Larson-Miller / Hollomon-Jaffe tempering parameter

Tempering, stress relief and post-weld heat treatment are all diffusion-controlled processes, and diffusion depends exponentially on absolute temperature but only linearly on time. That is why a modest temperature increase buys far more than a long extension of soak time. The Larson-Miller parameter — used in the same algebraic form as the Hollomon-Jaffe tempering parameter — captures the trade-off in a single number: LMP = T(C + log₁₀ t) / 1000, with T the absolute temperature in kelvin and t the holding time in hours.

Two heat treatments with the same parameter should produce approximately the same degree of tempering, the same drop in hardness and the same relief of residual stress. This lets you answer the question that comes up constantly on site: a vessel was soaked at 620 °C for 2 hours instead of the specified 650 °C for a shorter period — is that acceptable? Convert both to a parameter and compare. It also underlies the standard trade-off tables in ASME VIII-1 UCS-56, which permit a lower PWHT temperature if the holding time is increased.

The constant C is material dependent. C = 20 is the conventional value for carbon and low-alloy steel tempering and is the default here; some Cr-Mo creep work uses 19.5 or a fitted value. Using the same C for both sides of a comparison is what matters; the absolute parameter value only means something against a curve for the same material and the same C.

Two limits are worth remembering. The parameter has nothing to say about the heating and cooling rates, which codes control separately to avoid distortion and re-hardening, and it says nothing about staying below the lower critical temperature Ac1. Exceeding Ac1 — roughly 720 °C for plain carbon steel and lower for some alloys — re-austenitises the steel and the whole basis of the equivalence collapses. Equivalence calculations are a tool for evaluating what happened, not a licence to substitute an unqualified cycle for the one in the procedure.

T[K] = T[°C] + 273.15
LMP = T[K] × (C + log₁₀ t) / 1000    t in hours, C typically 20
Equivalent time at T₂:  t₂ = 10^( LMP × 1000 / T₂[K] − C )