Page 219 - Mechanics Analysis Composite Materials

204 Mechanics and analysis of composiie materials

where

(4.162)

Axial stress, ax,should provide the stress resultant equal to aa (see Fig. 4.72), Le.,

7 a,dy= aa
-a12

This condition allows us to determine the axial strain as
a
E=---
& '
where

E,=E,+ [1+- 1,(I -itanh A)] (4.163)

is the apparent modulus of an angle-ply specimen.
Consider two limiting cases. First, assume that G.rz = 0, Le., that the plies are not
bonded. Then, A = 0 and because

1
lim -tanhI = 1 ,
x-0 I
E,r =E,'. Second, assume that G,, + 00, Le., that the interlaminar shear stiffness is
infinitely high. Then 14 ca and Eq. (4.163) yields

(4.164)

This result coincides with Eq. (4.131), which specifies the modulus of an angle-ply
layer.
For finite values of Gxz,parameter I in Eqs. (4.162) is rather large because it
includes the ratio of the specimen width, a, to the ply thickness, 6, which is, usually,
a large number. Taking into account that tanh I < 1 we can neglect the last term in
Eq. (4.163) in comparison with unity. Then, this equation reduces to Eq. (4.164).
This means that tension of angle-ply specimens allows us to measure material
stiffness with proper accuracy despite the fact that the fibers are cut on the
longitudinal edges of the specimens.
However, this is not true for strength. Distribution of stresses over the half-width
of the carbon-epoxy specimen with properties given above and alii = 20,@= 45" is