Comportement elastoplastique des aciers lors de Ia mise en forme : theorie micromecanique, simulations numeriques et resultats experimentaux.

Authors

  • Marcel Berveiller Laboratoire de Physique et Mecanique des Materiaux URA CNRS, /SGMP /le du Saulcy, 57045 Metz
  • Joseph Morreale Laboratoire d'Etude et de Developpement des Produits Plats (LEDEPP- SOLLAC) 17, avenue des Tilleuls, 57191 Florange
  • Eric Reubrez Laboratoire de Physique et Mecanique des Materiaux URA CNRS, /SGMP /le du Saulcy, 57045 Metz

Keywords:

plasticity, polycrystal, steel, texture, anisotropy, micromechanics, simulation, forming, residual stresses, slip, dislocations, grains

Abstract

Recent developments concerning the modelisation of the elastoplastic behaviour of steel sheets using micromechanical models are presented. For the polycrystalline grains, the connection of moving dislocations and the global slip rate a well as the hardening matrix describing the slip systems interaction are introduced in order to describe the behaviour of the single crystals. The field equations for heterogeneous elastoplastic metals are transformed into an integral equation which is approximate by the self consistent assumption. New results concerning hardening, plastic anisotropy, crystallographic texture evolution are compared to experimental measurements.

 

Downloads

Download data is not yet available.

References

[ASA 83] ASARO R.J., Micromechanics of crystal and polycrystals, Adv. in Appl. Mechanics

Vo123 p. 1 - 115 (1983)

[BER 87] B ERADAI CH., B ERVEILLER M., LIPINSKI P., Int. J. Plasticity 3 (1987) 13

[BER 93] BERVEILLER M., MULLER D., KRATOCHVIL J., Non local versus local elastoplastic

behavior of heterogeneous materials. Int. J. Plasticity 9 (1993) 633 - 652

[BER 81] BERVEILLER M., ZAOUI A. Methodes self consistantes en mecanique des solides

heterogenes. Comp. rheologique et structure des materiaux. Ed. ENPC, Paris (C. HUET,

A. ZAOUI Ed) (1981) p. 175- 198

[BER 84] BERVEILLER M., ZAOUI A., Modelling of the plastic behavior of inhomogeneous

media. J. Engng Mat. and Technology 106 (1984) p. 295- 299

[BER 86] BERVEILLER M., ZAOUI A., Some applications of the self consistent scheme in the

yield of plasticity and texture of metallic polycrystals in "lArge deformations of solids"

Ed. J. Gittus., J. Zarka, S. Nemat- Nasser Elsevier Applied Science (1986)

[DEW 73] DE WITT R., Theory of disclinations : Continuous and discrete disclinations in

anisotropie elasticity. J. of Research of the NBS 77 A ( 1973) 49 - 100

[DED 73] DEDERICHS P.H., ZELLER R., Variational treatment of the elastic constants of

desordered materails, Z. Phys. 259 (1973) 103

[DIE 91] DIEPOLDER W., MANNE V., LIPPMANN H., The Cosserat continuum, a model for

grain rotations in metals, Int. J. Plasticity 7 (1991) 313- 328

[ESH 57] ESHELBY J.D., The determination of the elastic field of an ellipsoidal inclusion and

related problems. Proc. Roy. Soc. London A241 (1957)

[FRA 80] FRANCIOSI P., B ERVEILLER M., ZAOUI A., Latent hardening in cooper and

aluminium single crystals. Acta Met 28 (1980) 273- 283

[HAN 91] HANSEN N., JENSEN D.J., Microscopic and crystallographic Aspect of flow stress

anisotropy. Proc. Plasticity 91 Grenoble

[HIH 85] HIHI A., B ERVEll..LER M., ZAOUI A., Nouvelle formulation du schema autocoherent

en plasticite des polycristaux metalliques. J. Nee. Theorique et Appl. 4 (1985) 201 - 219

[HIL 65] HILL R., A self consistent mechanics of composites materials J. Nech.Phys. Solids

(1965) 213

[HIL 72] HILL R., On constitutive macrovariables for heterogeneous solids at finite strain.

Proc. Roy. Soc. London A326 (1972) 131

[HIL 60] HDL R., The mathematical theory of plasticity. Clarendon Press Oxford (1960)

[HIL 65] HILL R., Continuum micro mechanics of elastoplastic polycrystals J. Rech. Phys.

Solids 13 (1965) 89

[HIL 72] HDL R., RICE J.R., Constitutive analysis of elastic - plastic crystals at arbitrary

strain, J. Mech. Phys. Solids 20 (1972) 401

[HUT 70] HUTCHINSON J.W., Elastic plastic behavior of polycristalline metals and

composites. Proc. Roy. Soc. London A319 (1970) 247

[OED 73] DEDERICHS P.H., ZELLER R., Variational treatment of the elastic constants of

disordered materials, Z Phys 259 (1953) 103

[IWA 84] IWAKUMA T., NEMAT- NASSER S., Finite elastic - plastic deformation of

polycrystalline metals. Proc. Roy. Soc. (London) A 394 (1984) 87

[KRO 58] KRONER E., Berechnung der elastichen Konstanten des Vielkristalls aus den

Konstanten des Einkristalls. Z. Phys. 151 (1958) 504

[KRO 58] KRONER E., Kontinuums theoric der versetzungen und Eigenspannungen Springer

(1958) Berlin

[KRO 61] KRONER E., Zur plastichen verformung des Vielkristalls Acta Met. 9 (1961) 155

[LEM 90] LEMAITRE J., CHABOCHE J.L., Mechanics of solid materials. Cambridge University

Press (1990)

[LIP 89] LIPINSKI P., BERVEILLER M., Elastoplasticity of micro in homogeneous metals at

large strains. Int. J. Plasticity 5 (1989) p. 149- 172

[LIP 90] LIPINSKI P., KRIER J., BERVEILLER M., Elastoplasticite des metaux en grandes

deformations : comportement global et evolution de la structure interne. Rev. Phys. Appl.

(1990) 361 - 388

[LIP 81] LIPMANN H., Mechanik des plastischen FliessBens Springer (1981) Berlin

[MAU 92] MAUGIN G.A., The thermomechanics of plasticity and fracture. Cambridge Texts

in applied Mathematics Clarendon Press

[MAN 71] MANDEL J., Plasticite classique et viscoplasticite, Lecture Notes CISM udineSpringer

Verlag Vienna (1971)

[MUG 88] MUGHRABI H., Dislocation clustering and long range internal stresses in

monotonically and cyclically deformed metal crystals. Rev. Phys. Appl - 23 - (1988) 367

[ORO 42] OROWAN E., A type of plastic deformation new in metals Nature 149 (1942) 643-

[PEA 50] PEACH and KOEHLER J.S., The forces excerted on dislocations and the yields

produced by them. Phys. Rev. SO, (1950) 436-439

[REU 92] REUBREZ E.,Optimal crystallographie texture in Modelling of Plastic deformation

th RISO Int. Sipmposium 1992 p 403-408

[SCH 24] SCHMIDT E., Proc.lnt. Congr. Applied Rech. Delft 342 (1924)

[TA Y 38] TAYLOR G.l., Plastic strain in metals. J. lnst. Metals 62 (1938) 307

Downloads

Published

1994-04-25

How to Cite

Berveiller, M. ., Morreale, J. ., & Reubrez, E. (1994). Comportement elastoplastique des aciers lors de Ia mise en forme : theorie micromecanique, simulations numeriques et resultats experimentaux. European Journal of Computational Mechanics, 3(4), 491–514. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/3601

Issue

Section

Original Article