Phase field simulation of monotectic transformation for liquid Ni-Cu-Pb alloys

Luo, Bing; Wang, Haipeng; Wei, B.

doi:10.1007/s11434-009-0018-5

Cited by 14 publications

(10 citation statements)

References 19 publications

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“…Otherwise, the growth distance continues evolving according to eq. (20). (4) After the above mentioned steps, the state variables of each cell on the boundaries and their neighboring cells are updated, and the microstructural evolution of the CA model proceeds.…”

Section: Coarsening Controlled By Diffusion Along Grain Boundariesmentioning

confidence: 99%

“…In contrast, numerical modeling of static coarsening is an effective approach which not only enables visible reproduction of the virtual microstructural evolution, but also systematic and comprehensive investigation of the effects of volume fraction, morphology, and initial grain size on the coarsening process. The most used models for this purpose are the cellular automata method (CA) [13][14][15], the Monte Carlo method [16,17], and the phase field method [18][19][20]. Recently, many researchers have begun to simulate the grain coarsening of single phase alloys or multi-phase alloys in a single phase field.…”

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confidence: 99%

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Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method

Yang

2013

Chin. Sci. Bull.

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A cellular automata (CA) method was employed to model static coarsening controlled by diffusion along grain boundaries at 1173 K and through the bulk at 1213 and 1243 K for a two-phase titanium alloy. In the CA model, the coarsening rate was inversely proportional to the 3rd power of the average grain radius for coarsening controlled by diffusion along grain boundaries, and inversely proportional to the 2nd power of the average grain radius for coarsening controlled by diffusion through the bulk. The CA model was used to predict the morphological evolution, average grain size, topological characteristics, and the coarsening kinetics of the Ti-6Al-2Zr-1Mo-1V (TA15) alloy during static coarsening. The predicted results were found to be in good agreement with the corresponding experimental results. In addition, the effects of the volume fraction of the  phase (V f ) and the initial grain size on the coarsening were discussed. It was found that the predicted coarsening kinetic constant increased with V f and that a larger initial grain size led to slower coarsening. Two-phase titanium alloys have been widely used in the aerospace industry because of their excellent moderate room-temperature and high-temperature strength [1][2][3]. For these types of alloys, static coarsening occurs easily during their application at higher temperatures, which usually has a large effect on the grain size, morphology, and phase volume fraction and, in turn, on the mechanical properties of the final parts. Therefore, investigation of the coarsening mechanism of such alloys at high temperatures is necessary for microstructure design and process control. Over the years, many researchers have carried out experiments to study the static coarsening of two-phase titanium alloys in the single phase field or the  two-phase field. It is generally believed that the static coarsening process can be expressed as a power law as a function of aver-where d is the average grain diameter during coarsening, d 0 is the initial value at time t 0 , K is the coarsening rate constant, and n is the coarsening exponent. Different values of n represent different coarsening mechanisms. Gil and Planell [4], Semiatin et al. [5], and Ivasishin et al. [6] investigated the static coarsening behavior of Ti-6Al-4V alloy in the  single phase field, and found that the value of n deviated from the theoretical value of 2 for pure metals under all temperatures tested. The authors attributed this difference to the effect of solute atoms, precipitates, or impurities [7]. However, for two-phase titanium alloys the coarsening mechanism in the  two-phase field is much more complicated than that in the  single phase field. Some authors, including Hu and Rath [8] and Grewal and Ankem [9,10],

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Section: Coarsening Controlled By Diffusion Along Grain Boundariesmentioning

confidence: 99%

mentioning

confidence: 99%

Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method

Yang

2013

Chin. Sci. Bull.

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“…When a single-phase liquid is undercooled into the gap, the liquid-liquid phase transformation takes place and the liquid separates into two liquids [1]. Many investigations on the solidification process of the immiscible alloys have been carried out by using the experimental method and numerical simulation [2][3][4][5][6]. The progress in the solidification control has been made to obtain the refinement microstructure.…”

Section: Introductionmentioning

confidence: 99%

Liquid phase separation and microstructure characterization in a designed Al-based amorphous matrix composite with spherical crystalline particles

Hai-quan

Yang

et al. 2010

Journal of Alloys and Compounds

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“…Recently, various numerical simulation techniques such as Potts-Monte Carlo models (MC) [11][12][13], phase field models [14,15] and cellular automaton models (CA) [16][17][18] have been gradually used to model the microstructure evolution on the mesoscale [19]. The CA methods have been widely used in these investigations, and have some advantages [20].…”

mentioning

confidence: 99%

Static coarsening of titanium alloys in single field by cellular automaton model considering solute drag and anisotropic mobility of grain boundaries

Yang

et al. 2012

Chin. Sci. Bull.

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Static coarsening is an important physical phenomenon that influences microstructural evolution and mechanical properties. How to simulate this process effectively has become an important topic which needs to be dealt with. In this paper, a new cellular automaton (CA) model, which considers the effect of solute drag and anisotropic mobility of grain boundaries, was developed to simulate static grain coarsening of titanium alloys in the beta-phase field. To describe the effect of the drag caused by different solute atoms on coarsening, their diffusion velocities in beta titanium were estimated relative to that of titanium atoms (Ti). A formula was proposed to quantitatively describe the relationship of the diffusion velocity of Ti to that of solute atoms; factors influencing the diffusion velocity such as solute atom radius, mass, and lattice type were considered. The anisotropic mobility of grain boundaries was represented by the parameter c 0 , which was set to 1 for a fully anisotropic effect. These equations were then implemented into the CA scheme to model the static coarsening of titanium alloys Ti-6Al-4V, Ti17 (Ti-5Al-4Mo-4Cr-2Sn-2Zr, wt%), TG6 (Ti-5.8Al-4.0Sn-4.0Zr-0.7Nb-1.5Ta-0.4Si-0.06C, wt%) and TA15 (Ti-6Al-2Zr-1Mo-1V, wt%) in the beta field. The predicted results, including coarsening kinetics and microstructural evolution, were in good agreement with experimental results. Finally, the effects of time, temperature, and chemical composition on grain coarsening and the limitations of the model were discussed. The mechanical properties of titanium alloys such as the creep resistance, fracture toughness and crack propagation resistance are determined by their grain sizes in the beta phase field [1,2]. However, the grains are prone to static coarsening when held in the beta phase field because of the structural characteristics of beta-titanium and relatively high stacking fault energy at high temperatures [3]; this results in a marked decrease in the mechanical properties of final products. Therefore, it is necessary to understand and to control static coarsening of titanium alloys in a single phase field to obtain the expected mechanical properties. Previously, many experimental investigations have focused on the static coarsening behaviors of titanium alloys in the beta phase field. Ivasishin et al. [4,5] investigated the effect of texture evolution on the values of the static coarsening exponent n and activation energy for Ti-6Al-4V alloy in the beta field. They found values of n ranging from 0.22 to 0.31 at different temperatures, but there were marked deviations attributed to different materials and experiments when the results were compared with those of others. Recently, Semiatin et al. [6][7][8] investigated the static grain coarsening of Ti-6Al-4V alloy via a series of heat treatments at typical temperatures. They found that the coarsening process of primary alpha particles was controlled by the volume diffusion of solute elements at lower temperatures and the growth exponent was equal to 0.33.

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Phase field simulation of monotectic transformation for liquid Ni-Cu-Pb alloys

Cited by 14 publications

References 19 publications

Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method

Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method

Liquid phase separation and microstructure characterization in a designed Al-based amorphous matrix composite with spherical crystalline particles

Static coarsening of titanium alloys in single field by cellular automaton model considering solute drag and anisotropic mobility of grain boundaries

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