Comptes Rendus
no. 11-12
Plastic yielding and work hardening of single crystals in a soft device
[Déformation antiplane et écrouissage d'un monocristal lors d'un essai à bord libre]
K.C. Le1  ; Q.S. Nguyen2
1 Ruhr-Universität Bochum, Lehrstuhl für Allgemeine Mechanik, Universitaetsstr. 150, 44780 Bochum, Germany
2 LMS, École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 709-715.

On propose une solution analytique du problème de déformation antiplane d'un monocristal lors d'un essai à bord libre dans le cadre de la théorie mathématique des dislocations. La dépendance de la contrainte limite en fonction de la taille du cristal dévie légèrement de la relation de Hall–Petch. On montre que le comportement d'écrouissage obtenu dans ce cas dissipatif est pratiquement identique au cas du monocristal sous déplacement controlé au bord.

An analytical solution to the problem of an anti-plane constrained shear of single crystals placed in a soft device within the continuum dislocation theory is found. The dependence of the nucleation stress on the grain size exhibits a modest deviation from the Hall–Petch relation. It is shown that, as soon as the dissipation is taken into account, the hardening behavior becomes nearly identical to that of single crystals in a hard device.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.10.004
Keywords: Continuum mechanics, Crystal, Twist boundary, Dislocation, Yielding, Hardening
Mot clés : Milieux continus, Cristal, Joint de torsion, Dislocation, Déformation, Écrouissage
K.C. Le 1 ; Q.S. Nguyen 2

1 Ruhr-Universität Bochum, Lehrstuhl für Allgemeine Mechanik, Universitaetsstr. 150, 44780 Bochum, Germany
2 LMS, École polytechnique, 91128 Palaiseau cedex, France 
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     title = {Plastic yielding and work hardening of single crystals in a soft device},
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K.C. Le; Q.S. Nguyen. Plastic yielding and work hardening of single crystals in a soft device. Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 709-715. doi : 10.1016/j.crme.2009.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.10.004/

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[4] V.L. Berdichevsky; K.C. Le Dislocation nucleation and work hardening in anti-plane constrained shear, Continuum Mech. Thermodyn., Volume 18 (2007), pp. 455-467

[5] K.C. Le; S. Sembiring Analytical solution of plane constrained shear problem for single crystals within continuum dislocation theory, Arch. Appl. Mech., Volume 78 (2008), pp. 587-597

[6] K.C. Le; S. Sembiring Plane constrained shear of single crystal strip with two active slip systems, J. Mech. Phys. Solids, Volume 56 (2008), pp. 2541-2554

[7] D.M. Kochmann; K.C. Le Dislocation pile-ups in bicrystals within continuum dislocation theory, Int. J. Plasticity, Volume 24 (2008), pp. 2125-2147

[8] D.M. Kochmann; K.C. Le A continuum model for initiation and evolution of deformation twinning, J. Mech. Phys. Solids, Volume 57 (2009), pp. 987-1002

[9] W.T. Read; W. Shockley Dislocation models of crystal grain boundaries, Phys. Rev., Volume 78 (1950), pp. 275-289

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