H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
549–554
DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE
LASER-BEAM-WELDING PARAMETERS FOR JOINING
TITANIUM TUBES
RAZVOJ NUMERI^NEGA MODELA OPTIMIZACIJE
PARAMETROV LASERSKEGA VARJENJA ZA MEDSEBOJNO
SPAJANJE CEVI IZ TITANA
Haitham M. Alswat
Department of Mechanical Engineering, College of Engineering, Shaqra University, Dawadmi, Riyadh 11911, Saudi Arabia
Prejem rokopisa – received: 2024-06-19; sprejem za objavo – accepted for publication: 2024-08-16
doi:10.17222/mit.2024.1220
In this work Nd:YAG laser beam welding (LBW), which requires a low heat input, was applied to join grade-2 titanium tubes.
The pulse duration and pulse energy were varied according to a two-factor three-level central composite face-centred (CCFC)
design to join grade-2 titanium tubes. A numerical model was developed to correlate LBW process parameters and ultimate ten-
sile strength (UTS). Validation of the developed model was done using the analysis of variance. Pulse duration has a more sig-
nificant impact compared to pulse energy. The highest and lowest values of each process parameter produced a weak UTS,
which was less than 338 MPa. The change in the UTS for each process parameter was analysed with metallurgical studies of the
joints. Optimised process parameters for improved UTS were identified and reported.
Keywords: laser beam welding, numerical model, titanium tube joints, ultimate tensile strength, optimisation
V ~lanku avtorji opisujejo raziskavo laserskega varjenja (LBW, angl.: laser beam welding) z Nd:YAG laserskim snopom, ki
na~eloma poteka z manj{im vnosom toplotne energije in so ga uporabili za medsebojno spajanje cevi iz titana kakovosti 2
(Ti-2). Med preizkusi so avtorji analizirali vpliv spreminjanja ~asa impulzov in koli~ine vne{ene energije na tri-nivojsko
centralno-~elni na~in medsebojnega spajanja (CCFC, angl: central composite face-centred design) cevi iz Ti-2. Avtorji so razvili
numeri~ni model, ki medsebojno povezuje procesne parametre LBW in kon~no natezno trdnost (UTS; angl.: ultimate tensile
strength) zvarnih spojev. Za ovrednotenje in veljavnost razvitega modela so avtorji uporabili metodo analize variance. ^as
trajanja impulzov je mnogo bolj vplival na kakovost zvarov kot koli~ina vne{ene toplotne energije. Najvi{ja in najni`ja vrednost
obeh izbranih parametrov je rezultirala v najni`jih vrednostih kon~ne natezne trdnosti in sicer manj kot 338 MPa. Spremembo
kon~ne natezne trdnosti za vsak izbrani parameter varjenja so analizirali s pomo~jo metalur{kih preiskav na izdelanih zvarnih
spojih. V ~lanku poro~ajo o optimalnih procesnih parametrih, ki dajejo navi{jo kon~no natezno trdnost zvarnih spojev.
Klju~ne besede: varjenje z laserskim snopom, numeri~ni model, spajanje cevi iz titana, natezna trdnost, optimizacija
1 INTRODUCTION
Titanium alloys are commonly used in aerospace and
marine industries due to their high strength and low den-
sity. The desirable properties of titanium alloys include
excellent resistance to corrosion, high creep strength,
high-temperature resistance, high specific strength, etc.
Titanium weldment is required in structural and mechan-
ical equipment such as gas turbine blades, rocket engine
cases, engine frames, heat exchangers and landing gear
of the aircraft and propeller shaft, pressure vessels and
fasteners.
1–3
The joining of titanium tubes is widely used
in nuclear power plants, marine industry heat exchangers
and fuel pipelines for transferring fluids because of its
outstanding properties. Titanium alloys have been suc-
cessfully joined using fusion welding techniques, such as
tungsten inert gas welding (TIG) and electron beam
welding (EBW). However, defects, poor ductility and a
wide heat affected zone caused by TIG welding, and
maintaining a high vacuum and a clean environment for
EBW are the challenges for the manufacturing industry
with respect to joining titanium alloys.
4–5
These chal-
lenges can be avoided using friction stir welding (FSW).
In FSW, tool manufacturing is another challenge for the
joining of titanium alloys.
6
Thus, the advantages of laser
beam welding (LBW) appreciably increase the demand
in the manufacturing industry. Reduced distortion, a nar-
row heat-affected zone (HAZ), high-intensity light
source, and high scanning speed are the major advan-
tages of LBW for achieving good welds. The complex
geometry of a weld is likely to require LBW allowing a
reduced production time, high strength, and good
microstructural properties.
7
Several studies on joining ti-
tanium alloys have confirmed that welding speed, laser
power, pulse duration, focal distance, pulse energy, laser
frequency, shielding gas, etc., are important process pa-
rameters in LBW.
8–15
Akbari et al.
8
developed an artificial neural network
model to analyse the input parameter on the weld bead
geometry. Squillace et al.
9
studied different weld bead
Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554 549
UDK 621.791.724:546.82 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(5)549(2024)
*Corresponding author's e-mail:
halswat@su.edu.sa (Haitham M. Alswat)

geometries, fatigue and tensile strength based on differ-
ent LBW process parameters. Cao et al.
10
studied differ-
ent kinds of porosity formation of LBW joints for differ-
ent welding process parameters. Titanium alloys with a
thickness of 1.5 mm were successfully joined and the
microstructure of the joints was analysed for different
welding speeds.
11
Liu et al.
12
reported that laser power
has a significant effect on determining the metallurgical
properties of LBW joints. The production time and cost
are the major challenges in the manufacturing industry,
which can be reduced by developing a numerical model
to identify and optimise the process parameters for better
results. Different methods for predicting and optimising
the LBW process parameters are available. Design of ex-
periment (DOE) is one of the techniques used for a better
prediction and optimisation.
13,14
The tensile strength of
LBW joints is determined based on the process parame-
ters used during welding.
Casalino et al.
15
investigated the joining of a titanium
alloy with LBW using the Taguchi technique to develop
the statistical model ANOVA for validation by consider-
ing the welding speed, laser power and plate thickness as
input parameters. Xiansheng et al.
16
varied the pulse
shape, pulse frequency, laser power, weld speed, focal
length and shielding gas for welding the titanium shell of
a neuro-stimulator using Nd:YAG laser welding. They
optimised the welding parameters based on the weld
bead geometry using the Taguchi matrix method. Praba-
karan et al.
13
varied the laser power, welding speed, and
focal distance according to the L9 orthogonal array to
optimise the process parameters based on the UTS of
LB-welded dissimilar steels. Sivagurumanikandan et al.
17
developed a numerical model using an ANN and RSM to
predict and optimise the process parameters for a better
tensile strength of Nd:YAG LB-welded steel. The study
reported that the process parameters including laser
power, focal position, pulse frequency and welding speed
have a significant effect on selecting the UTS of LBW
joints. Shanthos Kumar et al.
18
optimised process param-
eters using an RSM with a central composite face-cen-
tred design (CCFCD) to join dissimilar alloys by com-
bining the pulse duration, pulse energy and welding
speed as the input process parameters of an Nd:YAG la-
ser whereas the tensile strength was the output process
parameter. Based on ANOVA, they found that the weld-
ing speed has the most significant effect on selecting the
tensile strength, followed by pulse energy and pulse du-
ration. According to a literature analysis, LBW of a
grade-2 titanium tube using a combination of pulse en-
ergy and pulse duration, based on CCFCD, is required to
meet the demand of the manufacturing industry. Thus,
this investigation was made to identify and optimise the
optimum process parameters to improve the tensile be-
haviour of LB-welded grade-2 titanium tubes using a
RSM with CCFCD.
2 EXPERIMENTAL WORK
LBW has various welding parameters such as laser
power, welding speed, focal distance, pulse duration,
pulse energy, pulse frequency, pulse shape, shielding gas,
etc. Pulse duration and pulse energy are considered as in-
put parameters and their levels are presented in Table 1.
These ranges of the parameters were identified using a
trial experiment. The developed design matrix used to
conduct the experimental work is presented in Table 2.
Table 1: Process parameters and their levels
Process parameter
Levels
–1 0 1
Pulse duration, ms 9 11 13
Pulse energy, J 11 13 15
Table 2: Two-parameter three-level central composite face-centred de-
sign
Trail
No.
Two-parameter three-level
design matrix
Response (ultimate tensile
strength, MPa)
Pulse dura-
tion (T)
Pulse energy
(E)
Experimental
value, MPa
Predicted
value, MPa
1 –1 –1 314.77 314.99
2 1 –1 309.05 309.27
3 –1 1 316.51 316.73
4 1 1 301.31 301.53
5 –1 0 322.39 321.95
6 1 0 311.93 311.49
7 0 –1 333.54 333.10
8 0 1 330.54 330.10
9 0 0 338.79 337.69
10 0 0 336.00 337.69
11 0 0 336.00 337.69
12 0 0 338.00 337.69
13 0 0 338.79 337.69
A grade-2 titanium tube was selected. The chemical
composition (in w/%) of the commercial grade-2 tita-
nium included 99.69 % Ti and a few other elements –
0.04 % C, 0.10 % Fe, 0.01 % N, 0.09 % O, and 0.007 %
H. The outer diameter of the tube was 60 mm, the length
of the tube was 75 mm, and the thickness of the tube was
approximately 4 mm. Acetone was used to clean the
edges of the tube to remove contaminants. Pieces of the
tube were clamped usinga3j a wchuck with a proper
alignment. A tack weld was produced before the welding
to avoid misalignment. Argon was used as the shielding
gas with a flow rate of 15 lpm. An Nd:YAG laser was
H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
550 Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554
Figure 1: Sample of the LBW grade-2 titanium tube

used to join the tubes. The upper bead of the weld was
protected by keeping the weld shoe inside the tube. A
sample of the welded tubes is shown in Figure 1.
Tensile specimens as per ASTM E8-04 standard and
metallurgical specimens were extracted using a wire
EDM machine. Tensile-tested values are presented in Ta-
ble 2. The metallurgical specimens were polished before
etching with Kroll’s reagent (4 % HNO
3
,2%HF ,96%
H
2
O). After etching, macrographs of the welds were cap-
tured using a stereo microscope. To analyse the grain
structure of different zones, electron backscattered dif-
fraction (EBSD) was used.
3 RESULTS
3.1 Development of an RSM-based numerical model
A central composite face-centred design (CCFCD)
matrix has star points at the centre of each face of facto-
rial space. Thirteen welds were obtained according to the
design matrix and the results are presented in Table 2.
The relationship between the lower welding process pa-
rameters (pulse duration and pulse energy) and the ulti-
mate tensile strength of LBW joints can be presented as
a mathematical expression using experimental data. The
RSM-based numerical equation for two parameters
(pulse duration and pulse energy) with three levels is as
follows:
Y=F(T,E) (1)
where:
Y: response (UTS)
T: input parameter 1 (pulse duration)
E: input parameter 2 (pulse energy)
The second-order polynomial equation for the UTS
of LBW joints with two parameters is presented by
Equation (2) below.
UTS=b
0
+b
1
T+b
2
E+b
11
T
2
+b
22
E
2
+b
12
TE (2)
Here, b
0
is the response coefficient for the centre
point; b
1
and b
2
are the coefficients of linear terms asso-
ciated with pulse duration and pulse energy, respectively;
b
11
and b
22
are the coefficients for the squared terms as-
sociated with pulse duration and pulse energy, respec-
tively; b
12
is the coefficient combining pulse duration and
pulse energy. The Design-Expert software version 13
was used to compute all the coefficient values. The re-
gression model developed in a coded form is shown in
Equation (3).
UTS = 337.69 – 5.23T – 1.5E – 20.97T
2
–
– 6.09E
2
– 2.37TE (3)
3.2 Adequacy of the developed numerical model
The adequacy of the mathematical model was as-
sessed using ANOVA and the results are presented in Ta-
ble 3. The fitness of statistics of the developed model is
presented in Table 4.
Table 4: Fitness of statistics of the developed model
Std. dev. 1.15 R² 0.9955
Mean 325.2 Adjusted R² 0.9924
C.V. % 0.3525 Predicted R² 0.9906
Adequate precision 46.44
The F-values of the developed model (312.88) indi-
cate that the model is significant. Insignificant lack of fit
is good for the developed model. The P-values suggest
including significant terms to improve the model. The
H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554 551
Table 3: ANOVA of the developed model
Source Sum of squares DOF Mean square F-value P-value
Model 2055.22 5 411.04 312.88 < 0.0001
significant
T 164.12 1 164.12 124.92 < 0.0001
E 13.5 1 13.5 10.28 0.0149
TE 22.47 1 22.47 17.1 0.0044
T² 1214.64 1 1214.64 924.56 < 0.0001
E² 102.47 1 102.47 78 < 0.0001
Residual 9.2 7 1.31
Lack of fit 1.12 3 0.3731 0.1848 0.9016 not significant
Pure error 8.08 4 2.02
Cor. total 2064.41 12
Figure 2: Normal probability of the developed model

P-values of linear, quadratic, and interaction terms are
significant as they are less than 0.0500. T, E, T
2
and E
2
are significant terms. The coefficient of determination
values (R
2
) should be 0.6 to 1. In this developed model,
the values are more than 0.9. The values of R
2
, adjusted
R
2
and predicted R
2
agree well. The difference between
the predicted R
2
and adjusted R
2
is less than 0.2. The sig-
nal-to-noise ratio can be obtained from the adequate pre-
cision values.
14
The acceptable range for this ratio is
more than 4. The developed model has a ratio of 44.21,
which indicates that the developed model is adequate.
The normal probability chart for the UTS is shown in
Figure 2. All the residuals fall in a line, indicating that
the error is low for the developed model. A scatter graph
was done for experimental and predicted values. All the
values are close to the 45-degree line as shown in Fig-
ure 3. According to the above analysis, the developed
model for the LBW of titanium tubes is adequate to use.
A perturbation graph is shown in Figure 4, demon-
strating the effect of each process parameter on the UTS
of the LBW titanium tube. This graph indicates the prog-
ress of the responses or output. Although all input pa-
rameters deviate from the reference point, the remaining
values do not.
4 DISCUSSION
4.1 Effect of the pulse duration and pulse energy on
the UTS
The impact of pulse duration and pulse energy on the
UTS of titanium tube joints produced by LBW is pre-
sented in a response graph, as shown in Figure 5.
The response graph illustrates the effects of process
parameters and the underlying reasons. An increase in
the pulse duration and pulse energy increases the heat in-
put of the LBW, which creates porosity in the joints.
Low pulse energy and short pulse duration produce a re-
duced heat input, which creates undercut defects; this
agrees with the work done by Shanthos Kumar et al.
18
High pulse energy and long duration produce a higher
heat input, creating porosity in the WZ. Thus, the opti-
mum heat input is required to produce defect-free joints,
allowing better mechanical and metallurgical properties
than those obtained at higher and lower heat input. The
UTS of the titanium tube joints increases with an in-
H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
552 Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554
Figure 3: Scatter diagram of the developed model of the LBW of tita-
nium tubes
Figure 5: a) Response surface graph of the LBW of titanium tubes;
b) contour graph of the LBW of titanium tubes
Figure 4: Perturbation diagram of the developed model of the LBW of
titanium tubes

crease in the pulse energy from7Jto10J.Further incre-
ment in the pulse energy, from 10 J to 13 J, decreases the
UTS of the LBW joints.
It was observed from the microstructure analysis that
the lowest UTS occurred due to a low heat input at the
lowest pulse energy, resulting in defects at the bottom of
the WZ, as shown in Figure 6a. The highest pulse en-
ergy of 13 J produced an enormous amount of heat at the
joints, creating porosity (Figure 6f) and causing tensile
failure during a tensile-strength test. A similar trend was
observed with the pulse duration. Increasing the pulse
duration from 9 ms to 11 ms increases the UTS, and
from 11 ms to 13 ms, it decreases the UTS. Undercut and
porosity are observed at the lowest and highest pulse du-
ration, respectively. Both pulse energy and pulse dura-
tion significantly impact the weld bead geometry. The
width of the WZ is almost the same from top to bottom
at a pulse energy of 10 J and a pulse duration of 11 ms.
The WZ is nearly parallel to the joint line at the optimum
heat input. It was possible to study the effect of process
parameters on the penetration of the joints as part of this
work. Grain-size variation was observed in the EBSD
images of the LBW of titanium tubes, as shown in Fig-
ure 7. The BM, HAZ and WZ have different grain sizes.
The changes in the microstructure occurred due to the
thermal cycle during LBW. The grain-size difference be-
tween the WZ and BM is clearly visible. At the same
time, the grain-boundary difference between the WZ and
HAZ is unclear. Labelling is approximately carried out at
the grain border by taking into account the weld root and
weld toe position.
7
The HAZ and WZ have coarse grains.
Elongated grains are observed in the HAZ, indicating
that the formation of a columnar grain structure accrued
at the initial stage of solidification.
The columnar grain structure orients itself along the
direction of heat flow during LBW. There are a few defi-
nite limits to the width of the HAZ. The uneven and
coarse granular grains in the weld zone are caused by the
epitaxial growth that occurs during solidification. Li et
al.
11
identified a columnar structure in the WZ of pure ti-
tanium joints produced by LBW. Similarly, columnar
grain structures with irregular coarse grains are observed
after the LBW of titanium. Porosity formation is un-
avoidable with fusion welding methods, including laser
welding. The fatigue strength and UTS are determined
by the porosity.
7,19
4.2 Optimisation
RSM is a simple and appropriate technique for de-
signing, analysing, and optimising the process parameter
combination for better responses. In RSM, response and
H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554 553
Figure 7: EBSD images of the LBW of titanium tubes comprising
WZ, HAZ and BM
Figure 6: Micrographs of the LBW of titanium tubes: a) pulse duration of 9 ms and pulse energy of 10 J; b) pulse duration of 13 ms and pulse en-
ergy of 10 J; c) pulse energy of 7 J and pulse duration of 11 ms; d) pulse energy of 13 J and pulse duration of 11 ms; e) pulse duration of 11 ms
and pulse energy of 10 J; f) observed porosity in the WZ

contour plots developed by the numerical model are the
indicators used to identify the best process parameters al-
lowing optimised conditions.
13,14
The developed response
and contour plots with optimised conditions for the LBW
of titanium tubes are presented in Figure 5. These plots
can predict the output in any range of experimental com-
binations. The maximum UTS values were taken from
the vertex of the response plot. The contour plot was
used to predict the optimised values for a better UTS.
The vertex point in the contour plot provided the x and
y-axis values used to predict the process parameters. The
optimised UTS value is 338 MPa, and the corresponding
values are a pulse duration of 11 ms and pulse energy of
10 J. In accordance with ANOVA, the process parame-
ters were ranked from the F-ratio. Based on the F-ratio
from ANOVA, the pulse duration impacts the UTS more
than the pulse energy.
5 CONCLUSION
This study yields the following findings:
• The LBW of titanium tubes was successfully done by
considering the pulse duration and pulse energy as
the input parameters.
• Using a RSM, a numerical model for optimizing the
process parameters of the LBW of titanium tubes was
successfully developed.
• Pulse duration and pulse energy are significant pro-
cess parameters for producing the heat input during
LBW, determining the UTS.
• Defects such as undercut and porosity are associated
with with low and high heat input, respectively.
• A coarse grain microstructure in the WZ, along with
a small HAZ, was identified.
• A pulse duration of 11 ms and a pulse energy of 10 J
were the best input parameters for obtaining the high-
est UTS of 338 MPa.
6 REFERENCES
1
D. Banerjee, J. C. Williams, Perspectives on Titanium Science and
Technology, Acta Materialia, 61 (2013), 844–879, doi:10.1016/
j.actamat.2012.10.043
2
W. Zhang, Z. Zhu, C. Y. Cheng, A literature review of titanium met-
allurgical processes, Hydrometallurgy, 108 (2011), 177–188,
doi:10.1016/j.hydromet.2011.04.005
3
Y. Lee, J. Cheon, B. K. Min, C. Kim, Optimization of gas shielding
for the vacuum laser beam welding of Ti–6Al–4 V titanium alloy,
The International Journal of Advanced Manufacturing Technology,
123 (2022), 1297–1305, doi:10.1007/s00170-022-10257-5
4
A. Karpagaraj, N. Sivashanmugam, K. Sankaranarayanasamy, Some
studies on mechanical properties and microstructural characterization
of automated TIG welding of thin commercially pure titanium
sheets, Materials Science and Engineering A, 640 (2015), 180–189,
doi:10.1016/j.msea.2015.05.056
5
M. Wu, R. Xin, Y. Wang, Y. Zhou, K. Wang, Q. Liu, Microstructure,
texture and mechanical properties of commercial high-purity thick ti-
tanium plates jointed by electron beam welding, Materials Science
and Engineering A, 677 (2016) 50–57, doi:10.1016/j.msea.
2016.09.030
6
P. D. Edwards, M. Ramulu, Material flow during friction stir welding
of Ti-6Al-4V, Journal of Materials Processing Technology, 218
(2015), 107–115, doi:10.1016/j.jmatprotec.2014.11.046
7
R. Palanivel, Effect of laser power on microstructure and mechanical
properties of Nd:YAG laser welding of titanium tubes, Journal of
Central South University, 30 (2023), 1064–1074, doi:10.1007/
s11771-023-5292-x
8
M. Akbari, S. Saedodin, A. Panjehpour, M. Hassani, M. Afrand, M.
J. Torkamany, Numerical simulation and designing artificial neural
network for estimating melt pool geometry and temperature distribu-
tion in laser welding of Ti6Al4V alloy, Optik, 127 (2016),
11161–11172, doi:10.1016/j.ijleo.2016.09.042
9
A. Squillace, U. Prisco, S. Ciliberto, A. Astarita, Effect of welding
parameters on morphology and mechanical properties of Ti–6Al–4V
laser beam welded butt joints, Journal of Materials Processing Tech-
nology, 212 (2012), 427–436 doi:10.1016/j.jmatprotec.2011.10.005
10
X. Cao, A. S. H. Kabir, P. Wanjara, J. Gholipour, A. Birur, J. Cuddy,
M. Medraj, Global and Local Mechanical Properties of Auto-
genously Laser Welded Ti-6Al-4V, Metallurgical and Materials
Transactions A, 45 (2014), 1258–1272, doi:10.1007/s11661-013-
2106-z
11
C. Li, K. Muneharua, S. Takao, H. Kouji, Fiber laser-GMA hybrid
welding of commercially pure titanium, Materials and Design, 30
(2009), 109–114, doi:10.1016/j.matdes.2008.04.043
12
S. Liu, G. Mi, F. Yan, C. Wang, P. Jiang, Correlation of high-power
laser welding parameters with real weld geometry and micro-
structure, Optics and Laser Technology, 94 (2017), 59–67,
doi:10.1016/j.optlastec.2017.03.004
13
M. P. Prabakaran, G. R. Kannan, Optimization of laser welding pro-
cess parameters in a dissimilar joint of stainless steel AISI316/
AISI1018 low carbon steel to attain the maximum level of mechani-
cal properties through PWHT, Optics and Laser Technology, 112
(2019), 314–322, doi:10.1016/j.optlastec.2018.11.035
14
R. Palanivel, S. P. Vigneshwaran, Y. Alqurashi, M. A. Rasheed, Ten-
sile-shear-strength prediction of friction-melt-bonded dissimilar spot
joints using RSM, Mater. Tehnol., 57 (2023), 57–62,
doi:10.17222/mit.2022.689
15
G. Casalino, F. Curcio, F. Memol Capece Minutolo, Investigation on
Ti6Al4V laser welding using statistical and Taguchi approaches,
Journal of Materials Processing Technology, 167 (2005), 422–428,
doi:10.1016/j.jmatprotec.2005.05.031
16
N. Xiansheng, Z. Zhenggan, W. Xiongwei, L. Luming, The use of
Taguchi method to optimize the laser welding of sealing neuro-
stimulator, Optics and Lasers in Engineering, 49 (2011), 297–304,
doi:10.1016/j.optlaseng.2010.11.005
17
N. Sivagurumanikandan, S. Saravanan, G. Shanthos Kumar, S. Raju,
K. Raghukandan, Prediction and optimization of process parameters
to enhance the tensile strength of Nd: YAG laser welded super du-
plex stainless steel, Optik, 157 (2018), 833–840, doi:10.1016/j.ijleo.
2017.11.146
18
G. Shanthos Kumar, K. Raghukandan, S. Saravanan, N. Siva-
gurumanikandan, Optimization of parameters to attain higher tensile
strength in pulsed Nd: YAG laser welded Hastelloy C-276–Monel
400 sheets, Infrared Physics and Technology, 100 (2019), 1–10,
doi:10.1016/j.infrared.2019.05.002
19
N. Kashaev, V. Ventzke, V. Fomichev, F. Fomin, S. Riekehr, Effect of
Nd: YAG laser beam welding on weld morphology and mechanical
properties of Ti–6Al–4V butt joints and T-joints, Optics and Lasers
in Engineering, 86 (2016), 172–180, doi:10.1016/j.optlaseng.2016.
06.004
H. M. ALSWAT: DEVELOPING A NUMERICAL MODEL TO OPTIMISE THE LASER-BEAM-WELDING PARAMETERS ...
554 Materiali in tehnologije / Materials and technology 58 (2024) 5, 549–554