Partition of plastic work into heat and stored energy in metals

Hodowany, J.; Ravichandran, G.; Rosakis, A. J.; Rosakis, Phoebus

doi:10.1007/bf02325036

Cited by 315 publications

(196 citation statements)

References 14 publications

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“…even if c ε (x, s) = c ε (x), the homogenized heat coefficient c 0 (x, s) does depend in general on s (see Theorem 6.1, where explicit formulas are given in the case of a material made of layers of some given homogeneous phases). This mathematical result is in accordance with recent experiments and theoretical mechanical studies based on a temperaturedependent fraction of plastic work converted into heating (see [10], [12] and [13]). Indeed the heat coefficient c is given by c = β ρh , where h is the specific heat coefficient and β the rate of plastic work converted into heating, a quantity which is related to the rearrangement of crystals during deformation.…”

Section: ë òóý º ëø ò ö × ùø ñ ð øó ñ ¸ α < X < B¸0 < T < T¸øsupporting

confidence: 92%

Homogenization of stratified thermoviscoplastic materials

Charalambakis

Murat

2006

Quart. Appl. Math.

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Abstract. In the present paper we study the homogenization of the system of partial differential equations, posed in a < x < b, 0 < t < T , completed by boundary conditions on v ε and by initial conditions on v ε and θ ε . The unknowns are the velocity v ε and the temperature θ ε , while the coefficients ρ ε , µ ε and c ε are data which are assumed to satisfy. This sequence of one-dimensional systems is a model for the homogenization of nonhomogeneous, stratified, thermoviscoplastic materials exhibiting thermal softening and a temperature-dependent rate of plastic work converted into heat.Under the above hypotheses we prove that this system is stable by homogenization. More precisely one can extract a subsequence ε for which the velocity v ε and the temperature θ ε converge to some homogenized velocity v 0 and some homogenized temperature θ 0 which solve a system similar to the system solved by v ε and θ ε , for coefficients ρ 0 , µ 0 and c 0 which satisfy hypotheses similar to the hypotheses satisfied by ρ ε , µ ε and c ε . These homogenized coefficients ρ 0 , µ 0 and c 0 are given by some explicit (even if sophisticated) formulas. In particular, the homogenized heat coefficient c 0 in general depends on the temperature even if the heterogeneous heat coefficients c ε do not depend on it.Résumé. Dans cet article, nousétudions l'homogénéisation du système d'équations aux dérivées partielles Cette suite de problèmes unidimensionnels modélise l'homogénéisation de matériaux thermoviscoplastiques hétérogènes dont la résistance diminue avec la température et dont le taux de travail plastique converti en chaleur dépend de la température. Sous les hypothèses ci-dessus, nous démontrons que ce système est stable par homogénéisation. Plus précisément, on peut extraire une sous-suite ε pour laquelle la vitesse v ε et la température θ ε convergent vers une vitesse homogénéisée v 0 et une température homogénéisée θ 0 qui sont solution d'un système similaireà celui dont v ε et θ ε sont solution, pour des coefficients ρ 0 , µ 0 et c 0 qui satisfont des hypothèses analoguesà celles satisfaites par ρ ε , µ ε et c ε . Les coefficients homogénéisés ρ 0 , µ 0 et c 0 sont donnés par des formules explicites (même si elles sont assez compliquées). En particulier le coefficient thermique homogénéisé c 0 dépend en général de la température, même si les coefficients thermiques hétérogènes c ε n'en dépendent pas.

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Section: ë òóý º ëø ò ö × ùø ñ ð øó ñ ¸ α < X < B¸0 < T < T¸øsupporting

confidence: 92%

Homogenization of stratified thermoviscoplastic materials

Charalambakis

Murat

2006

Quart. Appl. Math.

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“…Since c 5 2 Setting φ (t) = t 0 γ(t ) ϕ (t )dt and observing that φ (0) = 0 and that φ = γϕ ≤ ≤ γδ + γφ , an easy computation shows that every solution ϕ of inequality (3.24) satisfies for every t, When the data coincide, i.e. when ( f , v, u 0 ) = ( f , v , u 0 ), then δ (t) = 0 for every t, 0 ≤ t ≤ T , and (3.25) implies that ϕ (t) = 0 for every t, 0 ≤ t ≤ T .…”

Section: Proof Of the Uniqueness And Continuity Theorem 31mentioning

confidence: 99%

“…In almost all works concerned with this problem under adiabatic conditions, β is supposed to be a constant which is equal to 0.9. However recent experimental work of Hodowany et al [5] based on a Kolski bar technique, and theoretical studies by Rosakis et al [8] suggest that β can depend, among others, on the temperature. We actually prove in our paper [3] that homogenization of nonhomogeneous, stratified, thermoviscoplastic materials where c depends only on x produces an homogenized material where c in general does depend on the temperature.…”

Section: Introductionmentioning

confidence: 99%

Approximation by finite elements, existence and uniqueness for a model of stratified thermoviscoplastic materials

Charalambakis

Murat

2006

Ricerche mat.

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In the present paper we consider for a < x < b, 0 < t < T , the system of partial differential equationscompleted by boundary conditions on v and by initial conditions on v and θ . The unknowns are the velocity v and the temperature θ , while the coefficients ρ, µ and c are Carathéodory functions which satisfyCommunicated by the Editor-in-Chief This one dimensional system is a model for the behaviour of nonhomogeneous, stratified, thermoviscoplastic materials exhibiting thermal softening and temperature dependent rate of plastic work converted into heat. Under the above hypotheses we prove the existence of a solution by proving the convergence of a finite element approximation. Assuming further that µ is Lipschitz continuous in s, we prove the uniqueness of the solution, as well as its continuous dependence with respect to the data. We also prove its regularity when suitable hypotheses are made on the data. These results ensure the existence and uniqueness of one solution of the system in a class where the velocity v, the temperature θ and the stress σ = µ(x, θ ) ∂ v ∂ x belong to L ∞ ((0, T ) × (a, b)).

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“…The remaining part of plastic power, which is not converted into heat power, is stored in the material [22]. This effect is often modelled using the assumption of Taylor and Quinney [23], which states that 5% to 15% of the plastic work is stored in the material.…”

Section: Thermal Modelmentioning

confidence: 99%

Automatic correction of the time step in implicit simulations of thermomechanical problems

et al. 2016

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Abstract. The accurate numerical modelling of thermomechanical systems is important in several industrial applications. A new staggered coupling strategy is proposed to deal with thermo-elasto-plastic problems involving large deformations and rotations, which is combined with an automatic time-step control technique. The proposed strategy is based on the isothermal split approach. It differs from the classical scheme since, in each increment, there are two phases of interchange of information, instead of only one. In each increment, the solution procedure is divided in a prediction phase and a corrector phase, and the interchange of information is performed on both. The proposed strategy was implemented in the in-house quasi-static finite element code DD3IMP. Its performance is analysed and compared with the classical strategy and the iterative one, which are commonly employed for solving thermomechanical problems. The results indicate that the propose strategy contributes for improving the accuracy of the numerical solution, with a reasonable computational cost.

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Partition of plastic work into heat and stored energy in metals

Cited by 315 publications

References 14 publications

Homogenization of stratified thermoviscoplastic materials

Homogenization of stratified thermoviscoplastic materials

Approximation by finite elements, existence and uniqueness for a model of stratified thermoviscoplastic materials

Automatic correction of the time step in implicit simulations of thermomechanical problems

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