Dynamical Dislocation Theory of Crystal Plasticity. II. Easy Glide and Strain Hardening

Gillis, Peter P.; Gilman, John J.

doi:10.1063/1.1702999

Cited by 43 publications

(16 citation statements)

References 10 publications

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“…It is mentioned that although the form for v might not adequately describe the dislocation motion of all solid materials [13], it is desirable to develop a model that when integrated within a multi-dimensional framework is guaranteed not to exceed a saturation level in the event of over-stress. In the model for f, taken from [12], the exponent can be varied arbitrarily to accommodate the desired non-linearity, but here we restrict the range to 0 :S: n :S: 1 to conform with the requirement that the deformations asymptote to a maximum in the limit of finite strains Cp-+ oo. Note that an alternative approach to introducing a mechanism for strain hardening proposed in [12] is to take f = 1 and modify the characteristic drag stress to be some function of the plastic strain such that the dislocation velocity increases with increasing plastic strain.…”

Section: Closure Modelsmentioning

confidence: 99%

“…In the model for f, taken from [12], the exponent can be varied arbitrarily to accommodate the desired non-linearity, but here we restrict the range to 0 :S: n :S: 1 to conform with the requirement that the deformations asymptote to a maximum in the limit of finite strains Cp-+ oo. Note that an alternative approach to introducing a mechanism for strain hardening proposed in [12] is to take f = 1 and modify the characteristic drag stress to be some function of the plastic strain such that the dislocation velocity increases with increasing plastic strain. This approach is taken in [24] where it is suggested that non-linear hardening can be accounted for by assuming the drag stress is a polynomial of higher order: D = P(cp)· In fact both interpretations are equivalent and choosing either makes no difference to the final form of Eq.…”

Section: Closure Modelsmentioning

confidence: 99%

“…Thus constitutive models employ only continuum parameters such as invariants of stress and onedimensional plastic strain, yet reflect microscopic changes in response to macroscopic disturbances. Much of the dislocation theory is now well established and is attributed to the early efforts of Orowan [28], Taylor [32] and Gillis and Gilman [9][10][11][12]. It is this physically consistent theory that forms the basis of successful continuum plasticity models [35].…”

Section: Introductionmentioning

confidence: 99%

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On Computational Modelling Of Strain-Hardening Material Dynamics

Barton

Romenski

2012

Commun. comput. phys.

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Abstract. In this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strainhardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposed model within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

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Section: Closure Modelsmentioning

confidence: 99%

Section: Closure Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Computational Modelling Of Strain-Hardening Material Dynamics

Barton

Romenski

2012

Commun. comput. phys.

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“…Therefore, in order to close the model we require a equation of evolution for the dislocation densities. Processes resulting in changes in dislocation density include production by fixed sources, such as Frank-Read sources, breeding by double cross slip and pair annihilation (see [37] for a review; see also [38,39,40,41,42,43]). Although the operation of fixed FrankRead sources is quickly eclipsed by production due to cross slip at finite temperatures, it is an important mechanisms at low temperatures.…”

Section: Dislocation Evolution: Multiplication and Attritionmentioning

confidence: 99%

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Cuitiño

Stainier

Wang

et al. 2001

Journal of Computer-Aided Materials Design

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In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.

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“…Our analytical solution, in conjunction with Franciosi's relations, completely determines the hardening relations of the crystal in terms of the density of dislocations in all slip systems. To obtain a closed set of constitutive relations, we draw on the work of Gillis and Gilman (1965) and Essmann and Rapp (1973) to formulate the requisite equations of evolution for the dislocation densities as a function of slip activity.…”

Section: Introductionmentioning

confidence: 99%

Computational modelling of single crystals

Cuitiño

Ortiz

1993

Modelling Simul. Mater. Sci. Eng.

347

224

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Abstract. The physical basis of computationally uactable models of crystalline plasticity iS reviewed. A statistical mechanical model of dislocation motion throu@ forest dislocations is formulated. Following Franciosi and co-workers, the strength of lhe ShoR-range oblacles introduced by the forest dislocations is allowed to depend on the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading. with Vansienft in the densiry of fomt dislocations accounled for. This solution, coupled wilh svilable equations of evolution for the dislocation densities, provides a complete descripticn of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in CU single crys& illustrate the versatility of the m e t h o d .

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Dynamical Dislocation Theory of Crystal Plasticity. II. Easy Glide and Strain Hardening

Cited by 43 publications

References 10 publications

On Computational Modelling Of Strain-Hardening Material Dynamics

On Computational Modelling Of Strain-Hardening Material Dynamics

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Computational modelling of single crystals

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