A unified model for inelastic deformation of polycrystalline materials — application to transient behavior in cyclic loading and relaxation

Garmestani, Hamid; Vaghar, M. R.; Hart, Edward W.

doi:10.1016/s0749-6419(00)00089-9

Cited by 16 publications

(12 citation statements)

References 24 publications

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“…Pourétudier le comportement en relaxation, Hart [19,20] a développé une théorie pour initialement décrire la déformation plastique intragranulaire d'un solide polycristallin soumisà une traction monotone. Ce modèle est fondé sur l'existence d'une relation constitutive reliant la contrainte, la vitesse de déformation noń elastique avec le paramètre de dureté qui gouverne le comportement inélastique du matériau.…”

Section: Matériaux Et Expérimentationunclassified

“…Dans une seconde partie, nous proposons d'étudier le comportement en relaxation par indentation car il aété montré qu'il pouvaitêtre utilisé pour classer les matériaux selon leur sensibilité au fluage [16][17][18].À partir des travaux de Hart [19,20], nous déterminons le coefficient d'homothétie déduit de la droite de translation permettant de construire une courbe maîtresse unique. L'intérêt de ce coefficient est qu'il est lié au coefficient de sensibilitéà la contrainte obtenu par fluage, le premierétant l'inverse de l'autre.…”

Section: Introductionunclassified

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Fluage et relaxation par indentation d’aciers au chrome

Kamta

Chicot

Roudet

et al. 2017

Matériaux & Techniques

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Reçu le 7 décembre 2016, accepté le 24 mars 2017Résumé -L'étude du comportement en fluage et en relaxation de matériaux soumisà des conditions sévères en termes de température, de contrainte et de déformation est nécessaire mais parfois coûteuse avec les essais classiques. En effet, ces essais, particulièrement celui du fluage, sont très consommateurs de temps, ils peuvent durer plus d'une année. Pour ramener cette durée d'essaisà quelques minutes, nous proposons d'utiliser l'indentation instrumentée qui, avec l'évolution des conditions d'application de la charge et du déplacement de l'indenteur, permet de solliciter le matériau dans des conditions de chargement proches de celles imposées dans les essais classiques. Dans cetteétude, nous proposons d'étudier le comportement de deux aciers au chrome utilisés pour la fabrication d'appareils sous pression. Il s'agit des aciersà 9 % de chrome (T91) età 2,5 % de chrome (T22), l'objectifétant de classer les matériaux selon leur sensibilité au fluage età la relaxation. Dans ce travail, nous nous limitonsà l'indentationà température ambiante pouŕ etudier l'applicabilité de la technique d'indentation. En fluage, nous déterminons le coefficient de sensibilité a la contrainte et en relaxation le coefficient d'homothétie défini dans la théorie de Hart. L'intérêt de ces deux coefficients est qu'ils sont liés, l'un est l'inverse de l'autre, ce qui permet de comparer les deux modes de sollicitation. Mots clés : Fluage / relaxation / indentation / modélisation / aciers T91 et T22Abstract -Creep and relaxation by indentation of chromium-based steels. Study of creep and relaxation behaviours of materials submitted to severe conditions in terms of temperature, stress and strain is necessary but sometimes very expensive with classical tests. Indeed, these tests, mainly the creep one, are very time-consuming since it can last more than one year. In order to drastically reduce this duration, we suggest the use of the instrumented indentation test which allows testing the material with loading conditions comparable to that of the classical tests. This is now possible thanks to the development of the instrumented indentation. In this work, we propose to study the mechanical behaviour of two based chromium steels, 9 wt.% Cr (T91) and 2.5 wt.% Cr (T22), the objective being to classify the materials according to their creep and relaxation sensibilities. We limit our work to indentation experiments at room temperature in order to study the applicability of the indentation technique. With creep indentation, we determined the stress exponent and with relaxation by indentation the homothetic coefficient defined in the Hart's theory. The main advantage to study these two coefficients is that there are linked by a simple relation, one being the reciprocal of the other, thus allowing to easily compare these two solicitation modes.

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Section: Matériaux Et Expérimentationunclassified

Section: Introductionunclassified

Fluage et relaxation par indentation d’aciers au chrome

Kamta

Chicot

Roudet

et al. 2017

Matériaux & Techniques

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“…The third application involves stress relaxation of thin strips of metal. This application, which uses a modified Hart's model [30] and is described in Section 5.3, is a threedimensional problem discretized using finite elements. Our final application arises from an optimization problem.…”

Section: Applicationsmentioning

confidence: 99%

“…A modified Hart's model [30] (derived from Hart's model [36]), provides the governing equations for the system. The finite element discretization is described in detail in [62,Chapter 5].…”

Section: Holdingmentioning

confidence: 99%

Preconditioners for Generalized Saddle-Point Problems

Siefert¹,

Sturler²

2006

SIAM J. Numer. Anal.

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Generalized saddle point problems arise in a number of applications, ranging from optimization and metal deformation to fluid flow and PDE-governed optimal control. We focus our discussion on the most general case, making no assumption of symmetry or definiteness in the matrix or its blocks. As these problems are often large and sparse, preconditioners play a critical role in speeding the convergence of Krylov methods for these problems. We first examine two types of preconditioners for these problems, one block-diagonal and one indefinite, and present analyses of the eigenvalue distributions of the preconditioned matrices. We also investigate the use of approximations for the Schur complement matrix in these preconditioners and develop eigenvalue analysis accordingly. Second, we examine new developments in probing methods, inspired by graph coloring methods for sparse Jacobians, for building approximations to Schur complement matrices. We then present an analysis of these techniques and their accuracy. In addition, we provide a mathematical justification for their use in approximating Schur complements and suggest the use of approximate factorization techniques to decrease the computational cost of applying the inverse of the probed matrix.Finally, we consider the effect of our preconditioners on four applications.Two of these applications come from the realm of fluid flow, one using a finite element discretization and the other using a spectral discretization.The third application involves the stress relaxation of aluminum strips at low stress levels. The final application involves mesh parameterization and flattening.iii For these applications, we present results illustrating the eigenvalue bounds on our preconditioners and demonstrating the theoretical justification of these methods. We also present convergence and timing results, showing the effectiveness of our methods in practice. Specifically the use of probing methods for approximating the Schur compliment matrices in our preconditioners is empirically justified. We also investigate the h-dependence of our preconditioners one model fluid problem, and demonstrate empirically that our methods do not suffer from a deterioration in convergence as the problem size increases.iv AcknowledgmentsThere are many people deserving of thanks for their assistance in making this thesis a reality, but none more so than my advisor, Eric de Sturler.His sage advice, thoughtful insights and all-around good company played no small role in making this work happen. I am deeply grateful to him for everything he has done! I would also like to thank Michael Heath for his role as the Numerical Analysis group "patriarch." As the unofficial advisor to all of the graduate students, Mike's wisdom (and critique, when warranted) has helped me to hone my presentation skills and helped me to succinctly explain my work to my professional colleagues.The other members of my committee, Robert Skeel and Armand Beaudoin, are also deserving of special thanks, Bob for coming all the way b...

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“…Modeling of aging process only considers the thermodynamical features of the processing micromechanics (Kaneko and Oyamada, 2000). Other modeling attempts are based on the phenomenological aspect of the process using internal state variables representing anisotropy and internal stresses (Garmestani et al, 2001). A better understanding of this process requires integrated experimental and modeling efforts that attempt to relate crystallographic texture, anisotropy, and the inhomogeneous distribution of precipitates.…”

Section: Introductionmentioning

confidence: 99%

Modeling the evolution of anisotropy in Al–Li alloys: application to Al–Li 2090-T8E41

Garmestani

Kalidindi

Williams

et al. 2002

International Journal of Plasticity

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It is widely reported in current literature that the precipitation hardened Al-Li sheet alloys exhibit extremely high anisotropy in yield (and ultimate tensile) strength, which is well beyond what can be explained as purely a consequence of the strong crystallographic texture in the material (e.g. J. Mater. Sci. Eng. A265, 1999, 100). This paper presents a crystal plasticity based modeling framework that will (i) facilitate the segregation of the contributions to the overall anisotropy from crystallographic texture and precipitation hardening, and (ii) correlate the contribution from precipitate hardening to either co-planar slip activity or the noncoplanar slip activity in the cold-working step prior to the aging heat treatment. More specifically, a Taylor-type (fully-constrained) crystal plasticity model was formulated to predict the yield strength of the fully processed sheet and its anisotropy, while accounting for the initial texture in the hot-worked sheet, its evolution during the cold-working step prior to aging, and the inhomogeneous nucleation of the T 1 phase platelets (these are known to form on {111} planes, but not usually in equal amounts on the different {111} planes in a given crystal). In an effort to illustrate the methodology developed in the study, a limited set of experiments was conducted on Al-Li 2090-T8E41 alloy sheet. Off-axis stretches were applied on the sheet at room temperature prior to the aging treatment, and the mechanical anisotropy in the fully processed sheets was characterized by performing tension tests on coupons cut from the sheet at 0, 30, 45, 60 and 90 to the original rolling direction (RD). Both the initial texture in the sheet and its evolution during the different off-axis stretches were characterized. The alloys processed in this study showed pronounced anisotropy. The application of the methodology developed in this study revealed that much of the observed anisotropy in this particular data set could be explained by accounting for the texture in the sample in the processed condition. Although the data set available was inadequate to establish clear correlations of the anisotropy with preferential hardening mechanisms arising from either co-planar or non-co-planar slip activity during the off-axis stretch, there were indications favoring the latter. This case study, however, illustrates the application of the methodology developed in this study to obtain better insight into the nature of the anisotropy in these sheets and its physical origin. #

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A unified model for inelastic deformation of polycrystalline materials — application to transient behavior in cyclic loading and relaxation

Cited by 16 publications

References 24 publications

Fluage et relaxation par indentation d’aciers au chrome

Fluage et relaxation par indentation d’aciers au chrome

Preconditioners for Generalized Saddle-Point Problems

Modeling the evolution of anisotropy in Al–Li alloys: application to Al–Li 2090-T8E41

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