Journal of Minerals & Materials Characterization & Engineering, Vol. 10, No.8, pp.707-715, 2011
jmmce.org Printed in the USA. All rights reserved
707
Models for Assessment and Computational Analysis of Hardness of the
Heat Affected Zone in Water Cooled Alu minu m Weldment
C. I. Nwoye1*, C. N. Anyakwo2, E. Obidiegwu3 and N. E. Nwankwo1
*1Department of Metallurgical Engineering and Materials Engineering Nnamdi Azikiwe
University, Awka, Nigeria.
2Department of Materials and Metallurgical Engineering Federal University of Technology,
Owerri, Nigeria.
3Department of Metallurgical and Materials Engineering University of Lagos, Nigeria.
*Corresponding Author:
ABSTRACT
Models have been derived for assessment and computational analysis of the hardness of the
heat affected zone (HAZ) in aluminum weldment. The general model;
γ = 1.2714[(αβ/α + β)]
was found to predict the HAZ hardness of aluminum weldment cooled in water as a function
of the HAZ hardness of both mild steel and cast iron welded and cooled under the same
conditions. The maximum deviations of the model-predicted HAZ hardness values γ, α and β
from the corresponding experimental values γexp, αexp and βexp were less than 0.02%
respectively.
Keywords: Model, Hardness, Heat Affected Zone, Aluminum Weldments, Mild Steel, Cast
Iron.
1. INTRODUCTION
Heat-affected zone (HAZ) has been successfully investigated and reported [1] as basically the
area of base material, either a metal or a thermoplastic, which has had its microstructure and
properties altered by welding or heat intensive cutting operations. This change in the area
surrounding the weld results from the corporate inputs of the heat from the welding process
and subsequent re-cooling. The extent and magnitude of property change depends primarily
on the base material, the weld filler metal, as well as the amount and concentration of heat
input by the welding process used.

708 C. I. Nwoye, C. N. Anyakwo, E. Obidiegwu and N. E. Nwankwo Vol.10, No.8
It has been shown [1] that the thermal diffusivity of the base material plays very significant
role. High diffusivity results in high cooling rate of the material and this translates into
relatively small HAZ. Alternatively, a low diffusivity leads to slower cooling and a larger
HAZ. The amount of heat inputted by the welding process plays an important role as well, as
processes like oxyfuel welding use high heat input and increase the size of the HAZ.
Processes like laser beam welding and electron beam welding give a highly concentrated,
limited amount of heat, resulting in a small HAZ. Arc welding falls between these two
extremes, with the individual processes varying somewhat in heat input.
Recent report [2] has confirmed that weldment cracking results to low mechanical properties
such as hardness and impact strength in welded parts, the heat affected zone being located
adjacent to the immediate welded area or fusion. Studies [3] on HAZ have shown that the
most important mechanical property associated with it is the hardness since it gives an
indication of the degree of embrittlement there. Lancaster [3] found that the heat affected
zone hardness produced by any given welding operation depends on the cooling rate
experienced by the HAZ. Application of enhanced rapid rate of cooling favours the formation
of hard and brittle martensite in all the sub zones of the HAZ or increases the martensite
region in size relative to the other regions. The presence of martensite in the HAZ results in a
very high hardness value for the heat affected zone. Slow cooling favours a better
microstructure needed for engineering applications.
Nwoye [4] found that the hardness of HAZ in aluminum, cast iron and mild steel weldments
cooled in kerosene is the same as the hardness value of the same materials cooled in
groundnut oil [4]. This implies that
HG = HK (1)
Where
HG = Hardness of HAZ cooled in groundnut oil
HK = Hardness of HAZ cooled kerosene
Nwoye [4] reported that 8-10% less hardness than that from water occurs when kerosene or
groundnut oil is used as quenchant for HAZ. The researcher discovered that quenching the
HAZ with kerosene or groundnut oil gives approximately 8-10.7% more hardness than that
from quenching with air. The researcher found that palm oil gave the lowest hardness and
cooling rate on the HAZ.
Nwoye et al. [5] derived a model for the predictive analysis of hardness of the heat affected
zone in aluminum weldment cooled in groundnut oil. The general model;
β = 0.5997√(γα) (2)
was found to be dependent on the hardness of the heat affected zone (HAZ) in mild steel and
cast iron weldments cooled in same media. Re-arrangement of these models could be done to
evaluate the HAZ hardness of mild steel or cast iron respectively as in the case of aluminum.

Vol.10, No.8 Models for Assessment and Computational Analysis 709
α = β2 (3)
0.3596γ
γ = β2 (4)
0.3596α
The respective deviations of the model-predicted HAZ hardness values β, γ and α from the
corresponding experimental values was less 0.02%.
Quadratic and linear models [6] have been derived for predicting the heat-affected zone
(HAZ) hardness of water cooled cast iron weldment in relation to the combined and
respective values of the heat-affected zone hardness of aluminum and mild steel welded
and cooled under the same conditions. The quadratic model is expressed as:
θ = 3.0749β - γ + √ γ – 3.0749β 2 - γβ (5)
2 2
It was found that the validity of the quadratic model is rooted on the fractional expression;
γ/3.0749θ + γ/3.0749β + θ/3.0749β = 1. The respective deviations of the model-predicted
heat-affected zone hardness values of aluminum, cast iron and mild steel from the
corresponding experimental values were less than 0.01% which is quite insignificant,
indicating reliability of the model. The linear models expressed as: θ = 2.2051γ and θ =
1.8035β, on the other hand predict the HAZ hardness of cast iron weldment cooled in water
given the values of the HAZ hardness of aluminum or/and mild steel welded and cooled
under the same conditions are known.
Successful attempt [7] has been made to derive quadratic and linear models for predicting the
HAZ hardness of air cooled cast iron weldment in relation to the combined and respective
values of HAZ hardness of aluminum and mild steel welded and cooled under the same
conditions. It was discovered that the general model;
θ = [2.9774β – γ]/2 + √[((γ- 2.9774β)/2)2- γβ] (6)
predicts the HAZ hardness of cast iron weldment cooled in air as a function of the HAZ
hardness of both aluminum and mild steel welded and cooled under the same conditions. The
linear models; θ = 2.2391γ and θ = 1.7495β on the other hand predict the HAZ hardness of
cast iron weldment cooled in air as a function of the HAZ hardness of aluminum or mild steel
welded and cooled under the same conditions. It was found that the validity of the model is
rooted on the fractional expression; γ/2.9774θ + γ/2.9774β + θ/2.9774β = 1 since the actual
computational analysis of the expression was also equal to 1, apart from the fact that the
expression comprised the three metallic materials. The respective deviations of the model-

710 C. I. Nwoye, C. N. Anyakwo, E. Obidiegwu and N. E. Nwankwo Vol.10, No.8
predicted HAZ hardness values θ, γ, and β from the corresponding experimental values θexp,
γexp, and βexp was less than 0.003%.
Models have been derived [8] for the evaluation of the HAZ hardness of cast iron weldment
cooled in groundnut oil in relation to the respective and combined values of HAZ hardness of
aluminum and mild steel welded and cooled under the same conditions. The linear models; α
= 2.2330γ, α = 1.7934β and β = 1.2451γ, were found to predict the HAZ hardness of cast iron
weldment cooled in groundnut oil as a function of the HAZ hardness of aluminum or mild
steel welded and cooled under the same conditions. It was also discovered that the general
model;
α = 1.7391γ + 0.3967β (7)
can predict the HAZ hardness of cast iron weldment cooled in groundnut oil as a function of
the HAZ hardness of both aluminum and mild steel welded and cooled under the same
conditions. The respective deviations of the model-predicted HAZ hardness values γ, β and α
from the corresponding experimental values γexp, βexp,and αexp, was less 0.8% indicating the
reliability and validity of the model.
The present study aims at deriving models for assessment and computational analysis of the
hardness of the heat affected zone (HAZ) in water cooled aluminum weldment, as a function
of the respective and combined values of HAZ hardness of mild steel and cast iron welded
and cooled under the same conditions.
2. MATERIALS AND METHODS
Aluminum, mild steel and cast iron were cut and welded using the shielded metal arc welding
technique and the hardness of the HAZ (cooled in water maintained at room temperature)
tested. The hardness of the HAZ is as presented in Table 2. The full details of the
experimental procedures and equipment used are presented in the previous report [4]. Table 1
shows the welding current and voltage used.
Table 1: Variation of materials with welding current and voltage [4].
Materials Current Type Welding
Current
Welding Voltage
(V)
Aluminum
Cast Iron
Mild Steel
Direct (d.c)
Alternating
(a.c)
Alternating
(a.c)
120
180
180
280
220
220

Vol.10, No.8 Models for Assessment and Computational Analysis 711
Table 2: Hardness of HAZ in weldments [4]
3. MODEL FORMULATION
Results of experiment [4] carried out at Metallurgical and Materials Engineering Department
of Federal University of Technology, Owerri were used for this work. Computational analysis
of the experimental results [4] shown in Table 2 resulted in Table 3.
Table 3: HAZ Hardness ratio between aluminum, mild steel, and cast iron weldments
cooled in water.
Table 3 shows that the hardness of HAZ in aluminum weldment cooled in water is a function
of the hardness of HAZ in cast iron and mild steel weldment also cooled in water. Therefore,
γ = 0.4535α (8)
γ = 0.8179β (9)
α = 1.8036β (10)
Adding eqns. (8) and (9) as arranged in Table 2;
γ + γ = 0.4535 + 0.8179 (11)
α β
γβ + γα = 1.2714 (12)
αβ
γβ + γα = 1.2714αβ (13)
γ(β + α) = 1.2714αβ (14)
γ = 1.2714 αβ (15)
α + β
The derived model (general model) is equation (15)
Materials HAZ Hardness
(VHN)
Aluminum
Cast Iron
Mild Steel
458
1010
560
Ratio of
symbols
designating
HAZ hardness
Ratio of HAZ
hardness
values
Results of the
Ratio of HAZ
hardness values
γ/α
γ/β
α/β
458/1010
458/560
1010/560
0.4535
0.8179
1.8036

712 C. I. Nwoye, C. N. Anyakwo, E. Obidiegwu and N. E. Nwankwo Vol.10, No.8
Where
γ = Model-predicted hardness of HAZ in aluminum weldment cooled in water (VPN)
β = Model-predicted hardness of HAZ in mild steel weldment cooled in water (VPN)
α = Model-predicted hardness of HAZ in cast iron weldment cooled in water (VPN)
4. BOUNDARY AND INITIAL CONDITIONS
The welding process was carried out under atmospheric condition. After welding, weldments
were also maintained under atmospheric condition. Welding current and voltage used are
180A and 220V respectively. SiO2-coated electrodes were used to avoid oxidation of weld
spots. The coolants used were maintained at 250C (room temperature). Volume of coolants
used; 1000cm3. No pressure was applied to the HAZ during or after the welding process. No
force due to compression or tension was applied in any way to the HAZ during or after the
welding process. The sides and shapes of the samples are symmetries.
5. MODEL VALIDATION
The derived model was validated by evaluating the model-predicted values of HAZ hardness
in aluminum weldment cooled in water γ and comparing them with the corresponding values
obtained from the experiment γexp [4]. Following re-arrangement of the model equation; (15),
the values of α and β were also evaluated as;
α = 1.2714 _ 1 -1
γ β (16)
β = 1.2714 _ 1 -1
γ α (17)
and compared with their respective corresponding experimental values αexp and βexp to further
establish the validity of the model. The model-predicted values of γ, α and β are shown in
Table 3.
Analysis and comparison between the model-predicted values γ, α, β and the respective
corresponding experimental values γexp, αexp and βexp reveal deviations of model data from the
experimental data. This is attributed to the non-consideration of the chemical properties of the
coolant and the physiochemical interactions between the materials (aluminum, mild steel and
cast iron) and the coolant which is believed to have played vital roles in modifying the
microstructure of the HAZ during the coolant process. These deviations necessitated the
introduction of correction factor to bring the model-predicted values to exactly that of the
corresponding experimental values.
Deviation (Dv) of the model-predicted HAZ hardness values (γ, α and β) from the
corresponding experimental values γexp, αexp and βexp is given by

Vol.10, No.8 Models for Assessment and Computational Analysis 713
Dv = MH - EH x 100 (18)
EH
Correction factor (Cf) is the negative of the deviation i.e.
Cf = -Dv (19)
Where
Dv = Deviation of the model-predicted HAZ hardness values from the corresponding
experimental values
Cf = Correction factor
MH = Model-predicted HAZ hardness values
EH = HAZ hardness values from the experiment [4]
Therefore
Cf = -100 MH - EH (20)
EH
Introduction of the value of Cf from equation (20) into the models give exactly the
corresponding experimental values γexp, αexp and βexp [4].
6. RESULTS AND DISCUSSION
A comparison of the HAZ hardness values from experiment and those of the model show
model values very much within the range of the experimental values. Results of this
comparison are presented in Tables 4 and 5. Model values of γ evaluated from equations (8)
and (9) and tabulated in Table 4 show that all the equations are valid since all of them gave
almost the same corresponding experimental values γexp.
Table 4: Comparison of the hardness of HAZ in aluminum, mild steel and cast iron
weldments cooled in water as obtained from experiment [4] and as predicted by derived
model (each material as a function of 1- material).
The value of α in equation (10) was evaluated to establish the validity of the model. It was
found that the model-predicted α value was also almost the same as the corresponding
experimental value αexp. This is a clear indication that the HAZ hardness of any of aluminum,
mild steel and cast iron weldments cooled in water can be predicted as a function of the HAZ
hardness of any of the other two materials, providing each pair was cooled in water. Table 5
also indicates that the model-predicted value of α is approximately the same as the
corresponding experimental value.
N Models derived MH EH Dv (%) Cf (%)
1
1
1
γ = 0.4535α
γ = 0.8179β
α = 1.8036β
458.0350
458.0240
1010.0160
458.00
458.00
1010.00
+0.0076
+0.0052
+0.0016
-0.0076
-0.0052
-0.0016

714
Table 5: Comparison of the hardness of HAZ in aluminum, mild steel and cast iron
weldments cooled in water as obtained from experiment [4] and as predicted by derived
model (each material as a function of 2- materials).
N = No. of materials constituting the corresponding model as independent variable
It can also be seen from Table 5 that the model-predicted values of α and β are also almost
the same as the corresponding experimental values of αexp and βexp respectively. Tables 4 and
5 indicate that the respective deviations of the model-predicted HAZ hardness values γ, α and
β from those of the corresponding experimental values γexp, αexp and βexp are all less than
0.02% which is quite negligible and within the acceptable model deviation range from
experimental results. Furthermore, the values of α and β (from equations (16) and (17)
respectively) evaluated to be approximately equal to the respective corresponding
experimental values αexp and βexp confirm the validity of the model. This also implies that the
general model; equation (15) can predict the HAZ hardness of any of aluminum, mild steel
and cast iron weldments cooled in water as a function of the HAZ hardness of the other two
materials, providing the three materials constituting the model (aluminum, mild steel and cast
iron) were cooled in water. Equation (15) is regarded as the general model equation because
it comprises of the HAZ hardness of all the materials considered for the model formulation.
Based on the foregoing, the models in equations (8), (9) and (10) are valid and very useful for
predicting HAZ hardness of aluminum, mild steel and cast iron weldments cooled in water
depending on the material of interest and the given HAZ hardness values for the other
materials.
7. CONCLUSION
The derived models; γ = 0.4535α, γ = 0.8179β, and α = 1.8036β, can predict the HAZ
hardness of aluminum weldment cooled in water as a function of the HAZ hardness of mild
steel or cast iron welded and cooled under the same conditions. Similarly, the general model;
γ = 1.2714[(αβ/α + β)] can predict the HAZ hardness of aluminum weldment cooled in water
as a function of the HAZ hardness of both mild steel and cast iron welded and cooled under
the same conditions. Furthermore, re-arrangement of these models could be done to evaluate
the HAZ hardness of mild steel or cast iron respectively as in the case of aluminum. The
respective deviations of the model-predicted HAZ hardness values γ, α and β from the
corresponding experimental values γexp, αexp and βexp was less 0.02% indicating the reliability
and validity of the model.
N Models derived MH EH Dv (%) Cf (%)
2
2
2
γ = 1.2714 [(αβ/α + β)]
α = [(1.2714/γ – 1/β)]-1
β = [(1.2714/γ – 1/α)]-1
458.028
559.910
1010.101
458.00
560.00
1010.00
+0.0061
-0.0161
+0.0100
-0.0061
+0.0161
-0.0100

715
ACKNOWLEDGEMENT
The authors are grateful to the management of Federal University of Technology, Owerri for
providing the equipment used for this work.
REFERENCES
[1] Weman, K. (2003) Welding Process Handbook. CRC Press LLC, New York.
[2] Nnuka, E. E., Ovat, F. A., and Oseni, M. I., (2008) Effect of Electrode Types on the
Mechanical Properties and Structure of Welded Steel Joints. JMME, 3(1):7-13.
[3] Lancaster, J. F., (1987) Metallurgy of Welding: The Mechanical Properties of the Heat
Affected Zone, 4th Edition, Allen and University, London. p45.
[4] Nwoye, C. I. (2008) Comparative Studies of the Cooling Ability of Hydrocarbon Based
Media and their Effects on the Hardness of the Heat Affected Zone (HAZ) in Weldments
JMME 3(1):35-38.
[5] Nwoye, C. I., Odumodu, U., Nwoye, C. C., Obasi, G. C., and Onyemaobi, O. O. (2009)
Model for Predictive Analysis of Hardness of the Heat Affected Zone in Aluminum
Weldment Cooled in Groundnut Oil Relative to HAZ Hardness of Mild Steel and Cast
Iron Weldments Cooled in Same Media. New York Science Journal, 2(6): 93-98.
[6] Nwoye, C. I. (2009) Quadratic Model for Predicting the Hardness of Heat Affected Zone
in Water Cooled Cast Iron Weldment In Relation to Similarly Cooled Aluminum and
Mild Steel Weldments. Journal of Mineral and Materials Characterization and
Engineering, 8(10):765-773.
[7] Nwoye, C. I. (2009) Quadratic and Linear Models for Predicting the Hardness of Heat
Affected Zone in Air Cooled Cast Iron Weldment in Relation to the HAZ Hardness of
Aluminum and Mild Steel Weldments Cooled in Same Media. Researcher Journal,
1(4):1-6.
[8] Nwoye, C. I., and Mbuka, I. E. (2010) Models for Predicting HAZ Hardness in cast iron
Weldment Cooled in Groundnut Oil in Relation to HAZ Hardness of Aluminum and Mild
Steel Weldments Cooled in Same Media. Materials Research Innovation, 14(4):312-315