Page 168 - Engineered Interfaces in Fiber Reinforced Composites

150 Engineered interfaces in $her reinforced composites

fundamental limitation of generating interface properties only valid in the
comparative sense for given conditions that seldom represent those of practical
composites of large fiber 6. In this regard, the use of multiple fiber composite
specimens (made from real composites or from model composites with a regular
fiber arrangement for the surrounding composite medium) can eliminate such a
limitation of the single fiber pull-out test. Details of the experimental technique have
yet to be developed although significant difficulties are envisaged in specimen
preparation with the current technology. In fact, the micro-bundle pull-out test has
recently been devised (Qiu and Schwartz, 1991), although still in its early stage of
development, to account for the high fiber volume fraction of real composites.

4.4. Fiber push-out

4.4.1. Solutions for stress distributions
Many investigators have studied the micromechanics analyses of fiber push-out,
notably Bright et al. (1989, 1991), Hsueh (1990b, c), Keran and Parthasarathy
(1991), Lau and Mai (1990, 1991), Marshall (1992), Marshall and Oliver (1987,
1990), Shetty (1988), Singh and Sutcu (1991), Liang and Hutchinson (1993), and
more recently Zhou and Mai (1995). Among these, Keran and Parthasarathy (1991),
Marshall (1992) and Liang and Hutchinson (1993) took into account the effects of
the axial residual stresses in the fiber in addition to the residual radial stresses across
the interface, both of which are caused by the matrix shrinkage during the
processing of the composite. The influence of redistribution of residual stress due to
slicing the composite in preparation of the specimen (Liang and Hutchinson, 1993)
is also specifically addressed. The effects of fiber surface roughness on push-out have
also been analysed by Liu et al. (1995). Numerical analysis based on the finite
element method (Grande et al., 1988; Tsai et al., 1990; Chen and Young, 1991;
Kallas, 1992; Meda et al., 1993; Mital et al., 1993; Ananth and Chandra, 1995;
Chandra and Ananth, 1995; Majumda and Miracle, 1996; Ho and Drzal, 1996) is
also becoming increasingly popular with this loading geometry. Similar to the
microbundle pull-out test a fiber bundle push-out test has also been proposed for
CMCs and a theoretical analysis has been given recently by Zhou and Mai (1994).
However, some theoretical treatment considers only the special case of friction
sliding of a single fiber along a mechanically bonded interface, particularly for some
ceramic matrix composites, where the Coulomb friction law applies. See for example
Zhou and Mai (1995) and Shetty (1988). Assuming a constant friction at the fiber-
matrix interface and neglecting the Poisson effects, Shetty (1988) reported a simple
force balance equation for the frictional shear strength, qr

Tfr = -Wo . (4.125)

qo is determined from the data for the maximal frictional push-out stress, qr, when
the sliding length reaches the entire embedded fiber length (i.e. e = L). qr is given by