Abstract
This paper pursues the interest in characterizing stress concentrations in composites for the purpose of providing more reliable input into statistical theories about composite strength. A previous paper estimated stress concentration parameters in a fibre-matrix composite by numerical maximum likelihood, using the chain of bundles model of Harlow and Phoenix. An assumption of the model is that bundles are independent. Here, a model is proposed which allows for a dependence across bundles, usually due to the extent to which a fibre becomes unstressed in the region of a break. The model is demonstrated using experimental data on a carbon-epoxy hybrid composite, and arrays of tungsten-cored silicon carbide fibres embedded in resin. It is shown, via the method of maximum likelihood, how inferences may be made about stress concentrations and also parameters describing single fibre strength.
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References
L. C. Wolstenholme and R. L. Smith, J. Mater. Sci. 24 (1989) 1559.
D. G. Harlow and S. L. Phoenix, J. Compos. Mater. 12 (1978) 195.
Idem, ibid. 12 (1978) 314.
Idem, Int. J. Fracture 17 (1981) 347.
Idem, ibid. 17 (1981) 601.
M. G. Bader and M. J. Pitkethly, Probabilistic aspects of the strength and modes of failure of hybrid fibre composites in, “Mechanical Characterisation of Fibre Composite Materials”, edited by R. Pyrz (Aalborg University, Denmark, 1986).
B. W. Rosen, AIAA J. 2 (1964) 1985.
C. Zweben and B. Rosen, J. Mech. Phys. Solids 18 (1970) 189.
C. Zweben, AIAA J. 6 (1968) 2325.
D. A. Clarke and M. G. Bader, in “Proceedings of ICCM-VI and ECCM-2”, edited by F. L. Matthews, N. C. R. Buskell, J. M. Hodgkinson and J. Morton (Elsevier, London, 1987) pp. 5.382–92.
D. A. Clarke, PhD thesis, University of Surrey (1988).
J. D. Kalbfleisch and R. L. Prentice, “The Statistical Analysis of Failure Time Data” (Wiley, New York, 1980).
W. Nelson, “Applied Life Data Analysis” (Wiley, New York, 1982).
C. Cunnane, J. Hydrology 37 (1978) 205.
G. Blom, “Statistical Estimates and Transformed Beta Variables” (Wiley, New York, 1958).
I. I. Gringorten, J. Geophys. Res. 68 (1963) 813.
A. Hazen, Trans. Amer. Soc. Civ. Eng. 77 (1914) 1547.
E. L. Kaplan and P. Meier, J. Amer. Stat. Assoc. 53 (1958) 457.
L. C. Wolstenholme, PhD thesis, University of Surrey (1989).
A. P. Basu and J. P. Klein, Some recent results in competing risks theory, in Institute of Mathematical Statistics Lecture notes, Vol. 2, “Survival Analysis”, edited by J. Crowley and R. A. Johnson (1982).
M. Ambramowitz and I. A. Stegun, “Handbook of mathematical functions with formulas, graphs and mathematical tables” (Dover, New York, 1972).
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Wolstenholme, L.C. A dependent bundles model for estimating stress concentrations in fibre-matrix composites. J Mater Sci 26, 4599–4614 (1991). https://doi.org/10.1007/BF00612394
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DOI: https://doi.org/10.1007/BF00612394