Page 195 - Mechanics Analysis Composite Materials

I80 Mechanics and analysis of composite materials

Section 3.3. Then, material stiffnesses are given by Eqs. (4.124). The corresponding
results are also presented in Fig. 4.47. As follows from this figure, all three models
give close results for the burst pressure (which is natural because << Sf) but
different strains.
The problem of analysis of cracked cross-ply composite laminate was studied by
Tsai and Azzi (1966), Hahn and Tsai (1974), Vasiliev et al. (1970), Vasiliev and
Elpatievskii (1967), Reifsnaider (1977), Hashin (1987) and many other authors. In
spite of this, the topic is still receiving repeated attention in the literature (Lungren
and Gudmundson, 1999). Taking into account that matrix degradation leads to
reduction of material stiffness and fatigue strength, absorption of moisture and
many other consequences that can be hardly predicted but are definitely undesirable
it is surprising how many efforts were undertaken to study this phenomenon rather
than to avoid it. At the first glance, the problem looks simple - all we need is to
synthesize unidirectional composite whose ultimate elongations along and across
the fibers, i.e., El and E2, are the same. Actually, the problem is even more simple,
because E2 can be less than 81 by the factor that is equal to the safety factor of the
structure. This means that matrix degradation can occur but at the load that exceeds
the operational level (safety factor is the ratio of the failure load to the operational
load and can vary from 1.25 up to 3 and more depending on the application of a
composite structure). Returning to Table 4.2 in which El and & are given for typical
advanced composites we can see that El > E;! for all the materials and that for
polymeric matrices the problem could be, in principle, solved if we could increase E2
up to about 1%.
Two main circumstances hinder the direct solution of this problem. The first is
that being locked between the fibers, the matrix does not show the high elongation
that it has under uniaxial tension and behaves as a brittle material (see Section
3.4.2). To study this effect, epoxy resins were modified to have different ultimate
elongations. The corresponding curves are presented in Fig. 4.48 (only the initial
part of curve 4 is shown in this figure, the ultimate elongation of this resin is 60%).
Fiberglass composites that were fabricated with these resins were tested under
transverse tension. As can be seen in Fig. 4.49, the desired value of E2 (that is about
1%) is reached if the matrix elongation is about 60%. However, the stiffness of this

0 I ,4 ,,60%
0 4 8 12 16 20Em’?
Fig. 4.48. Stress-strain curves for epoxy matrices modified for diff‘erent ultimate elongations.