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Phase-Field Modeling for the Three-Dimensional Space-Filling Structure of Metal Foam Materials

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DOI: 10.4236/ojmsi.2015.33013    3,214 Downloads   3,780 Views   Citations
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ABSTRACT

Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Uehara, T. (2015) Phase-Field Modeling for the Three-Dimensional Space-Filling Structure of Metal Foam Materials. Open Journal of Modelling and Simulation, 3, 120-125. doi: 10.4236/ojmsi.2015.33013.

References

[1] Banhart, J. (2001) Manufacture, Characterization and Application of Cellular Metals and Metal Foams. Progress in Materials Science, 46, 559-632.
http://dx.doi.org/10.1016/S0079-6425(00)00002-5
[2] Lefebvre, L.-P., Banhart, J. and Dunand D. (2008) Porous Metals and Metallic Foams: Current Status and Recent Developments. Advanced Engineering Materials, 10, 775-787.
http://dx.doi.org/10.1002/adem.200800241
[3] Weaire, D and Phelan, R. (1994): A Counter-Example to Kelvin’s Conjecture on Minimal Surfaces. Philosophical Magazine Letters, 69, 107-110.
http://dx.doi.org/10.1080/09500839408241577
[4] Sye, R.I. and Sethian, J.A. (2013) Multiscale Modeling of Membrane Rearrangement, Drainage, and Rupture in Evolving Foams. Science, 340, 720-724.
http://dx.doi.org/10.1126/science.1230623
[5] Uehara, T. (2014) Numerical Simulation of Foam Structure Formation and Destruction Process Using Phase-Field Model. Advanced Materials Research, 1042, 65-69.
http://dx.doi.org/10.4028/www.scientific.net/AMR.1042.65
[6] Uehara, T. and Suzuki, H. (2012) Numerical Simulation of Homogeneous Polycrystalline Grain Formation Using Multi-Phase-Field Model. Applied Mechanics and Materials, 197, 2610-2614.
http://dx.doi.org/10.4028/www.scientific.net/AMM.197.628
[7] Uehara, T. (2012) Grain-Size Equalization Model Using Multi-Phase-Field Model. Proceedings of the 7th International Workshop on Modeling Crystal Growth, Taipei, 28-31 October 2012, 82-83.
[8] Steinbach, I., Pezzolla, F., Nestler, B., Seeselberg, M., Prieler, R., Schmitz, G.J. and Rezende, J.L.L. (1996) A Phase Field Concept for Multiphase Systems. Physica D, 94, 135-147.
http://dx.doi.org/10.1016/0167-2789(95)00298-7
[9] Steinbach, I. and Pezzolla, F. (1999) A Generalized Field Method for Multiphase Transformations Using Interface Fields. Physica D, 134, 385-393.
http://dx.doi.org/10.1016/S0167-2789(99)00129-3
[10] Nestler, B., Wendler, F. and Selzer, M. (2008) Phase-Field Model for Multiphase Systems with Preserved Volume Fractions. Physical Review E, 78, Article ID: 011604.
http://dx.doi.org/10.1103/physreve.78.011604

  
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