Page 65 - Engineered Interfaces in Fiber Reinforced Composites

48 Engineered interfaces in fiber reinforced composites

41

a

-2 11,.,1....1....
7 7.5 0 8.5 9 9.5 IO
(a) Ln(Fiber axial stress, MPa)

Fig. 3.4. Ln-Ln plot of fiber fragment length as a function of fiber stress (a) for Kevlar 29 fiber-epoxy
matrix composite and (b) for a carbon fiber-epoxy matrix composite. Yabin et al. (1991).

where of" is the average fiber tensile strength and a, the fiber radius. A non-
dimensional correction factor x has been introduced later to take into account the
statistical distribution of tensile strength and fragment length of the fiber

where CTTS is fiber tensile strength at the critical transfer length. It is noted that
x = 0.75 (Ohsawa et al., 1978, Wimolkiatisak and Bell, 1989) is taken as a mean
value if the fiber fragment lengths are assumed to vary uniformly between (L)c and
(2L),. In a statistical evaluation of fiber fragment lengths and fiber strength, Drzal
et al. (1980) expressed the coefficient in terms of the gamma function, r, and
Weibull modulus, m, of the strength distribution of a fiber of length, I, as