Micromechanics and Inhomogeneity pp 599-622 | Cite as

# Theory of Plasticity for a Class of Inclusion and Fiber-Reinforced Composites

## Abstract

Based on the theoretical framework recently established by Tandon and Weng (1988), a multiaxial theory of plasticity is developed for a class of composites containing unidirectionally aligned spheroidal inclusions. The aspect ratio of inclusions may range from that of a thin disk all the way to that of a continuous fiber, and its influence on the transversely isotropic elastoplastic behavior of the composite is investigated. Under a combined stress the secant moduli of the composite and the average stress concentration factors of the matrix are derived. It is shown that the yield condition of the composite generally depends on the hydrostatic pressure, contributing most significantly for the disk and fiber-reinforced cases. Both the initial yield stress and the work-hardening modulus of the anisotropic composite are also seen to be strongly influenced by the shape of inclusions; the disks are found to be most effective in the transverse plane but the fibers are so along the axial direction. Finally, a rather detailed account on the elastoplastic behavior of fiber-reinforced composites is given, and a comparison of the stress-strain curve with experiment is also demonstrated.

### Keywords

Boron Hexagonal Posite Verse Prolate## Preview

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### References

- Accorsi, M. L. and Nemat-Nasser, S. (1986), Bounds on the overall elastic and instan-taneous elastoplastic moduli of periodic composites,
*Mech. Materials*, 5, 209–220.Google Scholar - Adams, D. F. (1970), Inelastic analysis of a unidirectional composite subjected to transverse normal loading,
*J. Composite Materials*,**4**, 310–328.CrossRefGoogle Scholar - Arsenault, R. J. and Taya, M. (1987), Thermal residual stress in metal matrix composite,
*Acta Metallurgica*,**35**, 651–659.CrossRefGoogle Scholar - Benveniste, Y. (1987), A new approach to the application of Mori—Tanaka theory in composite meterials,
*Mech. Materials*,**6**, 147–157.CrossRefGoogle Scholar - Berveiller, M. and Zaoui, A. (1979), An extension of the self-consistent scheme to plastically-flowing polycrystals,
*J. Mech. Phys. Solids*,**26**, 325–344.CrossRefGoogle Scholar - Budiansky, B. (1959), A reassessment of deformation theories of plasticity,
*J. Appl. Mech*.,**26**, 259–264.MathSciNetGoogle Scholar - Dvorak, G. J. and Bahei-El-Din, Y. A. (1987), A bimodal plasticity theory of fibrous composite materials,
*Acta Mech*,**69**, 219–241.Google Scholar - Dvorak, G. J., Bahei-El-Din, Y. A., Macheret, Y., and Liu, C. H. (1988), An experimental study of elastic-plastic behavior of a fibrous boron-aluminum composite,
*J. Mech. Phys. Solids*,**36**, 655–687.Google Scholar - Eshelby, J. D. (1957), The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London, A241, 376–396.Google Scholar
- Hashin, Z. and Shtrikman, S. (1963), A variational approach to the theory of the elastic behavior of multiphase materials,
*J. Mech. Phys. Solids*,**11**, 127–140.MathSciNetADSMATHCrossRefGoogle Scholar - Hashin, Z. (1965), On elastic behavior of fibre reinforced materials of arbitrary trans-verse phase geometry,
*J. Mech. Phys. Solids*,**13**, 119–134.ADSCrossRefGoogle Scholar - Hill, R. (1948), A theory of the yielding and plastic flow of anisotropic metals,
*Proc. Roy. Soc. London*,**A193**, 281–297.ADSMATHCrossRefGoogle Scholar - Hill, R. (1963), Elastic properties of reinforced solids: Some theoretical principles,
*J. Mech. Phys. Solids*,**11**, 357–372.ADSMATHCrossRefGoogle Scholar - Hill, R. (1964a), Theory of mechanical properties of fibre-strengthened materials: I. Elastic behavior,
*J. Mech. Phys. Solids*,**12**, 199–212.MathSciNetADSCrossRefGoogle Scholar - Hill, R. (1964b), Theory of mechanical properties of fibre-strengthened materials: II. Inelastic behavior,
*J. Mech. Phys. Solids*,**12**, 213–218.MathSciNetADSCrossRefGoogle Scholar - Hill, R. (1965), Continuum micro-mechanics of elastoplastic polycrystals,
*J. Mech. Phys. Solids*,**13**, 89–101.ADSMATHCrossRefGoogle Scholar - Hutchinson, J. W. (1970), Elastic-plastic behavior of polycrystalline metals and composites,
*Proc. Roy. Soc. London*,**A319**, 247–272.ADSCrossRefGoogle Scholar - Kröner, E. (1961), Zur plastischen verformung des vielkristalls,
*Acta Metallurgica*,**9**, 155–161.CrossRefGoogle Scholar - Luo, H. A. and Weng, G. J. (1987), On Eshelby’s inclusion problem in a three-phase spherically concentric solid, and a modification of Mori-Tanaka’s method,
*Mech. Materials*,**6**, 347–361.CrossRefGoogle Scholar - Luo, H. A. and Weng, G. J. (1989), On Eshelby’s S-tensor in a three-phase cylindrically concentric solid, and the elastic moduli of fiber reinforced composites,
*Mech. Materials*,**8**(in press).Google Scholar - Mori, T. and Tanaka, K. (1973), Average stress in the matrix and average elastic energy of materials with misfitting inclusions,
*Acta Metallurgica*,**21**, 571–574.CrossRefGoogle Scholar - Mura, T. (1987),
*Micromechanics of Defects in Solids*, 2nd ed., Martinus Nijhoff, Dordrecht. Pedersen, O. B. (1983), Thermoelasticity and plasticity of composites-I. Mean field theory,*Acta Metallurgica*,**13**, 1795–1808.Google Scholar - Tandon, G. P. and Weng, G. J. (1984), The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites,
*Polymer Composites*,**5**, 327–333.CrossRefGoogle Scholar - Tandon, G. P. and Weng, G. J. (1986), Average stress in the matrix and effective moduli of randomly oriented composites,
*Composite Sci. Tech*.,**27**, 111–132.CrossRefGoogle Scholar - Tandon, G. P. and Weng, G. J. (1988), A theory of particle-reinforced plasticity,
*J. Appl. Mech*.,**55**, 126–135.ADSCrossRefGoogle Scholar - Teply, J. L. and Dvorak, G. J. (1988), Bounds on overall instantaneous properties of elastic-plastic composites,
*J. Mech. Phys. Solids*,**36**, 29–58.Google Scholar - Wakashima, K., Suzuki, Y., and Umekawa, S. (1979), A micromechanical prediction of initial yield surfaces of unidirectional composites,
*J. Composite Materials*,**13**, 288–302.CrossRefGoogle Scholar - Weng, G. J. (1982), A unified, self-consistent theory for the plastic-creep deformation of metals,
*J. Appl. Mech*.,**49**, 728–734.ADSMATHCrossRefGoogle Scholar - Weng, G. J. (1984), Some elastic properties of reinforced solid, with special reference to isotropic ones containing spherical inclusions,
*Int. J. Engng. Sci*.,**22**, 845–856.MATHCrossRefGoogle Scholar - Weng, G. J. (1988), Theoretical principles for the determination of two kinds of composite plasticity, in
*Mechanics of Composite Materials*, edited by Dvorak, G. J. and Laws, N., AMD-Vol.**92**, ASME, New York, pp. 193–208.Google Scholar - Zhao, Y. H., Tandon, G. P., and Weng, G. J. (1989), Elastic moduli for a class of porous materials,
*Acta Mech*,**76**, 105–130.MATHCrossRefGoogle Scholar