Page 75 - Mechanics Analysis Composite Materials

60 Mechanics and analysis of composite materials

Fig. 3.9. Atoms’ interaction curve (-) and its sine approximalion(- -- -).

Introducing strain

we arrive at

cr = O,sin 2ns .

Now, we can calculate modulus as

Thus

E
at=-.
2n
This equation yields a very high value for the theoretical strength. For example, for
a steel wire, at = 33.4 GPa. By now the highest strength reached in 2 pm diameter
monocrystals of iron (whiskers) is about 12 GPa.
The model under study allows us to introduce another important characteristic
of the material. The specific energy that should be spent to destroy the material
can be presented in accordance with Fig. 3.9 as

-x
2y = /”cr(a)da . (3.9)
a)

As material fracture results in formation of two new free surfaces, y can be referred
to as specific surface energy (energy spent to form the surface of unit area).