Page 299 - Mechanics Analysis Composite Materials

284 Mechanics and analysis of composite materiols

MPa
-160 -120 -80 40 0 40 (329
Fig. 6.15. Failure envelope for glass-cpoxy unidirectional coinposite in plane (02, ~12). (-)
approximation criterion, Eqs. (6.12) and (6.16); (- -- -) approximation criterion, Eqs. (6.17); (0)
experimental data.
In conclusion it should be noted that there exist more complicated polynomial
strength criteria than considered above, e.g., the fourth-order criterion of Ashkenazi
(1966) and cubic criterion proposed by Tennyson et al. (1980).
6.1.3. Interlaminar strength

The failure of composite laminates can be also associated with interlaminar
fracture caused by transverse normal and shear stresses cr3 and 213, 223 or aiand
z,,, zu3.(see Fig. 4.18). Because 03 = crz and shear stresses in coordinates (I, 2, 3) are
linked with stresses in coordinates (x, y, z) by simple relationships in Eqs. (4.67) and
(4.68), the strength criterion is formulated here in terms of stresses oz,z.~=,z,~which
can be found directly from Eqs. (5.73). Since the laminate strength in tension and
compression across the layers is different, we can use the polynomial criterion
similar to Eq. (6.14). For the stress state under study, we get
+(;) 2
crz(+-&) = 1 , (6.18)

where
2, =4- = 4-

is the resultant transverse shear stress and Z, determines the interlaminar shear
strength of the material.
In thin-walled structures, transverse normal stress is usually small and can be
neglected in comparison with shear stress. Then, Eq. (6.18) can be simplified and
written as
z, = zi . (6.19)
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