the thermal-shock parameter R′
The plain parameter R judges a material as if every shock were infinitely fast, giving the surface no chance to share its heat with the interior. Real shocks are quick but not instant, and a material that spreads heat rapidly never lets a steep temperature gradient build up in the first place. R' fixes this by folding thermal conductivity into the score: it is the shock-resistance parameter for moderate, finite-rate quenches, and it explains a fact that R alone cannot — why some only-moderately-strong ceramics are superb at surviving thermal shock.
R' is simply R multiplied by the thermal conductivity k: R' = k times sigma_f times (1 - nu) divided by (E times alpha), where k is conductivity, sigma_f strength, nu Poisson ratio, E modulus, and alpha expansion. It applies when heat transfer is fast but finite — a moderate Biot number — so conduction has time to relieve part of the gradient. The logic is intuitive: pump heat away from the surface quickly and the surface never gets as far out of step with the core, so the thermal stress stays smaller. A high k earns a material a big R' even if its strength is unremarkable.
This is exactly why silicon carbide and silicon nitride are the darlings of thermal-shock engineering: their conductivity is high (SiC around 120 W/m/K), so despite only moderate strength they ride out savage temperature swings that would shatter a stronger but poorly conducting oxide. R' is the quantitative form of the design maxim high conductivity helps. It is also the second member of a whole family: R'' brings in the rate of temperature change, while Hasselman's R''', R'''' and the like recast the problem in terms of stored elastic energy and toughness to rank crack propagation and damage resistance rather than initiation. Which parameter you use depends on how fast the shock is and whether you care about starting a crack or living with one.
Compare silicon carbide and alumina under a fast air quench. SiC has lower strength than a top alumina but roughly four times the conductivity, so its R' comes out far higher and it survives quenches that crack the alumina — the everyday reason SiC is chosen for heat exchangers, burner nozzles, and kiln furniture.
Under finite-rate shock, conductivity can matter more than strength: R' captures why high-k SiC beats stronger oxides.
R and R' are not competing rankings; they apply in different regimes. R governs the extreme, near-instant quench where conductivity is useless, and R' governs the more common finite-rate shock — pick the one that matches your actual heat-transfer conditions.