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# Multiple tempering or stress-relieving heat treatment effect

Where tempering treatments are all carried out at the same temperature, the effects are additive, and the times are simply summed. (An allowance for the time elapsed during heating and cooling cycles is discussed below). Softening generally occurs, but in secondary hardening steels the hardening produced by precipitation is superimposed on this softening. Where further heat treatment is carried out on a quenched and tempered steel, significant softening will generally not occur at temperatures lower than the original tempering temperature. If the further heat treatment is a stress-relieving treatment, the intended stress relieving temperature will influence selection of the temperature for the original tempering.

Where treatments are carried out at different temperatures it is, in effect, the metallurgical changes which must be added. This can be achieved by using the Hollomon-Jaffetime-temperature parameter, H, which is used for both C-Mn and low alloy steels, and which is given by:

H = T (20 + log t) x 10 -3

where T is the temperature in K, and t is the heating time in hours. As the metallurgical changes which occur follow a logarithmic time law, the time appears as a logarithmic term; H values are therefore not additive. Where periods of heating occurred at different temperatures, the effective times at a common temperature must be evaluated. It is then these effective times which are added. For post-weld stress relieving treatments carried out on C-Mn and low alloy steels, H values are typically in the range 17 to 20.

Where heating and cooling rates are low, as in the heat treatment of thick sections, the time spent nearly at temperature during heating and cooling cycles can make a significant contribution to the metallurgical changes. Such effects can be allowed for by determining additional equivalent times. For the relevant equation and a graphical representation see reference below. The equivalent additional time, Δt, is

Δt = T/[2.3 S (20 - log S)]

where S (K/hour) is the heating or the cooling rate (ignoring the change of sign of the slope).

A value of 20 for the constant in the equations given above is appropriate to C-Mn and low alloy steels. Whilst a value of 30 is commonly used for 9%Cr steels, a value of 20 is probably more appropriate.

## Reference

1. Gulvin T F, Scott D, Haddrill D M and Glen J: 'The influence of stress relief on the properties of C and C-Mn pressure vessel plate steels', J. West of Scotland Iron and Steel Institute, 1972-3 80 149-175 and 282-285.