Materials for engineering, 3rd Edition - (Malestrom)

136
Materials for engineering
where σ is the actual stress observed. But σ * varies with time and we can
write it in terms of the Biot modulus as
σ * = 0.31β [4.4]
A modified thermal shock resistance factor R′ can now be written
∆T
f
= R′
S
1
0.31r h
m
where
Kσ
f (1 – ν)
R′ =
[4.5]
α E
Thus, in addition to the factors mentioned earlier, good resistance to thermal
stress failure also required a high thermal conductivity in the material.
4.1.3 Toughening of glass
Glass shows very high strength in compression: its compressive breakage
strength is over 1 GPa. This high value has been used in the design of
submarine ocean research devices. These are glass spheres (filled with electronic
instruments) which successfully withstand the high hydrostatic pressures
near the ocean bed. The modulus of rupture of window glass is 50 MPa and
this weakness of glass in tension is due to the presence of small surface
cracks (Griffith cracks) arising from normal handling of the material. The
toughness of glass (G c ) is only about 1 J m –2 , and its Young’s modulus is
74 GPa, so that the Griffith equation [2.12] suggests that microcracks of the
order of 10 µm in depth are present.
In order to increase the strength of glass, these surface cracks must be
prevented from spreading by ensuring that they do not experience a tensile
stress. This is achieved by inducing surface compressive stresses into the
glass, which can be done by thermal or chemical toughening.
Thermal toughening
The piece to be toughened is heated above its glass transition temperature
and the surface is rapidly chilled, for example by a series of air-jets played
upon it. The surface cools and contracts while the inside is still soft and at
high temperature. Later, the inside cools, hardens and contracts, but the outer
layers cannot ‘give’ and are thus compressed. In other words, the original
temperature gradient, induced by the air-jets, is replaced by a stress gradient
in the glass (the outer layers being in a state of compression), with a stress
of about –100 MPa, the interior being in tension. Any internal strains influence
the passage of polarized light through the glass, so that when one looks
through a car windscreen while wearing polarizing spectacles it is possible
to see the pattern of the air jets used in the toughening treatment.