Page 104 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ply 89
-

c
c .__,
c
c
t
t
02-
02-
c
c
c
c
c --I --I
c
Aa
Fig. 3.38. Microstructuralmodel of the second-order.
The strain in the matrix can be determined with the aid of Fig. 3.38 and Eq. (3.84),
i.e.,
Aa Aa
Em = - - - - 82 (3.86)
l(a) - a - 2R sin CI

where in accordance with Eq. (3.82)

2R
A=-=>. 421 (3.87)
a n
Assuming that there is no strain in the matrix in the fiber direction and there is no
stress in the matrix in the x3-direction we have

om=-. Em Em (3.88)
1 -v;

Substituting o2 from Eq. (3.85) and om,from Eq. (3.88) into Eq. (3.83) and using
Eq. (3.86) to express E~ we arive at

Calculating the integral and taking into account Eq. (3.87) we finally get

(3.89)

where
E-;.
= ctan-'
1
I-A