Academic literature on the topic 'Phase-filed modeling'

The Brillouin function, the phase transition and the related magnetic properties in La0.62Er0.05Ba0.33Fe0.2Mn0.8O3 perovskite have been studied using Bean-Rodbell model. The Brillouin function allows determining the total momentum J and the mean filed exchange parameter λ of the perovskite. The mean-filed equation draws the system to second order phase transition. These constants were used to stimulate the experimental isotherms M (H, T) by meanfield theory. The predicted results are compared to the available experimental data. It is noted that a good agreement has been found, with minor discrepancies, between theoretical and experimental data.

AbstractPitting corrosion damage is a major problem affecting material strength and may result in difficult to predict catastrophic failure of metallic material systems and structures. Computational models have been developed to study and predict the evolution of pitting corrosion with the goal of, in conjunction with experiments, providing insight into pitting processes and their consequences in terms of material reliability. This paper presents a critical review of the computational models for pitting corrosion. Based on the anodic reaction (dissolution) kinetics at the corrosion front, transport kinetics of ions in the electrolyte inside the pits, and time evolution of the damage (pit growth), these models can be classified into two categories: (1) non-autonomous models that solve a classical transport equation and, separately, solve for the evolution of the pit boundary; and (2) autonomous models like cellular automata, peridynamics, and phase-field models which address the transport, dissolution, and autonomous pit growth in a unified framework. We compare these models with one another and comment on the advantages and disadvantages of each of them. We especially focus on peridynamic and phase-filed models of pitting corrosion. We conclude the paper with a discussion of open areas for future developments.

In a recent study, a manufacturing batch-size and end-product shipment problem with outsourcing, multi-shipment, and rework was investigated using mathematical modeling and derivatives in its solution procedure. This study demonstrates that a simplified two-phase algebraic approach can also solve the problem and decide the cost-minimization policies for batch-size and end-product shipments. Our proposed straightforward solution approach enables the practitioners in the production planning and controlling filed to comprehend and efficiently solve the best replenishing batch-size and shipment policies of this real problem.

To understand the dendrite formation during solidification phase-field model has become a powerful numerical method of simulating crystal growth in recent years. Two phase-field models due to Wheeler et al. and Karma et al., respectively, have been employed for modeling the dendrite growth worldwidely. The comparison of the two models was performed. Then using the adaptive finite element method, both models were solved to simulate a free dendrite growing from highly undercooled melts of nickel at various undercoolings. The simulated results showed that the discrepancy between the two phase-field models is negligible. Careful comparison of the phase-filed simulations with LKT(BCT) theory and experimental data were carried out, which demonstrated that the phase-field models are able to quantitatively simulate the dendrite growth of nickel at low undercoolings, however, at undercoolings above ten percent of the melting point (around 180K), the simulated velocities by Wheeler and Karma model as well as the analytical predictions overestimated the reported experiment results.

This paper explores the dynamics of the collaborative innovation network of China’s agricultural biotechnology, from a spatial-topological perspective. The data pertain to a collection of patent applications jointly filed by universities, research institutes and enterprises on the mainland of China during 1985–2017. Using the logistic model, we first identify the developing phases of China’s agricultural biotechnology. By dismantling the collaborative innovation network into spatial and topological networks, the dynamics are analyzed from these two dimensions at the three levels of nodes, edges and whole network. The results indicate that with the technology developing from the introduction to the growth-to-maturity phase, the collaborative innovation network exhibits dynamics as follows: as the scale expands, collaborations in the network are concentrated core cities, while dispersing to more innovators; enterprises replace universities and become the main innovation forces; the network attributes of small-world, scale-free and core-edge structures are apparent. Multi proximity factors including geographical, cognitive and organizational, play key roles in driving the dynamics, and the main factor evolves from geographical proximity to cognitive as well as organizational proximity.

Abstract. The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified data-derived model. For this purpose we use deterministic methods of nonlinear dynamics, together with a probabilistic approach of statistical physics. In this paper we discuss the mathematical aspects of such a combined analysis. In particular we introduce a new method of embedding analysis based on the notion of a mean-field dimension. For a given level of averaging in the system the mean-filed dimension determines the minimum dimension of the embedding space in which the averaged dynamical system approximates the actual dynamics with the given accuracy. This new technique is first tested on a number of well-known autonomous and open dynamical systems with and without noise contamination. Then, the dimension analysis is carried out for the correlated solar wind-magnetosphere database using vBS time series as the input and AL index as the output of the system. It is found that the minimum embedding dimension of vBS - AL time series is a function of the level of ensemble averaging and the specified accuracy of the method. To extract the global component from the observed time series the ensemble averaging is carried out over the range of scales populated by a high dimensional multi-scale constituent. The wider the range of scales which are smoothed away, the smaller the mean-field dimension of the system. The method also yields a probability density function in the reconstructed phase space which provides the basis for the probabilistic modeling of the multi-scale dynamical features, and is also used to visualize the global portion of the solar wind-magnetosphere coupling. The structure of its input-output phase portrait reveals the existence of two energy levels in the system with non-equilibrium dynamical features such as hysteresis which are typical for non-equilibrium phase transitions. Further improvements in space weather forecasting tools may be achieved by a combination of the dynamical description for the global component and a statistical approach for the multi-scale component.Key words. Magnetospheric physics (solar wind– magnetosphere interactions; storms and substorms) – Space plasma physics (nonlinear phenomena)

We present a continuum thermodynamical framework for simulating multiphase Stefan problem. For alloy solidification, which is marked by a diffuse interface called the mushy zone, we present a phase filed like formalism which comprises a set of macroscopic conservation equations with an order parameter which can account for the solid, liquid, and the mushy zones with the help of a phase function defined on the basis of the liquid fraction, the Gibbs relation, and the phase diagram with local approximations. Using the above formalism for alloy solidification, the width of the diffuse interface (mushy zone) was computed rather accurately for iron-carbon and ammonium chloride-water binary alloys and validated against experimental data from literature.

This article employed the fused deposition modelling (FDM) method and gas-pressure infiltration to manufacture alumina/AlSi12 composites. Porous ceramic skeletons were prepared by FDM 3D printing of two different alumina powder-filed filaments. The organic component was removed using a combination of solvent and heat debinding, and the materials were then sintered at 1500 °C to complete the process. Thermogravimetric tests and DTA analysis were performed to develop an appropriate degradation and sintering program. Manufactured skeletons were subjected to microstructure analysis, porosity analysis, and bending test. The sintering process produced porous alumina ceramic samples with no residual carbon content. Open porosity could occur due to the binder’s degradation. Liquid metal was infiltrated into the ceramic, efficiently filling any open pores and forming a three-dimensional network of the aluminium phase. The microstructure and characteristics of the fabricated materials were investigated using high-resolution scanning electron microscopy, computer tomography, hardness testing, and bending strength testing. The developed composite materials are characterized by the required structure—low porosity and homogenous distribution of the reinforcing phase, better mechanical properties than their matrix and more than twice as high hardness. Hence, the developed innovative technology of their manufacturing can be used in practice.

The high-strength/high-performance concretes are prone to cracking at early age due to low water/binder ratio. The replacement of cement with mineral additives such as fly ash and blast-furnace slag reduces the hydration heat during the hardening phase, but at the same time, it has significant influence on the development of mechanic and viscoelastic properties of early age concrete. Its potential benefit to minimize the cracking risk was investigated through a filed experiment carried out by the Norwegian Directorate of Roads. The temperature development and strain development of the early age concrete with/without the fly ash were measured for a “double-wall” structure. Based on experimental data and well-documented material models which were verified by calibration of restraint stress development in TSTM test, thermal-structural analysis was performed by finite element program DIANA to assess the cracking risk for concrete structures during hardening. The calculated and measured temperature and strain in the structure had good agreement, and the analysis results showed that mineral additives such as flay ash are beneficial in reducing cracking risk for young concrete. Furthermore, parameter studies were performed to investigate the influence of the two major factors: creep and volume change (autogenous shrinkage and thermal dilation) during hardening, on the stress development in the structure.

Precipitation-hardened alloys are one of the most technologically significant materials that are used for structural applications, where an important mode of strengthening is due to the impediment to the movement of dislocations. The alloys, particularly possessing coherent precipitate-matrix interface, give rise to the coherency strain fields producing the coherency stresses in the matrix, which further interact with the dislocations to provide necessary strengthening. In this context, the control of the shape and distribution of the precipitates as a function of material and process parameters is important. In this thesis, we propose a diffuse-interface approach in order to compute the equilibrium shape of precipitates, which also allows us to minimize the grid-anisotropy related issues that occur in the classical sharp interface methods. The method is based on the minimization of the functional consisting of the elastic free energy and the interfacial energy, while the volume of the precipitate is conserved. Using this technique we reproduce the shape bifurcation diagram from 2D simulations for isotropic, inhomogeneous elastic energy with dilatational misfit, which is compared against the analytical solution provided by Johnson-Cahn and an existing sharp interface FEM technique. Thereafter the model has been utilized for the investigation of equilibrium shapes for different combinations of elastic misfit matrices and cubic anisotropy. Additionally, we incorporate the anisotropy in the interfacial energy, which has not been studied by previous sharp interface techniques and investigate its influence on shape bifurcation. Finally, we extend the model to calculate the equilibrium shapes of the precipitate in 3D which resembles the precipitate structures observed in real microstructures. We notice that the nature of shape bifurcation diagram in 3D is different than that observed in 2D, which is principally because there exist multiple variants of precipitate shapes for the same precipitate size e.g. prolate-like or oblate-like structures that are not equivalent. We also compute a range of equilibrium shapes in 3D, that can form as a result of symmetry breaking for different forms of anisotropy in the elastic energy. In the next part of the thesis, we extend the phase-field model for computing the equilibrium shape of single precipitates for consideration of multiple variants that allows us to investigate the equilibrium configurations of precipitates. Here, given the properties of the material such as the magnitude of misfit strain and its signs, the magnitude of the shear moduli and the size of the precipitate, one can determine the equilibrium configuration that can form during solid-state precipitation reactions. Using this method, we investigate three solid-state precipitation reactions, i.e. formation of a core-shell type of precipitates in the microstructure and two symmetry-breaking transitions namely, cubic to tetragonal (typically observed in the superalloys with γ' − γ'' microstructure) and hexagonal to orthorhombic (formation of multi-variant precipitate pattern in Ti-based alloys). We evaluate the criteria for the formation of core-shell type microstructures and show that while the formation of such structures is purely due to interfacial conditions (satisfying the wetting condition), the reaction pathway leading to their formation is assisted by elastic interactions between the precipitates. In the symmetry-breaking transitions, we investigate the formation of equilibrium configurations of the multi-variant precipitates using energetic calculations. Here, we observe that the formation of such configurations involving multiple variants is favored over the nucleation of a single precipitate of the same equivalent volume beyond a certain precipitate size. In the last part of the thesis, we relax the condition of volume preservation of the precipitates and study precipitate growth in a supersaturated matrix in the presence of anisotropy in the elastic energy. To achieve this, we utilize a phase-field model based on the grand-potential formulation for coupling the chemical driving forces with coherency stresses. Using this model we investigate the specific problem of solid-state dendrite formation occurring during certain precipitation reactions. Here, we find that the anisotropy in the elastic energy gives rise to the formation of the dendrite-like structures that are typically observed in solidification microstructures as an effect of the Mullins-Sekerka in stabilities. We determine the dendrite tip shape and tip velocity, as the precipitate grows in size as a function of different materials parameters such as the magnitude of misfit strain, supersaturation in the matrix, and the anisotropy strength in both the energies. We notice that in all the cases, the dendrite tip shape and tip velocity does not achieve steady-state which is in contrast with the dendrites observed during solidification. This modification is due to the presence of coherency stresses.

Abstract Gas and water transport behavior, which is controlled by the pore characteristics and capillarity in hydrate-bearing sediments (HBS), is one of the key factors affecting the gas production. Hydrate distribution morphology (HDM) can significantly influence the pore structures of HBS, affecting the relative permeabilities of gas and water. To elucidate the impacts of HDM in microscopic scale, a phase-field lattice Boltzmann (LB) model is developed to describe the gas and water transport in HBS.To simulate the transport of immiscible fluids, which exist obvious density and viscosity contrasts, a phase-field LB model with the conservative form of interface-tracking equation is developed to suppress the spurious currents at phase interfaces. To describe the fluid-solid interactions, the bounce-back condition is applied for both solid phases (hydrate and grains) to achieve the non-slip condition and the wettability condition is applied for grains and hydrate to describe the wettability behavior. To improve the numerical stability, the multi-relaxation-time (MRT) collision operator is applied and the discretization schemes with 8th order accuracy for the gradient operator are selected. In this work, we first validated our model by applying several benchmark cases aiming at fluids with obvious density contrasts such as the layered Couette/Poiseuille flows, Rayleigh–Taylor instability. Then the synthetic geometries of the pore-filling and grain-coating HBS with several hydrate saturation (Shyd) were constructed by guaranteeing the same extent of connectivity. Then the steady-state relative permeability measurement and drainage capillary pressure measurement processes were simulated by the LB model for two HDM cases under several Shyd. The results showed that in the hydrophilic HBS, the relative permeability of gas in the pore-filling case is obviously larger than that in the grain-coating case at the same Shyd, and larger capillary pressure can be obtained in the pore-filling case. In addition, as the Shyd increased, it would notably enhance these differences of fluids relative permeability and capillary pressure between two HDM cases. Because the HDM can not only influence the pore space structures but also the wettability of the porous medium by creating solid surfaces of varying wettability, the distribution and transport of fluid phases in different HDM cases can be obviously affected. The phase-filed LB model applied in this study is capable to handle and suppress the spurious currents at phase interfaces, ensuring a satisfactory numerical stability and accuracy. Thus, the real density and viscosity contrasts between the water and gas under the in-situ thermodynamic conditions can be considered in the simulation. The impacts of HDM on the gas and water transport were quantitively analyzed by simulating multiphase flow processes in HBS.

Abstract Advances in high-resolution micro computed tomography (micro-CT) allow obtaining high-quality rock images with a resolution of up to a few micrometres. Novel direct numerical simulation methods provide the opportunity to precisely predict the flow properties in the resolved pore space. However, a large fraction of porosity lies below the resolution of modern micro-CT scanners. These, so called, micro-pores may significantly affect the physics of flow in geologically complex dual-porosity heterogeneous formations (carbonates, shales, and coals) and are currently not accounted for in traditional micro-CT based simulations. In this work, we have employed a multiphase multi-scale Darcy-Brinkman approach to simulate immiscible two-phase flow in a hybrid system containing both macro-porous solid-free regions and a micro-porous permeable matrix. This approach solves the Navier-Stokes based volume of fluid equations system in macro-pores and accounts for multiphase Darcy equations in micro-porous regions. By combining available information on micro-porosity with relative permeability curves estimated from the synthetically generated image with both macro- and micro-porous regions fully resolved, we solve the inverse problem to account for micro-porous contribution in our Darcy-Brinkman simulation. This approach allows us to estimate relative-permeability curves in the micro-porous region and correct the multi-scale simulation so it coincides with the data from the fully-resolved image. As a result, we were able to account for the impact of micro-porosity on the residual saturation and correct the shape of relative permeability curves and their end-points in the micro-porous domain. The proposed approach provides a workflow which can be used to history-match the Darcy-Brinkman pore-scale simulation with core-scale petrophysical data with respect to the relative permeability. Thus, it is possible to account for heterogeneity in complex rock formations by incorporating the whole range of porosity. The inclusion of micro-porosity in pore-scale image-based simulations for predicting relative permeability curves may help in a more reliable modelling and estimation of filed-scale subsurface flows, production profiles, recoverable reserves and carbon capture and storage mechanisms.