Page 162 - Engineered Interfaces in Fiber Reinforced Composites

144 Engineered interfaces in fiber reinforced composites

@+ 1) sinh[&(L-z)] +2sinh(&z)
- Y2 sinh (&L) 1

Finite element analysis (FEA) is also developed in parallel to validate the results
generated from the micromechanical model. Both the composites containing single
and multiple fibers are considered for the present FEA. The geometry, the loading
method and the boundary conditions are selected to represent those of the actual
experimental technique for both the single and multiple fiber composites, as
illustrated in Fig. 4.30, which are analogous to those used in the corresponding
micromechanics analyses. For the axi-symmetric loading geometry of a two
dimensional model, a uniformly distributed constant stress, ~s = 100 MPa, is applied
to the partially embedded fiber at the surface (z = 0). The boundary conditions are
imposed such that the bottom surfaces of the matrix and composite medium are
fixed at z = 2L, and the axis of symmetry (r = 0) is fixed where there is no
displacement taking place.
Specific results are calculated for Sic fiber-glass matrix composites with the
elastic constants given in Table 4.1. A constant embedded fiber length L = 2.0 mm,
and constant radii a = 0.2mm and B = 2.0mm are considered with varying matrix
radius b. The stress distributions along the axial direction shown in Fig. 4.31 are
predicted based on micromechanics analysis, which are essentially similar to those
obtained by FE analysis for the two extremes of fiber volume fraction, fi, shown in
Fig. 4.32. The corresponding FAS distribution calculated based on Eqs. (4.90) and
(4.120), and IFSS at the fiber-matrix interface of Eqs. (4.93) and (4.132) are plotted
along the axial direction in Fig. 4.32.
The three-cylinder composite model predicts that both the FAS and IFSS
decrease from a maximum near the loaded fiber end towards zero at the embedded
fiber end. Increase in fi (and the equivalent improvement of stiffness in the
composite medium) increases slightly both the maximum IFSS and the stress
gradient, without changing the general trend of the stress fields. For small fi, stress
distributions in the single fiber composite model are equivalent to those of the three-
cylinder model. In sharp contrast, the stress fields change drastically in the single
fiber composite model when vf is large. The FAS values in the central portion of the
fiber are approximately constant and do not diminish to zero at the embedded fiber
end. More importantly, the IFSS displays two peaks at the ends of the fiber, the one
at the embedded end being increasingly greater than the other at the loaded end with