A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Edmiston, John; Steigmann, David J.; Johnson, George C.; Barton, Nathan R.

doi:10.1016/j.ijengsci.2012.10.001

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…As the authors demonstrate, inclusion of DDT in the yield function introduces an additional length-scale into the macroscopic theory. Using this length-scale as a parameter, [38] have shown the formation of dislocation microstructures with spatially localized DDT similar to our work. For similar structures, the value of the length-scale in the theory are also similar to the range of intermediate asymptotic length scales that we estimated are needed to obtain a field description of the DDT from the DD simulations.…”

Section: Discussionsupporting

confidence: 83%

“…Such models form alternatives to the crystal-plasticity formulations based on active slip systems. For example, [38] include the DDT in the yield function, and develop a rate-independent macroscopic theory based on material symmetry. As the authors demonstrate, inclusion of DDT in the yield function introduces an additional length-scale into the macroscopic theory.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, a direct comparison of the dislocation density tensor field (DDT) resulting from the evolution of the dislocation distribution in the case of DD and from the plastic deformation in the case of CP has not been considered thus far. However, the inclusion of the DDT as an independent field or a parameter in the flow rules and yield criteria of single-crystal plasticity models has been explored, see [30][31][32][33][34][35], and can be used to model length-scale effects [36,37], predict different dislocation microstructures [38], and allows comparison with EBSD and X-ray micro-diffraction data [39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

Jones

Zimmerman

2016

JMSR

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The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused on the system-level material response that use DD-generated information to enhance the fidelity of plasticity models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity flow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density tensor fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations, we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Our results show that, for the case of torsion, the two material models can produce comparable spatial dislocation density distributions.

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Section: Discussionsupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

Jones

Zimmerman

2016

JMSR

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“…The introduction in that recent paper provides an extensive bibliography of such research, and the substantial analysis in two dimensions provided there is based in part on the availability of an infinite family of energy wells (as was the case in [1] and [2]) and on the requirement of frame-indifference, ingredients that will enter into a future analysis of yielding, hysteresis, and dissipation, based on the results on energetics of structured deformations in the present paper. Another recent article [14] provides a critical review of an essential element of "physically based" plasticity theories and gives an alternative approach to conventional treatments.…”

Section: Spatial Localizationmentioning

confidence: 99%

Upscaling and spatial localization of non-local energies with applications to crystal plasticity

Matías

Morandotti

Owen

et al. 2020

Mathematics and Mechanics of Solids

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We describe multiscale geometrical changes via structured deformations [Formula: see text] and the non-local energetic response at a point x via a function [Formula: see text] of the weighted averages of the jumps [Formula: see text] of microlevel deformations [Formula: see text] at points y within a distance r of x. The deformations [Formula: see text] are chosen so that [Formula: see text] and [Formula: see text]. We provide conditions on [Formula: see text] under which the upscaling “[Formula: see text]” results in a macroscale energy that depends through [Formula: see text] on (1) the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text], (2) the “horizon” r, and (3) the weighting function [Formula: see text] for microlevel averaging of [Formula: see text]. We also study the upscaling “[Formula: see text]” followed by spatial localization “[Formula: see text]” and show that this succession of processes results in a purely local macroscale energy [Formula: see text] that depends through [Formula: see text] upon the jumps [Formula: see text] of g and the “disarrangement field”[Formula: see text] alone. In special settings, such macroscale energies [Formula: see text] have been shown to support the phenomena of yielding and hysteresis, and our results provide a broader setting for studying such yielding and hysteresis. As an illustration, we apply our results in the context of the plasticity of single crystals.

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“…To derive a simple relation for plastic spin under the cubic symmetry group it is assumed that Ω is independent of α. It is also required, based on phenomenological considerations, that Ω is an odd function of S. The simplest representation of Ω is a third order polynomial in S given by [9]…”

Section: Wmentioning

confidence: 99%

Plane strain problem in elastically rigid finite plasticity

Gupta¹,

Steigmann²

2014

The Quarterly Journal of Mechanics and Applied Mathematics

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A theory of elastically rigid finite deformation plasticity emphasizing the role of material symmetry is developed. The fields describing lattice rotation, dislocation density, and plastic spin, irrelevant in the case of isotropy, are found to be central to the present framework. A plane strain characteristic theory for anisotropic plasticity is formulated wherein the solutions, as well as the nature of their discontinuities, show remarkable deviation from the classical isotropic slipline theory.

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A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Cited by 10 publications

References 26 publications

Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

Comparison of Dislocation Density Tensor Fields Derived from Discrete Dislocation Dynamics and Crystal Plasticity Simulations of Torsion

Upscaling and spatial localization of non-local energies with applications to crystal plasticity

Plane strain problem in elastically rigid finite plasticity

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