R. PALANIVEL et al.: NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING ... 25–31 NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING OF A HIGH-TEMPERATURE MATERIAL NUMERI^NI MODEL ZA OPTIMIZACIJO PARAMETROV LASERSKEGA VARJENJA VISOKOTEMPERATURNIH MATERIALOV Ramaswamy Palanivel 1* , Thiyagarajan Muthu Krishnan 2 , Yousef Alqurashi 1,3 , Mohammad Abdur Rasheed 4 1 Department of Mechanical Engineering, College of Engineering, Shaqra University, Dawadmi, Riyadh 11911, Saudi Arabia 2 Department of Mechanical Engineering, SRM Valliammai Engineering College, Kattankulathur 603203, Tamil Nadu, India 3 Saudi Railway Research Group, Department of Mechanical Engineering, College of Engineering, Shaqra University, Dawadmi, Riyadh 11911, Saudi Arabia 4 Department of Civil Engineering, College of Engineering, Shaqra University, Dawadmi, Riyadh 11911, Saudi Arabia Prejem rokopisa – received: 2023-09-06; sprejem za objavo – accepted for publication: 2023-12-04 doi:10.17222/mit.2023.990 Ferritic stainless steel (FSS) is one of the high-temperature materials, used in many industries for sustainable applications such as power plants, automotive, offshore and chemical industries. Joining these materials is challenging due to the formation of an intermetallic and the grain growth with high-heat-input welding methods. Laser beam welding (LBW) that uses a low heat input was used successfully to join AISI 409 FSS tubes. In this work the welding speed and focal distance were varied as per a two-factor, three-level face-centred central composite design (FCCCD) to join AISI 409 FSS. A numerical model was developed to correlate the relationship between the ultimate tensile strength (UTS) and LBW process parameters. The validation of the de- veloped model was carried out using the analysis of variance. Both welding speed and focal distance have a significant effect on determining the UTS. The optimised process parameters provided for a better UTS as reported in this paper. Keywords: laser beam welding, high-temperature materials, ferritic stainless steel, sustainable manufacturing Feritna nerjavna jekla (FSS, angl.: Ferritic Stainless Steels) so ena izmed mnogih vrst materialov oziroma kovinskih zlitin, ki se uporabljajo pri visokih in povi{anih temperaturah v mnogih industrijah kot so naprimer ladjedelni{tvo, termo- in nuklearne elektrarne ter kemijska industrija za trajnostne aplikacije. Spajanje teh materialov je zahtevno zaradi tvorbe trdih in krhkih intermetalnih spojin ter pretirane rasti kristalnih zrn zaradi velikega vnosa toplote med varjenjem. Varjenje z laserskim snopom (LBW, angl.: laser beam welding) je tehnika pri kateri se uporablja manj{i vnos toplote za spajanje cevi iz nerjavnega jekla vrste AISI 409. V tem ~lanku avtorji opisujejo vpliv spreminjanja hitrosti laserskega varjenja in `ari{~ne razdalje na spajanje tri nivojskega dizajna centralno ploskovno centriranega kompozita (CCFC, angl.: three-level central composite face-centred de- sign) iz nerjavnega jekla vrste AISI 409. Avtorji so razvili numeri~ni model za napoved korelacije med kon~no natezno trdnostjo (UTS, angl.: ultimate tensile strength)in parametri laserskega varjenja. Razviti model so ovrednotili z uporabo tehnike analize variance. Oba izbrana parametra, to je hitrost varjenja in `ari{~na razdalja imata pomemben vpliv na kon~no natezno trdnost spoja. V ~lanku avtorji opisujejo postopek optimizacije procesnih parametrov za izbolj{anje kon~ne natezne trdnosti spojev izbrane konstrukcije oziroma dizajna. Klju~ne besede: lasersko varjenje, visoko temperaturni materiali, feritna nerjavna jekla, trajnostna proizvodnja 1 INTRODUCTION Ferritic stainless steel (FSS) has a body-centred cubic structure (BCC) at a normal temperature and good corro- sion resistance due to 12–25 w/% of chromium (Cr), which acts as a protective layer against the atmosphere. Joining FSS tubes is essential for meeting the demand of power plants and petrochemical industries to transfer flu- ids from one end to another. 1 The weldability of FSS is good with the fusion welding method. 2 Inappropriate fu- sion welding techniques produce incomplete joints, less penetration and defects that can weaken the joints. A higher amount of heat input restricts the expected joint properties. The growth of grains in the heat-affected zone (HAZ) is higher because of a slower cooling rate. 3 Most of the defects take place due to an insufficient or excess heat input. Also, the joints become weaker due to the formation of intermetallic phases sigma ( ) and chi ( ) with the fusion welding method. 4,5 So, the selection of the joining technique and process parameters is neces- sary for producing defect-free joints. LBW is an appro- priate method for joining FSS because of its merits such as a lower heat input, smaller HAZ, higher production rate and higher level of automation. The joint properties obtained with LBW are determined by the process pa- rameters such as laser power, welding speed, focal dis- tance, pulse width, pulse frequency, etc. 6–8 RSM is one of the methods based on statistical tech- niques of DOE, which uses input parameters to investi- gate the output parameters and optimise the inputs for better outputs or responses. There are different tech- niques of RSM, of which the central composite face-cen- Materiali in tehnologije / Materials and technology 58 (2024) 1, 25–31 25 UDK 621.791.725:669.14.018.62 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(1)25(2024) *Corresponding author's e-mail: rpalanivelme@gmail.com (Ramaswamy Palanivel) tred (CCFC) factorial design technique has more valida- tion with minimum logical experiments. 9 Cao et al. 10 studied the LBW process parameters of 3 mm thick AISI 316L using GA and RBFNN. They found that the laser power and welding speed are the deciding factors for good joint properties. Optimization of process parame- ters for hybrid laser–TIG welding of 5.6 mm thick AISI316L steel was carried out by Ragavendran et al. 11 They concluded that the pulse frequency, laser power and pulse duration are the significant input parameters for the bead width and depth of penetration. Jiang et al. 12 devel- oped a finite element model to optimise the LBW param- eters for 3 mm thick 316L stainless steel. The welding speed, laser power and focal distance were the input pa- rameters, whereas the depth of penetration and bead width were the output parameters for their study. Torabi et al. 13 used the response surface method (RSM) and a simulated annealing algorithm to develop a mathematical model for predicting the UTS of a thin AISI316L sheet after LBW. They concluded that the RSM is one of the best techniques for analysing the interaction between in- put parameters and responses. The effects of the welding speed, focal distance and laser power of CO 2 laser weld- ing on medium-carbon steel was investigated by Benyounis et al. 14 using the RSM technique. Chatterjee et al. 9 used the DOE technique with an RSM-based face-centred central composite design (FCCCD) matrix to conduct the LBW of 0.45 mm thin sheets of AISI 316. Vahiddastjerdi et al. 15 used the RSM technique for the LBW of high-Mn TWIP steel. They used the laser power, welding speed and spot size as the input parame- ters and concluded that the laser power had the major in- fluence on defining the UTS responses. Olabi et al. 16 op- timised LBW process parameters using the RSM for dissimilar joints between low-carbon steel and austenitic steel AISI316. They reported that the welding speed was the most effective parameter, compared to the laser power and focal position, for defining the weld-bead di- mensions and UTS of the joints. Kumar et al. 17 used the RSM to compare the joint properties of AISI304 and AISI 316 stainless steel joined with LBW. They reported that the most significant factor for defining the UTS was the pulse width compared to the welding speed and laser power. Pakmanesh 18 et al. optimized the process parame- ters to minimise the LBW underfill and undercut defects of 316L stainless steel using RSM. They reported that the laser power had the greatest impact on the defects. Undercut and underfill defects increased with increased pulse duration, frequency and laser power. According to a literature analysis, very limited studies on the LBW of FSS are available. The existing studies only focus on plates. So, in this work the joining of AISI 409 FSS tubes was investigated successfully and the process pa- rameters were optimised using the RSM technique with a FCCCD matrix. 2 EXPERIMENTAL WORK AISI 409 FSS tubes were 4 mm thick, their outer di- ameter was 44 mm and the length was 150 mm; a chemi- cal composition (in w/%) of 86.39 % Fe, 12.65 % Cr, 0.74 % Mn, 0.46 % Si, 0.11 % Ni, with few traces of Al, Cu, Co, C, P and S was selected for this investigation. The tube edges were cleaned using solvents and clamped firmly to the rotating chuck. The process parameters and their levels were selected based on trial experiments. Based on the process parameters, the FCCCD matrix was selected as presented in Table 1. Helium was used as the shielding gas with a gas flow rate of 15 lpm. The angle R. PALANIVEL et al.: NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING ... 26 Materiali in tehnologije / Materials and technology 58 (2024) 1, 25–31 Table 1: Laser-welding process-parameter levels along with the FCCCD matrix and response LBW welding parameter Levels –1 0 1 Welding speed, m/min 1.3 2.3 3.3 Focal distance, mm 13 18 23 Face-centered central composite design matrix (two parameters, three levels) Response (ultimate tensile strength, MPa) Percentage of error (E–P/P) x100 Welding speed (S) Focal distance (D) Experimental value (E), MPa Predicted value (P), MPa –1 –1 490 482.77 1.50 1 –1 467 477.05 –2.11 –1 1 484 484.51 –0.11 1 1 460 469.31 –1.98 –1 0 496 490.39 1.14 1 0 470 479.93 –2.07 0 –1 494 501.54 –1.50 0 1 492 498.54 –1.31 0 0 501 506.79 –0.55 0 0 504 506.79 –0.55 0 0 502 506.79 0.24 0 0 504 506.79 –0.55 0 0 504 506.79 –0.55 of incident was normal to the welding. LBW was carried out using a developed design matrix and experimental set-up. A sample of welded tubes is shown in Figure 1. Three tensile specimens were extracted from the welded tube as per the ASTM E8M-04 standard and the samples are shown in Figure 1. After each tensile test, the UTS average value was recorded as the ultimate tensile strength or response in Table 1. Specimens for micro- structural studies were prepared as per the standard met- allurgical technique. Etching of a prepared specimen was done for 2 min with a mixture of 10 mL glycerol, 5 mL HNO 3 and 15 mL HCl to reveal the microstructures of LBW joints. A field emission scanning electron micro- scope (FESEM) and electron backscatter diffraction (EBSD) were used to observe the microstructures of the LBW samples. Tensile fracture samples were observed using the FESEM to analyse the mode of fracture. 3 RESULTS 3.1 Development of an RSM-based numerical model The relationship between the two input parameters (welding speed and focal distance) and the output (the UTS of the LBW joints) were derived from the 13 sets of experimental data using the RSM RSM-based FCCCD matrix. Mathematically, the relationship between the welding speed and focal distance to the response UTS of LBW joints is expressed with Equation (1). UTS = F (S, D) (1) Here, S – welding speed, D – focal distance The second-order polynomial equation of the UTS of LBW joints with two parameters is Equation (2) below: UTS = b 0 + b 1 S + b 2 D + b 11 S 2 + b 22 D 2 + b 12 SD (2) where b 0 is the constant value; b 1 and b 2 are the first-or- der terms related to the welding speed and focal dis- tance, respectively; b 11 and b 22 are the second-order terms related to the welding speed and focal distance, respectively; b 12 is the interaction term between the welding speed and focal distance. The above-mentioned coefficients are calculated using Design Expert 13 soft- ware and the developed equation in coded form is in- cluded in Equation (3). UTS = 506.79 – 5.23S – 1.5D – 21.63S 2 – 6.75D 2 – – 2.37SD (3) R. PALANIVEL et al.: NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING ... Materiali in tehnologije / Materials and technology 58 (2024) 1, 25–31 27 Figure 1: LBW tube with a tensile sample Table 2: ANOVA for second-order quadradic models Source Sum of squares Degrees of free- dom Mean square F-value p-value Model 2055.22 5 411.04 312.88 < 0.0001 Significant S 164.12 1 164.12 124.92 < 0.0001 D 13.50 1 13.50 10.28 0.0149 SD 22.47 1 22.47 17.10 0.0044 S² 1214.64 1 1214.64 924.56 < 0.0001 D² 102.47 1 102.47 78.00 < 0.0001 Residual 9.20 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 R² Adjusted R² Predicted R² Adequate precision 0.9955 0.9924 0.9906 46.44 Figure 2: Scatter plot for LBW of the AISI 409 tube 3.2 Validation of the developed model using ANOVA ANOVA was done to validate the developed model and its results are presented in Table 2. The developed numerical model F-value of 312.88 infers the model is significant. An F-value this large might arise owing to noise only 0.01 % of the time. In this model, S, D, SD, S 2 and D 2 are considered as the significant terms as their p values are less than 0.05. An insignificant lack of fit is good for any developed numerical model for validation. The R 2 and adjusted R 2 values for the predicted model are in good agreement with each other. In general, the R 2 and adjusted R 2 values should be 0.6–1; in this case, they are close to 1. The signal-to- noise ratio for the developed numerical model is 46.44, which indicates that the model has an adequate signal. A scatter plot was drawn for the predicted and experimental values and all the values are very close to the 45° line as shown in Figure 2. In the light of the above, the devel- oped model is adequate to use. 9,19 R. PALANIVEL et al.: NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING ... 28 Materiali in tehnologije / Materials and technology 58 (2024) 1, 25–31 Figure 4: EBSD images of the WZ of the AISI 409 FSS tube: a) welding speed of 1.3 m/min, b) welding speed of 3.3 m/min, c) focal distance of 13 mm, d) focal distance of 23 mm, e) welding speed of 2.3 m/min and focal distance of 18 mm Figure 3: FESEM micrograph of the AISI 409 tube after LBW 3.3 Microstructure A FESEM micrograph of AISI 409 after LBW is shown in Figure 3. Three different zones are observed: the base metal, HAZ and weld zone or fusion zone. The fusion zone was analysed with EBSD to observe the grain structure and the results are presented in Figure 4. The tensile fracture morphology of tensile specimens was also analysed as shown in Figure 5. 4 DISCUSSION 4.1 Effect of the welding speed and focal distance The LBW process parameters including the welding speed and focal distance have an impact on the UTS of the joints as presented in the response and contour graphs in Figure 6, depicting the overall relationship be- tween the causes and effects. The laser welding speed increasing from 1.3 m/min to 2.3 m/min increased the UTS of the LBW joints; later a decrement in the UTS was observed with a further in- crement in the welding speed from 2.3 m/min to 3.3 m/min. Microstructural variation is seen due to the heat energy variation during the welding (Figure 3). The highest heat and related rate of cooling drop as one moves far from the laser beam. The effect of heat energy fades away at a certain distance when the basic-metal grains remain unchanged. It is worth noting that a very small region of the heat-affected zone is observed. In the FZ, a dendric structure is observed. Further, the observed EBSD microstructure of the FZ for different process pa- rameters is shown in Figure 4. It is obvious that there is a dendritic microstructure throughout the image. The un- even features within the dendritic structure, in contrast to a well-defined grainy structure, prevented an estimation of the grain size. However, it is noted that as the welding speed increases, the dendritic structure’s size becomes more precise. The decrease in the heat input and greater cooling rate may be attributed to this change. The rate at which solidifying steel cools from its molten state to room temperature controls the changes to the dendritic structure. 20 According to Figure 4, there is a longer time available for the formation of the dendritic micro- structure at 1.3 m/min than at 3.3 m/min. A shorter time is available at higher welding speeds, consuming a larger amount of heat. As a result, the dendritic structure gradu- ally shrinks. The welding speed of 3.3 m/min allows less tensile strength due to an undercut defect formed at the bottom of the weld zone. Lakshminarayanan et al. 21 ob- served incomplete penetration at higher welding speeds. The lowest welding speed produces a high amount of heat in the weld area, which can create pores. So, high and low welding speeds produce less tensile strength. An increase in the focal distance from 13 mm to 18 mm leads to an increasing trend of the UTS of the LBW joints, which starts to decrease with an increase from 18 mm to 23 mm. The power density can be changed by the focal distance, also affecting the mode of weld, width R. PALANIVEL et al.: NUMERICAL MODEL FOR OPTIMIZING THE PARAMETERS FOR LASER-BEAM WELDING ... Materiali in tehnologije / Materials and technology 58 (2024) 1, 25–31 29 Figure 5: Fracture surface of the AISI 409 FSS tube after LBW with a welding speed of 2.3 m/min and focal distance of 18 mm Figure 6: a) Response plot between the welding speed and focal distance, b) contour plot with predicted values for better process parameters of weld and depth of penetration. 8 Insufficient and exces- sive penetrations occur at the lowest and highest focal distances, respectively, which may affect the strength of the joints. A fine dendritic structure is observed with the EBSD analysis at a high focal distance due to a low power density, which causes the heat input to decrease and the cooling rate to increase. Figure 5 shows heavily packed fine voids on the fracture surface. The failure originates from well-developed and interrelated voids. The ductile mode of failure occurs. These striations propagate the fracture further. The collapse, meanwhile, does not occur suddenly, exhibiting the traits of a normal ductile failure. 4.2 Optimisation of LBW process parameters In order to obtain an optimised process parameter combination for a better UTS of LBW AISI 409, we can use the response and contour graphs developed by the numerical model and presented in Figure 6. These re- sponse contours can be used for any section of the exper- imental region to help predict the outcome (UTS). 9 The vertex of the response graph is used for determining the highest attainable UTS. The optimised process parame- ters are identified visually with the help of the contour graph. It is difficult to develop a contour graph for a sec- ond-order model compared to a first-order numerical model. Characterizing a response surface close to a mo- tionless spot may be necessary once it has been located. Characterization entails determining if the motionless spot is a saddle point, maximum or minimum response. Examining it through a contour graph makes categoriza- tion easy. The process parameters can be ranked based on the F-ratio calculated using ANOVA. As per the F-ra- tio, the welding speed has a more significant effect than the focal distance in determining the UTS. The obtained maximum UTS is found to be 506 MPa, corresponding to a welding speed of 2.3 m/min and focal distance of 18 mm. 5 CONCLUSIONS The conclusions of this research work are as follows: • Tubes of AISI 409 FSS were joined successfully us- ing LBW. • The RSM with a face-centered central composite fac- torial design was suitable for developing a numerical model with minimum logical experiments. • The welding speed and focal distance have signifi- cant effects on the UTS of the AISI 409 FSS tubes. • EBSD micrographs of the WZ show significant ef- fects of different welding speeds and focal distances. • The welding speed of 2.3 m/min and focal distance of 18 mm were identified as the best process parameter combination for achieving the maximum UTS of 506 MPa. Acknowledgment The authors extend their appreciation to the Deanship of Scientific Research at the Shaqra University, Saudi Arabia, for funding this research work through project number SU-ANN-2023031. 6 REFERENCES 1 M. A. 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