Page 74 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics qf a unidirectionalply 59

be used to make fibers with the strength exceeding the strength of such traditional
structural materials as aluminum or steel (see Table 1.1). The general answer is well
known: strength of a thin wire is usually much higher than the strength of the
corresponding bulk material. This is demonstrated in Fig. 3.7 showing that the wire
strength increases while the wire diameter is reduced.
In connection with this, two questions arise. First, what is the upper limit of
strength that can be predicted for an infinitely thin wire or fiber? And second, what
is the nature of this phenomenon?
The answer for the first question is given in Physics of Solids. Consider an
idealized model of a solid, namely a regular system of atoms located as shown in
Fig. 3.8 and find the stress, 6,that destroys this system. Dependence of G on the
atomic spacing following from Physics of Solids is presented in Fig. 3.9. Point 0
of the curve corresponds to the equilibrium of the unloaded system, while point
U specifies the ultimate theoretical stress, 0,.Initial tangent angle, u, characterizes
material modulus of elasticity, E. To evaluate at, we can use the following sine
approximation (Gilman, 1959) for OU segment of the curve
a - ao
fJ= a, sin 2n- .
a0

' d,mm
0.4 0.8 1.2 1.6
Fig. 3.7. Dependence of high-carbon steel wire strength on the wire diameter.

0

0

Fig. 3.8. Material model.