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The prediction of maximum HAZ hardness in various regions of multiple pass welds

Joanna M Nicholas and David J Abson

Paper presented at the 17th International Conference 'Computer Technology in Welding and Engineering' Held at the University of Cranfield, 18-19 June 2008.


In a previous study, equations for the prediction of the maximum HAZ hardness in single pass welds in C-Mn and low alloy steel were reviewed. In the present study, the benefits of an approach for estimating the hardness of the heat affected zone after tempering by the deposition of subsequent welds has been considered. Multipass welding, which imposes repeated thermal cycles to parts of a weldment, may result in increases in hardness rather than decreases where the initial microstructure does not contain high percentages of martensite and the steel contains secondary hardening elements. For hardness-critical applications (such as sour service) where a maximum hardness limit is imposed, the prediction of maximum HAZ hardness, and of the effect of changes in welding parameters, can effect considerable savings in time and cost.

The parameters used to describe a heat treatment cycle (heating rate, soak temperature, soak time and cooling rate) are often combined into a temper parameter, such as the Hollomon-Jaffe temper parameter. Multipass welding can be viewed as an extremely rapid postweld heat treatment cycle. In principle, the sub-critical part of a welding cycle can therefore also be described by such a parameter. However, as the heating and cooling rates are constantly changing, some form of modification to the determination of such a parameter is required. The Rosenthal equations have been used to determine time-temperature response, and this was discretised assuming a series of instantaneous temperature increases and finite hold times. This discretised thermal cycle was then used to determine an appropriate Hollomon-Jaffe temper parameter.

Okumura et al[11] devised an empirical method to determine the change in hardness after PWHT, in which the composition of the material and the Hollomon-Jaffe parameter were used. This method was adopted in the present study, with the Hollomon-Jaffe parameter determined as described above, along with the method of computing the maximum HAZ hardness determined in the previous study, the final hardness can be calculated. It should be noted that trends associated with varying composition or welding parameters rather than exact hardness values are best predicted in this fashion, as the uncertainties associated with any prediction are compounded with increased assumptions at each stage.

This approach was tested against welds deposited with varying heat inputs; for the welds examined, it generated a reasonable agreement with the measured values.


Increasingly, fabrication codes and customers call for a limit on the maximum hardness achieved in the weld region. In most cases, this applies to the weld metal cap or root, or the heat affected zone (HAZ), and procedure development and qualification welding trials are carried out to attain the required properties and welding conditions. A number of investigations[1-8] have determined empirical relationships between steel compositions and the welding parameters to predict the as-welded HAZ hardness, but no empirical relationships have been determined for multipass welds. Oddy et al[9] have determined a method and finite element model for determining the hardness of a multipass weld in a 2.25Cr-1Mo steel. This method requires intimate knowledge of the thermal properties of the steel (TTT diagram, phase diagram, absolute martensite and bainite hardness levels), which are not necessarily readily available. Oddy's approach uses the Hollomon-Jaffe parameter (HJP)[10] to describe the effect of the thermal cycle, as does an approach taken by Okumura et al[11] for describing the maximum HAZ hardness after postweld heat treatment (PWHT). Application of HJP to an isothermal heat treatments, such as welding cycles, is more complex, as some method of transforming such a heat treatment to an HJP value is necessary. In this paper, a semi-empirical method of determining the maximum hardness in the heat affected zone of multipass welds is presented.



In order to determine a starting point for the determination of hardness in multipass welds, a number of issues need to be considered. A multipass weld results in material experiencing a number of thermal cycles, varying as the welding parameters and the distance from the weld pool change. This results in a complex microstructure (Fig.1) and a consequent distribution of hardness. In a single-pass weld, the hardness along the HAZ, adjacent to the fusion boundary (grain-coarsened HAZ, GCHAZ) can be described with knowledge of the parent steel composition and the welding parameters (or cooling time from 800°C to 500°C (t8/5) recorded during welding). The hardness in the HAZ reduces with increasing distance from the fusion boundary, as the peak temperature experienced reduces. The effect of tempering by multiple weld passes, could be considered to be a number of an isothermal postweld heat treatments. Okumura et al[11] use a 'change in hardness' algorithm, which was selected for use in this work, to apply to the subcritically reheated grain-coarsened HAZ (SCGCHAZ). This method uses the HJP to describe the thermal cycle experienced by the weld.

Fig.1. Schematic showing zones present in the cap region of a multipass weld
Fig.1. Schematic showing zones present in the cap region of a multipass weld

Determination of the Hollomon-Jaffe Parameter

For a given set of welding conditions (thickness, joint geometry, heat input, preheat), the thermal cycle can be estimated from the Rosenthal equations, at various locations from the weld centreline.[12,13] Having determined the temperature profile with respect to time, the effective HJP for the sub-critical thermal cycle can be evaluated by discretisation of the thermal profile as follows:

At t=t0, T=T0
At t=t1, T=T1
At t=tn, T=Tn

Where t is time in hours and T is temperature in Kelvin.

The stepwise evaluation of the HJP re-evaluates an effective time at the next temperature, and assumes an instantaneous jump to that temperature, as shown in an exaggerated form in Fig.2.

Fig.2. A simplified schematic representation of how the weld thermal cycle equates to a series of isothermal heat treatments for evaluation of the effective HJP
Fig.2. A simplified schematic representation of how the weld thermal cycle equates to a series of isothermal heat treatments for evaluation of the effective HJP
Where a weldment is subjected to heating at different temperatures, the times are additive only if adjusted, by means of the HJP, to a common temperature. This approach is similar to that used by Alberry. [14]


The HJP increases to a maximum value for a given position in the weld zone (Fig.3).

Fig.3. A diagram of how the HJP and temperature vary with time for a given location in the weld zone during welding
Fig.3. A diagram of how the HJP and temperature vary with time for a given location in the weld zone during welding

Determination of as-welded HAZ hardness

The maximum HAZ hardness of the first weld bead was established by using the approach recommended by Nicholas and Abson[14], utilising the parent material composition, and the t8/5 determined for the first pass.

The maximum as-welded hardness is generally described by:


where C is the carbon content in wt%


all elements in wt%


all elements in wt%


all elements in wt%

t8/5 is the cooling time from 800°C to 500°C for a given weld pass, in s.

At the extremes of t8/5, the expression is modified, such that at t8/5=tm, tm is substituted for t8/5 in all cases to account for the maximum hardness possible (i.e. 100% martensite).


For cases where t8/5 ≥ tb, tb is substituted for t8/5 in the first part of the equation, to account for a fully bainitic microstructure, with continual softening to allow for subsequent grain growth.


i.e. for t8/5 ≥ tb


Thus, for a given composition, the as-welded hardness varies with t8/5 in the manner shown in Fig.4. The 95% confidence interval for this prediction is ±56HV.

Fig.4. An example of how predicted as-welded hardness varies with increasing cooling time (heat input or preheat), for a given composition
Fig.4. An example of how predicted as-welded hardness varies with increasing cooling time (heat input or preheat), for a given composition

Determination of reheated HAZ hardness

After a second or subsequent pass, the following method, put forward by Okumura et al [11], to estimate the maximum HAZ hardness, was applied:

HV = HVweld - ΔHV

Where HVweld is the as-welded maximum hardness and ΔHV is the change in hardness as a result of subsequent heat treatments.


M = 0.5 - 0.455arctan(x)


t8/5, tm and tb relate to the initial as-welded hardness values.

The tempering (softening) effect is influenced by the term M, and the relevant HJP calculated, and secondary hardening, as a parabolic nature for each of V, Nb and Mo to as minimum secondary hardening at values of HJP 18,18 and 17.3 respectively.

Welding trials

In order to validate the predictions of hardness, a series of submerged arc welds were deposited. So that the desired extent of bead overlap could be achieved with the minimum number of trial welds, the welds were bead in groove welds, with a second weld bead deposited in a groove running at an angle to the first weld bead (Fig.5). The parent steel compositions are given in Table 1 and the welding parameters, parent material thickness and IIW carbon equivalent are given in Table 2.

Fig.5. Schematic example of the two weld beads deposited, indicating divergent welds in order to ensure that the overlap of the beads was optimised at a certain location in the plate
Fig.5. Schematic example of the two weld beads deposited, indicating divergent welds in order to ensure that the overlap of the beads was optimised at a certain location in the plate

Table 1. Plate compositions.

 Element, wt%
Plate CodeCSiMnPSCrMoNiAlCuNbTiV
1A624 0.10 0.38 1.35 0.024 0.020 0.020 0.008 0.047 0.004 0.060 <0.002 0.002 0.002
1B819 0.14 0.20 1.05 0.015 0.004 0.550 <0.004 0.230 0.039 0.280 <0.002 0.002 0.054
1B458 0.07 0.28 1.36 0.007 0.002 0.014 0.003 0.015 0.037 0.009 0.014 0.011 0.002
1B168 0.19 0.23 1.44 0.015 0.006 0.022 0.013 0.023 0.025 0.025 0.023 0.002 0.005

Table 2 Detail of the welding parameters used.

Weld CodePlate CodePlate Thickness
IIW CECurrent
Travel Speed
Heat Input
Measured t8/5 (s)Calculated t8/5 (s)
W7 1B168 50 0.44 500 28 550 1.5 --- 8.1
W8 1B168 50 0.44 700 32 225 6.0 --- 31.6
W10 1B819 15 0.48 600 30 430 2.5 37.8 31.9
W11 1B458 30 0.30 600 30 430 2.5 13.1 13.3
W12 1B819 15 0.48 500 28 550 1.5 12.8 11.8
W13 1A624 10 0.31 500 28 500 1.5 22.9 26.5
W14 1B458 30 0.30 700 32 225 6.0 51.9 45.1
W15 1B168 50 0.44 600 30 430 2.5 12.8 13.3

The welds were sectioned at a location that gave appropriate overlap of the two weld beads, and polished using standard metallographic preparation techniques. The samples were etched in 2% Nital, and a detailed hardness survey of all the zones of interest carried out.


The equations given above were incorporated into a FORTRAN computer model to predict the hardness of the regions of the HAZ, namely the GCHAZ; grain-refined HAZ (GRHAZ); intercritically-reheated grain-coarsened HAZ (ICGCHAZ) and SCGCHAZ.

The computer model was used to predict the hardness of these zones for double-pass bead in groove, submerged arc welds, with an offset of the secondary groove; see Fig.5. This section revealed the various reheated zones of the weld (Fig.6). The Vickers hardness in each of the zones of interest was measured using a 5kg load, and the results compared with the predicted value.

Fig.6. An example of the overlap of two weld beads, giving a subcritically reheated grain coarsened heat affected zone in the location indicated by the arrow
Fig.6. An example of the overlap of two weld beads, giving a subcritically reheated grain coarsened heat affected zone in the location indicated by the arrow

The predicted and measured values of hardness are given in Table 3. The agreement of the absolute values of prediction was generally good, shown graphically in Fig.7 for the SCGCHAZ. The agreement for subcritically reheated regions is ±53HV, which is within the limitations established for earlier work on the prediction of hardness in single-pass welding, i.e.±56HV[15].

The experimental work indicated that the grain refined HAZ (GRHAZ) had a hardness approximately equal to 0.77GCHAZ. This approximation was subsequently included in the model.

None of the welds sampled demonstrated secondary hardening, in that each sample had a lower hardness in the reheated region than in the as-welded locations. However, the predictions also indicated that bulk softening was more likely than secondary hardening.

Table 3 Comparison of predicted and measured Vickers hardness values.

WeldMaximum GCHAZ HardnessGrain Refined HAZ Hardness
(0.77 x GCHAZ)
Sub-critically ReheatedHeat Input
ActualPredictionActual-PredictedActualPredictedActual-PredictedActual 1Actual 2Predicted(kJ/mm)
W07 407 370 37 283 284 -1 268 274 309 1.5
W08 280 252 28 229 194 35 238 237 263 6.0
W10 262 267 -5 187 205 -18 225 237 261 2.5
W11 215 200 15 178 154 24 193 196 196 2.5
W12 329 344 -15 262 264 -2 254 272 307 1.5
W13 187 207 -20 156 159 -3 169 170 188 1.5
W14 192 185 7 165 142 23 164 179 183 6.0
W15 358 320 38 227 246 -19 288 296 290 2.5
Fig.7 Predicted maximum HAZ hardness values compared with those measured, for the as-welded GCHAZ and the SCGCHAZ.

Fig.7. Predicted maximum HAZ hardness values compared with those measured, for the as-welded GCHAZ and the SCGCHAZ



The calculation of the HJP from this discretised thermal cycle was used, in conjunction with an equation put forward by Okumura et al[11] for the change in hardness as a result of a postweld heat treatment. The effective post-weld heat treatment considered here was the subcritical reheating imposed by a second weld pass which overlaps the first.

The assumptions and uncertainties inherent in the prediction did not affect the accuracy of the prediction of absolute maximum hardness, in that the prediction remained within the limits determined in previous work for single pass welds.[15] This agreement suggests that the approach, evaluating HJP over a weld thermal cycle, and using that in the relevant equations to determine as-welded maximum HAZ hardness and the subsequent change in hardness is valid.

The predictions were better for absolute values of maximum HAZ hardness than for determining the change in hardness for a given situation. This is because the use of the value of tm from the original equations compensates for any over or under prediction in the prediction of as-welded maximum HAZ hardness. However, the method is potentially useful for evaluating the effect of changes in welding parameters on maximum HAZ hardness, for example where a specified maximum HAZ hardness has not been achieved in a weld procedure qualification test. Calculations such as those carried out here would indicate the likely hardness change for any proposed procedural changes.

Summary and conclusions

From the steel compositions and weld thermal cycles examined in this work, the maximum hardness of different regions of the HAZ has been calculated, and compared with values measured in the HAZ of overlapped submerged arc bead in groove welds, made at a range of heat inputs, in steels of varying thickness and composition. From this work, the following conclusions can be drawn:

  1. The hardness of the sub-critically reheated grain-coarsened HAZ can be estimated successfully from the as-welded GCHAZ hardness, a HJP from the relevant thermal cycle, and the use of equations which describe the tempering behaviour as a function of the steel composition and HJP.
  2. For the steels considered, an approximation of the GRHAZ hardness can be obtained by multiplying the prediction for single-pass grain coarsened HAZ by a factor of 0.77.
  3. The data generated in this work for the GCHAZ hardness was in agreement with the method put forward by earlier work.


The algorithms and approach used in this work have been incorporated into a FORTRAN computer program, which can provide the welding engineer with a useful tool to provide estimates of the maximum hardness in different regions of the HAZ. For applications where the maximum HAZ hardness is important, this prediction should be used to assist in weld procedure qualification. However, as the scatter-band for the original single pass hardness prediction is large (two standard deviations = ±56HV) the trends predicted are of more value than the absolute values of hardness.


The assistance of colleagues at TWI is gratefully acknowledged. Special thanks are due to W Martin, M Tiplady and L Smith. This work was funded by member companies of TWI as part of the core research programme.


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