Page 132 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress transfer 1 I5

fiber ends are smaller than the interface shear bond strength, Zb, (Le. r;(a,z) < Zb).
Substituting this requirement (along with 01 = 0 and e= 0) into Eq. (4.60) gives

(4.71)

Under this circumstance, the external stress corresponding to the fiber fragmenta-
tion, 0, = cof, is obtained from Eq. (4.59)

(4.72)

Because Eq. (4.72) also has to satisfy the condition for full bonding at the interface
governed by Eq. (4.71), the condition for fiber fragmentation while the interface is
fully bonded requires

42 sinh( p2L) (4.73)
" Zy"TS(2L)cosh(/%2L) 1
~
The critical combination of the interface bond strength, Zb, and the fiber length, 2L,
required for the initial interface debonding is plotted according to Eq. (4.73) in Fig.
4.1 1. The regions above and below the curve represent full bonding and partial
debonding at the interface, respectively, with the average fiber tensile strength
estimated from Eq. (4.40). Therefore, for a given value of TI,, one can evaluate the
minimum fiber length (215)~ for interfacial debonding during the fiber fragmentation
process by taking the value of the curve. For example, (2L), z 2.71 mm for
zh = 72.7MPa

n Debonding

ki 7
c
- 0 7
C
0 5 10 15 1 0
Mean fiber fragment length 2L (mm)
Fig. 4.1 1. Plot of interface shear bond strength, Q , as a function of fiber length, 2L, showing the interface
debond criteria, according to Eq. (4.71). After Kim et al. (1993b).