Thermal Shock Resistance (Kingery R′)

First and second thermal-shock parameters for brittle ceramics — the max temperature drop a part survives, and how conductivity buys margin.

InputR′ = σ_f·(1−ν) / (E·α) , R‴ = R′·k

Fracture strength σ_f (MPa)or enter ksi — converts to MPaPoisson's ratio νYoung's modulus E (GPa)or enter Msi — converts to GPaCTE α (1e-6/K)Thermal conductivity k (W/m·K)

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The engineering

For a brittle ceramic quenched instantly, the surface wants to shrink but the hot interior restrains it, generating tensile stress σ = E·α·ΔT/(1−ν). Setting that equal to the fracture strength gives R′ — the critical temperature drop the material can withstand before it cracks under an infinitely fast (Biot → ∞) quench. Reach for it when comparing candidate materials for nozzles, thermal barriers, or anything that sees a fast temperature transient.

R′ alone assumes the worst case — perfect thermal contact. Real quenches are finite, so conductivity matters: multiplying by k gives R‴, the parameter that ranks materials under moderate heat-transfer conditions. That's why fused silica (low α, low E) survives a torch-and-plunge that shatters a stiff, high-expansion oxide even though the latter is 'stronger.' Watch units: α is entered in 10⁻⁶/K, and the result is a temperature difference, not an absolute temperature.

Where this math comes from

W. David Kingery, working at MIT in the early 1950s, put ceramic thermal-shock behavior on a quantitative footing. His 1955 Journal of the American Ceramic Society paper laid out a family of resistance parameters — R, R′, R″, R‴ — each matched to a different quench severity, so an engineer could pick the right figure of merit instead of arguing about which ceramic was 'toughest.'

Kingery went on to write Introduction to Ceramics, the field's defining textbook, and these parameters remain the first screen a materials engineer runs. Hasselman later extended the picture in 1969 to crack propagation and the 'thermal shock damage resistance' regime, explaining why some materials crack gradually rather than failing catastrophically.

1955W. David KingeryDefines the R, R′, R″, R‴ thermal-shock resistance parameters for brittle ceramics.
1960W. D. KingeryIntroduction to Ceramics codifies the parameters as standard practice.
1969D. P. H. HasselmanExtends the theory to crack initiation vs. propagation and damage resistance.

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