Abstract
This paper describes a model of stress relaxation in broken fibers in unidirectional metal matrix composites reinforced with long brittle fibers. A cylindrical cell with a broken fiber embedded in a power law creeping matrix is employed, and the broken fiber is assumed to have a bilinear distribution of axial stress. Then, on the basis of energy balance in the cell, a relaxation equation of interfacial shear stress acting on stress recovery segments is derived in a simple form. Under constant overall strain the relaxation equation is approximated rationally and integrated to obtain an analytical solution, which is shown to agree fairly well with the numerical analysis of Du and McMeeking (1995). Moreover, the relaxation equation is combined with Curtin’s (1991) model, so that rupture lime in long term creep is evaluated analytically and explicitly on the assumption of global load sharing. It is shown that the resulting relation represents well the dependence of creep rupture time on applied stress observed experimentally on a unidirectional metal matrix composite.
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References
Curtin, W.A. (1991) Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Soc. 74, 2837–2845.
Du, Z.-Z. and McMeeking, R.M. (1995) Creep models for metal matrix composites with long brittle fibers. J Mech. Phys. Solids 43, 701–726.
Goda, K. (1993) Estimation of creep rupture life of a B/A1 composite using Monte Carlo simulation method. Proc. 12th Symposium on Material and Structural Reliability (in Japanese), p. 45–49. The Society of Materials Science, Japan
Lyengar, N. and Curlin, W.A. (1997) Time-dependent failure in fiber-reinforced composites by matrix and interface shear creep. Acta Mater, (to appear).
Kelly, A. and Tyson, W.R. (1965) Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum. J. Mech. Phys. Solids 13, 329–350.
Kelly, K.W. and Barbero, E. (1993) The effect of fiber damage on the longitudinal creep of a CFMMC. Int. J. Solids Struct. 30, 3417–3429.
Lagoudas, D.C., Hui, C.-Y. and Phoenix, S.L. (1989) Time evolution of overstress profiles near broken fibers in a composite with a viscoelastic matrix. Int. J. Solids Struct. 25, 45–66.
Lifshitz, J.M. and Rotem, A. (1970) Time-dependent longitudinal strength of unidirectional fibrous composites. Fibre Sci. & Technol. 3, 1–20.
Mason, D.D., Hui, C.-Y. and Phoenix, S.L. (1992) Stress profiles around a fiber break in a composite with a nonlinear, power law creeping matrix. Int. J. Solids Struct. 29, 2829–2854.
McLean, M. (1985) Creep deformation of metal-matrix composites. Compos. Sci. & Technol. 23, 37–52.
Ohno, N., Fujita, T., Miyake, T., Nakatani, H. and Imuta, M. (1996) Creep rupture of a unidirectional SCS-6/Beta21S metal matrix composite at 450, 500 and 550°C. Mater. Sci. Res. Int. 2, 199–205.
Ohno, N., Okamoto, N Miyake, T., Nishide, S. and Masaki Jr., S. (I994a) Acoustic emission and fiber damage in creep of a unidirectional SCS-6/Ti-15-3 metal matrix composite at 450°C. Scripta Metall. Mater. 31, 1549–1554.
Ohno, N., Toyoda, K., Okamoto, N., Miyake, T. and Nishide, S. (1994b) Creep behavior of a unidirectional SCS-6/Ti-15-3 metal matrix composite at 450°C. ASME J. Engng Mater. Technol. 116, 208–214.
Ohno, N. and Yamakawa, T. (1996) A model for shear stress relaxation around a fiber break in unidirectional metal matrix composites. JSME Int. J., Ser. A 39, 517–525.
Otani, H., Phoenix, S.L. and Petrina, P. (1991) Matrix effects on lifetime statics for carbon fibre-epoxy microcomposites in creep rupture. J. Mater. Sci. 26, 1955–1970.
Phoenix., S.L., Schwartz, P. and Robinson IV, H.H. (1988) Statics for the strength and lifetime in creep-rupture of model carbon/epoxy composites. Compos. Sci. & Technol. 32, 81–120.
Rosen, B.W. (1964) Tensile failure of fibrous composites. A1AA J. 2, 1985–1991.
Schwenker, S.W., Evans, D.J. and Eylon, D. (1993) Longitudinal creep behavior and damage in SCS-6/Ti-6A1-4V metal matrix composites. Titanium’ 92, Science and Technology (ed. F.H. Froes and I. Caplan), p. 2593–2600. The Minerals, Metals & Materials Society.
Song, Y., Bao, G. and Hui, C.Y. (1995) On creep of unidirectional fiber composites with fiber damage. Acta Metall. Mater. 43, 2615–2623.
Weber, C.H., Du, Z.-Z. and Zok, F.W. (1996) High temperature deformation and fracture of a fiber reinforced titanium matrix composite.Acta Mater. 44, 683–695.
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© 1999 Kluwer Academic Publishers
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Ohno, N., Kawabe, H., Miyake, T., Mizuno, M. (1999). A Model for Shear Stress Relaxation Around a Fiber Break in Unidirectional Composites and Creep Rupture Analysis. In: Wang, R. (eds) IUTAM Symposium on Rheology of Bodies with Defects. Solid Mechanics and its Applications, vol 64. Springer, Dordrecht. https://doi.org/10.1007/0-306-46937-5_13
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DOI: https://doi.org/10.1007/0-306-46937-5_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5297-6
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