A "quasi-elastic" affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

European Journal of Mechanics, A/Solids

Volumn 21, Issue 6, 2002, Pages 943-960

  Brenner, R ^a   Masson, R ^b   Castelnau, O ^a   Zaoui, A ^c  

^a UNIVERSITÉ PARIS 13   (France)

^b EDF R AND D   (France)

^c LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

Homogenisation; Nonlinear viscoelasticity; Polycrystal

Indexed keywords

APPROXIMATION THEORY; CREEP; LAPLACE TRANSFORMS; LOADS (FORCES); POLYCRYSTALS; STRAIN; STRESSES; VISCOELASTICITY;

HOMOGENIZATION; NONLINEAR VISCOELASTICITY; PHASE STRESSES;

COMPOSITE MATERIALS;

EID: 0037828482     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7538(02)01247-0     Document Type: Article

References (36)

1. Beurthey S., Zaoui A. Structural morphology and relaxation spectra of viscoelastic heterogeneous materials. Eur. J. Mech. A Solids. 19:2000;1-16.
2. Brenner, R., 2001. Influence de la microstructure sur le comportement en fluage thermique d'alliages de zirconium : analyse experimentale et mise en oeuvre de méthodes d'homogénéisation. Ph.D. thesis, Université Paris XIII, France.
3. Brenner, R., Béchade, J.-L., Castelnau, O., Bacroix, B., 2002. Thermal creep of Zr-Nb1%-O alloys: experimental analysis and micromechanical modelling. J. Nucl. Mater., to appear.
4. Brenner R., Castelnau O., Gilormini P. A modified affine theory for the overall properties of nonlinear composites. C. R. Acad. Sci. Paris Sér. IIb. 329:2001;649-654.
5. Brown G.M. A self-consistent polycrystalline model for creep under combined stress state. J. Mech. Phys. Solids. 18:1970;367-381.
6. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. London Ser. A. 241:1957;376-396.
7. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series and Products. 1965;Academic Press, New York.
8. Harren S.V. The finite deformation of rate-dependent polycrystals - II. A comparison of the self-consistent and Taylor methods. J. Mech. Phys. Solids. 39:1991;361-383.
9. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids. 13:1965;89-101.
10. Hutchinson J.W. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. Roy. Soc. London Ser. A. 348:1976;101-127.
11. Kröner E. Zur plastischen Verformung des Vielkristalls. Acta Metall. 9:1961;155-161.
12. Laws N., McLaughlin R. Self-consistent estimates for the viscoelastic creep compliances of composite materials. Proc. Roy. Soc. London Ser. A. 359:1978;251-273.
13. Lebensohn R.A., Tomé C.N. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall. 41:1993;2611-2624.
14. Letouzé, N., Brenner, R., Castelnau, O., Béchade, J.-L., Mathon M.-H., 2002. Residual strain distribution in Zircaloy-4 measured by neutron diffraction and estimated by homogenization techniques. Scripta Mater., to appear.
15. Mandel J. Mécanique des Milieux Continus. 1966;Gauthier-Villars, Paris.
16. Masson R., Bornert M., Suquet P., Zaoui A. An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. J. Mech. Phys. Solids. 48:2000;1203-1227.
17. Masson R., Zaoui A. Self-consistent estimates for the rate-dependent elastoplastic behavior of polycrystalline materials. J. Mech. Phys. Solids. 47:1999;1543-1568.
18. Molinari A. Averaging models for heterogeneous viscoplastic and elastic viscoplastic materials. J. Eng. Mat. Tech. 124:2002;62-70.
19. Molinari A., Ahzi S., Kouddane R. On the self-consistent modeling of elastic-plastic behavior of polycrystals. Mech. Materials. 26:1997;43-62.
20. Molinari A., Canova G.R., Ahzi S. A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. 35:1987;2983-2994.
21. Nemat-Nasser S., Obata M. Rate-dependent finite elstoplastic deformation of polycrystals. Proc. R. Soc. London Ser. A. 407:1986;343-375.
22. Paquin A., Sabar H., Berveiller M. Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials. Arch. Appl. Mech. 69:1999;14-35.
23. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids. 39:1991;45-71.
24. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids. 44:1996;827-862.
25. Pouya A., Zaoui A. Linéarisation et homogénéisation en viscoélasticité C. R. Acad. Sci. Paris Sér. IIb. 327:1999;365-370.
26. Rougier Y., Stolz C., Zaoui A. Représentation spectrale en viscoélasticité linéaire des matériaux hétérogènes. C. R. Acad. Sci. Paris Sér. II. 316:1993;1517-1522.
27. Rougier Y., Stolz C., Zaoui A. Self-consistent modelling of elastic-viscoplastic polycrystals. C. R. Acad. Sci. Paris Sér. II. 318:1994;145-151.
28. Schapery R.A. Approximate methods of transform inversion for viscoelastic stress analysis. Proc. U.S. Nat. Congr. Appl. Mech. ASME 4th. 2:1962;1075-1085.
29. Suquet P. Elements of homogenization for inelastic solid mechanics. Sanchez-Palencia E., Zaoui A. Homogenization Techniques for Composite Media. 1985;193-278 Springer-Verlag, Berlin.
30. Suquet P. Overall potentials and extremal surfaces of power law or ideally plastic composites. J. Mech. Phys. Solids. 41:1993;981-1002.
31. Turner P.A., Tomé C.N. Self-consistent modeling of visco-elastic polycrystals: application to irradiation creep and growth. J. Mech. Phys. Solids. 41:1993;1191-1211.
32. Turner P.A., Tomé C.N., Woo C.H. Self-consistent modelling of nonlinear visco-elastic polycrystals: an approximate scheme. Phil. Mag. A. 70:1994;689-711.
33. Weng G.J. Self-consistent determination of time dependent behavior of metals. J. Appl. Mech. 48:1981;41-46.
34. Weng G.J. A self-consistent relation for time-dependent creep of polycrystals. Int. J. Plasticity. 9:1993;181-198.
35. Zaoui A. Effets de la désorientation des grains sur la viscoplasticité de polycristaux C.F.C. Int. J. Solids Structures. 8:1972;1089-1101.
36. Zaoui A., Raphanel J.L. Investigation of inter- and intragranular plastic inhomogeneity. Lowe T.C., Rollett A.D., Follansbee P.S., Daehn G.S. Modeling the Deformation of Crystalline Solids. 1991;51-59 TMS.