A ceramic has a flexural strength of 300 MPa, a Young's modulus of 380 GPa, a Poisson's ratio of 0.22 and a coefficient of linear thermal expansion of 8.0×10⁻⁶ K⁻¹. Which value is closest to the rough temperature difference at which thermal shock from rapid quenching begins to crack it, ΔTc = σf(1 − ν)/(Eα)?

Answer: A. About 77 K

Eα = 380×10⁹ × 8.0×10⁻⁶ = 3.04×10⁶ Pa/K and σf(1 − ν) = 300×10⁶ × 0.78 = 2.34×10⁸ Pa, so ΔTc = 2.34×10⁸/(3.04×10⁶) ≈ 77 K. About 99 K forgets to multiply by (1 − ν), and about 127 K divides by (1 − ν) instead. Thermal shock resistance is greater the higher the strength and the lower the Young's modulus and thermal expansion coefficient. Fused silica, with a very small thermal expansion coefficient of about 0.5×10⁻⁶ K⁻¹, is extremely resistant to thermal shock. A high thermal conductivity also helps, because it keeps the temperature difference between the surface and the interior small.