Page 293 - Mechanics Analysis Composite Materials

278 Mechanics and analysis of composite materials

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Fig. 6.10. Failure envelope for carbon+arbon unidirectional composite in plane (m,512). (-)
maximum stress criterion, Eqs. (6.2);(0)experimental data.

The simplest way to induce a combined stress state for the unidirectional ply is to
use the off-axis tension or compression discussed in Section 4.3.1. Applying stress
as in Figs. 4.22 and 4.23 we have stresses al, a2 and 712 specified by Eqs. (4.78).
Then, Eqs. (6.2) yield the following ultimate stresses:
For a, > 0

For a, < 0

Actual ultimate stress is the minimum Sr value of three values provided by Eqs. (6.5)
for tension or Eqs. (6.6) for compression. Experimental data of S.W. Tsai taken
from Jones (1999) and corresponding to a glass-epoxy unidirectional composite are
presented in Fig. 6.1 1. As can be seen, the maximum stress criterion (solid lines)
demonstrates fair agreement with experimental results for angles close to 0" and 90"
only. An important feature of this criterion belonging to a structural type is its
ability to predict the failure mode. Curves 1, 2, and 3 in Fig. 6.1 1 correspond to the
first, the second and the third equations of Eqs. (6.5) and (6.6). As follows from Fig.
6.I l(a), the fiber failure occurs only for 4 = 0".For 0" < 4, < 30°, material failure is
associated with in-plane shear, while for 30" < 4 < 90" it is caused by transverse
normal stress 02.
Maximum strain failure criterion is similar to the maximum stress criterion
discussed above, but is formulated in terms of strains, i.e.