Page 128 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress transfer 111

.Zm(Y1Z) = az,(u,z) + [b21n(r/u) - v] [q~,,(b,z) - 0'~(a,z)1 (4.53)
(b2 - a*)[( 1 + y) In(b/a) - 1/21 1

where (T'm(u7z)(= a$-(.)) and a',(b,z) are the MASS at the fiber-matrix interface
(Y = u) and the cylindrical surface (at Y = b), respectively. Further, combining Eqs.
(4.50) and (4.52) yields the MAS at the cylindrical surface

(4.54)

where the coefficient & is a function of the elastic properties and geometric factors
of the constituents, and is given by

(4.55)

Therefore, combining Eqs. (4.12) and (4.50E(4.54) gives a differential equation for
the FAS as

(4.56)

where

11 (1 + ;)
B"- u2 [(!)2- (4.57)
2-
(1 +7){(;j41n(;) -+-f[(:)'+l]} .

The solution of Eq. (4.56) and the corresponding solutions for thc IFSS arc obtaincd
for the boundary conditions

(4.58)
O-gW. - e)) = CJt
for the partially debonded interface as a general case. Thus:

(4.59)

(4.60)

The corresponding solutions for the fully bonded interface can be obtained by
substituting ap = 0 when e= 0 in Eqs. (4.59) and (4.60).