Page 286 - Mechanics Analysis Composite Materials

Chapter 6

FAILURE CRITERIA AND STRENGTH OF LAMINATES

Consider a laminate consisting of orthotropic layers or plies whose principal
material axes 1, 2, 3, in general, do not coincide with global coordinates of the
laminate (x, y, z) and assume that this layer or ply is in the plane stressed state as
in Fig. 6.1. It should be emphasized that, in contrast to the laminate that can be
anisotropic and demonstrate coupling effects, the layer under consideration is
orthotropic and is referred to its principal material axes. Using the procedure that is
described in Section 5.10 we can find stresses 01, ~2,and 712 corresponding to a
given system of loads acting on the laminate. The problem that we approach now is
to evaluate the laminate load-carrying capacity, Le., to calculate the loads that cause
the failure of the individual layers and the laminate as a whole. For the layer, this
problem can be readily solved if we have a failure or strength criterion
F(Cl,Q,T12) = 1 , (6-1)
specifying the combination of stresses that causes the layer fracture. In other words,
the layer works while F < 1, fails if F = 1, and does not exist as a load-carrying
structural element if F > 1. In the space of stresses q,Q,TI~, Eq. (6.1) specifies the
so-called failure surface (or failure envelope) shown in Fig. 6.2. Each point of the
space corresponds to a particular stress state, and if the point is inside the surface,
the layer resists the corresponding combination of stresses without failure.
Thus, the problem of strength analysis is reduced to a construction of a failure
criterion in its analytical, Eq. (6.1), or graphical (Fig. 6.2) form. By now, numerous
variants of these forms have been proposed for traditional and composite structural
materials (Gol’denblat and Kopnov, 1968; Wu, 1974; Tsai and Hahn, 1975;
Rowlands, 1975; Vicario and Toland, 1975; etc.) and described by the authors of
many text-books in Composite Materials. Omitting the history and comparative
analysis of particular criteria that can be found elsewhere we discuss here mainly the
practical aspects of the problem.

6.1. Failure criteria for an elementary composite layer or ply

There exist, in general, two approaches to construct the failure surface, the first
of which can be referred to as the microphenomenological approach. The term

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