G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
485–494
OPTIMIZATION OF PROCESS PARAMETERS FOR A
SOLID-STATE-WELDED AISI 430 STEEL JOINT WITH THE GRG
REINFORCED RESPONSE SURFACE METHODOLOGY
OPTIMIZACIJA PROCESNIH PARAMETROV TORNEGA VARJENJA
JEKLA VRSTE AISI 430 Z GRG METODOLOGIJO OJA^ANEGA
ODGOVORA POVR[INE
G. Senthilkumar
1*
, V. Vinodkumar
2
, T. Mayavan
1
, G. Rathinasabapathi
1
,
Amos Gamaleal David
1
1
Department of Mechanical Engineering, Panimalar Engineering College, Chennai, Tamilnadu, India
2
Department of Mechanical Engineering, Chennai Institute of Technology and Applied Research, Chennai, Tamilnadu, India
Prejem rokopisa – received: 2023-05-04; sprejem za objavo – accepted for publication: 2023-07-28
doi:10.17222/mit.2023.873
High-temperature applications such as heat exchangers and burner tubes employ AISI 430 steel. A larger heat-affected zone, un-
desired metallurgical changes and higher hardness in the weld area occur when fusion welding this type of steel. The study in-
vestigates the feasibility of welding ferritic stainless steel AISI 430, utilizing a solid-state method (continuous drive friction
welding). The experiment uses an L27 orthogonal array and three levels of variation in the welding parameters such as frictional
pressure, forging pressure, friction time, forging time and rotational speed. Tensile strength, axial shortening and impact tough-
ness are the observed quality characteristics. In an integrated approach of the grey incidence reinforced response surface meth-
odology, the benefits of the grey relational theory are merged with the statistical analysis of the response surface methodology to
determine the ideal friction welding inputs (frictional pressure – 59.95 MPa, friction time–4s,upsetpressure – 68.5 MPa, forg-
ingtime–3sandrotational speed – 1399 min
–1
). The AISI 430 steel joint’s qualities are improved by 2.25, 12.74 and 7.89 % in
terms of the maximum ultimate tensile strength, axial shortening and impact toughness, respectively.
Keywords: friction welding, optimization, response surface methodology, microstructure
Za visokotemperaturne aplikacije kot so toplotni izmenjevalniki in cevi gorilcev se uporablja feritno nerjavno jeklo vrste AISI
430. Ve~ja toplotno vplivana cona, ne`eljene metalur{ke spremembe in vi{je trdote v podro~ju zvarov so rezultat
konvencionalega varjenja te vrste jekla, zaradi visokih temperatur in prisotnosti taline. Avtorji v tem ~lanku opisujejo {tudijo
izvedljivosti varjenja feritnega nerjavnega jekla vrste AISI 430 z metodo varjenja v trdnem stanju (kontinuirno varjenje s
trenjem in me{anjem oziroma gnetenjem). Za preizkuse so izbrali ortogonalno matrico tipa L27 in tri nivoje variacij parametrov
varjenja in sicer: tlak kovanja, ~as trenja in hitrost vrtenja. Izbrani kriteriji kvalitete izdelanih zvarov so bili njihova natezna
trdnost, osno skraj{anje in udarna `ilavost. Z integriranim pristopom pojava v "sivem" z uporabo metodologije oja~anega
odgovora povr{ine so avtorji uporabili prednosti te metodologije oz. teorije v sivini (megli) in z znanjem na podro~ju statisti~ne
analize RSM (angl.: Response Surface Methodology) dolo~ili idealne vhodne parametre varjenja (trenjski tlak – 59,95 MPa, ~as
trenja – 4 s, za~etni tlak – 68,5 MPa, ~as gnetenja – 3 s in hitrost vrtenja – 1399 min
–1
). Kakovost zvarov jekla AISI 430 so na ta
na~in izbolj{ali in sicer njihovo kon~no natezno trdnost za 2,25 %, aksialno skraj{anje za 12,74 % in udarno `ilavost za 7,89 %.
Klju~ne besede: torno varjenje, optimizcija, metodologija odgovora povr{ine, mikrostruktura.
1 INTRODUCTION
Pressure vessels and boilers are two common uses for
the AISI 430 steel. The predominant choice for tubes and
pipes in heat exchangers that carry hot fluids is AISI 430
steel due to its excellent tensile strength and impact
toughness. The use of traditional liquid-state joining
techniques to join AISI 430 steel raises several issues. A
greater heat affected zone (HAZ) and the resulting
changes in the parent metal’s metallurgy occur with fu-
sion welding processes. Liquid-state welding leads to
microscopic corrosion along grain boundaries. This
might have an impact on the joint’s mechanical charac-
teristics, which matter in applications involving high
temperatures and stresses. Thus, joining AISI 430 steel
in the solid state may increase the likelihood that such
undesirable mechanical and metallurgical changes are
minimized.
Since the temperature required for solid-state pro-
cessing is far lower than the parent material’s melting
point, there is little to no HAZ produced. At the joint in-
terface, the plastic flow of the material is seen. To limit
the quantity of flash produced, the process governing the
plastic flow of material at the weld contact is crucial. To
lessen axial shortening, a reasonably lower flash is al-
ways preferred.
1
Observations of United Launch Alli-
ance, Inc., detail crucial hardware advancements used to
make joints in the solid state.
2
The mechanical properties
of joints were shown to be considerably influenced by
the friction welding inputs, including frictional pressure,
upset pressure, burn-off length and rotational speed.
3
Grey relational analysis was used to optimize the param-
Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494 485
UDK 669.14.018.8:621.791 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 57(5)485(2023)
*Corresponding author's e-mail:
senthilngt1978@gmail.com (G. Senthilkumar)

eters of a typical TIG welding method used to join nu-
clear grade austenitic stainless steel 321. This improved
the mechanical properties of the weld joints.
4
It was dis-
covered that the temperature rise played a significant role
in changing the qualitative characteristics of the bonds in
the joints made between AISI 1050 and AISI 4140 steel.
It was also discovered that the initial temperature in-
crease was the highest, followed by a constant rise with
continuous rotation, and the joints had no empty gaps.
5
The unaffected zone, moderately deformed zone and
fully deformed zone are typically present at a solid-state
friction welded interface. The fully distorted and moder-
ately deformed zones show the most microstructural al-
terations.
6
By choosing the right values for the friction
duration and rotational speed, a nearly flawless bonding
strength that is close to that of the parent material can be
achieved. The welding parameters have the biggest im-
pact on how hot a friction interface becomes.
7
Due to the
development of precipitates, friction-welded joints of
high-strength nickel alloys show a tougher and stronger
weld zone.
8
It was discovered that the distribution of temperature
and the plastic flow of material at the weld contact area
is influenced by the rotational speed and frictional pres-
sure.
9
For Al 6061 and an austenitic stainless steel joint,
there is an increase in the efficiency of the fric-
tion-welded joint with a little increase in the frictional
contact duration and a considerable increase in the upset
pressure.
10
The friction-welded joint of AISI 304 with Al
6063 may have the best elbow bend ductility due to the
high forging pressure.
11
Multi-objective friction welding
of EN 10028 P 355 GH steel results in respectable
amounts of tensile strength improvement and material
savings.
12
The central composite design method for fric-
tion-welded ASTM A516 steel grade 70 leads to im-
provements in the tensile strength, impact toughness and
reduced axial shrinkage.
13
Even without a model for the
process, the genetic algorithm is a useful tool for experi-
mental welding optimization; however, it is challenging
to establish its parameters, such as population size and
the number of generations for adequate sweeping of the
search space. Though it suffers in an erratic experimental
zone, the RSM technique was found to achieve a better
compromise between evaluated results.
14
RSM is used to
optimize the friction welding inputs for connecting UNS
S32205 steel parts. For an experiment, the central com-
posite design (CCD) was employed. To maximize the
hardness and tensile strength, the upset pressure, friction
pressure and speed of rotation were found to be the three
most important parameters.
15
For the optimization of
process parameters and modeling of the response values
of diverse processes, hybrid approaches were applied.
The advantages of the algorithms can now be combined
benefits to these integrated techniques. The RSM ap-
proach and grey relational analysis are used for response
modeling and optimization.
16
Being a statistical tool for
optimization, the method is used to produce response
surfaces to investigate how different design variables in-
teract with one another. The two most popular response
surface designs are typically the central composite de-
sign and the Box-Behnken design
17
.
The TIG welding procedure was used to join a
Fe-2.25Cr-1Mo steel tube with a carbon steel tube while
employing a filler material that contained chromium.
The weld’s corrosion resistance behavior was enhanced
by the production of Cr
2
O
3
caused by the presence of
chromium.
18
A forged low-alloy steel tube and a drawn
low-alloy steel tube are successfully joined by solid-state
friction welding and the input parameters are optimized
with the response surface methodology to enhance the
required properties.
19
A surge in the friction force in-
creases the heat generation at the interface and tends to
make better bonding of the material, leading to a high
tensile strength.
20
The carbide-free interface obtained
with the friction welding of A516 steel and 316L steel
shows no sensitization during the process.
21
The
load-carrying ability of an asymmetric friction-welded
joint depends upon the grain size in the microstructure.
22
Even though AISI 430 steel has significant applica-
tions in heat exchanger tubes, there is not enough infor-
mation in the literature about the solid-state joining of
this material. Furthermore, scientific literature pays little
attention to designing welding parameters for AISI 430
steel. In order to provide instructions and a welding data-
base for joining AISI 430 steel with the friction welding
technique, this work investigates the feasibility of gener-
ating high-quality welded connections utilizing continu-
ous drive friction welding. Although orthogonal ar-
rays-based RSM is used in some manufacturing
processes, there is little information about it in the litera-
ture. Thus, by using a hybrid approach of the grey rela-
tional analysis and reinforced response surface method-
ology for the optimal parameter design, the potential for
simultaneous optimization of numerous responses is in-
creased in the proposed work.
2 MATERIALS AND METHODS
The AISI 430 steel used for heat exchanger tubes was
procured in the form of a rod with a diameter of 16 mm.
The chemical composition and material properties of the
parent material are listed in Tables 1 and 2, respectively.
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
486 Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494
Table 1: Composition of AISI 430 steel by maximum weight
Ele-
ment
C Mn Si Cr P Mo Ni Fe
% 0.13 1.58 0.41 16.38 0.038 0.21 0.46
Re-
maining
Table 2: Material properties of AISI 430 steel
S. No. Properties Value Unit
1 Yield strength 410 N/mm
2
2 Ultimate tensile strength 555 N/mm
2
3 Impact toughness 28 J

The friction welding of rods, cut to a length of 130 mm
each, was done in a friction welding machine made by
RV Machine Tools in Coimbatore, India.
The device has a hydraulic chuck with a spindle set
to 12 kW and a maximum speed of 3000 min
–1
. The fric-
tion welding settings are accurately set by "Indra Control
VCP-02" at the operator terminal, and the slide is driven
by a servomotor gearbox.
The machine contains a built-in "Rexroth controller"
component made by Bosch Rexroth’s automated assem-
bly section in Germany. A smooth transition between
various stages of a joint development is ensured with the
necessary parameter setup. Figures 1 and 2 show the be-
ginning of the friction welding process, the upset that oc-
curs, and the development of flash at the weld contact.
Preliminary experiments were used to determine the val-
ues of different parameters, resulting in bonds with no
visible flaws or failures. Based on the prior instructions
from scientific literature, trials were carried out to deter-
mine the ranges of various parameters. The levels of var-
ious welding parameters employed in experimentation
are shown in Table 3.
During friction welding, Rexroth spindle drive was
used to accurately control one half of the joint while
holding the other half motionless and ready to slide. Af-
ter verifying that both of the components to be joined
had an equal amount of overhang, they were then permit-
ted to come into contact. A smooth transition between
various stages of the joint development was ensured with
the necessary parameter setup. The tests were carried out
using Taguchi’s orthogonal array (L
27
), which made it
possible to investigate the essential interactions between
different design variables. Axial shortening (AS), impact
toughness (IT) and ultimate tensile strength (UTS) were
the quality attributes. The experiments were carried out
at random to lessen the influence of uncontrollable cir-
cumstances, and the created joints were examined for
quality attributes. The sample joints formed are shown in
Figure 3. After preparing a specimen in accordance with
ASTM E8, a tension test was carried out in an Instron
computerized tension tester. The reduction in the length
of the final joint obtained with friction welding was iden-
tified as axial shortening. An indicator of the toughness
of a sample is the amount of energy absorbed by the
specimen during fracture as seen during the impact test.
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494 487
Figure 2: Upset and flash formation
Table 3: Levels of various friction-welding inputs
Input parameters Unit
Sym-
bol
Levels
Level
1
Level
2
Level
3
Friction pressure (FP) N/mm
2
A4 05 06 0
Upset pressure (UP) N/mm
2
B5 06 07 0
Friction time (FT) s C 3 5 7
Upset time (UT) s D 3 5 7
Speed min
–1
E 1000 1200 1400
Table 4: Experimental results for friction welded AISI 430 steel joints
Trial
Process parameters Responses
FP
(MPa)
UP
(MPa)
FT
(s)
UT
(s)
Speed
(min
–1
)
UTS
(MPa)
AS
(mm)
IT
(J)
1 40 50 3 3 1000 518 10.93 14
2 40 50 5 5 1200 514 10.88 16
3 40 50 7 7 1400 519 10.53 20
4 40 60 3 5 1400 508 5.75 18
5 40 60 5 7 1000 515 5.98 21
6 40 60 7 3 1200 507 6.30 18
7 40 70 3 7 1200 518 17.78 23
8 40 70 5 3 1400 517 17.20 15
9 40 70 7 5 1000 519 17.51 19
10 50 50 3 3 1000 507 35.51 16
11 50 50 5 5 1200 510 34.30 18
12 50 50 7 7 1400 515 33.87 19
13 50 60 3 5 1400 530 14.53 23
14 50 60 5 7 1000 523 12.67 15
15 50 60 7 3 1200 521 13.31 19
16 50 70 3 7 1200 523 16.65 16
17 50 70 5 3 1400 525 15.43 20
18 50 70 7 5 1000 521 16.12 18
19 60 50 3 3 1000 507 17.78 18
20 60 50 5 5 1200 510 17.58 23
21 60 50 7 7 1400 514 17.60 15
22 60 60 3 5 1400 523 18.08 20
23 60 60 5 7 1000 521 17.95 18
24 60 60 7 3 1200 532 18.68 19
25 60 70 3 7 1200 534 8.89 18
26 60 70 5 3 1400 532 18.68 19
27 60 70 7 5 1000 536 9.53 15
Figure 1: Application of friction pressure in the initial phase

This provides the opportunity for additional research on
the ductile-brittle transition. According to the ASTM
E23 standard, Charpy V-notch testing (the pendulum
type) was done. The experimental results obtained are
shown in Table 4.
3 GREY RELATIONAL GRADE REINFORCED
RESPONSE SURFACE METHODOLOGY
The RSM is a statistical method featuring a module
for modeling design variables and a desirability analysis
module for enhancing the results. 3D surface graphs are
used to demonstrate how parameters affect responses.
The ability of the grey incidence analysis to handle un-
certainty is combined with RSM modeling skills in the
integrated strategy of the grey incidence reinforced re-
sponse surface technique and the process parameters are
optimized with the grey relational gradient reinforced re-
sponse surface methodology.
12
The grey relational gradi-
ent is one of the methods for converting a multi-objective
function into a single-objective function for the optimi-
zation of process parameters.
4
Previously several investi-
gations had been tried to find the optimum conditions
based on trials, but minimum literature is available on
the optimization of friction welding parameters for maxi-
mizing the tensile strength. Multi-objective optimization,
increasing the impact toughness and tensile strength, and
reducing axial shrinkage of friction welded joints is al-
most non-existent. Therefore, in this work, multi-objec-
tive optimization for surging the impact toughness and
tensile strength, and reducing axial shrinkage of friction
welded joints was integrated with the grey relational gra-
dient reinforced response surface methodology. The
step-by-step procedure of the grey relational grade rein-
forced response surface methodology is as follows.
3.1 Stage 1: Grey relational grade (GRG) analysis
In the first stage, the S/N ratio is calculated from the
experimental data. The normalization of the S/N ratio
converts experimental values from zero to one. The nor-
malized data is further processed, being projected as the
single quantity of various output responses obtained
from experimentations.
Step 1: Calculation of the S/N ratio for each response
using the exact equation based on its quality require-
ments. The larger-the-best type of quality characteristics
is used for maximizing the tensile strength and impact
toughness while the smaller-the-best type is used for
minimizing the axial shortening. The S/N ratio ( ) values
for responses are obtained with Equations (3.1) and
(3.2).
Larger-the-best:
S
Nn y
i
i
n
ratio( ) lg  =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =
∑
10
11
2
1
(3.1)
Smaller-the-best:
S
Nn
y
i
i
n
ratio( ) lg  =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =
∑
10
1
2
1
(3.2)
where n = No. of replications, y
i
= observed output val-
ues, i = 1,2,3… n.
Step 2: Normalized S/N ratio (Z
i
) estimated using
Equation (3.3)
Z
yy in
yi n y
i
ii
i
=
−=
=−
min( , , ,..., )
max( , , ,..., ) min(
12
12
i
in , , ,..., ) =12
(3.3)
Step 3: Calculation of grey relational coefficient ( )
values using Equation (3.4)
y
i
i
j
oj
=
+
+
ΔΔ
ΔΔ
min max
() max
  (3.4)
Δ
oj j
zizi =−
0
() (), z
0
(i) is the reference sequence z
0
(i)=
1; I = 1, 2,…,n), z
j
(i) is the smallest value of z
j
(i), and
’ ’ is the distinguishing coefficient 0 1 which is
taken as 0.5.
Step 4: Calculation of grey relational gradient (GRG)
values ( i
) for every trial using Equation (3.5)
GRG
n
ii
i
n
=
=
∑
1
1
()  (3.5)
3.2 Stage II: Grey relational grade (GRG) reinforced
RSM
A single-quality measure representing various out-
puts in terms of GRG is obtained. This GRG value is uti-
lized with the RSM technique to generate a second order
model. The influences of input parameters are observed
in the response surface plots.
Step 5: ANOV A with GRG values is used to deter-
mine the substantial contribution of process parameters.
Step 6: A second order model is developed to associ-
ate the GRG with the inputs and their interactions.
Step 7: The desirability analysis is used to find the
optimum welding conditions. The influence of input pa-
rameters on the GRG is studied with the response surface
plot. The optimized results are validated by the experi-
mentation.
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
488 Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494
Figure 3: Samples of friction welded joints

3.3 Grey incidence analysis and GRG values of friction
welded ferritic stainless steel
The S/N ratios and normalized values of S/N ratios
for quality characteristics of the friction welded AISI
430 joints are presented in Table 5. The grey relational
coefficient, GRC, grey relational gradient, GRG, and
GRG values predicted from the developed model for all
the trials are included in Table 6.
Table 5: S/N ratio and normalized S/N ratio for AISI 430 steel friction
welded joints
Trial
S/N ratio Normalized S/N ratio
UTS AS IT UTS AS IT
1 54.100 -15.193 22.923 0.000 1.000 0.000
2 54.151 -19.956 24.609 0.106 0.699 0.391
3 54.270 -20.812 24.444 0.352 0.645 0.817
4 54.287 -28.165 24.082 0.386 0.180 0.269
5 54.117 -24.711 23.522 0.036 0.398 0.139
6 54.185 -24.428 25.105 0.177 0.416 0.506
7 54.202 -25.506 24.609 0.212 0.348 0.391
8 54.185 -28.787 27.235 0.177 0.140 1.000
9 54.100 -28.787 26.444 0.000 0.140 0.817
10 54.151 -15.534 24.609 0.106 0.978 0.391
11 54.287 -25.144 26.444 0.386 0.371 0.817
12 54.353 -29.994 26.848 0.525 0.064 0.910
13 54.403 -29.367 26.444 0.628 0.104 0.817
14 54.253 -28.787 24.609 0.317 0.140 0.391
15 54.270 -29.127 26.444 0.352 0.119 0.817
16 54.253 -30.238 27.235 0.317 0.049 1.000
17 54.320 -29.571 27.235 0.456 0.091 1.000
18 54.287 -29.686 26.848 0.386 0.083 0.910
19 54.420 -20.749 24.082 0.662 0.649 0.269
20 54.370 -28.818 26.444 0.559 0.138 0.817
21 54.583 -30.832 24.609 1.001 0.011 0.391
22 54.567 -29.066 24.609 0.967 0.123 0.391
23 54.403 -28.818 24.082 0.628 0.138 0.269
24 54.370 -29.686 24.609 0.559 0.083 0.391
25 54.453 -28.787 24.609 0.730 0.140 0.391
26 54.583 -30.906 26.444 1.001 0.006 0.817
27 54.453 -31.005 27.235 0.730 0.000 1.000
Table 6: Calculations of the GRG of the AISI 430 friction welded
joints
Trial
Grey relational coefficient
(GRC)
Actual
(GRG)
Predicted
(GRG)
UTS AS IT
1 0.333 1.000 0.333 0.5556 0.5712
2 0.359 0.624 0.451 0.4779 0.4815
3 0.435 0.585 0.732 0.5839 0.5898
4 0.449 0.379 0.406 0.4113 0.4251
5 0.341 0.454 0.367 0.3875 0.3956
6 0.378 0.461 0.503 0.4474 0.4912
7 0.388 0.434 0.451 0.4243 0.4615
8 0.378 0.368 1.000 0.5818 0.5776
9 0.333 0.368 0.732 0.4776 0.4618
10 0.359 0.959 0.451 0.5894 0.5514
11 0.449 0.443 0.732 0.5411 0.5518
12 0.513 0.348 0.848 0.5696 0.5612
13 0.573 0.358 0.732 0.5543 0.5216
14 0.423 0.368 0.451 0.4137 0.4218
15 0.435 0.362 0.732 0.5097 0.4903
16 0.423 0.344 1.000 0.5889 0.5756
17 0.479 0.355 1.000 0.6111 0.6212
18 0.449 0.353 0.848 0.5500 0.5715
19 0.597 0.587 0.406 0.5300 0.5416
20 0.531 0.367 0.732 0.5434 0.5318
21 1.000 0.336 0.451 0.5960 0.5625
22 0.938 0.363 0.451 0.5840 0.5714
23 0.573 0.367 0.406 0.4488 0.4361
24 1.000 0.335 0.732 0.6892 0.6915
25 0.650 0.368 0.451 0.4894 0.4866
26 0.531 0.353 0.451 0.4451 0.4619
27 0.650 0.333 1.000 0.6609 0.6306
Figure 4 shows the variations in the GRG values for
the 27 experimental runs. The maximum value of the
GRG was 0.6892 (24
th
trial), closely matching experi-
mental conditions, being a near-optimal value.
4 RESULTS AND DISCUSSION
4.1 Quadratic model for the GRG (AISI 430 steel)
The Design-Expert software was used to create a
quadratic model for the GRG, i.e., Equation (4.1):
GRG = 3.5025 – 0.0116A – 0.0915B – 0.0566C –
0.0724D + 0.0001E + 0.0002AB + 0.0119CD +
0.0006B
2
(4.1)
Table 7 presents the ANOV A of the GRG reinforced
RSM model for a friction welded AISI 430 steel joint.
The F-value of 8.31 and p-value of 0.0001 attained for
this second-order model show that this model is signifi-
cant. A p-value of less than 0.05 indicates a significant
importance of parameters (A, B, D and E) and their in-
teractions (AB and CD). The second order of term A was
also significant in influencing the GRG and hence the re-
sponses. The R-square value of 0.7869, the predicted
R-square value of 0.5089, and the adjusted R-square
value of 0.6921 are near to 1 showing this model is rele-
vant. The adequate precision is 12.2354, which is greater
than 4, thus signifying the sufficiency of the model. Fig-
ure 5 shows the closeness of the actual and predicted
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494 489
Figure 4: Graph of GRG values for L
27
OA experimental runs

values of response (GRG) for the 27 trials. The predicted
and actual GRG values are very close on the diagonal.
This shows that the developed model is relevant.
12
Fig-
ure 6 shows the graph of internally studentized residuals.
The bulk residuals are positive or along the diagonal line,
with a nearly symmetric distribution and no discernible
trends. The fit of the produced model for the response is
further determined by the randomness in the residual
plot.
Table 7: ANOV A for the response surface quadratic model for an
AISI 430 FW joint
Source
Sum of
squares
DOF
Mean
sum of
square
F-value p-value
Re-
marks
Model 0.1256 8 0.0157 8.31 0.0001
Significant
A – Frictional
pressure
0.0215 1 0.0215 11.31 0.0049
B – Upset
pressure
0.0245 1 0.0245 12.89 0.0009
C – Friction
time
0.0007 1 0.0007 0.375 0.5477
D – Forging
time
0.0116 1 0.0116 6.15 0.0233
E – Rotational
speed
0.0129 1 0.0129 6.78 0.0065
AB 0.0077 1 0.0077 4.07 0.0588
CD 0.0137 1 0.0137 7.25 0.0149
B
2
0.0223 1 0.0223 11.79 0.0030
Residual 0.0340 18 0.0019
Cor. total 0.1596 26
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
490 Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494
Figure 7: a) Effect of parameters on GRG A and B, b) Effect of parameters on GRG C and D
Figure 5: Plot of predicted versus actual GRG values
Figure 6: Graph of internally studentized residuals

4.2 Analysis of response surface plots (AISI 430 steel)
The response surface plots in Figure 7a show that a
high value of frictional pressure of 59.95 MPa produces
a better response. Figure 7b shows a low level of friction
time of 4 seconds, which was sufficient to generate the
temperature and heat at the interface. A larger value of
upset pressure of 68.5 MPa allowed a larger GRG, which
is shown in Figure 7a and hence, an improved response.
4.3 Ramp graph and desirability analysis of GRG val-
ues (AISI 430 steel)
The desirability analysis is a method of finding a
good set of conditions that meet all the goals. The point,
at which the maximum desirability function gives the op-
timum operating conditions, is equal to one.
16
The opti-
mal conditions were determined in terms of input param-
eters that produced the highest values of desirability
(A – 59.95 MPa, B – 68.5 MPa,C–4s ,D–3sa n d
E – 1399 min
–1
). The desirability analysis output is pre-
sented in Table 8. Figure 8 shows the optimal levels of
input parameters. The input parameters with the highest
desirability are shown in the ramp graphs. The highest
desirable levels of all input parameters in the range of
permissible levels are marked as red dots, hence indicat-
ing that the highest value of GRG is 0.6908. This value
lies between the 95 % confidence level lower limit of
0.6259 and the upper limit of 0.7556. This shows that the
predicted optimum conditions have a chance ofa5%e r -
ror.
4.4 Confirmation test for a friction welded AISI 430
steel joint
The outputs of the experimental trial No. 24 with the
highest computed value of GRG (0.6892) were com-
pared to the outputs anticipated by the grey incidence re-
inforced response surface approach with the optimal
setup of the welding inputs. The quality attributes of the
joint formed with optimal welding inputs were im-
proved, proving the methodology used for the multi-re-
sponse optimization was efficient. The joint properties
including an ultimate tensile strength (UTS) of 544 MPa
and impact toughness (IT) of 20.5 J are obtained under
optimal conditions and the properties of the base metal
are UTS = 555 MPa and IT = 28 J. The axial shortening
of 16.3 mm obtained with the optimal setting of welding
inputs was substantially remarkable. As a result, a good
bond with good mechanical properties can be achieved
using only modest shortening values.
The enhancement of the properties including the
maximum ultimate tensile strength, impact toughness
and axial shortening obtained for the AISI 430 steel joint
is (2.25, 7.89 and 12.74) %, respectively. The increase in
the forging pressure is the reason for the improvement in
the strength and the decrease in the friction time is the
reason for bringing down the axial shrinkage.
23
These de-
tails are listed in Table 9.
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494 491
Figure 8: Ramp graphs with optimal levels of friction welding inputs
Table 8: Welding input parameters at optimal levels for AISI 430 steel
Symbol Welding inputs Low level High level Optimum level
A Friction pressure 40 60 59.95
B Upset pressure 50 70 68.5
C Frictional time 3 7 4
D Forging time 3 7 3
E Rotational speed 1000 1400 1399
Response Prediction SE mean 95 % CI high 95 % CI low
GRG 0.69088 0.0308 0.7556 0.6259

Table 9: Comparison of the results for optimal setting of welding in-
puts
Responses
Initial
setting
Optimal
set
esetting
Enhance-
ment
%E n -
hance-
ment
GRG 0.6892 0.6908 0.0016 –
Ultimate Tensile
Strength (MPa)
532 544 12 2.25
Axial Shortening
(mm)
18.68 16.30 2.38 12.74
Impact Toughness
(J)
19 20.5 1.5 7.89
5 MACROSCOPIC AND MICROSCOPIC
EXAMINATIONS
The thermal input required for the softening of mate-
rial closer to the weld contact is produced by the heat
flux as a result of the frictional pressure and rotational
speed. Applying the right amount of upset pressure
causes plastic flash, or radial outward displacement of
the material closer to the interface. The weld penetration
was fully accomplished because there was no longer any
trace of the weld line, and the curl of the parent material
was visible in the form of a flash. A closer look at the
flash under a microscope reveals that it is consistent in
breadth, demonstrating the strength of the bond. The heat
generation of friction welding is completely different
from the metal fusion welding technique, but the unifor-
mity of the temperature distribution is observed from the
weld interface to the unaffected zone. Various micro-
structures are identified between the weld interface and
the base metal due to the temperature gradient.
24
The microstructures of the unaffected zone, heat af-
fected zone, weld interface and plastically deformed
zone are shown in Figures 9a to 9d, obtained with the
optical microscope. The unaffected region shows that the
plastic flow has stopped and the parent material is begin-
ning to move away from the joint interface on both sides,
as seen in Figure 9a.
The chromium carbides seen at the ferritic bound-
aries in the microstructure of the heat affected zone in
Figure 9b show that chromium does not transform to
austenite because of heating. Therefore, the weld inter-
face in Figure 9c shows increased evidence of material
softening caused by the thermal input. The remaining
portion of the parent material is not impacted by the tem-
perature or stress, minimizing the probability of unfavor-
G. SENTHILKUMAR et al.: OPTIMIZATION OF PROCESS PARAMETERS FOR A SOLID-STATE-WELDED AISI 430 STEEL ...
492 Materiali in tehnologije / Materials and technology 57 (2023) 5, 485–494
Figure 9: a) Unaffected zone, b) heat affected zone, c) weld interface, d) plastically deformed zone

able microstructural changes and property degradation in
fusion welded joints.
The plastically deformed zone contains a finer grain
structure, whereas the partially deformed zone contains a
coarse grain structure as shown in Figure 9d. Due to
faster rotating speeds, the microstructure at the weld
contact exhibits dynamic recrystallization. Due to the
high temperature, stress and distortion that it experi-
enced, the weld interface seems to be considerably
darker than the other regions. Due to the torque that the
rotation experiences at higher temperatures, the grains
appear to be dragged into the zone of moderate deforma-
tion. It was discovered that the advancing portion of the
joint has more drag than the retreating portion.
6 CONCLUSIONS
A successful attempt to join AISI 430 steel pieces in
the solid state was made, and the potential for creating
high-quality welded joints utilizing continuous drive
friction welding was investigated. Using the integrating
strategy of the grey incidence incorporated response sur-
face methodology for the optimal parameter selection,
the potential for a concurrent optimization of numerous
responses is increased. The usage of the L
27
orthogonal
array in experimental trials, as opposed to more tradi-
tional approaches that used CCD or BBD, with the stan-
dard RSM to determine the ideal friction welding inputs
resulted in a significant reduction in the number of ex-
periments.
The maximum ultimate tensile strength, impact
toughness and axial shortening for the highest GRG of
friction welded AISI 430 steel are 532 MPa, 19 J and
18.68 mm, respectively. The maximum ultimate tensile
strength, impact toughness and axial shortening obtained
under optimum conditions are 544 MPa, 20.5 J and 16.3
mm, respectively. The improvement in the maximum ul-
timate tensile strength, impact toughness and axial short-
ening of the desired joint is (2.25, 7.89 and 12.74) %, re-
spectively. Improvements of nearly 98 % for the ultimate
tensile strength and 73.21 % for the impact toughness are
achieved when compared to the parent material. In terms
of linking various welding inputs and forecasting the
outcomes in terms of grey relational grade, the created
quadratic model was sufficient and efficient. It was dis-
covered that the anticipated and experimentally observed
values were rather close, proving the model’s suitability.
The quality characteristics of the joints were discovered
to be influenced by both the individual welding settings
and their interactions. The study can be extended further
to modeling the temperature at a weld interface.
Acknowledgment
The authors would like to extend their sincere grati-
tude for the facilities provided by the Panimalar Engi-
neering College, Department of Mechanical Engineering,
Chennai, India.
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