Page 324 - Mechanics Analysis Composite Materials

Chapter 7. Environmental, special loading, and manufacturing effeeis 309

Consider an orthotropic layer referred to coordinate axes x, y making angle Cp with
the principal material coordinate axes (see Fig. 7.2). Using Eqs. (7.14) instead of
Eqs. (4.56) and repeating the derivation of Eqs. (4.71) we arrive at

(7.17)

where A,,l are specified by Eqs. (4.72) and the thermal terms are

(7.18)

Here

T
ET2 = E: + VI'S;, E;l E; + VZlE,
and E:, E: are determined by Eqs. (7.13). The inverse form of Eqs. (7.17) is

Ev + E,T , YxyT = y.r,v +rryT . (7.19)
&.rT = 8.r + e.rT 7 ETT
Here, E,, E,,, and yxy are expressed in terms of stresses a,, c,,,and z.~?with Eqs. (4.73,
while the thermal strains are

Introducing thermal expansion coefficients in xy coordinate frame with the
following equations:

and using Eqs. (7.13) we get

(7.21)

As follows from Eqs. (7.19), in an anisotropic layer, uniform heating induces not
only normal strains, but also the shear thermal strain. As can be seen in Fig. 7.4,