A computer simulation of strength of metal matrix
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I.
INTRODUCTION
IN most metal matrix composites, chemical reaction at the fiber-matrix interface occurs when they are exposed at high temperatures. This interfacial chemical reaction has been known as one of the causes in reducing the strength of composites.t-~z To account for this degradation due to the reaction, various mechanisms have been considered. ~3 Among them, Heitman et al.,S Metcalfe and Klein,l'80chiai et a1.,~4-2~ and Shorshorov et al. 22 have attempted to explain the reduction in strength by considering that, as the reaction layer is brittle in most cases, the layer fractures at small strains, and this premature fracture of the layer plays a role as a notch on the fiber surface. This mechanism has been formulated by Metcalfe and Klein, 1'80chiai e t a / . , 14:5A7'2° and Shorshorov et al. 22 in detail, and it was found that this mechanism can essentially account for the degradation in boron-aluminum, ~8 boron-titanum, ~'8'~9 graphitealuminum, ~9 and SiC-coated boron-titanum2~ composites. The formulations of the above authors are, however, based on a single fiber model, which gives a limit of its application, since composites are usually composed of multi-fibers. The aim of the present paper is to study the strength of multi-fiber composites by means of a computer simulation technique. II.
TENSILE S T R E N G T H OF FIBER C O A T E D WITH R E A C T I O N LAYER ON THE BASIS OF THE SINGLE FIBER M O D E L
On the basis of the single fiber model, 14"~5:7the tensile strength of a fiber coated with reaction layer as a function of the thickness of reaction layer for the case where the inter-
SHOJIRO OCHIAI, Associate Researcher, and KOZO OSAMURA, Professor, are with the Department of Metallurgy, Kyoto University, Sakyo-ku, Kyoto 606, Japan. Manuscript submitted November 4, 1985.
METALLURGICALTRANSACTIONS A
facial bonding strength is strong enough to suppress debonding is briefly described as follows. Noting the strength of uncoated fiber as or~u, the fiber stress at which reaction layer fractures and a notch is formed on fiber surface as o-~ and the fiber stress at which the notch extends into fiber as o-/*, the er~ is given by
{31"?= O'Or(l/Vr)|/mrr(l + I/mr)(E//Er)
[1]
assuming that the strength of reaction layer obeys the Weibull distribution, 23 where Vr is the volume, or0r and mr the Weibull constants, Er the Young's modulus of the reaction layer, F is the gamma function, and EI is the Young's modulus of fiber, and the or/* is given by o-7 =
(I/I.12)(EyG*/Trc) ~'2
[2]
where c is the thickness of the reaction layer and G* is the strain energy release rate of fiber, when the c is small enough compared with the diameter of the fiber. The strength of fiber o-f. is given by the sequence of o-7., o'~, and or:*. There are six sequences among them. For the sequences of o':* > o'~ > o-~ (named as S1 type), o-~ > or:* > o-~. (S2 type), and or~ > or~ > or:* (S3 type), the reaction layer does not fracture, no notch is formed on fiber surface, and o-:. is given by o-~. For the sequence of or/* > or~. > o-
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