The mechanics of deformation–induced subgrain–dislocation structures in metallic crystals at large strains

Aubry, Sylvie; Ortiz, Michael

doi:10.1098/rspa.2003.1179

Cited by 43 publications

(36 citation statements)

References 41 publications

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“…Finally, following [42,4] for simplicity we study the limiting case of crystals exhibiting infinitely strong latent hardening. We take this property to signify that the crystal must necessarily deform in single slip at all material points.…”

Section: Introductionmentioning

confidence: 99%

Dislocation Microstructures and the Effective Behavior of Single Crystals

Conti

Ortiz

2005

Arch. Rational Mech. Anal.

117

122

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We consider single-crystal plasticity in the limiting case of infinite latent hardening, which signifies that the crystal must deform in single slip at all material points. This requirement introduces a nonconvex constraint, and thereby induces the formation of fine-scale structures. We restrict attention throughout to linearized kinematics and deformation theory of plasticity, which is appropriate for monotonic proportional loading and confers the boundary value problem of plasticity a well-defined variational structure analogous to elasticity. We first study a scale-invariant (local) problem. We show that, by developing microstructures in the form of sequential laminates of finite depth, crystals can beat the single-slip constraint, i. e., the macroscopic (relaxed) constitutive behavior is indistinguishable from multislip ideal plasticity. In a second step, we include dislocation line energies, and hence a lengthscale, into the model. Different regimes lead to several possible types of microstructure patterns. We present constructions which achieve the various optimal scaling laws, and discuss the relation with experimentally known scalings, such as the Hall-Petch law.

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Section: Introductionmentioning

confidence: 99%

Dislocation Microstructures and the Effective Behavior of Single Crystals

Conti

Ortiz

2005

Arch. Rational Mech. Anal.

117

122

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“…The numerical examples reported in this paper also illustrate that ad hoc element enhancements are unlikely to result in any significant relaxation. The application to single crystals also demonstrates an evident but nevertheless compelling fact: the explicit knowledge of the relaxation of a problem results in an enormous reduction of computational cost, and a correspondingly vast improvement in performance, with respect to methods that construct subgrid microstructures numerically "on the fly" (see, e.g., [4]). This strongly suggests that explicit relaxation results such as those collected in section 4 will inevitably play a decisive role in rendering multiscale computing feasible.…”

Section: Discussionmentioning

confidence: 99%

“…Of course, the sequentially laminated energy (5.1) is not guaranteed to have a minimum over X, but the approach has proven useful in elastoplasticity [53,54,4,22,12].…”

Section: Sequential Laminationmentioning

confidence: 99%

“…More general concurrent multiscale computing schemes based on modern calculus of variations tools have been proposed recently [13,53,54,28,8,26,21,4,12,46,55]. These schemes allow a fully nonlinear analysis of the energy to be performed at the subgrid scale and generate microstructures "on-the-fly" by a variety of algorithms such as sequential lamination [40,41,42] and recursive faulting [55].…”

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confidence: 99%

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Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single‐Crystal Plasticity

Conti¹,

Hauret²,

Ortiz³

2007

Multiscale Model. Simul.

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Abstract. This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced-strain elements; and we illustrate the approach in an important area of application, namely, single-crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general.Key words. multiscale computing, relaxation, microstructure, finite elements, enhanced strain, single-crystal plasticity AMS subject classifications. 74G65, 74C05DOI. 10.1137/0606623321. Introduction. The problem addressed in this paper concerns the effective modeling of deformation microstructures within a concurrent multiscale computing framework. In many applications of interest, materials develop fine microstructure on multiple length and time scales in response to loading [5,53,58,49]. Examples of such microstructures include martensite; subgrain dislocation structures; dislocation walls and networks; ferroelectric domains; shear bands; spall planes; and others. In addition, materials such as polycrystalline metals may exhibit processing microstructure from the outset, prior to the onset of deformation. The macroscopic behavior of such materials is too complex to be amenable to modeling based on simple representational schemes, such as afforded by continuum thermodynamics, symmetry groups, linearization, polynomial approximations, empirical fitting and calibration, and other similar schemes. Indeed, empirical models are a major source of error and uncertainty in engineering applications, and the empirical paradigm does not offer a systematic means of reducing such error and uncertainty.Multiscale modeling aims to eliminate empiricism and uncertainty from material models by systematically identifying the rate-controlling mechanisms at all scales and the fundamental laws that govern those mechanisms, and by bridging the relevant

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“…For the necessary background and more references on dislocations, plasticity and microstructures we refer to [1,4,5,27,28].…”

Section: Introductionmentioning

confidence: 99%