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Phase Field Method to the Interaction of Phase Transformations and Dislocations at Nanoscale | ||
| AUT Journal of Mechanical Engineering | ||
| مقاله 12، دوره 1، شماره 2، اسفند 2017، صفحه 243-246 اصل مقاله (676.23 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2017.11892.5209 | ||
| نویسندگان | ||
| M. Javanbakht* 1؛ V. I. Levitas2 | ||
| 1Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran | ||
| 2Iowa State University, Departments of Mechanical and Aerospace Engineering, Ames, IA, USA | ||
| چکیده | ||
| In this paper, a new phase field method for the interaction between martensitic phase transformations and dislocations is presented which is a nontrivial combination of the most advanced phase field methods to phase transformations and dislocation evolution. Some of the important points in the model are the multiplicative decomposition of deformation gradient into elastic, transformational and plastic parts, defining a proper energy to satisfy thermodynamic equilibrium and instability conditions, including phase-dependent properties of dislocations. The system of equations consists of coupled elasticity and phase field equations of phase transformations and dislocations. Finite element method is used to solve the system of equations and applied to study the growth and arrest of martensitic plate and the evolution of dislocations and phase in a nanograined material. It is found that dislocations play a key role in eliminating the driving force of the plate growth and their arrest which creates athermal friction. Also, the dual effect of plasticity on phase transformations is revealed; due to dislocations pile-up and its stress concentration, the phase transformation driving force increases and consequently, martensitic nucleation occurs. On the other hand, the dislocation nucleation results in decreasing the phase transformation driving force and consequently, the phase transformation is suppressed. | ||
تازه های تحقیق | ||
[1] F. D. Fischer, G. Reisner, E. Werner, K. Tanaka, G. Cailletaud, T. Antretter, A new view on transformation induced plasticity (TRIP), Int J Plast, 16 (2000) 723-748. [2] V. I. Levitas, Continuum mechanical fundamentals of mechanochemistry, In: Ed. Y. Gogotsi and V. Domnich, High Pressure Surface Science and Engineering. Section 3, Institute of Physics Publishing, 159-292, 2004. [3] V. I. Levitas, High-pressure mechanochemistry: conceptual multiscale theory and interpretation of experiments, Phys Rev B, 70 (2004) 184118. [4] G. B. Olson, M. Cohen, Dislocation theory of martensitic transformations, In: Ed. F R N. Nabarro, Dislocations in solids, Amsterdam, North-Holland, 297-407, 1998. [5] V. I. Levitas, Structural changes without stable intermediate state in inelastic material. Parts I and II, Int. J. Plast, 16 (2000) 805-849 and 851-892. [6] A. V. Idesman, V. I. Levitas, E. Stein, Structural changes in elastoplastic materials: a unified finite element approach for phase transformation, twinning and fracture, Int. J. Plast, 16 (2008) 893-949. [7] Y. Wang, A. G. Khachaturyan, Multi-scale phase field approach to martensitic transformations, Mater Sci Eng A, 438&440 (2006) 55-63. [8] J. Kundin, D. Raabe, H. Emmerich, A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite, J Mech Phys Solids, 59 (2011) 2082-2102. [9] V. I. Levitas, M. Javanbakht, Advanced phase field approach to dislocation evolution, Phys Rev B, 86 (2012) 140101. [10] V. I. Levitas, Phase-field theory for martensitic phase transformations at large strains, Int J Plast, 49 (2013) 85- 118. [11] V. I. Levitas, M. Javanbakht, Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms, Nanoscale, 6 (2014) 162- 166. [12] V. I. Levitas, M. Javanbakht, Phase field approach to interaction of phase transformation and dislocation evolution, Appl Phys Lett, 102 (2013) 251904. [13] Y. U. Wang, Y. M. Jin, A. M. Cuitino, A. G. Khachaturyan, Application of phase field microelasticity theory of phase transformations to dislocation dynamics: model and three-dimensional simulations in a single crystal, Philos Mag, 81 (2001) 385-393. [14] V. I. Levitas, M. Javanbakht, Surface tension and energy in multivariant martensitic transformations: phase-field theory, simulations, and model of coherent interface, Phys Rev Lett, 105 (2011) 165701. [15] V. I. Levitas, M. Javanbakht, Phase-field approach to martensitic phase transformations: effect of martensite-martensite interface energy, Int J Mat Res, 102 (2011) 652-665. [16] V. I. Levitas, Phase field approach to martensitic phase transformations with large strains and interface stresses, J. Mech Phys Solids, 70 (2014) 154-189. [17] V. I. Levitas, M. Javanbakht, Surface-induced phase transformations: multiple scale and mechanics effects and morphological transitions, Phys Rev Lett, 107 (2011) 175701. [18] M. Javanbakht, V. I. Levitas, Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples, J Mech Phys Solids, 82 (2015) 164-185. | ||
| کلیدواژهها | ||
| Phase field؛ Interaction؛ Phase transformations؛ Dislocations؛ Nanoscale | ||
| مراجع | ||
|
[1] F. D. Fischer, G. Reisner, E. Werner, K. Tanaka, G. Cailletaud, T. Antretter, A new view on transformation induced plasticity (TRIP), Int J Plast, 16 (2000) 723-748.
[2] V. I. Levitas, Continuum mechanical fundamentals of mechanochemistry, In: Ed. Y. Gogotsi and V. Domnich, High Pressure Surface Science and Engineering. Section 3, Institute of Physics Publishing, 159-292, 2004.
[3] V. I. Levitas, High-pressure mechanochemistry: conceptual multiscale theory and interpretation of experiments, Phys Rev B, 70 (2004) 184118.
[4] G. B. Olson, M. Cohen, Dislocation theory of martensitic transformations, In: Ed. F R N. Nabarro, Dislocations in solids, Amsterdam, North-Holland, 297-407, 1998.
[5] V. I. Levitas, Structural changes without stable intermediate state in inelastic material. Parts I and II, Int. J. Plast, 16 (2000) 805-849 and 851-892.
[6] A. V. Idesman, V. I. Levitas, E. Stein, Structural changes in elastoplastic materials: a unified finite element approach for phase transformation, twinning and fracture, Int. J. Plast, 16 (2008) 893-949.
[7] Y. Wang, A. G. Khachaturyan, Multi-scale phase field approach to martensitic transformations, Mater Sci Eng A, 438&440 (2006) 55-63.
[8] J. Kundin, D. Raabe, H. Emmerich, A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite, J Mech Phys Solids, 59 (2011) 2082-2102.
[9] V. I. Levitas, M. Javanbakht, Advanced phase field approach to dislocation evolution, Phys Rev B, 86 (2012) 140101.
[10] V. I. Levitas, Phase-field theory for martensitic phase transformations at large strains, Int J Plast, 49 (2013) 85- 118.
[11] V. I. Levitas, M. Javanbakht, Phase transformations in nanograin materials under high pressure and plastic shear: nanoscale mechanisms, Nanoscale, 6 (2014) 162- 166.
[12] V. I. Levitas, M. Javanbakht, Phase field approach to interaction of phase transformation and dislocation evolution, Appl Phys Lett, 102 (2013) 251904.
[13] Y. U. Wang, Y. M. Jin, A. M. Cuitino, A. G. Khachaturyan, Application of phase field microelasticity theory of phase transformations to dislocation dynamics: model and three-dimensional simulations in a single crystal, Philos Mag, 81 (2001) 385-393.
[14] V. I. Levitas, M. Javanbakht, Surface tension and energy in multivariant martensitic transformations: phase-field theory, simulations, and model of coherent interface, Phys Rev Lett, 105 (2011) 165701.
[15] V. I. Levitas, M. Javanbakht, Phase-field approach to martensitic phase transformations: effect of martensite-martensite interface energy, Int J Mat Res, 102 (2011) 652-665.
[16] V. I. Levitas, Phase field approach to martensitic phase transformations with large strains and interface stresses, J. Mech Phys Solids, 70 (2014) 154-189.
[17] V. I. Levitas, M. Javanbakht, Surface-induced phase transformations: multiple scale and mechanics effects and morphological transitions, Phys Rev Lett, 107 (2011) 175701.
[18] M. Javanbakht, V. I. Levitas, Interaction between phase transformations and dislocations at the nanoscale. Part 2: Phase field simulation examples, J Mech Phys Solids, 82 (2015) 164-185. | ||
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