Page 302 - Mechanics Analysis Composite Materials

Chapter 6. Failure criteria and strength of laminutes 387

the overbar denotes, as earlier, the ultimate value of the corresponding stress. In the
general case, ;s:5 # 7yj. Indeed, for a unidirectional composite, stress induces
tension of the fibers, while ziS causes compression of the fibers, and the
corresponding ultimate values can be different. Using results presented in Section
2.4 we can conclude that for the loading case shown in Fig. 6.17(a), 01= ti5!
o2= -5I;S and z12 = 0, while for the case in Fig. 6.17(b), CJI = -5ij, 02 = zj5
and ~~2 = 0. Applying strength criterion in Eq. (6.22) for these loading cases we
arrive at

In general, these two equations give different solutions for R&. The unique solution
exists if the following compatibility condition is valid:

(6.23)

If the actual material strength characteristics do not satisfy this equation, then the
strength criteria in Eq. (6.22) cannot be applied to this material. If they do, then
coefficient RY2 can be found as

(6.24)

For further analysis, consider for the sake of brevity a special orthotropic material
shown in Fig. 6.18 for which 5: = 8; = ai = 5, = &J,T& = 7Tj = 745 and 712 = 70.
As can be seen, Eq. (6.23) is satisfied in this case, and the strength criterion,
Eq. (6.22), referred to the principal material coordinates (I, 2) in Fig. 6.18 acquires
the form

(6.25)

where in accordance with Eq. (6.24)

(6.26)