Phase-field simulation of irradiated metals: Part I: Void kinetics

We present a phase-field model of void formation and evolution in irradiated metals by spatially and temporally evolving vacancy and self-interstitial concentration fields. By incorporating a coupled set of Cahn–Hilliard and Allen–Cahn equations, the model captures the processes of point defect generation and recombination, annihilation of defects at sinks, as well as void nucleation and growth in the presence of grain boundaries. Illustrative results are presented that characterize the rate of void growth or shrinkage due to supersaturated vacancy or interstitial concentrations, void nucleation and growth kinetics due to cascade-induced defect production, as well as void denuded and peak zones adjacent to grain boundaries.     

Reinforced cast metals: Part II Evolution of the interface

Interface evolution in metal-matrix composites is a thermodynamic necessity and interface design a kinetics challenge. The synergistic interaction between processing science and surface engineering has led to considerable progress in understanding, modelling and tailoring the fibre–matrix interface at the microstructural, crystallographic and atomic levels. The chemical, morphological, crystallographic and thermoelastic compatibilities between the fibre and the matrix influence the interfacial adhesion strength. This article examines the role of material properties and fabrication conditions in chemical interactions between the fibre and the matrix in metal-matrix composites synthesized using the solidification and casting techniques. © 1998 Chapman & Hall     

Phase-field simulations of gas density within bubbles in metals under irradiation

Phase-field simulations are used to study the evolution of gas density within irradiation-induced bubbles in solids. In our simulations, which use copper as a model material, the dpa rate, gas production rate, and defect diffusivities are systematically varied to understand their effect on bubble nucleation rates, bubble densities, and the distribution of gas concentration within bubbles and in the solid regions. We find that gas densities within bubbles fluctuate drastically in the early nucleation stages, when growth rates are highest, but converge to steady-state values during the later coarsening stages. The steady-state gas densities within bubbles correspond with the ratio of total accumulated vacancy content divided by the total accumulated gas content, in agreement with a thermodynamic analysis concerning free-energy minimization.     

Si-Ni合金中小晶面枝晶生长的相场法模拟

相场法作为一种有效预测过冷熔体凝固过程的数值模拟计算方法,在模拟枝晶生长方面得到了广泛应用。应用界面能的校正形式,建立二元合金小晶面枝晶生长的相场模型,对Si-Ni二元合金小晶面枝晶生长进行了模拟。结果表明,当各向异性强度系数超过临界值υ=1/15时,枝晶生长表现出小晶面生长形态,尖端曲率效应消失,呈现出棱角状的不连续结构;同时在枝晶主支上产生大量侧向分支。实验观察验证了小晶面枝晶生长相场模型的有效性。     

Phase-field model of interface migration and powder consolidation in additive manufacturing of metals

Consolidation phenomena are of fundamental importance for additive manufacturing since the quality of metal parts produced by selective laser melting (SLM) is greatly dependent on residual porosity. The most recent studies use the lattice Boltzmann method (LBM) to analyze conjugated multiphase flow, heat transport, and phase transitions in the molten zone. A phase-field approach suggested in this paper retains all advantages of LBM and provides an alternative tool for theoretical analysis of SLM. In case of consolidation of composite powders where wetting phenomena are crucial at the matrix-inclusion interfaces, the phase-field method is more suitable. In this paper, the problem of metallic powder consolidation is numerically studied and the dynamics of pore and gas bubbles evolution in the molten zone is described. A two-step mechanism of consolidation is proposed which differs from a single-step mechanism typical for additive manufacturing of polymer powders. The consolidation time for different particle orderings is studied and an algorithm for the parameter selection in the widely used viscoplastic model is derived.     

Large inelastic deformation of glassy polymers. Part II: numerical simulation of hydrostatic extrusion

Oriented polymers may be successfully produced by the warm mechanical process of hydrostatic extrusion. This forming process is analyzed here using the constitutive model for the large inelastic deformation of glassy polymers developed in the companion paper. The model is numerically integrated and incorporated into a finite element code. The numerical results for the quantities of die swell, shrinkage stress, and pressure vs. velocity compare favorably with those obtained in documented experiments. The effects of strain rate, temperature, and friction on the process are also examined.     

Phase-field simulation of multilayer microstructure of Cr-enriched phase induced by alternating strain

International Journal of Mechanics and Materials in Design - Strain-induced microstructures have special effects on the mechanical properties of alloys. Alternating tensile/compressive strains can...     

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part II: Experimental validation

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers considering metastable region and separated flow has been developed in Part I of this paper. The developed numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions and metastable region. The accuracy of the detailed simulation model is demonstrated in this part (Part II) of the paper by comparing simulation results with a wide range of steady state experimental data from the technical literature, which include the refrigerant mass flow rate, outlet suction line temperature, and temperature profile along concentric and lateral capillary tube–suction line heat exchangers. Of the 196 data points evaluated for mass flow rate 96.4% are within an error of ±15%, 81.1% are within ±10% with a mean deviation of ±6.3%. Of the 143 data points evaluated for outlet suction line temperature 89.5% are within an error of ±2 °C, with a mean deviation of ±0.98 °C.The numerical results obtained are used to understand the refrigerant flow behavior inside non-adiabatic capillary tubes. Some divergence problems in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the heat exchanger zone; this aspect needs special attention while modeling the non-adiabatic capillary tube flow. Other important parameter to be evaluated experimentally with special care is the capillary tube internal diameter due to its strong influence on the refrigerant flow results (results of any study based on the nominal diameter are to be used with caution).     

DEM simulation of single bubble flotation: Implications for the hydrophobic force in particle–bubble interactions

A 3D Discrete Element Method simulation model for a single bubble was developed in order to investigate the capture of hydrophobic particles. The bubble was considered stationary at the centre of the working space. Particle–particle and particle–bubble contacts were simulated using a linear spring-dashpot model. Gravitational, buoyancy, drag and hydrophobic forces were taken into account. The hydrophobic force was estimated through a single exponential decay law which depends on a pre-exponential parameter K and a decay length λ. It was observed that when λ was less than 10 nm, the number of the particles that were collected was independent of the strength of the hydrophobic force. In contrast, for values of λ within the range of 10–500 nm, the capture efficiency increased significantly with the strength of the hydrophobic force and λ. We have also demonstrated how these two parameters affect the particle trajectory around the bubble and thus produce a significant difference in particle collection when the strength and range of the hydrophobic force were varied.     

Reinforced cast metals: Part I Solidification microstructure

The solidification process in fibre- and particle-reinforced metals is modified due to solute screening, thermal shielding, heterogeneous nucleation, fluid damping, particle pushing and morphological instabilities at the liquid–solid–fibre boundary. These factors lead to considerable variations in grain size, grain morphology, microsegregation and macro-segregation, and reinforcement distribution in the matrix. This article examines the roles of the above factors in the evolution of solidification microstructure in composites under controlled growth as well as under normal casting conditions. © 1998 Chapman & Hall     

Impact compression of alkali metals: Computer-aided simulation

This article describes a method for calculation of the potential of the embedded atom model (EAM), suitable for calculation of the properties of alkali metals in highly compressed states. For the first time, sequential consideration of the thermal energy and thermal pressure of collective electrons has been introduced into the EAM flowchart. The parameters of the EAM potential have been calculated, which make it possible to obtain good agreement in terms of pressure and energy for five alkali metals under impact compression. The properties of the molecular dynamic models of alkali metals at 300 and 0 K are compared with the data of static compression. The agreement between them is sufficient up to pressures of 15–20 GPa, and at higher compression rates divergences become significant. A lack of experimental data makes it impossible to understand whether the reason for these divergences is incomplete adequacy of the EAM potential or systematic errors contained in the experimental data in the range of high pressures. The proposed potentials make it possible to calculate the thermodynamic, structural, and diffusion properties of alkali metals in highly compressed states at temperatures up to 20000–30000 K.     

A new directional simulation method for system reliability. Part II: application of neural networks

A challenge in directional importance sampling is in identifying the location and the shape of the importance sampling density function when a realistic limit state for a structural system is considered in a finite element-supported reliability analysis. Deterministic point refinement schemes, previously studied in place of directional importance sampling, can be improved by prior knowledge of the limit state. This paper introduces two types of neural networks that identify the location and shape of the limit state quickly and thus facilitate directional simulation-based reliability assessment using the deterministic Fekete point sets introduced in the companion paper. A set of limit states composed of linear functions are used to test the efficiency and possible directional preference of the networks. These networks are shown in the tests and examples to reduce the simulation effort in finite element-based reliability assessment.     

A general dynamic simulation model for evaporators and condensers in refrigeration. Part II: simulation and control of an evaporator

A mathematical model of an evaporator based on one-dimensional partial differential equations representing mass conservation, and tube wall energy has been formulated. These equations are then restructured and linked to a program data base of all major refrigerants and refrigerant mixtures. The result is a simulation model of an evaporator that is general and flexible. The model is tested over a wide range of operating conditions and a simple controller is implemented to demonstrate the effectiveness of the model for controller and systems design.

Résumé

On a établi un modèle mathématique d'un évaporateur basé sur des équations aux dérivés partielles unidimensionnelles qui représentent la conservation de masse et l'énergie de la paroi du tube. Ces équations ont été restructurées ensuite, puis reliées à une base de données sur les principaux frigorigènes purs et en mélanges. De cette manière, on obtient un modèle d'évaporateur d'application générale et souple. Ce modèle a été éprouvé dans des conditions de fonctionnement très variées et on a employé un système de régulation simple pour montrer l'efficacité du modèle pour la conception et la régulation des systèmes.     

Numerical simulation of bubble growth in expanding perlite

Aiming to improve the comprehension of the expansion process of perlite, a numerical study has been carried out, concerning the water vapour bubble growth in softened perlite melt. The physical properties of the melt and temperature history during the expansion process are varied, in order to determine the most influencing parameters. Calculated bubble growth results are compared to experimental data obtained in a previous study, and to industrial expansion results. An extensive literature review has been done to determine the physical properties of raw and expanded perlite, as input values to the numerical model.     

Multiscale modelling of defect kinetics in irradiated iron.

Changes in microstructure and mechanical properties of nuclear materials are governed by the kinetics of defects produced by irradiation. The population of vacancies, interstitials and their clusters can however be followed only indirectly, for example by macroscopic resistivity measurements. The information on the mobility, recombination, clustering or dissociation of defects provided by such experiments is both extremely rich and difficult to interpret. By combining ab initio and kinetic Monte Carlo methods, we successfully reproduce the abrupt resistivity changes-so-called recovery stages-observed upon annealing at increasing temperatures after electron irradiation in alpha-iron. New features in the mechanisms responsible for these stages are revealed. We show that di-vacancies and tri-interstitials contribute to the stages attributed to mono-vacancy and di-interstitial migration respectively. We also predict the effect of the unexpected low migration barriers found for tri- and quadri-vacancies, and discuss the challenging questions raised by the mobility of larger defect clusters.     

CFD simulation of particle segregation in a rotating drum. Part II: Effects of specularity coefficient

Segregation of binary particle mixture in a rotating drum is numerically studied using the Eulerian multiphase computational fluid dynamics (CFD) simulations coupling the solid phase kinetic theory of granular flow model. The corresponding solid kinetic viscosities of the two particulate phases are determined by the previous granular bed surface fitting (BSF) method. The effects of the specularity coefficients used in the simulations on the segregation patterns in the rotating drums are systematically studied by using the specularity coefficient values ranging from 0.15 to 1.0. When using a smaller specularity coefficient value in the simulation, the momentum transferring from the drum wall to the particulate phase is poorer, lowering the kinetic energy of the particulate phase. The lower particulate phase kinetic energy causes slower particle motion in the bed and hence delays the segregation core/band formation. At the same simulation time, the concentration of the smaller particles in the segregation core increases with the increasing of the specularity coefficient value used in the simulation. When the specularity coefficient values larger than 0.4 are used in our simulations, the realistic three-dimensional segregation structures are well predicted. A proper specularity coefficient value should be adopted in Eulerian multiphase CFD simulations of granular flows.     

Transcritical carbon dioxide microchannel heat pump water heaters: Part II - System simulation and optimization

This paper presents the development of a transcritical CO₂ heat pump water heating system model incorporating analytical heat exchanger models and an empirical compressor model. This study investigated the effects of a suction line heat exchanger (SLHX) and once-through versus recirculating water heating schemes. The once-through systems outperformed the recirculating systems by 10% for the system without an SLHX and 15% with an SLHX. However, a gas cooler twice as large is required. The SLHX was shown to benefit system performance at higher evaporator temperatures with improvements of 16.5% for the once-through and 4% for the recirculating systems. This study can be used to improve the design of microchannel based transcritical CO₂ heat pumps; evaluate the impact of varying water inlet temperature, desired outlet temperature and evaporation temperature on system performance; and quantify the effect of differential diurnal electricity rates on system operating costs for these different operation schemes.     

Gas absorption and outgassing of metals

The solution of the diffusion equation is taken as a foundation of the theory of gas-metal interaction in high vacuum. The boundary conditions are formulated from the analysis of the gas balance equations on a metal surface and in a gas volume. The boundary conditions are generally non-linear but in some important cases linearization is permissible. In this way it is possible to obtain analytical expressions for the instantaneous gas flow on electron- and photon-induced desorption, low temperature thermal desorption and gettering at a constant pressure. By means of these formulae one can generalize the experimental data of various authors and calculate the kinetics of such processes as the outgassing of an electron collector, the gas desorption by synchrotron radiation in a vacuum chamber of electron or positron colliding-beam storage-rings, the degassing of an ultra-high vacuum system, the gas sorption by barium and titanium, etc.     

微孔发泡气泡非等温长大过程的数值模拟

针对微孔发泡气泡非等温长大过程,以PS/C02系统为例,考虑了温度对聚合物流变性质、亨利常数、扩散系数、表面张力的影响,基于细胞模型建立气泡非等温长大问题的数学模型,研究非等温条件下气泡长大情况的变化和不同工艺参数对气泡长大的影响.结果表明:冷却过程中亨利系数的增大和扩散系数的减小是导致气泡长大速度降低的主要因素;增加冷却速度是获得具有高密度、小尺寸泡孔形态微孔塑料的有效手段.这为微孔发泡气泡长大过程的控制提供了一定的理论依据.     

Computer simulation of fluid phase change: vapor nucleation and bubble formation dynamics

Using large scale molecular dynamics (MD) simulation techniques, two types of fluid–fluid phase changes were investigated. One is a homogeneous nucleation process from supersaturated vapor, in which we compare a Lennard–Jones system and water system. Another is a bubble formation (cavitation) process in stretched liquid, in which we compare one-component and two-component systems.