Hollomon-Jaffe Parameter: Minimizing negative effects through multiple PWHT Cycles

In 1945, Hollomon and Jaffe [1] published fundamental studies on the relationship between tempering temperature and tempering time required to achieve a specific hardness. If the tempering time is reduced, the tempering temperature must be increased to achieve the same hardness.

Hollomon and Jaffe defined this relationship between the interchangeability of tempering temperature and tempering time using the following equation, which incorporates the Hollomon-Jaffe parameter P:

Equation (1):

$P=\frac{T_S}{1000}\text{•}[C+lo{g}_{10}(t_{})]$

Where:

• P = Hollomon-Jaffe parameter [-]
• T_S = Tempering/holding temperature [Kelvin]
• t = Tempering duration/holding time of the heat treatment [h]
• C = A constant (dependent on the carbon content of the material):
• C = 15 for steels with 0.90 to 1.20 % carbon
• C = 19.5 for steels with 0.15 to 0.45 % carbon (in practice, the constant C = 20 is used for carbon steels and low-alloy C-Mn steels)
• C = 30 for higher-alloys

Example 1:

T_S = 863,15 K (= 590 °C; = 1094 °F)

t = 1,5 h

C = 20 (C-Stähle und niedriglegierte C-Mn-Stähle)

$P=\frac{\mathrm{863,15}}{1000}\text{•}[20+lo{g}_{10}(\mathrm{1,5})]$

P = 17,41

In post-weld heat treatment (PWHT), negative effects on strength and fracture toughness must be minimized by adhering to the permissible critical Hollomon-Jaffe parameters (P_crit). To this end, verification methods involving calculations can be used to determine optimal annealing specifications in order to comply with the critical values P_crit as specified in Section 11 of EN 13445-4, thereby avoiding the need for additional material testing.

Additional effects during the heating phase or cooling phase

Heat treatment of heavy and thick components is sometimes associated with long heating and cooling times. As a result, significant metallurgical changes can occur even during these phases.

These effects can be accounted for by applying time corrections—determined in addition to the holding time—when the heating or cooling rate is constant.

Equation (2): Time correction due to the heating phase in [h|

$$\mathrm{\Delta }{t}_{heat}=\frac{T_S}{\mathrm{2,3}\bullet K_1[20-lo{g}_{10}(K_1)]}$$

Equation (3): Time correction due to the cooling phase in [h]

$$\mathrm{\Delta }{t}_{cool}=\frac{T_S}{\mathrm{2,3}\bullet K_2[20-lo{g}_{10}(K_2)]}$$

Where:

∆t_heat = time correction during the heating phase in [h]

∆t_cool = time correction during the cooling phase in [h]

K₁ = heating rate [Kelvin/h]

K₂ = cooling rate [Kelvin/h]

20 = constant (for C and C-Mn steels); see above

The total duration t_corr for calculating the Hollomon-Jaffe parameter (see Equation (1)) is calculated in [h]:

t_corr= t + ∆t_heat + ∆t_cool = t + $\frac{T_S}{\mathrm{2,3}\bullet K_1[20-lo{g}_{10}(K_1)]}$ + $\frac{T_S}{\mathrm{2,3}\bullet K_2[20-lo{g}_{10}(K_2)]}$

Example 2 (Compared to Example 1, taking into account the heating and cooling phases):

K₁  heating rate  = 100 K/h;

K₂ cooling rate  = 50 K/h;

Holding time t = 1,5 h;

t_corr = t + ∆t_heat + ∆t_cool = t + $\frac{T_S}{\mathrm{2,3}\bullet K_1[20-lo{g}_{10}(K_1)]}$ + $\frac{T_S}{\mathrm{2,3}\bullet K_2[20-lo{g}_{10}(K_2)]}$ [h]

t_corr = 1,5 + $\frac{\mathrm{863,15}}{\mathrm{2,3}\bullet 100[20-lo{g}_{10}(100)]}$ + $\frac{\mathrm{863,15}}{\mathrm{2,3}\bullet 50[20-lo{g}_{10}(50)]}$ [h]

t_corr = 1,5 + 0,208 + 0,410 [h]

t_corr = 2,118 h

Using the corrected holding time t_corr = 2.118 h, the corrected Hollomo-Jaffe parameter P_corr can be calculated using Equation (1):

$P_{corr}=\frac{T_S}{1000}\text{•}[C+lo{g}_{10}(t_{corr})]$

$P_{corr}=\frac{\mathrm{863,15}}{1000}\text{•}[20+lo{g}_{10}(\mathrm{2,118})]$

P_corr = 17,54

Calculation of the annealing time and/or holding time for given Hollomon-Jaffe parameters

Some standards for pressure equipment, such as EN 13445-4, or material standards, such as EN 10028-2, specify critical Hollomon-Jaffe parameters (P_crit) from which specific heat treatment specifications can be derived, such as the hold time for PWHT annealing.

The hold time t and the tempering/annealing temperature T_S can be derived from the above formula (1).

Equation (4) for calculating the holding time:

$t={10}^{\frac{1000\cdot P}{T_S}-20}$ [h]

Calculation of the tempering or annealing temperature for given Hollomon-Jaffe parameters

Equation (5) for calculating the tempering or annealing temperature:

$T_S=\frac{1000\cdot P}{20+lo{g}_{10}(t_{})}$ [Kelvin]

Effect of Repeated Heat Treatments

In the case of repeated heat treatments (at the same reference temperature), the respective equivalence times can be calculated using Equation (4), and the sum of these times can then be substituted into Equation (1) above to determine the total Hollomon parameter P_total.

Using the Hollomon calculation tool, both the Hollomon parameter P for each individual annealing and the total Hollomon parameter Ptotal for multiple annealings can be easily determined using the actual annealing parameters.

Note: Although normal annealing is a heat treatment, it does not need to be taken into account.

Referenzen:

[1] Hollomon, J. H.; Jaffe, L. D.. (1945). Time–Temperature Relations in Tempering Steel.
Transactions of the American Institute of Mining and Metallurgical Engineers, Vol. 162, 1945, pp. 223–249.

[2] Gulvin, T.F.; Scott, D.; Haddrill, D.M.; Glen, J.. The Influence of Stress Relief on the Properties of C and C-Mn Pressure Vessel Plate Steels. Journal of the West of Scotland Iron and Steel Institute, 1972–1973, Vol. 80, pp. 149–175 and 282–285.