Shock-induced phase transition of iron studied with phase field method


  • Z Wang
  • X Guo
  • D Zhao
  • Q Zhang



To develop phase field method in high strain rate loading, it derived the governing equations of phase field model in the foundation of entropy functional, and the model adopted a diffusion interface, which made automatic tracking on interface possible. Added the order parameter to characterize the different phases of materials, and simulated the soften and phase transition in shock-induced loading. According to the conservation theorems and principle of entropy increasing, we established the governing equations of shock-induced phase transition in metal dielectric. Then the work discretized phase field model by using high order difference scheme, introducing the artificial viscosity, and obtained the numerical solution of the phase field model. Compared the numerical value with the theoretical solution, the accuracy of the developed phase field model was verified. Based on the model described above, the work study the a®e polymorphic phase transition of iron-base alloy induced by one-dimensional shock wave. Considering the spatial and temporal distribution of each parameter field and the Hugoniot data for iron, it further analyzed the coupling effect of wave and phase transition by tracking the changes of pressure and speed in each unit. The simulation results fitted well with the experimental results, which indicated that the phase field model developed was successful, and it would help people to understand the microstructural evolution of metallic materials under the shock wave.


Tang X J, Hu H B, Li Q Z, et al. Experimental studies on shock-induced phase transition in HR2 and other Fe-based materials[J]. Explosion & Shock Waves, 2006, 26(2):115-120.

Zhang X H, Tang Z P, Wei-Wei X U, et al. Experimental study on characteristics of shock-induced phase transition and spallation in FeMnNi alloy[J]. Explosion & Shock Waves, 2007, 27(2):103-108.

Chao L, Shi Y N, Qin C S, et al. Study of Shock-induced Polycrystalline Iron Phase Transition with DEM[J]. Acta Armamentarii, 2014, 35(7):1009-1015.

Penrose O, Fife P C. Thermodynamically consistent models of phase-field type for the kinetic of phase transitions[J]. Physica D Nonlinear Phenomena, 1990, 43(1):44-62.

Wang S L, Sekerka R F, Wheeler A A, et al. Thermodynamically-consistent phase-field models for solidification[J]. Physica D-nonlinear Phenomena, 1993, 69(1-2):189-200.

Kobayashi R, Warren J A, Carter W C.A continuum model of grain boundaries [J]. Physica, 2000, D140: 141-150.

Brown J M, Fritz J N, Hixson R S. Hugoniot data for iron[J]. Journal of Applied Physics, 2000, 88(9):5496-5498.

Barker L M, Hollenbach R E. Shock wave study of the α ⇄ ϵ phase transition in iron[J]. Journal of Applied Physics, 1974, 45(11):4872-4887.

Mao H, Bassett W A, Takahashi T. Effect of Pressure on Crystal Structure and Lattice Parameters of Iron up to 300kbar[J]. Journal of Applied Physics, 1967, 38(1):272-276.

Johnson P C, Stein B A, Davis R S. Temperature Dependence of Shock-Induced Phase Transformations in Iron[J]. Journal of Applied Physics, 1962, 33(2):557-561.

Bundy F P. Pressure—Temperature Phase Diagram of Iron to 200kbar, 900°C[J]. Journal of Applied Physics, 2004, 36(2):616-620.

Forbes J W. Experimental Investigation of the Kinetics of the Shock-Induced Alpha to Epsilon Phase Transformation in Armco Iron.[J]. 1976.

Boettger J C, Wallace D C. Metastability and dynamics of the shock-induced phase transition in iron[J]. Physical Review B Condensed Matter, 1997, 55(5):2840-2849.



How to Cite

Wang, Z., Guo, X., Zhao, D. and Zhang, Q. (2018) “Shock-induced phase transition of iron studied with phase field method”, The International Journal of Multiphysics, 12(2), pp. 131-146. doi: 10.21152/1750-9548.12.2.131.