Driving forces and boundary conditions in continuum dislocation mechanics

Acharya, Amit

doi:10.1098/rspa.2002.1095

Cited by 97 publications

(145 citation statements)

References 21 publications

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“…In contrast, in our work the rate of plastic distortion arises from an averaging of a fine scale theory (FDM) that incorporates the elastic theory of dislocations exactly; as for kinetics, some of the simplest realizations of the equation for dislocation density-evolution in FDM have been shown (Acharya 2003;Varadhan et al 2005) to lead to Hamilton-Jacobi equations for propagation of fronts, whose solutions can be interpreted as expansions of loops from Frank-Read sources allowing automatic annihilation.…”

Section: Introductionmentioning

confidence: 99%

“…This paper and its sequel provide a detailed account of this development and its predictions. A feature of our model that may be considered a desirable consistency property is that when the spatial averaging length scale tends to zero, our model reduces to a theory of the collective behavior of individual dislocations -applicable to finite bodies of arbitrary shape, and conveniently adapted for geometric, crystal elastic and dissipative nonlinearities as well as the effects of inertia -that can be exercised to probe mechanical behavior at the nanoscale and above, with emerging predictions representative of such (Acharya, 2001(Acharya, , 2003(Acharya, , 2004Miller and Acharya, 2004;Roy and Acharya, 2005;Varadhan et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

“…This feature is not preserved by the technique mentioned in the first line of this paragraph, borrowed from conventional plasticity. Moreover, accommodating ECDD within a nonequilibrium theory of plasticity takes some care (Acharya, 2003), especially in the finite deformation setting (Acharya, 2004).…”

Section: Introductionmentioning

confidence: 99%

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Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

Acharya¹,

Roy²

2006

Journal of the Mechanics and Physics of Solids

161

176

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A Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM) model is developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. PMFDM results from an elementary space-time averaging of the equations of Field Dislocation Mechanics (FDM), followed by a closure assumption from any strain-gradient plasticity model that attempts to model effects of geometricallynecessary dislocations (GND) only in work-hardening. The specific lower-order gradient plasticity model chosen to substantiate this work requires one additional material parameter compared to its conventional continuum plasticity counterpart. The further addition of dislocation mechanics requires no additional material parameters. The model a) retains the constitutive dependence of the free-energy only on elastic strain as in conventional continuum plasticity with no explicit dependence on dislocation density, b) does not require higher-order stresses, and c) does not require a constitutive specification of a 'back-stress' in the expression for average dislocation velocity/plastic strain rate. However, long-range stress effects of average dislocation distributions are predicted by the model in a mechanistically rigorous sense. Plausible boundary conditions (with obvious implication for corresponding interface conditions) are discussed in some detail from a physical point of view. Energetic and dissipative aspects of the model are also discussed. The developed framework is a continuous-time model of averaged dislocation plasticity, without having to rely on the notion of incremental work functions, their convexity properties, or their minimization. The tangent modulus relating stress rate and total strain rate in the model is the positive-definite tensor of linear elasticity, and this is not an impediment to the development of idealized microstructure in the theory and computations, even when such a convexity property is preserved in a computational scheme. A model of finite deformation, mesoscopic single crystal plasticity is also presented, motivated by the above considerations.Lower-order gradient plasticity appears as a constitutive limit of PMFDM, and the development suggests a plausible boundary condition on the plastic strain rate for this limit that is appropriate for the modeling of constrained plastic flow in three-dimensional situations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

Acharya¹,

Roy²

2006

Journal of the Mechanics and Physics of Solids

161

176

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“…In the 2003 research summary for this project, we reported on the development of a computational model for a dislocation mechanics based theory of plasticity building on earlier work (Acharya, 2001(Acharya, , 2003(Acharya, , 2004aRoy & Acharya, 2004). This model has been shown to make good predictions of 1. size effect 2. development of microstructure from homogeneous initial conditions under boundary conditions for homogeneous deformation in the conventional theory 3. development of a strong Bauschinger effect.…”

Section: Scope Of Workmentioning

confidence: 99%

NIAI Superalloy Modeling Based on Combined Dislocation Mechanics and Phenomenological Plasticity

Acharya¹

2005

Self Cite

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“…Current effort is directed at a parallel implementation of the Field Dislocation Mechanics framework, posed by Acharya [22][23][24][25] . Along with parallel codes for the incompatibility and equilibrium problems, an explicit (Galerkin-Least Squares) technique has been developed for the transport of excess dislocation density.…”

Section: B Amentioning

confidence: 99%

Determining the mechanical constitutive properties of metals as a function of strain rate and temperature: A combined experimental and modeling approach; Progress Report for 2004

Robertson¹,

Beaudoin²,

Lambros³

2005

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Determining the mechanical constitutive properties of metals as a function of strain rate and temperature: A combined experimental and modeling approach Progress report for 2004Development and validation of constitutive models for polycrystalline materials subjected to high strain rate loading over a range of temperatures are needed to predict the response of engineering materials to in-service type conditions (foreign object damage, high-strain rate forging, high-speed sheet forming, deformation behavior during forming, response to extreme conditions, etc.). To account accurately for the complex effects that can occur during extreme and variable loading conditions, requires significant and detailed computational and modeling efforts. These efforts must be closely coupled with precise and targeted experimental measurements that not only verify the predictions of the models, but also provide input about the fundamental processes responsible for the macroscopic response. Achieving this coupling between modeling and experimentation is the guiding principle of this program. Specifically, this program seeks to bridge the length scale between discrete dislocation interactions with grain boundaries and continuum models for polycrystalline plasticity. Achieving this goal requires incorporating these complex dislocation-interface interactions into the well-defined behavior of single crystals. Despite the widespread study of metal plasticity, this aspect is not well understood for simple loading conditions, let alone extreme ones. Our experimental approach includes determining the high-strain rate response as a function of strain and temperature with post-mortem characterization of the microstructure, quasi-static testing of predeformed material, and direct observation of the dislocation behavior during reloading by using the in situ transmission electron microscope deformation technique. These experiments will provide the basis for development and validation of physically-based constitutive models, which will include dislocation-grain boundary interactions for polycrystalline systems. One aspect of the program will involve the direct observation of specific mechanisms of micro-plasticity, as these will indicate the boundary value problem that should be addressed. This focus on the pre-yield region in the quasi-static effort (the elasto-plastic transition) is also a tractable one from an experimental and modeling viewpoint. In addition, our approach will minimize the need to fit model parameters to experimental data to obtain convergence. These are critical steps to reach the primary objective of simulating and modeling material performance under extreme loading conditions. To achieve these goals required assembling a multidisciplinary team, see Table 1, with key collaborators at the National Laboratories. One of the major issues for the team members was to learn about the expertise available and how to communicate across disciplines. The communication issue is a challenging one and is being addressed in part with weekly ...

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Driving forces and boundary conditions in continuum dislocation mechanics

Cited by 97 publications

References 21 publications

Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

NIAI Superalloy Modeling Based on Combined Dislocation Mechanics and Phenomenological Plasticity

Determining the mechanical constitutive properties of metals as a function of strain rate and temperature: A combined experimental and modeling approach; Progress Report for 2004

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