Page 113 - Engineered Interfaces in Fiber Reinforced Composites

96 Engineered interfaces in fiber reinforced composites

bonded (elastic) interface, the partially yielding interface and the partially slipped
(or debonded) interface. These interface conditions are controlled by the failure
mechanisms operating at the interface region, depending on the nature of interface
bonding and ductility of matrix material. Hsueh (1988) also presented an analytical
shear-lag model of stress transfer for both the bonded and debonded fiber ends.
However, solutions for the fiber fragment length or the critical transfer length have
not been generated in either of the above two studies.
More recently, Lacroix et al. (1992) obtained solutions for the critical transfer
length using the stress equations previously derived by Cox (1952) for the bonded
region and assuming either constant or varying frictional shear stress at the
debonded region. They proposed three different interface conditions depending on
the state of bonding at the interface, namely the full elastic bonding, the partially
elastic bonding and the fully unbonded models. From the plots of the mean
fragment length as a function of applied stress, the critical transfer length is found
not to be a material constant but to vary with the applied stress, which rather
contradicts with the findings of other investigators.
Apart from the shear-lag model without a distinct region in-between the fiber and
matrix, composite models with interlayers have also been proposed for the fiber
fragmentation loading condition, particularly based on FE analyses (Lhotellier and
Brinson, 1988; Daabin et al., 1992; DiAnselmo et al., 1992; Daoust et al., 1993; Ho
and Drzal, 1995a, b). In these studies, a cylindrical region of thin layer is included
around the fiber having mechanical properties different from those of the bulk
matrix material. Theoretical analyses for debond stresses in fiber pull-out models
have also been developed (Lu and Mai, 1995; Hsueh, 1991) for the microcomposites
containing plastic and visco-elastic coating layers. The effects of such an interlayer
or fiber coating on the mechanical performance and fracture behavior of the bulk
composites will be detailed in Chapter 7 from both the experimental and theoretical
viewpoints.
As mentioned in Chapter 3, a recent development in understanding the interface
states for the fiber fragmentation test geometry is that there are both bonded and
debonded interfaces present simultaneously during the fiber fragmentation process
of some polymer matrix composites (Favre and Jacques, 1990; Favre et al., 1991;
Gulino et al., 1991; Lacroix et al., 1992). In this context, a comprehensive treatment
is presented in the following sections of micromechanics analyses of the fiber
fragmentation test. Three distinct conditions for the fiber-matrix interface are
identified, i.e. full bonding, partial debonding and full frictional bonding, depending
on the interface properties and the fiber tensile strength for given elastic constants of
the composite constituents. It is assumed here that fiber breaks when the maximum
FAS obtained at the fiber center reaches the average tensile strength, and debond
crack propagates at the fiber ends when the debond criterion is satisfied whether a
fracture mechanics approach or shear strength criterion is employed. The
corresponding micromechanics analysis developed on the basis of the shear strength
criterion for interfacial debond (Kim et al., 1993b) is given in Section 4.2.4.
Considering the partial debonded interface as the most general case, a parametric
study is performed for a model composite of carbon fiber-epoxy matrix.