furthermore, lateral and forward interactions of the twin with tilt grain boundaries whose misorientation axes are normal to the coherent twin boundary show significantly different outcomes. For the forward interaction, the twin is absorbed and stacking faults are emitted when interacting for low misorientation angles (up to 30°) while the lateral interaction results in twin transmission, nucleation of a {$11\bar12$} twin, and emission of I 2 stacking faults. Finally, comparisons between twin interactions with symmetric and asymmetric tilt GBs with different GB structures show similar outcomes.
36 MATERIALS SCIENCE↗
Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems
Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.
Cheng, Tianle↗
Formation and self-organization of void superlattices under irradiation: A phase field study
Self-organized patterns, realized in non-equilibrium processes, have been widely observed in physics and chemistry. As a powerful tool to create far-from-equilibrium environments, irradiation produces a variety of types of defects, which can self-organize through physical interactions and chemical reactions. Such a process becomes complicated especially when both thermodynamics and kinetics play critical roles in pattern formation. Here, we explore the formation and self-organization mechanism of void superlattices in metals and alloys under irradiation through phase field modeling and simulations. For the first time, three different formation mechanisms of void superlattices are clearly distinguished according to their thermodynamic origin and reaction kinetics. It is discovered that the characteristic length and symmetry of an emerging superlattice is determined by the interplay of the thermodynamic driving force and the kinetic anisotropy of the system. Through parametric study, the effects of kinetic coefficients, such as atomic mobility and irradiation dose rate, on the nucleation, growth, coarsening, coalescence, and ordering of voids are systematically investigated. The theoretical model developed in this work may provide guidelines for designing desired self-organized microstructures under irradiation.
36 MATERIALS SCIENCE↗
Quantification of flexoelectricity in PbTiO 3 /SrTiO 3 superlattice polar vortices using machine learning and phase-field modeling
Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO 3 /SrTiO 3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO 3 and SrTiO 3 . Here, our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.
36 MATERIALS SCIENCE↗
Pressure-induced switching in ferroelectrics: Phase-field modeling, electrochemistry, flexoelectric effect, and bulk vacancy dynamics
Pressure-induced polarization switching in ferroelectric thin films has emerged as a powerful method for domain patterning, allowing us to create predefined domain patterns on free surfaces and under thin conductive top electrodes. However, the mechanisms for pressure-induced polarization switching in ferroelectrics remain highly controversial, with flexoelectricity, polarization rotation and suppression, and bulk and surface electrochemical processes all being potentially relevant. Here we classify possible pressure-induced switching mechanisms, perform elementary estimates, and study in depth using phase-field modeling. Finally, we show that magnitudes of these effects are remarkably close and give rise to complex switching diagrams as a function of pressure and film thickness with nontrivial topology or switchable and nonswitchable regions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Phase Field Modeling of Microstructure Development in Microgravity
This newly funded project seeks to extend our NASA-sponsored project on modeling of dendritic microstructures to facilitate collaboration between our research group and those of other NASA investigators. In our ongoing program, we have applied advanced computational techniques to study microstructural evolution in dendritic solidification, for both pure isolated dendrites and directionally solidified alloys. This work has enabled us to compute dendritic microstructures using both realistic material parameters and experimentally relevant processing conditions, thus allowing for the first time direct comparison of phase field computations with laboratory observations. This work has been well received by the materials science and physics communities, and has led to several opportunities for collaboration with scientists working on experimental investigations of pattern selection and segregation in solidification. While we have been able to pursue these collaborations to a limited extent, with some important findings, this project focuses specifically on those collaborations. We have two target collaborations: with Prof. Glicksman's group working on the Isothermal Dendritic Growth Experiment (IDGE), and with Prof. Poirier's group studying directional solidification in Pb-Sb alloys. These two space experiments match well with our two thrusts in modeling, one for pure materials, as in the IDGE, and the other directional solidification. Such collaboration will benefit all of the research groups involved, and will provide for rapid dissemination of the results of our work where it will have significant impact.
Dantzig, Jonathan A.↗
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↗
Evolution of Dendritic Extended 3D Patterns during Directional Solidification: Microgravity Experiments in DECLIC-DSI onboard ISS and Phase-field Modeling
To characterize the dynamical formation of three-dimensional (3D) arrays of dendrites under diffusive growth conditions, in situ monitoring of a series of experiments on a transparent succinonitrile – 0.46 wt% camphor model alloy was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. These experiments offer continuous interface observation and enable the construction of space-time evolution maps of dendrite location and primary spacing during directional solidification. We present the evolution of dendritic extended 3D patterns for a large range of parameters displaying different levels of side branching in both experiments and phase-field simulations. The combined and separate effects of macroscopic interface curvature and crystal mis-orientation are evidenced and detailed. In addition, the aligned dendritic array caused by the invasion of dendrites formed at the edge of the crucible border is investigated.
Kaihua Ji↗
Phase-field predictions of the influence of cooling rates during AM on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys
Additive manufacturing of single crystals made of Ni-based superalloys offers major cost savings for gas turbine engines with the inclusion of internal cooling channels. However, the lack of understanding of the effect of transient thermal conditions on solidification grain structure during additive manufacturing hinders the potential for process control to maintain the single crystal quality. The use of high-fidelity simulations through high performance computing to predict the evolution of the solidification microstructure will enhance the abilities to tailor the microstructures through process optimization. Phase field simulations are used to determine the effect local thermal conditions and defects on the stability of the solidification morphology, specifically with respect to the onset of columnar-to-equiaxed transition that results in the loss of the single crystal. The results are expected to be instrumental for developing future surrogate models to speed up the integration of design and manufacturing of turbine blades under the harsh in-service conditions.
36 MATERIALS SCIENCE↗