A continuum model of grain boundaries

Kobayashi, Ryo; Warren, James A.; Carter, W. Craig

doi:10.1016/s0167-2789(00)00023-3

Cited by 339 publications

(317 citation statements)

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“…Non-quadratic potentials are seldom in the phase field community. Examples can be found for the modelling of grain boundary migration and recrystallization [51,52]. Such nonlinear relations between generalized stresses and gradient terms lead to fundamentally new kinds of differential operators whose properties are essentially unknown.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

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Section: Introductionmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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“…There are different methods that are used for the modeling of the microstructure evolution, and among of them are the cellular automata (CA) models, 1) Monte Carlo Potts models, 2) the finite element method (FEM) based models, 3) the phase field models, 4,5) the front tracking method 6,7) and the vertex models.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Microstructure Evolution during Shape Rolling with the Use of Frontal Cellular Automata

Svyetlichnyy

2012

ISIJ Int.

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The objective of the paper is an application of the model of the microstructure evolution based on three-dimensional cellular automata (CA) for hot shape rolling simulation. A short description of frontal cellular automata (FCA) is presented. The model contains two parts: the deformation and the microstructure evolution. The CA cells do not remain as undistorted cubes, but they are deformed according to the strain tensor. The independence of the grain growing from the shape and the sizes of the cell is ensured by the so-called "virtual front tracking". The microstructural part of the model simulates two phenomena: the nucleation and the growth of nuclei. There are three issues considered in the paper: the creation of the initial microstructure, the recrystallization and the phase transformation. When recrystallization is simulated, the nucleation and the grain boundary migration depend on the deformation parameters such as: the temperature, the strain, the strain rate, the dislocation density and the crystallographic orientation. The nucleation during the phase transformation is a function of the cooling rate and the final microstructure. These phenomena along with the deformation can be modeled over a wide range of multi-stage deformation processes. The process of shape rolling is chosen as an example. The data needed for the FCA calculations is received from the modeling by the finite element method. The results of the simulation of the microstructure evolution, during the last three passes of the round bars rolling with the consequent phase transformation, are presented in the paper.

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“…Alternatively, local orientation is described by a single parameter whose value may assume a continuous range of orientations. For 2D problems, orientation can be described by a single angle, as developed in [15,16]. This technique was used, e.g., in [17] to simulate austenite to ferrite phase transformation in 2D.…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm for the solution of a phase-field model of polycrystalline materials

Dorr

Fattebert

Wickett

et al. 2010

Journal of Computational Physics

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We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.Key words: Phase-field model, polycrystalline microstructure, method of lines, Newton-Krylov methods 1991 MSC: 35Q99, 65F10, 65H10, 65M06, 65M12, 65M20, 65Z05 * Corresponding author.Email addresses: dorr1@llnl.gov (M. R. Dorr ), fattebert1@llnl.gov (J.-L. Fattebert ), wickett1@llnl.gov (M. E. Wickett ), belak1@llnl.gov (J. F. Belak ), turchi1@llnl.gov (P. E. A. Turchi ).

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A continuum model of grain boundaries

Cited by 339 publications

References 14 publications

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Simulation of Microstructure Evolution during Shape Rolling with the Use of Frontal Cellular Automata

A numerical algorithm for the solution of a phase-field model of polycrystalline materials

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