A phase-field model of twinning and detwinning coupled with dislocation-based crystal plasticity for HCP metals

Kondo, Ruho; Tadano, Yuichi; Shizawa, Kazuyuki

doi:10.1016/j.commatsci.2014.08.034

Cited by 59 publications

(23 citation statements)

References 46 publications

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“…In this article, we extend the previous studies of the twinning phase field coupled with elasticity, 18 single crystal plasticity, 20 and polycrystal plasticity 21 . More specifically, Lie algebra is utilized to interpolate the Schmid tensor within the phase field interfacial region to avoid introducing an additional set of slip systems for the dislocation slip within the twinning region.…”

Section: Introductionmentioning

confidence: 90%

“…It is also proved that the coupled free energy may not be convex, such that multiple local minima may exist and the initial guess is crucial in predicting the phase field evolution. Based on these preliminary studies, the twinning phase field is also coupled with crystal plasticity for single crystal 20 and polycrystal. 21 In these aforementioned models, an additional set of slip systems is introduced to characterize the dislocation slip within the twinning region, which may increase the computational cost during the stress update algorithm.…”

Section: Models For Deformation Twinningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

Sun

2020

Numerical Meth Engineering

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For some polycrystalline materials such as austenitic stainless steel, magnesium, TATB, and HMX, twinning is a crucial deformation mechanism when the dislocation slip alone is not enough to accommodate the applied strain. To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solvers that couple the crystal plasticity material model with a phase field twining model such that the twinning nucleation and propagation can be captured via an implicit function. While a phase field order parameter is introduced to quantify the twinning induced shear strain and corresponding crystal reorientation, the evolution of the order parameter is driven by the resolved shear stress on the twinning system. To avoid introducing an additional set of slip systems for dislocation slip within the twinning region, we introduce a Lie algebra averaging technique to determine the Schmid tensor throughout the twinning transformation. Three different numerical schemes are proposed to solve the coupled problem, including a monolithic scheme, an alternating minimization scheme, and an operator splitting scheme. Three numerical examples are utilized to demonstrate the capability of the proposed model, as well as the accuracy and computational cost of the solvers.

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Section: Introductionmentioning

confidence: 90%

Section: Models For Deformation Twinningmentioning

confidence: 99%

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Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

Sun

2020

Numerical Meth Engineering

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“…Since the direction of this isochoric inelastic deformation is purely that for twisting, and not extension/compression in axial and radial directions, the inelastic kinematic description physically corresponds to a plastically anisotropic material with a restricted set of glide or twin systems or one in which slip in certain directions is much easier than slip in other directions, for example molecular crystals with few system(s) [78], twinning in low-symmetry crystals [76], or basal slip in hexagonal crystals [79,80]. A similar prescription of torsional plastic distortion was used in a dislocation-based model of deforming single crystal rods [43].…”

Section: -26mentioning

confidence: 99%

Generalized pseudo-Finsler geometry applied to the nonlinear mechanics of torsion of crystalline solids

Clayton

2018

Int. J. Geom. Methods Mod. Phys.

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A continuum theory of the mechanical behavior of solid materials is presented wherein fundamental geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. This theory, referred to as generalized pseudo-Finsler geometric continuum mechanics, enables depiction of a very broad class of physical phenomena in deformable solid bodies. The general nonlinear theory is reported first, primarily summarizing prior work by the author. Next, a new application of the theory to torsional deformation of solids is presented, whereby a cylindrical sample of material may be simultaneously subjected to twisting, extension or compression along its axis, as well as possible radial confinement or contraction. The internal state variable, when normalized by a regularization length, is identified with an order parameter associated with inelastic deformation that may include slippage, fracture, and/or structural collapse. Evolution of the internal state follows a generalized Ginzburg–Landau type of kinetic equation. For axially homogeneous fields, a coupled system of nonlinear partial differential equations is obtained that can be integrated numerically. Results are first documented for generic solids representative of many crystals that exist in nature. Then solutions corresponding to realistic properties of crystals of boron carbide ceramic and ice are reported. Results for boron carbide predict a dominant effect of shearing over compression on the structural transformation process, in agreement with observations from atomistic simulations. Results for ice demonstrate periods of steady plastic flow under constant applied average shear stress as well as torsional rigidity varying with sample size. Existence of both phenomena agrees with experimental observations.

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“…Among them, dislocation-based crystal plasticity theory classified into continuum mechanics is preferable for reproducing actual phenomena because it can easily handle the spatial and time scales. The authors (Kondo et al, 2014) proposed a multi-physics model combining a phase-field model for twinning evolution in α-Mg with a dislocation-based crystal plasticity model for the deformation of HCP crystal, and an FE analysis was performed.…”

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confidence: 99%

Crystal plasticity FE simulation for kink band formation in Mg-based LPSO phase using dislocation-based higher-order stress model

Kimura

Ueta

Shizawa

2020

Mechanical Engineering Journal

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One way to reduce greenhouse gas emissions is by decreasing the energy of transportation equipment such as aircrafts and automobiles, so that it is necessary to develop light and strong structural materials. Since magnesium (Mg) is the lightest metal, the research and development of Mg and its alloys have been widely conducted in recent years. In particular, magnesium alloys with a long-period stacking ordered (LPSO) phase have excellent properties such as a light weight, high strength (Hagihara et al., 2010)(Inoue et al., 2001) and high incombustibility (Inoue et al., 2019), raising expectations for their practical use. Moreover, it has been clarified that the excellent mechanical properties of these alloys can be caused by kink deformation, which is also attracting attention as a new material-strengthening mechanism in the field of materials science. Kink deformation is a type of plastic buckling observed in a laminated structure, and a kink band is a deformation band such as a shear band or a twin. The LPSO phase has a structure in which a soft atomic layer of α-Mg and a rigid atomic layer with additional element clusters are laminated at the nanometer level. In a kink band of the LPSO phase, the basal plane of the hexagonal crystal is rotated with respect to the matrix above and below the kink band. Thus, the resulting kink band acts as a grain boundary in the dislocation motion of the basal slip system. This process is the mechanism of material strengthening originating from kink deformation. Kink deformation is modeled as the gliding of localized dislocations in the basal slip system, as proposed by Hess and Barrett (Orowan, 1942)(Hess and Barrett, 1949). When a material is compressed parallel to the basal slip plane of the basal slip system, so that resolved shear stress hardly occurs, the basal slip plane is locally inclined owing to the

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A phase-field model of twinning and detwinning coupled with dislocation-based crystal plasticity for HCP metals

Cited by 59 publications

References 46 publications

Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

Phase field modeling of coupled crystal plasticity and deformation twinning in polycrystals with monolithic and splitting solvers

Generalized pseudo-Finsler geometry applied to the nonlinear mechanics of torsion of crystalline solids

Crystal plasticity FE simulation for kink band formation in Mg-based LPSO phase using dislocation-based higher-order stress model

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