Page 113 - Mechanics Analysis Composite Materials

98 Mechanics and analysis of composite materials

o,,MPa
2000
1600

1200
aoo

4w

0
0 0.5 1 1.5
(a)

0 2 ; ,2. MPa
~
200 [
50 p-;2

E2+,'

0 12%
0 1 2 3

Fig. 3.41. Stress-strain curves for unidirectional carbon-epoxy composite material under longitudinal
tension and compression (a), transverse tension and compression (b), and in-plane shear (b).

(Section 3.3), material stiffness under tension across the fibers is higher than that of
a pure matrix (see Fig. 3.36).
For qualitative analysis of transverse strength, consider again the second-order
model in Fig. 3.38. As can be seen, stress distribution am(x3)is not uniform, and the
maximum stress in the matrix corresponds to a = 90". Using Eqs. (3.85), (3.86), and
(3.88) we obtain

Taking uy = Om and u2 = 02f, where am and a; are the ultimate stresses for
the matrix and for the composite material and substituting for A and E2 their
expressions in accordance with Eqs. (3.87) and (3.89) we arrive at

(3.105)