Materials for engineering, 3rd Edition - (Malestrom)

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