Transformation simulation

Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

Accepted Manuscript

Cellular automaton study on influencing factors of dynamic solid phase trans-formation kinetics

K.J. Song, Y.H. Wei, K. Fang, Z.B. Dong, X.H. Zhan, W.J. Zheng

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Received Date:Revised Date:Accepted Date:S0307-904X(15)00236-Xhttp://wendang.chazidian.com/10.1016/j.apm.2015.03.046APM 10529Appl. Math. Modelling29 May 20136 March 201531 March 2015

Please cite this article as: K.J. Song, Y.H. Wei, K. Fang, Z.B. Dong, X.H. Zhan, W.J. Zheng, Cellular automatonstudy on influencing factors of dynamic solid phase transformation kinetics, Appl. Math. Modelling (2015), doi:http://wendang.chazidian.com/10.1016/j.apm.2015.03.046

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Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

K.J. Song a, Y.H. Wei a, b*, K. Fanga, Z.B. Dong a, X.H. Zhan b, W.J. Zheng a

a State Key Laboratory of Advanced Welding and Joining, Harbin Institute of

Technology, Harbin 150001, China

b School of Materials

Astronautics, Nanjing 210016, China

Abstract

β to αalloy was simulated using virtual modified cellular automaton (CA) diffusion equations. transformation kinetics and microstructure exhibit desired with prediction result of Zener–Hillert equation and angle as well as kinetic parameters including solute diffusion and mobility coefficient on new phase morphologies and micro segregation. diffusion/mixed/interface controlled transformations are distinguished by deviation of interfacial solute concentration from initial solute concentration and equilibrium solubility of parent phase. Three transformation modes are simulated by varying diffusion coefficient, interface mobility coefficient and transformation driving force factor.

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Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

Keywords: Cellular automaton; Driving force model; Transformation kinetics;

Curvature effect; Diffusion/mixed/interface controlled

1. Introduction

During hotworking or heat treatment process for titanium, β to α or αdirectly results in the arrangement and morphology of constituent

by the heterogeneous grain size of parent phase, in different zones at different time, thermodynamics and kinetics, etc. Such complexity makes in transformation in Fe–C, steels [2,3] and other diffusion controlled kinds of transformations, since many confusing problems, i.e., solute drag, nonsteady state of interface frontier, sharp/

are always striving for better understanding of solid phase transformation models. The advanced models for solid phase transformation are mainly divided into classic analytic solutions, finite element method, phase field and CA. In early stages, analytic solutions and their corporation with finite element method were widely applied [7,8]. Most of these models dealt with complete diffusion controlled transformation of interstitial solutions. The outputs are the transformation fraction and 2

Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

interface moving velocity but transient interface characteristics or phase morphology. Phase field does not have to track the moving phase boundary explicitly but uses an uniform continuous function as governing equation for phase state transition. Mecozzi deviation of carbon concentration in austenite at the interface from equilibrium

carbon concentration. Still, there are many reports using Gibbs energy change according to phase state, in taking energy change as driving force [10,11]. Loginova et al. the Widmanstatten ferrite morphology with predefined properties. A transition from diffusion controlled to transformation is predicted when solute simulation of precipitation in smooth globular shape. Nakajima et al. [14] simulated of flake pearlite using multi–phase field model. It is found in ferrite and growth of cementite from the ferrite increase the determined by phase state and grain angles to reproduce austenite to ferrite transformation. However, the computational domain of phase field is limited due to the extremely thin interfacial thickness.

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Cellular automaton study on influencing factors of dynamic solid phase transformation kinetics

CA is popular for its computation efficiency, flexibility in multi–scale bridging and physical consistency. There are many application examples but mainly on austenite to ferrite transformation in multi–grains [16,17]. Quantification of transformation kinetics inherent to solute diffusion and interface mobility characteristics importance for practical applications of CA models. However, to knowledge, current phase transformation CA models have not yet sufficient

information about controlling factors of transformation the diffusion–controlled transformation, while in former solute partition is swallowed up by the fast moving coefficient increasing, interface shifts towards diffusion mode transformation, during which transformation rate and solute partition are

study [18], virtual front tracking CA approach was presented and to be very successful when studying the crystallographic characteristics of transformation. Attentions are more focused on the numerical solutions of CA model and quantitative capability there. The simulation is performed using a common transformation driving force model and a fixed transformation condition (constant temperature, diffusion and interface mobility coefficient). To do further study by 4