Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element(CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field(PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy.Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.

3D anisotropy simulation of dendrites growth with phase field method

The anisotropy problem of 3D phase-field model was studied,and various degrees of anisotropy were simulated by numerical calculation method.The results show that with the change of interface anisotropy coefficients,from smooth transition to the appearance of angle,equilibrium crystals shape morphology has a critical value,and 3D critical value is 0.3.The growth of dendrites is stable and the interface is smooth when it is less than critical value;the interface is unstable,rolling edge appears and the growth is discontinuous when it is more than critical value.With the increase of anisotropy coefficients,the dendrites grow faster under the same condition.

Simulation of faceted dendrite growth of non-isothermal alloy in forced flow by phase field method

Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.

Analysis on high-temperature oxidation and growth stress of iron-based alloy using phase field method

High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method （PFM） based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution axe predicted for Fe-Cr-A1-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.

Numerical Simulations of Equiaxed Dendrite Growth Using Phase Field Method

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in a metallic system. In this paper, the equiaxed dendrite evolution during the solidification of a pure material was numerically simulated using the phase field model. The equiaxed dendrite growth in a two-dimensional square domain of undercooled melt (nickel) with four-fold anisotropy was simulated. The phase field model equations was solved using the explicit finite difference method on a uniform mesh. The formation of various equiaxed dendrite patterns was shown by a series of simulations, and the effect of anisotropy on equiaxed dendrite morphology was investigated.

Multi-phase field simulation of grain growth in multiple phase transformations of a binary alloy

This work establishes a temperature-controlled sequence function, and a new multi-phase-field model, for liquid- solid-solid multi-phase transformation by coupling the liquid-solid phase transformation model with the solid-solid phase transformation model. Taking an Fe-C alloy as an example, the continuous evolution of a multi-phase transformation is simulated by using this new model. In addition, the growth of grains affected by the grain orientation of the parent phase （generated in liquid-solid phase transformation） in the solid-solid phase transformation is studied. The results show that the morphology of ferrite grains which nucleate at the boundaries of the austenite grains is influenced by the orientation of the parent austenite grains. The growth rate of ferrite grains which nucleate at small-angle austenite grain boundaries is faster than those that nucleate at large-angle austenite grain boundaries. The difference of the growth rate of ferrites grains in different parent phase that nucleate at large-angle austenite grain boundaries, on both sides of the boundaries, is greater than that of ferrites nucleating at small-angle austenite grain boundaries.

Phase field model for strong interfacial energy anisotropy of HCP materials

Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value（1/35）, the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.

GROWTH MORPHOLOGIES OF A BINARY ALLOY WITH LOW ANISOTROPY IN DIRECTIONAL SOLIDIFICATION

Two new classes of growth morphologies, called doublons and seaweed, were simulated using a phase-field method. The evolution of doublon and seaweed morphologies was obtained in directional solidification. The influence of orientation and velocity on the growth morphology was investigated. It was indicated that doublons preferred growing with its crystallographic axis aligned with the heat flow direction. Seaweed, on the other hand, could be obtained by tilting the crystalline axis to 45°. Stable doublons could only exist in a range of velocity regime. Beyond this regime the patterns formed would be unstable. The simulation results agreed with the reported experimental results qualitatively.

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.

Phase-field simulation of competitive growth of grains in a binary alloy during directional solidification

Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional(3-D) phasefield method. The result of phase-field simulation was verified by applying cold spray and directional remelting. In the simulation process, two competitive modes were designed: in Scheme 1, the monolayer columnar grains in multilayer columnar crystals had different orientations; while in Scheme 2, they had the same orientation. The simulation result showed that in Scheme 1, the growth of the dendrites, whose orientation had a certain included angle with the direction of temperature gradient, was restrained by the growth of other dendrites whose direction was parallel to the direction of temperature gradient. Moreover, the larger the included angle between the grain orientation and temperature gradient, the earlier the cessation of dendrite growth. The secondary dendrites of dendrites whose grain orientation was parallel to the temperature gradient flourished with increasing included angles between the grain orientation and temperature gradient. In Scheme 2, the greater the included angle between grain orientation and temperature gradient, the easier the dendrites whose orientation showed a certain included angle with temperature gradient inserted between those grew parallel to the temperature gradient, and the better the growth condition thereafter. Some growing dendrites after intercalation were deflected to the temperature gradient, and the greater the included angle, the lower the deflection. The morphologies of the competitive growth dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the two modes of competitive growth of dendrites characterized in the simulation do exist and frequently appear in practical solidification processes.

Grain growth in a nanostructured AZ31 Mg alloy containing second phase particles studied by phase field simulations

Phase field models were established to simulate the grain growth of a nanostructured AZ31 magnesium alloy,which contain spherical particles of differing sizes and volume fractions, under realistic spatial and temporal scales.The effect of the second phase particles on the nanostructure evolution was studied. The simulated results were compared with those of the conventional microstructured alloy.The expression of the local free energy density was improved by adding a second phase particle term. The right input parameters were selected for proper physical meaning. It was shown that the rules that govern the pinning effect of the second phase particles during the grain growth were different for the nanostructure and microstructure. There was a critical particle size value that affected the grain growth within the nanostructure. If the particle size was lower than the critical value, the pinning effect on grain growth increased with decreasing particle size. When the particle size was greater than the critical value, the particles had almost no pinning effect.However, in the conventional microstructured material,the larger particle size resulted in an enhanced pinning effect during grain growth for particle sizes smaller than 1 μm. The effect was reversed when the particle size was larger than the critical value. For the nanostructure, the critical value was200 nm when the particle content was 10 v.%, and the critical value decreased when the content increased. When the particle size was 30 nm, the particle pinning effect on the grain growth increased for increasing particle content.

Microstructure evolution and phase transitions in metals simulated by the multiphase-field method

The phase-field method has emerged as the method of choice for the description of microstructure evolution and phase transitions in metallic materials.Following general thermodynamic laws a set of evolution equations for the structural variables of the system,the so called phase-fields,are derived.The paper reviews shortly the theoretical background of the multi-phase-field.Different examples demonstrating the applicability of the method to technical steels will be presented ranging from deformation of the dendritic strand shell during peritectic transformation,grain growth in Austenite to stress driven growth of Pearlite.

Phase-field simulation of the coupled evolutions of grain and twin boundaries in nanotwinned polycrystals

Nanotwinned polycrystals exhibit an excellent strength-ductility combination due to nanoscale twins and grains. However, nanotwin-assisted grain coarsening under mechanical loading reported in recent experiments may result in strength drop based on the Hall-Petch law. In this paper, a phase-field model is developed to investigate the effect of coupled evolutions of twin and grain boundaries on nanotwin-assisted grain growth. The simulation result demonstrates that there are three pathways for coupled motions of twin and grain boundaries in a bicrystal under the applied loading, dependent on the amplitude of applied loading and misorientation of the bicrystal. It reveals that a large misorientation angle and a large applied stress promote the twinning-driven grain boundary migration. The resultant twin-assisted grain coarsening is confirmed in the simulations for the microstructural evolutions in twinned and un-twinned polycrystals under a high applied stress.

Morphological evolution and growth kinetics of Kirkendall voids in binary alloy system during deformation process-Phase field crystal simulation study

The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.

Phase-field simulation of dendritic growth for binary alloys with complicate solution models

A phase-field method for simulation of dendritic growth in binary alloys with complicate solution models was studied. The free energy densities of solid and liquid used to construct the free energy of a solidification system in the phase-field model were derived from the Calphad thermodynamic modeling of phase diagram. The dendritic growth of Ti-Al alloy with a quasi-sub regular solution model was simulated in both an isothermal and a non-isothermal regime. In the isothermal one, different initial solute compositions and melt temperatures were chosen. And in the non-isothermal one, release of latent heat during solidification was considered. Realistic growth patterns of dendrite are derived. Both the initial compositions and melt temperatures affect isothermal dendritic morphology and solute distributions much, especially the latter. Release of latent heat will cause a less developed structure of dendrite and a lower interfacial composition.

Numerical Simulation of Two-Dimensional Dendritic Growth Using Phase-Field Model

In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.

Site occupation evolution of alloying elements in L1_2 phase during phase transformation in Ni_(75)Al_(7.5)V_(17.5)

Correlation between site occupation evolution of alloying elements in L12 phase and growth of DO22 phase in Ni75Al7.5V17.5 was studied using microscopic phase field model. The results demonstrate that the growing process of DO22 phase can be divided into two stages. At the early stage, composition in the centre part of L12 phase almost remains unchanged, and the nucleation and growth of DO22 phase is controlled by the decrease of interface between L12 phases. At the late stage, part of V for growth of DO22 phase is supplied from the centre part of L12 phase and mainly comes from Al sublattice, the excess Ni spared from the decreasing L12 phase migrates into the centre part of L12 phase and occupies the Ni sublattices exclusively, while the excess Al mainly occupies the Al sublattice. At the late stage, the growth of DO22 phase is controlled by the evolution of antisite atoms and ternary additions in the centre part of L12 phase.

基于相场方法的铀枝晶生长电化学-流场耦合研究

铀枝晶生长是导致乏燃料后处理电解精炼装置发生意外短路的潜在威胁因素,同时会使铀产物夹杂大量熔盐,影响产物纯度。为了更好地理解铀枝晶生长的微观机理,掌握阴极沉积形貌的控制方法,基于相场方法建立了铀在阴极的电沉积模型,研究了铀枝晶的底部沉积宽度、主枝晶干高度和总沉积面积等形貌参数对流场速度变化的依赖规律。发现外加流场的引入会使铀枝晶的底部沉积宽度降低37.18%,主枝晶干高度降低30.5%,总沉积面积降低49.3%。说明外加流场可以抑制铀枝晶生长,改善铀沉积形貌,但同时也会使破碎的枝晶须重新溶解到熔盐体系中,降低铀电解精炼效率。另外,通过对流场与电解电压、初始浓度等沉积条件耦合影响下铀枝晶形貌特征相图的分析可知,在实际电解精炼过程中,应在保证电解精炼效率的基础上尽量选择高初始浓度和高电解电压的沉积条件,同时设置合理的流场速度以获得理想的铀枝晶沉积形貌。

镍基高温合金SLM过程中熔池内的微观结构演变数值模拟

采用有限元耦合相场的方法研究IN718高温合金在激光选区熔化过程中熔池内的竞争性生长和晶粒/枝晶结构的演变。通过有限元解决热演化问题,然后将结果输入相场模型,相场模拟涉及晶粒成核、晶粒外延生长和晶粒竞争的微观结构演变。基于对熔池横向和纵向截面微观结构演变的分析,讨论SLM过程中枝晶竞争性生长的机制,并量化计算熔池中溶质元素Nb的浓度分布。结果表明,枝晶竞争性生长受温度梯度和晶体学取向的影响,具有高错配角(>22.5°)的不利取向晶粒将很快被有利取向晶粒淘汰。

氧化铝陶瓷典型缺陷结构对电场分布的影响研究

在高电压环境下,显微缺陷结构的存在会导致绝缘材料内产生电场畸变,是影响氧化铝陶瓷绝缘强度的重要因素之一。为了研究高电压环境下氧化铝陶瓷典型缺陷结构对材料内电场分布的影响,建立了包含缺陷结构的细观陶瓷结构模型,并采用有限元软件分析了晶粒尺寸、玻璃相以及气孔的存在对电场分布的影响规律。结果表明:晶粒尺寸对电场畸变程度的影响较小,而玻璃相的存在对电场畸变程度的影响较大。玻璃相对电场畸变的影响与晶界方向有关,晶界与电场方向夹角越大,玻璃相处的电场畸变程度越大。与晶粒尺寸和玻璃相的影响相比,气孔缺陷的存在对氧化铝陶瓷内部电场畸变的影响最大,其中,晶粒内气孔导致场强最大值提高了46.8%,而晶界处的气孔导致场强最大值提高一倍以上。气孔尺寸对电场畸变的范围影响较大,而对场强最大值的影响较小。