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Materials for engineering, 3rd Edition - (Malestrom)

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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]

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