A computational procedure for rate-independent crystal plasticity

Anand, Lallit; Kothari, Mrityunjay

doi:10.1016/0022-5096(96)00001-4

Cited by 366 publications

(234 citation statements)

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“…Simple power-law relations such as the ones proposed here in Eq. (14) are commonly used in crystal plasticity continuum models (Anand and Kothari, 1996;Staroselsky, 1998;Anand, 2004;Roters et al, 2010;Lee et al, 2010;Zamiri and Pourboghrat, 2010;Choi et al, 2010a,). Note that other formulations using Voce-type law or more generally hyperbolic functions could also be used; but all generally present the same drawback of being exclusively dependent on the CRSS, occulting any dependence on the lattice defect population for example (Roters et al, 2010).…”

Section: Crystal Plasticity Continuum Formulationmentioning

confidence: 99%

“…Material parameters sensibility. For a given set of parameters, it is known that a unique set of active slip systems will be found (Anand and Kothari, 1996). However, it is not clear whether a calibration based on both considered stress-strain curves should be enough to guarantee the unicity of the set of parameters.…”

Section: Materials Parametersmentioning

confidence: 99%

“…If fcc and bcc crystal plasticity continuum models have already been extensively studied (Cuitiño and Ortiz, 1993;Anand and Kothari, 1996;Anand, 2004;Houtte et al, 2006;Zhao et al, 2007;Kuchnicki et al, 2008;Jérusalem et al, 2008;Roters et al, 2010;Lee et al, 2010;Liu et al, 2011;Thamburaja, 2010;Rossiter et al, 2010;Zamiri and Pourboghrat, 2010;Watanabe et al, 2010;Sung et al, 2010), similar efforts have been much scarcer for HCP metals (Staroselsky, 1998;Staroselsky and Anand, 2003;Graff et al, 2007;Mayeur and McDowell, 2007;Tang et al, 2009;Mayama et al, 2009;Prakash et al, 2009;Choi et al, 2010b;Choi et al, 2010a;Lévesque et al, 2010). Despite the relatively ancient interests in HCP metals, the intrinsic mechanisms of HCP crystalline deformation, such as twinning (generally more present than in fcc and bcc metals), twin-slip interaction, or twin polarization among others, are still, as of now, not fully understood (Jérusalem et al, 2008;Wang et al, 2009a;Yue et al, 2010;Shen et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

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Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Fernández

Prado

Wei

et al. 2011

International Journal of Plasticity

104

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a b s t r a c tLightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843-1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip hc + ai versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.

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Section: Crystal Plasticity Continuum Formulationmentioning

confidence: 99%

Section: Materials Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Fernández

Prado

Wei

et al. 2011

International Journal of Plasticity

104

View full text Add to dashboard Cite

show abstract

“…Although recent developments in these two approaches have now reached an advanced stage, the major improvements have been made by crystallographic models due to their ability to incorporate complex micromechanisms of slip within the flow and evolutionary equations of the single crystal models. These include the effects of dislocation interactions (for example, Meric and Cailletaud (1991) and Meric et al (1991)), hardening and strain gradient phenomena (for example, Gurtin (2000), Meissonnier et al (2001) and Stainer et al (2002)) and general anisotropic plastic and viscoplastic behaviour (for example Jordan and Walker (1992), Anand and Kothari (1996) and Busso and McClintock (1996)). A brief outline of the salient features of local and non-local crystal plasticity approaches are given below.…”

Section: Continuum Discretization Of a Boundary Value Problemmentioning

confidence: 99%

“…Owing to the severe restrictions placed on material properties, such as latent hardening, to ensure uniqueness in the mode of slip (for example Anand and Kothari (1996) and Busso and Cailletaud (2003)), and the associated difficulties in its numerical implementation, the use of rateindependent formulations has been somehow restricted and is much more limited than rate-dependent models. This has been compounded by the fact that, by calibrating their strain-rate sensitivity response accordingly, rate-dependent models have been successfully used in quasirate-independent regimes.…”

Section: Generic Local Crystallographic Frameworkmentioning

confidence: 99%

Multiscale modelling of nanomechanics and micromechanics: an overview

Ghoniem

Busso

Kioussis

et al. 2003

Philosophical Magazine

139

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Recent advances in analytical and computational modelling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum are reviewed. It is shown that multiscale modelling of materials approaches relies on a systematic reduction in the degrees of freedom on the natural length scales that can be identified in the material. Connections between such scales are currently achieved either by a parametrization or by a 'zoom-out' or 'coarse-graining' procedure. Issues related to the links between the atomistic scale, nanoscale, microscale and macroscale are discussed, and the parameters required for the information to be transferred between one scale and an upper scale are identified. It is also shown that seamless coupling between length scales has not yet been achieved as a result of two main challenges: firstly, the computational complexity of seamlessly coupled simulations via the coarse-graining approach and, secondly, the inherent difficulty in dealing with system evolution stemming from time scaling, which does not permit coarse graining over temporal events. Starting from the Born-Oppenheimer adiabatic approximation, the problem of solving quantum mechanics equations of motion is first reviewed, with successful applications in the mechanics of nanosystems. Atomic simulation methods (e.g. molecular dynamics, Langevin dynamics and the kinetic Monte Carlo method) and their applications at the nanoscale are then discussed. The role played by dislocation dynamics and statistical mechanics methods in understanding microstructure self-organization, heterogeneous plastic deformation, material instabilities and failure phenomena is also discussed.

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Crystal Plasticity and Evolution of Polycrystalline Microstructure

Miehé

Schotte

2004

Encyclopedia of Computational Mechanics

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The continuum slip theory of crystals provides a canonical framework of finite plasticity with physically well‐defined roots in the dislocation mechanics of metals. Reliable algorithmic settings of crystal plasticity are not only needed for structural analyses of single crystals but also provide a cornerstone for multiscale computations of evolving anisotropic microstructures in metallic polycrystals. This article summarizes a current status of computational crystal plasticity and its application to the texture analysis of polycrystals. It outlines a basic constitutive structure of crystal plasticity, alternative deformation‐driven stress update algorithms and a computational scheme for the nonlinear homogenization of polycrystalline aggregates. Particular emphasis is put on a canonical incremental variational formulation for Schmid‐type crystal plasticity with potential hardening where an incremental stress potential is obtained from a local minimization problem with respect to the internal variables. The existence of this stress potential allows the formulation of IBVPs for elastic–plastic crystals as a sequence of incremental minimization problems. Furthermore, the nonlinear homogenization of polycrystalline microstructures may be recast into a principle of minimum averaged incremental energy. Within this variational setting of homogenization, a quasi‐hyperelastic incremental macro‐stress potential is obtained from a global minimization problem with respect to the fine‐scale displacement fluctuation field. The performance of the formulations is demonstrated for benchmarks of single crystal plasticity and texture developments in polycrystals.

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A computational procedure for rate-independent crystal plasticity

Cited by 366 publications

References 14 publications

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Multiscale modelling of nanomechanics and micromechanics: an overview

Crystal Plasticity and Evolution of Polycrystalline Microstructure

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