A crystal plasticity model that incorporates stresses and strains due to slip gradients

Gerken, Jobie M.; Dawson, Paul R.

doi:10.1016/j.jmps.2007.07.012

Cited by 53 publications

(44 citation statements)

References 83 publications

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“…Several researchers pursuing nonlocal continuum theories of crystal plasticity use a plane strain solution assuming isotropic elasticity for the stress field surrounding the Volterra dislocation to compute either the internal stress field or a slip-system associated back stress (Evers et al, 2004a,b;Yefimov and van der Giessen, 2005a;Bayley et al, 2006;Geers et al, 2007;Gerken and Dawson, 2008;Hirschberger et al, 2011;Liu et al, 2011;Leung et al, 2015;Schulz et al, 2014). Leung et al (2015), incorporate a physical representation of the long-range internal stress by generalizing relations for the elastic interaction force between two dislocations from Hirth and Lothe (1982).…”

Section: Introductionmentioning

confidence: 99%

Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

Luscher

Mayeur

Mourad

et al. 2016

International Journal of Plasticity

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Please cite this article as: Luscher, D.J., Mayeur, J.R., Mourad, H.M., Hunter, A., Kenamond, M.A., Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions AbstractWe have developed a multi-physics modeling approach that couples continuum dislocation transport, nonlinear thermoelasticity, crystal plasticity, and consistent internal stress and deformation fields to simulate the single-crystal response of materials under extreme dynamic conditions. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. Nonlinear thermoelasticity provides a thermodynamically consistent equation of state to relate stress (including pressure), temperature, energy densities, and dissipation. Crystal plasticity is coupled to dislocation transport via Orowan's expression where the constitutive description makes use of recent advances in dislocation velocity theories applicable under extreme loading conditions. The configuration of geometrically necessary dislocation density gives rise to an internal stress field that can either inhibit or accentuate the flow of dislocations. An internal strain field associated with the internal stress field contributes to the kinematic decomposition of the overall deformation. The paper describes each theoretical component of the framework, key aspects of the constitutive theory, and some details of a one-dimensional implementation. Results from single-crystal copper plate impact simulations are discussed in order to highlight the role of dislocation transport and pile-up in shock loading regimes. The main conclusions of the paper reinforce the utility of the modeling approach to shock problems.

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Section: Introductionmentioning

confidence: 99%

Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

Luscher

Mayeur

Mourad

et al. 2016

International Journal of Plasticity

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“…It was used to study localization in smooth and notched cylindrical tensile specimens [13][14][15][16], tensile specimens with rectangular cross-section [17], plane-strain tension [18] and metal sheets [19,20]. It was also used to study the influence of more advanced material models, like strain gradient plasticity, on the necking phenomenon [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Simulation of large-strain behaviour of aluminium alloy under tensile loading using anisotropic plasticity models

Khadyko¹,

Dumoulin²,

Hopperstad³

2015

Computers & Structures

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Cylindrical smooth and notched AA6060 samples were tested in tension. The material was either cast and homogenized or extruded with strong cube texture. The textured specimens demonstrated unusual shapes of the fracture surface that deviated from elliptical and were more rectangular in shape. A phenomenological plasticity model was used in finite element simulations of the tensile tests, together with a crystal plasticity model. The phenomenological plasticity model could not reproduce the evolution of the cross-section of the specimens made from the textured material. The crystal plasticity finite element model on the other hand demonstrated behaviour closer to the experiments.

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“…Actually, the back stress, Part II in Eq. (58), will also induce elastic distortion of lattice, which has already been computed by Gerken and Dawson [30]. This lattice deformation will be relieved as the disappearance of this elastic incompatibility.…”

Section: Discussionmentioning

confidence: 61%

“…slip system 2, in the calculations. According to microscopic balance equations (30) and (31), we have the following equations…”

Section: Tension Stress-strain Relationshipmentioning

confidence: 99%

“…By introducing the defect energy into the work-conjugate strain gradient plasticity theories, a back stress corresponding to the defect-energy can be derived as a function of strain gradient. In this type of theory, the influence of strain gradient on flow stress is represented by a back stress hardening model [27][28][29][30][31]. This model has been successfully applied to the explanation of size effect and boundary layer in constraint plastic flow problems [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

et al. 2011

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The Bauschinger and size effects in the thinfilm plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the workconjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defectenergy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

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A crystal plasticity model that incorporates stresses and strains due to slip gradients

Cited by 53 publications

References 83 publications

Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions

Simulation of large-strain behaviour of aluminium alloy under tensile loading using anisotropic plasticity models

Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

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