Page 123 - Engineered Interfaces in Fiber Reinforced Composites

106 Engineered interfaces in fiber reinforced composites

Substituting the solutions for the three major stress components determined in the
bonded and debonded regions, a fiber-matrix interface debond criterion is derived
as

,
27~aGi, = B3u2 + C,(F + C)C + D3(F + c)~ (4.37)
where the coefficients B3, C3 and 03 are the complex functions of material properties
of the constituents and geometric factors, and are given in Appendix B. Therefore,
the stress applied to the matrix at the remote ends, o, = bod(= a(b2 - a2)/b2), for
debond crack propagation is obtained

2naGiC 'I2 - C3 +2D3
Yb2
Cod = a2 { [ (B3 + C3 + D3)2 + 4(B3 + C3 + 03) 2(B3 + C3 +D3)'} '
(4.38)

4.2.3.3. Fiber fragmentation
When the external stress is sufficiently high to cause the maximum FAS to reach
the local fiber tensile strength at the fiber center, the fiber fractures. A fiber tensile
strength model is used in this analysis to predict the average strength of the fiber
corresponding to a given gauge length based on the Weibull probability of failure
(Weibull, 195 1). According to the cumulative failure probability function proposed
by van der Zwaag (1989), the average fracture stress of length (2L0) is given by

(4.39)

where m and cu are the Weibull modulus and scale factor, and r is the gamma
function. Therefore, the average tensile strength of the fiber segment of length (215) is
given by

(4.40)

Since the loading is assumed to be perfectly symmetrical about the fiber center, fiber
breakage is always expected to occur at the center (z = 0)
4(0) = OTS(2L) . (4.41)

The maximum FAS at z = 0 can be determined from Eqs. (4.25) and (4.31)

.I> sech &(L - t) (4.42)