Summary
It is shown that elastic-plastic response of metal matrix composites reinforced by aligned continuous fibers can be described in terms of two distinct modes. In the matrix-dominated mode, the composite deforms primarily by plastic slip in the matrix, on planes which are parallel to the fiber axis. In the fiber-dominated mode, both phases deform together in the elastic and plastic range. Constitutive equations are derived for the matrix-dominated mode of deformation in composites with elastic-perfectly plastic matrices. Response in the fiber-dominated mode is approximated by the self-consistent and Voigt models. The two deformation modes give different branches of the overall yield surface which identify the state of stress that activates a particular mode, and indicate the conditions for mode transition in a given composite system. The matrix-dominated mode is found to exist in systems reinforced by fibers of large longitudinal shear stiffness, such as boron or silicon carbide. Systems reinforced by more compliant fibers, such as graphite, appear to deform exclusively in the fiber-dominated mode. The results show good agreement with experimental data, and with predictions obtained from a more accurate material model. They also help to reconcile several different plasticity theories of fibrous composites, and suggest limits of their validity.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Dvorak, G. J., Teply, J. L.: Periodic hexagonal array models for plasticity analysis of composite materials. In: Plasticity today: modelling, methods and applications, W. Olszak memorial volume (Sawczuk, A., Bianchi, V., eds.), p. 623. Elsevier 1985.
Teply, J. L., Dvorak, G. J.: Bounds on overall instantaneous properties of elastic-plastic composites. To appear in the Journal of the Mechanics and Physics of Solids.
Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids11, 357–372 (1963).
Walpole, L. J.: On the overall elastic moduli of composite materials. J. Mech. Phys. Solids17, 235–251 (1969).
Huang, W. C.: Plastic behavior of some composite materials. J. Composite Materials5, 320–338 (1971).
Yamada, Y., Yoshimura, N., Sakurai, T.: Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method. Int. J. Mech. Sci.10, 345–354 (1968).
Phillips, A., Liu, C. S., Justusson, J. W.: An experimental investigation of yield surfaces of elevated temperatures. Acta Mechanica14, 119–146 (1972).
Stowell, E. Z., Liu, T. S.: On the mechanical behavior of fiber-reinforced crystalline materials. J. Mech. Phys. Solids9, 242–260 (1961).
Kelly, A., Davies, G. J.: The principles of fiber reinforcement of metals. Metallurgical Reviews10, 1–77 (1965).
Cratchley, D.: Experimental aspects of fiber-reinforced metals. Metallurgical Reviews10, 79–144 (1965).
Mulhern, J. F., Rogers, T. G., Spencer, A. J. M.: A continuum model for fiber-reinforced plastic materials. Proc. Roy. Soc.301, 473–492 (1967).
Spencer, A. J. M.: Deformation of fibre-reinforced materials. Oxford University Press 1972.
Spencer, A. J. M. (editor): Continuum theory of the mechanics of fibre-reinforced composites. CISM courses and lectures No. 282. Springer 1984.
Helfinstine, J. D., Lance, R. H.: Yielding of fiber reinforced Tresca material. J. Engineering Mechanics Division ASCE,EM 4, 849–866 (1972).
Dvorak, G. J., Bahei-El-Din, Y. A.: Elastic-plastic behavior of fibrous composites. J. Mech. Phys. Solids27, 51–72 (1979).
Dvorak, G. J., Bahei-El-Din, Y. A.: Plasticity analysis of fibrous composites. J. Applied Mechanics49, 327–335 (1982).
Author information
Authors and Affiliations
Additional information
With 9 Figures
Prepared for the Symposium on Plasticity: Foundations and Future Directions. In Memory of Aris Phillips. January 28–30, 1987. University of Florida, Gainesville, U.S.A.
Rights and permissions
About this article
Cite this article
Dvorak, G.J., Bahei-El-Din, Y.A. A bimodal plasticity theory of fibrous composite materials. Acta Mechanica 69, 219–241 (1987). https://doi.org/10.1007/BF01175723
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01175723