Page 111 - Engineered Interfaces in Fiber Reinforced Composites

94 Engineered interfaces in fiber reinforced composites

that the load-bearing capability of a composite depends on the efficiency of stress
transfer, which is largely controlled by the nature of bonding at the interface region,
in addition to the mechanical properties of the fiber and matrix.
Theoretical analysis of interfacial debonding has received significant attention
especially for the fiber pull-out test. The condition of interface debonding has been
defined by two distinct approaches: the shear strength criterion and the fracture
mechanics approach. In the shear strength criterion, when the interface shear stress
(IFSS) reaches the interface shear bond strength, Zb, debonding occurs. In the
fracture mechanics approach, extension of a debond crack requires the potential
energy release rate of the composite constituents to reach a critical value, the
interface fracture toughness, Gi,. In these two debond criteria, both Zb and Gi, are
assumed to be material constants, the characteristic interface properties to be
determined in experiments.
Recognizing the significance of stress concentration at the fiber broken ends,
many researchers have inclined to employ numerical methods, particularly FE
analysis where the effects of specific end geometry as well as different matrix
behavior at the interface region can be properly evaluated. The use of FE method
allows a more accurate description of the interactions between neighboring fibers
and the IFSS fields near the singularity as demonstrated in the fiber fragmentation
test (MacLaughlin and Barker, 1972; Termonia, 1987, 1992; Fan and Hsu, 1992a, b;
Daabin et al., 1992; Daoust et al., 1993; Ho and Drzal, 1995a, b), the fiber pull-out
test (Atkinson et al., 1982; Wu and Claypool, 1991; Marotzke, 1993, 1994; Povirk
and Needleman, 1993; Kim et al., 1994a, b) and microindentation test (Grande et al.,
1988; Tsai, 1990; Kallas et al., 1992; Mital et al., 1993; Meda et al., 1993; Ho and
Drzal, 1996). The stress recovery around the fiber ends after fiber breaks is also
taken into account (Curtin, 1991) to describe the fragmentation distribution as a
function of the fiber’s underlying statistical strength and the interface bond strength.
In this chapter, the roles of the interface are discussed with regard to the efficiency
of stress transfer in various loading geometry of the three most popular single fiber
microcomposite tests, namely the fiber fragmentation test, the fiber pull-out test and
the fiber push-out test. Among many different failure mechanisms that may be
operative at the interface region, universally considered in this chapter as a
predominant failure mode is the debonding along the fiber-matrix interface. Except
for the fiber fragmentation test, only the fracture mechanics approach is employed
to define the debond process. Much of the discussion here is based on the theoretical
consideration of the micromechanics analysis using a shear lag model of the single
fiber composite and other models extended therefrom.

4.2. Fiber fragmentation test

4.2.1. Introduction
Cox (1952) first considered a shear-lag model where an elastic fiber is embedded in
an elastic matrix which is subjected to uniaxial tension. Perfect bonding is assumed