Microsoft Word - numero_56_art_07_3006 S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 84 Development of mathematical model and optimization of GMA welding parameters of IS 2062 grade A steel weldments Saadat Ali Rizvi University polytechnic, Jamia Millia Islamia, New Delhi India saritbhu@gmail.com, http://orcid.org/0000-0001-2345-6789 Wajahat Ali SCRIET, CCS University Meerut, India Wajahatali@rediffmail.com ABSTRACT. In this experimental work, the effects of Gas metal arc (GMA) welding process parameters, such as arc voltage, wire feed speed, and gas flow rate on the mechanical quality of IS 2062 structural steel of grade A have been studied. Process parameters play an important role in determining the weld quality. In this research work the response surface methodology (RSM) via the design expert version 12 (DOE) software was applied to determine the weld quality, for 3D plot, maximize desirability for all response, and also to develop a mathematical model that can predict the main effect of the listed parameters on weld quality i.e. toughness and hardness. A set of experiments has been conducted to collect the response data using a central composite design and ANOVA was used to predict the impact of welding parameters on toughness and hardness. The obtained and predicated results were compared and it was verified that toughness and hardness of weldments are significantly affected by arc voltage and wire feed speed while gas flow rate has a minor effect. KEYWORDS. Response surface methodology (RSM); Centre composite design (CCD); Modeling; Optimization; GMA welding; Mechanical quality. Citation: Rizvi, S. A., Ali., W., Development of mathematical model and optimization of GMA welding parameters of IS 2062 grade A steel weldments, Frattura ed Integrità Strutturale, 56 (2021) 84-93. Received: 31.01.2021 Accepted: 17.02.2021 Published: 01.04.2021 Copyright: © 2021 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION S 2062 structural steel is frequently used in fabrication industries due to its good weldability, good tensile strength (UTS), toughness, easy availability, economical etc. In this work, gas metal arc (GMA) welding process was used to join this grade A steel. Now a day’s gas metal arc welding process is frequently used to weld various materials as it is a semi automatic joining process and can even be used as automatic. In GMA welding process a copper coated mild steel I https://youtu.be/XExqfLyx8Lg S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 85 wire is used as a filler wire [1]. Several statistical and computational techniques such as response surface methodology, ANN, and Taguchi [2] techniques were applied to develop the mathematical modeling and process parameters optimization. Response surface methodology (RSM) is a powerful mathematical tool used to optimize the process parameters in processes such as machining, welding, and casting etc [3-5] and also used to develop a mathematical model [6] and it minimize the number of experiments. Muralimohan Cheepu et al [7] developed a mathematical model and optimize the welding process parameters during the laser welding of titanium alloys and compared the obtained results from response surface methodology with experimental results. Shekhar Srivastava and R.K. Garg[8] developed a mathematical model and optimized GMA welding process parameters during the welding of IS2062 via RSM approach . They verified that the wire feed speed has a significant effect, followed by arc voltage and travel speed. Sanjay A. Swami et al [9] investigated the effect of GMA welding parameters on the mechanical properties of mild steel by designing the experiments using central composite matrix. They concluded that on increasing the CO2 gas percentage in Ar gas ultimate tensile strength (UTS) increase up to some extend and then decreases. A G Kamble and R Venkata Rao [10] studied the effect of GMA welding process parameters on AISI 202 steel weldments and developed a model for mechanical properties and they showed in their results that higher the arc voltage decreases the hardness and mechanical quality but increases with increasing in welding speed. In the present experimental research work the effect of GMA welding process parameters on the toughness and hardness of IS2062 structural steel of grade A weldments were investigated and a mathematical model was developed by response surface methodology. Scanning electron microscopy (SEM) micro- morphology fracture surface of toughness test samples was studied to determine the ductile or brittle fracture. EXPERIMENTAL PROCEDURE n this research work, IS 2062 structural work of grade A in form of plate of size 300 mm x 60 mm x10 mm was used as parent metal. Gas metal arc (GMA) welding process was used to weld the parent metal in the shielding environment of 75% Ar+25% CO2 gas mixture. ER70S-6 of Ø 2 mm is used as filler wire to join the parent metal. Chemical composition of parent metal and filler wire is mentioned in Tab. 1. Material C Mn S P Si Fe IS 2062 0.22 1.5 0.049 0.05 0.37 Bal. ER70S-6 0.20 1.61 0.025 0.025 0.98 Bal. Table 1: Chemical composition of parent metal and filler wire (wt.%) Tab. 2 illustrates the different selected input parameters of GMA welding with their corresponding level, their notation, and unit in actual form. The proposed experimental design involves the variation of three factors (arc voltage, wire feed speed, and gas flow rate) at three levels. Welding trials were completely conducted based on central composite design of experiments associated with twenty numbers runs. Factors Notation Unit Level -1 0 +1 Arc Voltage V V 25 26 27 Wire feed speed WF IPM 300 350 400 Gas flow rate GF lpm 10 15 20 Table 2: Process parameters and their level Design matrix is shown in Tab. 3. Toughness test samples before fracture and after fracture are showed in Fig. 1. I S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 86 Std run Experimental run Arc voltage (V) Wire feed speed (Ipm) Gas flow rate (lpm) Toughness (J) Hardness (VHN) 9 1 24 350 15 200 178 6 2 27 300 20 156 181 16 3 26 350 15 266 161 5 4 25 300 20 188 186 13 5 26 350 6 258 199 20 6 26 350 15 261 159 3 7 25 400 10 186 165 1 8 25 300 10 242 171 15 9 26 350 15 274 165 19 10 26 350 15 255 162 12 11 26 434 15 188 182 2 12 27 300 10 214 196 8 13 27 400 20 190 180 10 14 28 350 15 208 206 18 15 26 350 15 268 150 4 16 27 400 10 192 181 14 17 26 350 23 194 186 17 18 26 350 15 260 155 11 19 26 266 15 156 189 7 20 25 400 20 202 175 Table 3: DOE table with responses Figure 1: toughness test samples. RESULT AND DISCUSSION Development of mathematical model n this work arc voltage (V), wire feed speed (F), and gas flow rate (L) were selected as welding process parameters. Mechanical properties, i.e. toughness and hardness of welded joints, are significantly affected by welding parameters and it is very clear from previous research work that toughness and hardness of IS 2062 steel weldments is I S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 87 considerably influenced by arc voltage and wire feed speed [11]. In regression analysis [12] as expressed by Eq. (1), an experimental mathematical model was generated in between the toughness, hardness, and independents variable [13] and check for its adequacy. Response surface methodology is also used based on central composite design (CCD) to develop a model to predict the mechanical quality and checked by ANOVA for its adequacy [14]. The mechanical properties dimensions response function can be expressed as Eqn. (1): Ytrans=f (x1,x2, x3, x4,...............xn) (1) where Ytrans is the power transformation of the welding parameters and xn represent the input parameters. x1=arc voltage, x2=wire feed speed, and x3=gas flow rate selected as welding input parameters in this experimental work. Usually 2nd order Eqn. (2) can be expressed [15] as:          k k k k o i i ii i ij i ji j i i y d d X d X d X X 2 1 1 (2) where y is the response (toughness and hardness) variable,xi is the uncoated level of the variables, ε is the fitting error, the coefficient do is the constant value or intercept, and coefficients di,dii, and dij represent the linear, quadratic, and interaction terms of the variable, respectively. Figure 2: Response surface plot showing the interation effect of (a) WFS Vs V,(b) GFR Vs and V and (c) GFR Vs WFS on toughness. Effect of welding parameters on mechanical properties (toughness) From the Tab. 4 it is very clear that quadratic is the best possible fit for toughness. As the main interaction and quadratic factors that contribute significant to toughness include arc voltage (A), gas flow rate (B), wire feed speed (C), arc voltage (a) (b) (c) S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 88 and gas flow rate (AB), arc voltage and wire feed speed (AC), gas flow rate and wire feed speed(BC),current (A2),gas flow rate (B2),and wire fed speed (C2). Model for toughness Developed mathematical model for toughness is represented by Eq.3             14402.13068 1066.54705 * 4.72138 * 5.50615 0.135000 * * 0.550000 * * 0.063000 * * 21.33451 * ² 0.013059 * ² 0.542253 * ²     Toughness A B C A B A C B C A B C (3) From Fig. 2 (a) and (b) it is very clear that as on increasing the wire feed speed toughness of weldment increases up to 350 IPM after that toughness start to reduce where as on increasing the voltage toughness tends to increases and it is obtained maximum at point 26V after that toughness tends to decreases it is due to increasing in the heat input. Fig.3 (a) & (b) repersent the normal probalility curve for toughness and hardness and this plot is used to check the adquancy of model. as all points are in a straight line,it can concluded that model is adequate[16-18]. Figure 3: residuals plot for the developed model (a) toughness (b) hardness. Design expert- 12 version software was used in this experimental work to develop and choose the suggented model that described the response factor in regression analysis and sequential F test was performed to test the significence of the regression model and determine the significent model terms of developed model. Data of Tab. 4 and 5 indicate that a quadratic model is statstically significant for the weldments mechancial quality i.e. toughness and hardness and can be used for further analysis in this investigation. Source Sequential p-value Lack of Fit p-value Adjusted R² Predicted R² Linear 0.5587 0.0002 -0.0476 -0.2908 2FI 0.7135 0.0001 -0.1650 -1.0345 Quadratic < 0.0001 0.0505 0.9088 0.6829 Suggested Cubic 0.0162 0.8845 0.9746 0.9803 Aliased Table 4: Statistics model for toughness test Source Sum of Squares df Mean Square F-value p-value Mean vs Total 9.496E+05 1 9.496E+05 Linear vs Mean 3340.00 3 1113.33 0.7125 0.5587 2FI vs Linear 2409.50 3 803.17 0.4622 0.7135 Quadratic vs 2FI 21231.24 3 7077.08 52.00 < 0.0001 Suggested Cubic vs Quadratic 1134.00 4 283.50 7.49 0.0162 Aliased Residual 227.06 6 37.84 Total 9.780E+05 20 48897.50 Table 5: Sequential model sum of square for toughness model. S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 89 Analysis of variance (ANOVA) ANOVA is a power full statically tool to determine which factor influence the response [19]. A model or model term is significant when p value is less than 0.05. In ANOVA p-term represent the probability of importance for each control parameters and higher signifies the use fullness of that parameters. Importance of design or control parameters can be determined and confirmed by ANOVA [20]. Tabs. 6 and 7 shows the ANOVA table for toughness and hardness of weldment. For both cases quadratic model was suggested. For both cases, as the value of R2 is closer to 1 hence model is accepted. Model 26980.75 9 2997.86 22.03 < 0.0001 significant A-Voltage 202.17 1 202.17 1.49 0.2509 B-Wire feed speed 41.54 1 41.54 0.3052 0.5928 C-Gas flow rate 3096.29 1 3096.29 22.75 0.0008 AB 364.50 1 364.50 2.68 0.1328 AC 60.50 1 60.50 0.4445 0.5200 BC 1984.50 1 1984.50 14.58 0.0034 A² 6559.46 1 6559.46 48.19 < 0.0001 B² 15361.09 1 15361.09 112.86 < 0.0001 C² 2648.42 1 2648.42 19.46 0.0013 Residual 1361.05 10 136.11 Lack of Fit 1135.05 5 227.01 5.02 0.0505 not significant Pure Error 226.00 5 45.20 Cor Total 28341.80 Std. Dev. 11.67 R² 0.9520 Mean 217.90 Adjusted R² 0.9088 C.V. % 5.35 Predicted R² 0.6829 Adeq Precision 13.7511 Table 6: ANOVA table for toughness. Model 3574.75 9 397.19 4.83 0.0108 significant A-Voltage 568.20 1 568.20 6.91 0.0252 B-Wire feed speed 146.78 1 146.78 1.79 0.2110 C-Gas flow rate 12.12 1 12.12 0.1474 0.7090 AB 0.1250 1 0.1250 0.0015 0.9697 AC 210.13 1 210.13 2.56 0.1409 BC 10.13 1 10.13 0.1232 0.7329 A² 1204.41 1 1204.41 14.66 0.0033 B² 674.99 1 674.99 8.21 0.0168 C² 1251.44 1 1251.44 15.23 0.0029 Residual 821.80 10 82.18 Lack of Fit 676.47 5 135.29 4.65 0.0584 not significant Pure Error 145.33 5 29.07 Cor Total 4396.55 Std. Dev. 9.07 R² 0.8131 Mean 176.35 Adjusted R² 0.6449 C.V. % 5.14 Predicted R² -0.2269 Adeq Precision 6.5677 Table 7: ANOVA table for hardness S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 90 Effect of welding parameters on mechanical properties (hardness) The moderate fit for hardness (VHN) also highlighted the quadratic relation as the possible best fit. From ANOVA table it is clear that as the main interaction and quadratic factors that contribute significant to hardness include arc voltage (A), gas flow rate (B), wire feed speed (C), arc voltage and gas flow rate (AB), arc voltage and wire feed speed (AC), gas flow rate and wire feed speed (BC), current (A2), gas flow rate (B2), and wire fed speed (C2).reduced ANOVA is tabulated in Tab. 7. Developed mathematical model for hardness is represented by Eq.4.            6262.89689 454.42813 * 2.11433 * 13.70422 * 0.002500 * * 1.02500 * * 0.004500 * * 9.14189 * ² 0.002738 * ² 0.372747 * ² HV A B C A B A C B C A B C (4) From Fig. 4 (a) and (b) it is very clear that as on increasing the arc voltage there is increment in the hardness of weldment where as on increasing the wire feed speed and gas flow rate there is little increment in the hardness. but from Fig. 4 (c) it is very clear on increasing the amount of gas flow rate hardness of weldment first increases and then decreases. Figure 4: Response surface plot showing the interation effect of (a) WFS Vs V,(b) GFR Vs and V and (c) GFR Vs WFS on hardness. Fig. 5 shows the effect of all the three welding process parameters on the weldment hardness at the centre point in the dsign space. Fractographic analysis Toughness test samples of IS 2062 steel weldments were tested for mode of fracture with the support of scanning electron microscope (SEM) to determine the nature of fracture i.e. ductile fracture of brittle fracture and it was observed that from Fig. 6 a- b having quasi-cleavage fracture [21] that consist a river patter and shows a brittle fracture but from Fig. 6 c it is very clear as there are a large number of dimples on fracture surface hence representing a ductile fracture. S. A. Rizvi et alii, Frattura ed Integrità Strutturale, 56 (2021) 84-93; DOI: 10.3221/IGF-ESIS.56.07 91 Figure 5: Perturbation plot showing the effect of all factor on the hardness of weldment. Figure 6: SEM image of fracture surface of samples. CONCLUSION his experimental work focuses on the GMA welding of IS 2062 structural steel of grade A. This study was carried out in order to determine the effect of GMA welding process parameters on the mechanical quality of weldments i.e. toughness and hardness. In addition, the interactions between the welding parameters were determined via 3D response plot and a mathematical model was proposed to predict the mechanical behavior of the weldments using response surface methodology (RSM). The following conclusions have achieved.  Response surface methodology approach can be effectively applied to determine the effect of process parameters on response i.e. on output.  RSM method is also used to plot the contour graph for various responses to show the interaction between the different process parameters.  The effective of both models i.e. toughness and hardness was checked according to R2 terms. As the R2 value in model is near to unity hence developed model represent good accuracy.  Ductile fracture was observed on SEM fractrography of toughness test samples T S. A. 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