Page 127 - Engineered Interfaces in Fiber Reinforced Composites

110 Engineered interfaces in fiber reinforced composites

related to a single parameter such as the interface bond strength, zb, as in
conventional analyses of the test given by Eq. (3.3).

4.2.4. An improved model based on a shear strength criterion

Although a fracture mechanics approach presented in Section 4.2.3 in general
deals with a more fundamental aspect of the interface debond problem for a given
loading configuration, a shear strength criterion has an important advantage in that
the interfacial shear strength, whether for the bonded or debonded regions, can be
directly determined from the experimental results of the fiber fragmentation test.
Therefore, in this section, a micromechanics analysis is presented based on the shear
strength criterion for interfacial debonding. A particular emphasis is placed on the
identification of the specific criteria required to satisfy each interface condition, i.e.
full bonding, partial debonding and full frictional bonding. The approximate
analysis given in this model leads to relatively simple, closed-form equations for all
basic solutions for the stress distributions in the constituents, the external stress
required for debonding or fiber fragmentation, and the mean fiber fragmentation
length for the three different interface conditions.

4.2.4.1. Solutions for stress distributions
For the cylindrical coordinates of the shear-lag model shown in Fig. 4.6, the
governing conditions adopted in this analysis are essentially the same as those
described in Section 4.2.3. There is one exception in that the mechanical equilibrium
condition between the external stress, 0, and the internal stress components given by
Eq. (4.11) is replaced by

b
b20 = a2+) +2/r8m(r,z)drdz (4.50)
a
It is assumed here that the axial displacements are independent of the radial
position, and the stress components in the radial and circumferential directions are
neglected for Eqs. (4.8) and (4.9). Also, the radial displacement gradient with respect
to the axial direction is neglected compared to the axial displacement gradient with
respect to the radial direction in Eq. (4.10). Combination of Eqs. (4.10) and (4.16)
for the boundary condition of the axial displacement continuity at the bonded
interface &e. u‘m(a,z) = U;(z)) and integration gives:

(4.51)

(4.52)

Therefore, from Eqs (4 8) (4.10) and (4.49), the MAS is obtained