Page 96 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 3. Measurements of interfacelinterlaminar properties 79

where x is the correction factor required to account for the end rotation and
deflection of the crack tip, giving the corrected compliance value

8(a + ~ h ) ~
C=N (3.23)
Ebh3

F and N are the correction factors for the stiffening of the specimen due to large
displacements (i.e. shortening of the beam) and the metal blocks bonded to the
specimen ends, respectively. These correction factors are a complex function of the
measured displacement, length of specimen arms, distance of the load-point above
the beam axis and other geometric factors, and are given in Hashemi et al., (1990b).
It is increasingly realized that crack bridging by misaligned fibers across the crack
faces gives rise to a crack-resistance or R-curve (Hu and Mai, 1993; Williams et al.,
1995) and that such an R-curve will be useful for material comparison. Indeed,
much earlier, Huang and Hull (1989) pointed out the importance of crack bridging
and Hu and Mai (1 993) indicated that this will affect the different compliance-based
equations to evaluate the delamination resistance.
Assuming the coefficient FIN in Eq. (3.22) is close to unity, Eq. (3.22) is then
simplified in the specification (ASTM D5528, 1994) to:

3 P6
G- (3.24)
IC - 2b(a + lAl) '

where A is the additional crack length arising from the end rotation and crack tip
deflection. A can be determined experimentally from a least squares plot of the cube
root of compliance, C1'3, as a function of crack length, a. Eq. (3.24) is called the
'modified beam theory' (MBT) method. This approach also allows the modulus, E,
to be determined as follows

64(a + 1A03P
E= ! (3.25)
Sbh3
which should be independent of delamination length.
Another approach developed on the basis of an empirical compliance calibration,
which was designed originally for isotropic brittle materials (Berry 1963), appears to
avoid certain problems associated with correction factors. The compliance is given
in the form of empirical equation

C=ka". (3.26)

The compliance values for a given crack length, a, are obtained from the slope of the
loading path in the loading-unloading experiments. A least squares line of a plot of
C versus a in a log-log plot allows the parameter k'and exponent n to be determined.
The effect of crack bridging will also influence the exponent n as discussed by Hu
and Mai (1993). Combining Eqs. (3.16) and (3.26),'Grc is given