Page 300 - Mechanics Analysis Composite Materials

Chapter 6. Failure criteria and strength of laminates 285

As an example, Fig. 6.16 displays the dependence of the normalized maximum
deflection w/R on the force P for the fiberglass-epoxy cross-ply cylindrical shell of
radius R loaded with a radial concentrated force P (Vasiliev, 1970). The shell failure
was caused by deiamination. The shadowed interval shows the possible values of the
ultimate force calculated with the aid of Eq. (6.19) (this value is not unique because
of the scatter of interlaminar shear strength).

6.2. Practical recommendations and discussion

As follows from the foregoing analysis, for practical strength evaluation of fabric
composites, we can use either maximum stress criterion, Eqs. (6.2) or second-order
polynomial criterion in Eq. (6.14) in conjunction with Eq. (6.15) for the case of
biaxial compression. For unidirectional composites with polymeric matrices, we can
apply Eqs. (6.3) and (6.4) in which function F is specified by Eq. (6.17). It should
be emphasized that experimental data have usually rather high scatter, and the
accuracy of more complicated and rigorous strength criteria can be more apparent
than real. It should be also noted that the simplicity of the recommended
polynomial criteria is associated with the fact that from the very beginning they
were introduced in this chapter as formal approximations of experimental data in
the principal material coordinates. In the literature, these criteria are sometimes
formulated in a tensor-polynomial form as linear combinations of mixed invariants
of the stress tensor aii and the strength tensors of different ranks Sii, Sijk,, etc., Le.

(6.20)
i.k i.k.m.11

Using the standard transformation for tensor components we can readily write this
equation for an arbitrary coordinate frame. However, the fact that the strength

P,kN
2

1.6
1.2

0.8

0.4
0 WlR
0 0.004 0.008 0.012 0.016 0.02

Fig. 6.16. Experimental dependence of the normalized maximum deflection of a fiberglass-epoxy
cylindrical shell on the radial concentrated force.