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Acta Metall Sin  2018, Vol. 54 Issue (8): 1204-1214    DOI: 10.11900/0412.1961.2017.00478
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A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System
Cheng WEI1,2, Changbo KE2, Haitao MA1,3, Xinping ZHANG2()
1 School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
2 School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China
3 Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou 510405, China;
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Abstract  

The materials design and fabrication based on predicting microstructure have been drawn increasing attention from scientists and engineers. Martensite microstructure, which is well observed in many materials, has significant influence on physical and mechanical properties of the materials. Some experimental studies have been launched to understand the featured microstructure and its evolution in martensitic transformations (MT). Meantime, numerical approaches are often employed to assist the experimental studies due to the complex and nonlinear nature of MT. The phase field method is one of the most powerful tools in predicting microstructure. Due to the diffuse-interface description, phase field method can be used to simulate arbitrary morphologies without tracking the interface. As a consequence, the interface must contain enough elements to obtain reasonable results by using finite element method. On the other hand, the width of the interface is several orders smaller than its real counterpart. More computational resources are required to resolve the phase field variables at the interface with the system size increased. Therefore, the simulation is restricted in smaller system even with state-of-the-art computer power. For arbitrary model formulations, the interfacial energy depends on the interfacial width and other specific properties of materials. However, the phase field models of martensitic transformation do not have enough degrees of freedom to increase the interfacial width without changing the interfacial energy. In the present study, a scalable phase field model by introducing a global modified function is constructed to study MT, the modified function takes into account the inhomogeneous nature of order parameter gradient across the interfacial region. Through adjusting the free energy density and gradient coefficient, meanwhile keeping the interfacial energy density unchanged, the interfacial width and system size are increased, yet the MT feature can be fully characterized. The simulation results show that the modified phase field model can well solve the drawbacks such as fast growth rate of martensite, artificial orientation relationship between the variants of martensite, and disordered martensite microstructure in large scale system.

Key words:  martensitic transformation      order parameter gradient      interfacial width      phase field method     
Received:  15 November 2017     
ZTFLH:  TF777.1  
Fund: Supported by National Natural Science Foundation of China (No.51205135) and Key Project Program of Guangdong Provincial Natural Science Foundation (No.S2013020012805)

Cite this article: 

Cheng WEI, Changbo KE, Haitao MA, Xinping ZHANG. A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System. Acta Metall Sin, 2018, 54(8): 1204-1214.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2017.00478     OR     https://www.ams.org.cn/EN/Y2018/V54/I8/1204

Fig.1  Global modification function (gp) vs equivalent gradient (νp) at different width ratios (λm/λ), in which gp does not adjust any coefficients in the non-interface region (νp=0, gp=1), but modifies the coefficients in the interfacial region (see points A and B)
Fig.2  Morphological evolution of new phase (red color) simulated in systems with scales of 134 nm×134 nm (a1~a3), 1072 nm×1072 nm (b1~b3) and 4288 nm×4288 nm (c1~c3) at time of t=0.00 s (a1~c1), t=0.15 s (a2~c2) and t=0.45 s (a3~c3), and change of the equivalent radius with time (In which each simulation system owns the same initial square nucleus size of 10.72 nm×10.72 nm) (d)
Fig.3  Morphological evolution of new phase (red color) simulated with employing the global modification function in systems with scales of 1072 nm×1072 nm (a1~a3) and 4288 nm×4288 nm (b1~b3) at time of t=0.00 s (a1, b1), t=0.15 s (a2, b2) and t=0.45 s (a3, b3), and change of the equivalent radius with time (In which each simulation system owns the same initial square nucleus size of 10.72 nm×10.72 nm) (c)
Fig.4  Morphological evolution of two R-phase variants in their initial states (variant 1 in blue and variant 2 in red) (a) simulated in systems with different scales of 101 nm×67 nm (b), 2010 nm×1340 nm (c) and 20100 nm×13400 nm (d), and change of strain energy density with time (e)
Fig.5  Morphologicl evolution of two R-phase variants (variant 1 in blue and variant 2 in red) simulated with employing the global modification function in systems with scales of 2010 nm×1340 nm (a) and 20100 nm×13400 nm (b), and change of strain energy density with time (c)
Fig.6  Schematic configuration of four R-phase variants in the (001) plane with variants 1 and 4 (a), and variants 1 and 2 (b)
Fig.7  Morphological evolution of B2-R phase transformation simulated in systems with scales of 101 nm×101 nm (a1~a3), 2010 nm×2010 nm (b1~b3) and 20100 nm×20100 nm (c1~c3) at time of t=0.05 s (a1~c1), t=0.50 s (a2~c2), t=40.10 s (a3), t=16.52 s (b3) and t=16.13 s (c3), and change of strain energy density with time (d) (In which the blue region stands for B2-phase, the light blue region stands for variant 1, the green region stands for variant 2, the yellow region stands for variant 3, and the red region stands for variant 4)
Fig.8  Morphological evolution of B2-R phase transformation simulated with employing the global modification function in systems with scales of 2010 nm×2010 nm (a1~a3) and 20100 nm×20100 nm (b1~b3) at time of t=0.05 s (a1, b1), t=0.50 s (a2, b2), t=67.71 s (a3), t=83.76 s (b3), and change of strain energy density with time (c) (In which the blue region stands for B2-phase, the light blue region stands for variant 1, the green region stands for variant 2, the yellow region stands for variant 3, and the red region stands for variant 4)
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