Elastic-Inelastic Self-Consistent Model for Polycrystals

[+] Author and Article Information
A. Abdul-Latif

ERBEM/GIM, Université Paris8, IUT de Tremblay, 93290 Tremblay-en-France, Francee-mail: aabdul@iut-tremblay.univ-paris8.fr

J. P. Dingli, K. Saanouni

GSM/LASMIS, Université de Technologie de Troyes, B. P. 2060, 10010 Troyes cedex, France

J. Appl. Mech 69(3), 309-316 (May 03, 2002) (8 pages) doi:10.1115/1.1427693 History: Received January 25, 2000; Revised April 30, 2001; Online May 03, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Sachs,  G., 1928, “Zur Ableitung einer Fliessbedingung,” Z. Ver. Dent. Ing., 72, p. 734.
Cox,  H. L., and Sompmith,  D. E., 1937, “Effect of Orientation on Stresses in Single Crystals and of Random Orientation on Strength of Polycrystalline Aggregates,” Proc. Phys. Soc. London, 49, p. 134.
Taylor,  G. I., 1938, “Plastic Strain in Metals,” J. Inst. Met., 62, p. 307.
Hershey,  A., 1954, “The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals,” ASME J. Appl. Mech., 21, p. 236.
Kröner,  E., 1958, “Berechnung der Elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Z. Phys., 151, p. 504.
Laws,  N., and McLaughlin,  R., 1978, “Self-Consistent Estimates for the Viscoelastic Creep Compliance of Composite Materials,” Proc. R. Soc. London, Ser. A, A359, p. 251.
Kouddane, R., Molinari, A., and Canova, G. R., 1993, “Self-Consistent Modeling of Heterogeneous Viscoelastic and Elasto-Viscoplastic Materials,” Large Plastic Deformation: Fundamentals and Applications to Metal Forming, C. Teodosiu, J. L. Raphanel, and F. Sidoroff, eds., Mecamat 91, A. A. Balkema, Rotterdam, p. 129.
Brown,  G. M., 1970, “A Self-Consistent Polycrystalline Model for Creep Under Combined Stress States,” J. Mech. Phys. Solids, 18, p. 367.
Rice,  J. R., 1970, “On the Structure of Stress-Strain Relations for Time Dependent Plastic Deformation in Metals,” ASME J. Appl. Mech., 37, p. 728.
Rice,  J. R., 1971, “Inelastic Constitutive Relations for Solids: An Internal-Variable Theory and Its Application to Metal Plasticity,” Trans. J. Mech. Phys. Solids, 19, p. 433.
Hutchinson,  J. W., 1976, “Bounds and Self-Consistent Estimate for Creep of Polycrystalline Materials,” Proc. R. Soc. London, Ser. A, A348, p. 101.
Molinari,  A., Canova,  G. R., and Ahzi,  S., 1987, “A Self-Consistent Approach of the Large Deformation Viscoplasticity,” Acta Metall., 35, p. 2983.
Weng,  G. J., 1993, “A Self-Consistent Relation for the Time-Dependent Creep of Polycrystals,” Int. J. Plast., 9, p. 181.
Lebensohn,  R. A., and Tomé,  C. N., 1993, “A Self-Consistent Anisotropic Approach for the Simulation of Plastic Deformation and Texture Development of Polycrystals: Application to Zirconium Alloys,” Acta Metall. Mater., 41, p. 2611.
Lebensohn,  R. A., Tomé,  C. N., 1994, “A Self-Consistent Viscoplastic Model: Prediction of Rolling Texture of Anisotropic Polycrystals,” Mater. Sci. Eng., A, A175, p. 71.
Lin,  T. H., 1957, “Analysis of Elastic and Plastic Strain of FCC Crystal,” J. Mech. Solids, 5, p. 143.
Kröner,  E., 1961, “Zur Plastichen Verformung des Vielkristalls,” Acta Metall., 9, p. 155.
Budianski, B., and Wu, T. T., 1962, “Theoretical Prediction of Plastic Strains of Polycrystals,” Proc. 4th U.S. Nat. Cong. Appl. Mech., ASME, New York, p. 1175.
Hill,  R., 1965, “Continuum Micro-mechanical Elastoplastic Polycrystals,” J. Mech. Phys. Solids, 13, p. 89.
Hutchinson,  J. W., 1970, “Elastic-Plastic Behaviour of Polycrystalline Metals and Composites,” Proc. R. Soc. London, Ser. A, A319, p. 247.
Berveiller,  M., and Zaoui,  A., 1979, “An Extension of the Self-Consistent Scheme to Plasticity Flowing Polycrystals,” J. Mech. Phys. Solids, 26, p. 325.
Weng,  G. J., 1982, “A Unified Self-Consistent Theory for the Plastic-Creep Deformation of Metals,” ASME J. Appl. Mech., 49, p. 728.
Iwakuma,  T., and Nemat-Nasser,  S., 1984, “Finite Elastic Deformation of Polycrystalline Metals,” Proc. R. Soc. London, Ser. A, A394, p. 87.
Nemat-Nasser,  S., and Obata,  M., 1986, “Rate-Dependent, Finite Elasto-Plastic Deformation of Polycrystals,” Proc. R. Soc. London, Ser. A, A407, p. 343.
Lipinski,  P., Krier,  J., and Berveiller,  M., 1990, “Elastoplasticité des Métaux en Grandes Déformations: Comportement Global et Evolution de la Structure Interne,” Rev. Phys. Appl., 25, p. 361.
Lipinski,  P., Naddari,  A., and Berveiller,  M., 1992, “Recent Results Concerning the Modeling of Polycrystalline Plasticity at Large Strains,” Int. J. Solids Struct., 92, p. 1873.
Rougier,  Y., Stola,  C., and Zaoui,  A., 1994, “Self-Consistent Modelling of Elastic-Viscoplastic Polycrystals,” C. R. Acad. Sci. Paris, 319, p. 145.
Molinari,  A., Ahzi,  S., and Kouddane,  R., 1997, “On the Self-Consistent Modeling of Elasto-Plastic Behavior of Polycrystals,” Mech. Mater., 26, p. 43.
Schmitt,  C., Lipinski,  P., and Berveiller,  M., 1997, “Micromechanical Modelling of the Elastoplastic Behavior of Polycrystals Containing Precipitates—Application to Hypo- and Hyper-eutectoid Steels,” Int. J. Plast., 13, p. 183.
Abdul-Latif,  A., Dingli,  J. Ph., and Saanouni,  K., 1998, “Modeling of Complex Cyclic Inelasticity in Heterogeneous Polycrystalline Microstructure,” J. Mech. Mater., 30, p. 287.
Schmid, E., 1924, Proc. Int. Congr. Appl. Mech, Delft, p. 342.
Abdul-Latif,  A., and Saanouni,  K., 1994, “Damaged Anelastic Behavior of FCC Poly-Crystalline Metals With Micromechanical Approach,” Int. J. Damage Mech., 3, p. 237.
Abdul-Latif,  A., and Saanouni,  K., 1996, “Micromechanical Modeling of Low Cycle Fatigue Under Complex Loadings—Part II Applications,” Int. J. Plast., 12, p. 1123.
Abdul-Latif,  A., and Saanouni,  K., 1997, “Effect of Some Parameters on the Plastic Fatigue Behavior With Micromechanical Approach,” Int. J. Damage Mech., 6, p. 433.
Saanouni,  K., and Abdul-Latif,  A., 1996, “Micromechanical Modeling of Low Cycle Fatigue Under Complex Loadings—Part I. Theoretical Formulation,” Int. J. Plast., 12, p. 1111.
Abdul-Latif,  A., 1999, “Unilateral Effect in Plastic Fatigue with Micromechanical Approach,” Int. J. Damage Mech., 8, p. 316.
Abdul-Latif,  A., Ferney,  V., and Saanouni,  K., 1999, “Fatigue Damage of Waspaloy Under Complex Loading,” ASME J. Eng. Mater. Technol., 121, p. 278.
Cailletaud,  G., 1992, “A Micromechanical Approach to Inelastic Behaviour of Metals,” Int. J. Plast., 8, p. 55.
Dingli, J. P., 1997, “Modélisation du Comportement Anélastique des Matériaux Polycristallins Hétérogènes,” Mémoire de DEA, Université de Technologie de Compiègne.
François, D., Pineau, A., and Zaoui, A., 1993, Comportement Mécanique des Matériaux, Hermens, Paris.
Kocks,  U. F., and Brown,  T. J., 1966, “Latent Hardening in Aluminum,” Acta Metall., 14, pp. 87–98.
Jackson,  P. J., and Basinski,  Z. S., 1967, “Latent Hardening and the Flow Stress in Copper Single Crystal,” Can. J. Phys., 45, p. 421.
Franciosi, P., 1978, “Plasticité à froid des monocristaux C.F.C.: Etude du Durcissement Latent,” Thèse d’état, Univ. of Paris XIII.
Dingli,  J. P., Abdul-Latif,  A., and Saanouni,  K., 2000, “Predictions of the Complex Cyclic Behavior of Polycrystals Using a New Self-Consistent Modeling,” Int. J. Plast., 16, p. 411.


Grahic Jump Location
Plot of comparison between tangent formulation-based (T) and simplified (S) models showing the overall stress evolution versus the strain for uniaxial tensile test under three strain rate values (1:0.1/s, 2: 0.01/s and 3:0.001/s)
Grahic Jump Location
Plots showing (a) a comparison between tangent formulation-based (T) and simplified (S) models for tension-compression loading, (b) the evolution of ηo versus time during tension-compression loading test
Grahic Jump Location
Overall stress-strain simplified model response showing its sensitivity to the phenomenological parameter (α) under monotonic tensile test
Grahic Jump Location
Effect of the parameter (α) on the evolution of the activated slip systems during monotonic tensile load
Grahic Jump Location
Effect of the parameter (α) on the heterogeneity of the elastic strain (εge) in 11 direction of each grain within the used aggregate at the end of the monotonic tensile load
Grahic Jump Location
Effect of the parameter (α) on the heterogeneity of the inelastic strain (εgin) in 11 direction of each grain within the used aggregate at the end of the monotonic tensile load




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In