Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation

Levitas, Valery I.; Ozsoy, Istemi B.

doi:10.1016/j.ijplas.2008.02.004

Cited by 105 publications

(47 citation statements)

References 47 publications

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“…In this paper we will focus on martensitic or diffusionless transformations (Ahluwalia et al, 2003;Artemev et al, 2001;Curnoe and Jacobs, 2001a,b;Jacobs et al, 2003;Jin et al, 2001;Levitas and Preston, 2002a,b;Levitas et al, 2003;Levitas and Lee, 2007;Lookman et al, 2003a,b;Rasmussen et al, 2001;Seol et al, 2003;Shenoy et al, 1999;Wang et al, 2001). Deformation of the crystal lattice of the austenite, A, the high-temperature phase, into the martensite, M, the low temperature phase, can be described by the transformation strain tensor e t (also called the Bain strain or spontaneous strain).…”

Section: Introductionmentioning

confidence: 99%

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Levitas

Lee

Preston

2010

International Journal of Plasticity

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140

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Section: Introductionmentioning

confidence: 99%

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Levitas

Lee

Preston

2010

International Journal of Plasticity

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140

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“…It also can be included for melting within grain boundaries [77] and at the interfaces between two solid phases [76,[78][79][80][81]. Note that reorientation of an interface may occur due to applied stresses and corresponding thermodynamic driving force is found in [82,83]. In PFA, such a reorientation will occur automatically.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses

Levitas

Warren

2015

Phys. Rev. B

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The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e., gradient energy) is an anisotropic function of the gradient of the order parameters in the current (deformed) state, which yields a nonsymmetric Cauchy stress tensor. This violates two fundamental principles: the angular momentum equation and the principle of material objectivity.Here, it is justified that for a noncontradictory theory the gradient energy must be an isotropic function of the gradient of the order parameters in the current state, which also depends anisotropically on the direction of the gradient of the order parameters in the reference state. A complete system of thermodynamically consistent equations is presented. We find that the main contribution to the Ginzburg-Landau equation resulting from small strains arises from the anisotropy of the interface energy, which was neglected before. The explicit expression for the free energy is justified.An analytical solution for the nonequilibrium interface and critical nucleus has been found and a parametric study is performed for orientation dependence of the interface energy and width as well as the distribution of interface stresses.2

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“…Upon exploiting the evolution equations (13) the consistency conditions (25) are rewritten in matrix representation as…”

Section: Consistency Conditions and Lagrangian Multipliersmentioning

confidence: 99%

“…Antretter et al [4], Idesman et al [17], Fischer et al [8,10], Leblond [23], Mahnken et al [30], Wolff et al [50], Wolff et al [51], Hallberg et al [15], amongst others. Considering micromechanical or multi-scale modeling we refer to Fischer and Reisner [10], Levitas and Ozsoy [25,26], Suiker and Turteltaub [43], Turteltaub and Suiker [46], Kouznetsova and Geers [22], Jacques et al [19], amongst others.…”

Section: Introductionmentioning

confidence: 99%

A thermodynamics framework and numerical aspects for transformation-induced plasticity at large strains

Mahnken

Schneidt

2009

Arch Appl Mech

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In this work, we present a macroscopic material model for simulation transformation-induced plasticity, which is an important phenomenon in metal forming processes. The model is formulated within a thermodynamic framework at large strains. In order to account for both, phase transformation and plasticity, yield functions are related to these effects. Then, applying the concept of maximum dissipation evolution equations are obtained for the inelastic strains, the transformation strains, a hardening variable and the volume fraction of martensite. Furthermore the numerical implementation of the constitutive equations into a finite element program is described. In a numerical example we investigate the austenite-to-martensite phase transformation in a shaft subjected to thermo-mechanical loading in a hybrid-forming process.

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Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation

Cited by 105 publications

References 47 publications

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses

A thermodynamics framework and numerical aspects for transformation-induced plasticity at large strains

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