# Hollomon–Jaffe parameter

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The Hollomon–Jaffe parameter, or HP, also generally known as the Larson-Miller parameter,[1] describes the effect of a heat treatment at a temperature for a certain time.[2] This parameter is especially used to describe the tempering of steels, so that it is also called tempering paramenter.

## Effect

The effect of the heat treatment depends on its temperature and its time. The same effect can be achieved with a low temperature and a long holding time, or with a higher temperature and a short holding time.

## Formula

In the Hollomon–Jaffe parameter, this exchangeability of time and temperature can be described by the following formula:

${\displaystyle H_{p}={\frac {(273.15+T)}{1000}}\cdot (C+\log(t))}$

This formula is not consistent concerning the units; the parameters must be entered in a certain manner. T is in degrees Celsius. The argument of the logarithmic function has the unit hours. C is a parameter unique to the material used. The Hollomon parameter itself is unitless and realistic numeric values vary between 15 and 21.

${\displaystyle H_{p}=T(C+\log(t))\,}$

where T is in kilokelvins, t is in hours, and C is the same as above.

Holloman and Jaffe determined the value of C experimentally by plotting hardness versus tempering time for a series of tempering temperatures of interest and interpolating the data to obtain the time necessary to yield a number of different hardness values. This work was based on six different heats of plain carbon steels with carbon contents varying from 0.35%–1.15%. The value of C was found to vary somewhat for different steels and decrease linearly with the carbon content of a steel grade. Holloman and Jaffe proposed that C = 19.5 for carbon and alloy steels with carbon contents of 0.25%–0.4%; and C = 15 for tool steels with carbon contents of 0.9%–1.2%.[3]