Materials for engineering, 3rd Edition - (Malestrom)
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Glasses and ceramics 135<br />
Table 4.1 Some properties of glasses<br />
Property Units Silica Soda-lime Borosilicate Glass<br />
glass glass glass ceramic<br />
Modulus of rupture MPa 70 50 55 >110<br />
Compressive strength MPa 1700 1000 1200 ~1200<br />
Young’s modulus GPa 70 74 65 92<br />
Thermal expansion 10 –6 K –1 0.62 7.8 3.2 1.0<br />
coefficient<br />
Thermal conductivity W m –1 K –1 1.8 1.8 1.5 2.4<br />
Toughness (G c ) J m –2 ~1 ~1 ~1 ~10<br />
αE∆T<br />
σ = 1 – ν<br />
[4.1]<br />
where α is the thermal expansion coefficient, E is Young’s modulus, ν is the<br />
Poisson ratio and ∆T is the temperature difference between the surface and<br />
the interior of the sample.<br />
The value of ∆T f required to generate the fracture stress of the material<br />
(σ f ) can be regarded as a merit index (R) <strong>for</strong> the thermal shock resistance of<br />
ceramics and glasses:<br />
∆T<br />
f<br />
σ f (1 – ν) = = R<br />
α E<br />
A shape factor S may be included, giving:<br />
∆T f = RS<br />
The value of the thermal expansion coefficient is thus of critical importance<br />
in this context and it is obvious from the data in Table 4.1 why borosilicate<br />
glasses are superior in this respect to soda-lime glass.<br />
This approach has made the implicit assumption that the surface temperature<br />
reaches its final value be<strong>for</strong>e there is any change in temperature in the bulk<br />
of the material – i.e. that an infinitely rapid quench has been applied. In<br />
practice, finite rates of heat transfer should be taken into account by considering<br />
the Biot modulus (β), defined by the equation:<br />
r<br />
β = m h<br />
[4.2]<br />
K<br />
where r m is the radius of the sample, h the heat transfer coefficient and K the<br />
thermal conductivity.<br />
If we define a non-dimensional stress σ * as the fraction of stress that<br />
would result from infinitely rapid surface quenching, then<br />
σ* =<br />
σ<br />
αE∆T/(1 – ν)<br />
[4.3]