Gradient single-crystal plasticity with free energy dependent on dislocation densities

Gurtin, Morton E.; Anand, Lallit; Lele, Suvrat P.

doi:10.1016/j.jmps.2007.02.006

Cited by 178 publications

(186 citation statements)

References 37 publications

(55 reference statements)

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“…At the same time, back stresses 3133) and additional dissipations due to the development of strain gradient or the evolution of plastic curvature and torsion 33,34) and other factors associated with GNDs will be important issues to be discussed. However, thorough discussions of these effects are beyond the objective of this study.…”

Section: )mentioning

confidence: 99%

Crystal Plasticity Analysis of Development of Intragranular Misorientations due to Kinking in HCP Single Crystals Subjected to Uniaxial Compressive Loading

et al. 2015

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The mechanism and the effective factors for the development of intragranular misorientations due to kinking is studied by a crystal plasticity finite element method. A single crystal with hexagonal close-packed (HCP) structure in which only basal slip system is activated is used as a model material. To activate basal slip system, the initial crystal orientations are set to be the ones whose basal planes are slightly deviated from the compressive direction. The result shows that basal slip and the development of intragranular misorientations are sometimes localized near the center of the specimen depending on the initial deviation angle, strain hardening rate, and strain rate sensitivity. The mechanism is discussed in terms of the nonuniform stress distribution and lattice rotation. The effect of slight changes in the boundary conditions shows significant effect on the positions of slip localization. In summary, the present numerical results suggest that there are a number of effective factors for the development of the intragranular misorientations due to kinking including initial crystal orientation, material parameters, and boundary conditions.

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Section: )mentioning

confidence: 99%

Crystal Plasticity Analysis of Development of Intragranular Misorientations due to Kinking in HCP Single Crystals Subjected to Uniaxial Compressive Loading

et al. 2015

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“…When the total misfit strain would be completely accommodated by plastic slip, the effective stresses in both phases would be similar and the misfit would effectively vanish. For the interface regions this is automatically ensured by the compatibility requirements, according to equation (5). Plastic deformation in one region causes a local stress redistribution across the two phases and a corresponding decrease of the misfit.…”

Section: Lattice Misfitmentioning

confidence: 99%

“…The existence of a strain gradient dependent back stress and its relevance for crystal plasticity of small components undergoing inhomogeneous plastic flow has been reported in several papers. The work of Gurtin and co-workers [2][3][4][5] is here emphasized in particular.…”

Section: Introductionmentioning

confidence: 99%

Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Tinga

Brekelmans

Geers

2008

Philosophical Magazine

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“…As an example of a gradient plasticity model for impenetrable GBs the set of equations in Table 1 is considered. The equations are very similar to those of Gurtin et al (2007). The microscopic counterpart of the classical traction vector t = σn is the microtraction Ξ = ξ · n. The classical linear momentum balance is supplemented by a microforce balance equation.…”

Section: Review Of Gradient Plasticity Models For Impenetrable Gbsmentioning

confidence: 96%

Micromechanical Simulation of the Hall‐Petch Effect with a Crystal Gradient Theory including a Grain Boundary Yield Criterion

Wulfinghoff

Bayerschen

Böhlke

2013

Proc Appl Math and Mech

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A viscoplastic strain gradient crystal plasticity theory based on the gradient of the equivalent plastic strain ∇γ eq is proposed. A grain boundary yield condition is introduced. The microstructural explanation of the Hall-Petch effect, accounting for notch-like stress concentrations at the grain boundary as a result of discrete slip bands, is reviewed. Periodic tensile test FEM simulation results illustrate the prediction of the numerical model. The requirements of modern products, like mechanical components for cars or airplanes, are demanding. Amongst other things they must be small, light-weight, robust and cheap. Therefore, a permanent product optimization is going on. This procedure demands high-performance materials and there is a significant industrial interest in material design and material development. The trend shows that material optimization as well as the design of new materials takes place. It is desired to develop materials by microstructural design. The preferred tool are simulations since these are often cheaper and faster than experiments. Additionally, the miniaturization trend requires micromechanical models for small systems. The problem is that these are often inadequate and/or computationally expensive material models. For example, they show weaknesses when size effects, interfaces or damage have to be modeled. Therefore, the focus of the contribution at hand is the modeling of metallic microstructures with interfaces (grain boundaries). This work is in accordance with [7]. The main new contribution constitutes details on the numerical solution based on a geometrical multigrid solver in combination with a locally refined mesh. This mesh has been obtained by deforming a perfectly cube shaped mesh. Effects to be ModeledThe effects to be modeled are the effects which determine the macroscopic behavior. As far as elastic anisotropy is concerned, excellent continuum models exist. The same holds for crystal plasticity dominated by forest hardening. The models for size effects (e.g. dislocation pile-ups) are limited. Extended research is going on in this field like in the region of grain boundaries. Here, we focus on pile-ups and grain boundaries. An external loading of a given grain aggregate provokes dislocation motion inside of the grains. The grain boundaries (GBs) represent obstacles for dislocation motion. One main reason is the grain misorientation. As a consequence, dislocations pile up at the GBs. Initially, the GBs are often assumed impenetrable for dislocations. When more and more dislocations pile up there is a certain break through: dislocations enter and leave the GB (the grain boundary yields). This effect is considered later. At first, a short review of gradient plasticity model for impenetrable GBs is given. Review of Gradient Plasticity Models for Impenetrable GBsFor simplicity a single slip setting at small strains is applied. As an example of a gradient plasticity model for impenetrable GBs the set of equations in Table 1 is considered. The equations are very similar to thos...

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Gradient single-crystal plasticity with free energy dependent on dislocation densities

Cited by 178 publications

References 37 publications

Crystal Plasticity Analysis of Development of Intragranular Misorientations due to Kinking in HCP Single Crystals Subjected to Uniaxial Compressive Loading

Crystal Plasticity Analysis of Development of Intragranular Misorientations due to Kinking in HCP Single Crystals Subjected to Uniaxial Compressive Loading

Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Micromechanical Simulation of the Hall‐Petch Effect with a Crystal Gradient Theory including a Grain Boundary Yield Criterion

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