Page 134 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ply 1 I9

(T;=+gm= 2 = -0 (3.129)
and that E: = E?. Substituting E; and E? from Eqs. (3.128) we get with due regard to
Eqs. (3.129)
I 1
-(Of + 2VfO) = -(O;" + 2v,a)
Ef E*,

In conjunction with Eq. (3.127) this equation allows us to find O: which has the
form

2a(&vm - Ernvf)urn
a; =
Efuf +Em urn
Simplifying this result under the condition Ef >> E, we arrive at

Of = 20- Vm urn .
Uf

Thus, the loading shown in Fig. 3.72 indeed induces tension of fibers that can be
revealed using the micromechanical model. The ultimate stress can be expressed in
terms of fibers' strength 8f as

1 2.r
@=-Sf-
2 Vmvm
The actual material strength is not as high as follows from this equation which is
derived under the condition that adhesion strength between the fibers and the
matrix is infinitely high. Tension of fibers is induced by the matrix that expands in
the 1-direction (see Fig. 3.72) due to the Poisson effect and interacts with fibers
through shear stresses whose maximum value is limited by the fiber-matrix adhesion
strength. Under high shear stress, debonding of fibers can occur reducing the
material strength that is, nevertheless, very high. This effect is utilized in composite
shell with radial reinforcement designed to withstand high intensity external
pressure (Koltunov et al., 1977).

3.7. References

Abu-Farsakh, G.A., Abdel-Jawad, Y.A.and Abu-Laila, Kh.M. (2000). Micromechanical characteriza-
tion of tensile strength of fiber composite materials. Mech. Composite Mater. Struct. 7(1), 105-122.
Bogdanovich. A.E. and Pastore, C.M. (1 996). Mechanics of Textile and Laminated Composites. Chapman
& Hall, London.
Chiao, T.T. (1979). Some interesting mechanical behaviors of fiber composite materials. In Proc. of Ist
USA-USSR Symposium on Fracture of Composite Moteriuls, Riga, USSK, 4-7 September, 1978
(G.C. Sih and V.P. Tamuzh eds.). Sijthoff and Noordhoff, Alphen aan den Rijn., pp. 385-392.
Crasto, A.S. and Kim, R.Y. (1993). An improved test specimen to determine composite compression
strength. In Proc. 9th Int. Conj: on Composite Materials (ICCM/9),Madrid, 12-16 July 1993. Vol. 6,
Composite Properties trnd Applications. Woodhead Publishing Ltd, pp. 621-630.