Hollomon-Jaffe Tempering Parameter
Trade soak time against temperature in steel tempering — compute the HJ parameter and solve the equivalent time at a second temperature.
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The engineering
Tempering is a diffusion-controlled process, so time and temperature trade against each other: a short soak at high temperature softens martensite about as much as a long soak at lower temperature. The Hollomon-Jaffe (Holloman) parameter collapses both onto one number — the same HP means the same hardness, so you can compare furnace schedules, qualify a shortened cycle, or predict where a weld's HAZ lands after PWHT. The optional second temperature solves the equivalent-time problem directly: what soak at T₂ matches the tempering effect of the entered cycle.
Two gotchas: time must be in hours and temperature in kelvin — feed it minutes or °C and every comparison is garbage. And C is not a universal constant; it drops with carbon content (roughly C ≈ 21.3 − 5.8·wt%C), with 20 the standard default for medium-carbon steels. HP itself also ignores heat-up and cool-down — for thick sections, count only the time actually at temperature, or integrate the ramp in segments.
Where this math comes from
In 1945, John H. Hollomon and Leonard Jaffe — both working on Army ordnance steel problems at Watertown Arsenal during the war — published "Time-temperature relations in tempering steel" in Transactions of AIME. They showed that hardness after tempering could be mapped onto a single rate parameter of the Arrhenius form T·(C + log t), turning a two-variable furnace scheduling problem into a one-number lookup. Hollomon went on to run General Electric's research laboratory; the parameter kept his name on every heat-treat traveler since.
The idea proved bigger than tempering. Larson and Miller borrowed the identical mathematical form in 1952 for creep-rupture life — the Larson-Miller parameter — and Grange and Baughman's 1956 hardness correlations gave shops direct HP-to-HRC curves for common carbon and alloy grades. George Krauss's Steels: Processing, Structure, and Performance (ASM International, updated 2015) remains the standard modern reference for the parameter and the C ≈ 20 convention this card defaults to.
- 1945J. H. Hollomon & L. D. JaffePublish the tempering parameter T·(C + log t) in Transactions of AIME.
- 1952F. R. Larson & J. MillerAdapt the same form to creep-rupture life — the Larson-Miller parameter.
- 1956R. A. Grange & R. W. BaughmanPublish hardness-vs-HP correlations for carbon and alloy steels.
- 2015George Krauss / ASM InternationalSteels: Processing, Structure, and Performance pins modern usage and the C ≈ 20 default.
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