Materials and Design 34 (2012) 759–767

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Materials and Design

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The modeling and process analysis of resistance spot welding on galvanizedsteel sheets used in car body manufacturing

S.M. Hamidinejad a,⇑, F. Kolahan b, A.H. Kokabi c

a Department of Mechanical Engineering, Islamic Azad University, Eghlid Branch, Eghlid, Iranb Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iranc Materials Science and Engineering Department, Sharif University of Technology, Tehran, Iran

a r t i c l e i n f o

Article history:Received 11 April 2011Accepted 28 June 2011Available online 7 July 2011

Keywords:A. Ferrous metals and alloysD. WeldingG. Destructive testing

0261-3069/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.matdes.2011.06.064

⇑ Corresponding author. Tel.: +98 9173520155; faxE-mail addresses: hamidinejad@iaueghlid.ac.ir, ham

Hamidinejad).

a b s t r a c t

In this study, the resistance spot welding (RSW) process of the galvanized interstitial free (IF) steel sheetsand galvanized bake hardenable (BH) steel sheets, used in the manufacturing of car bodies, has beenmodeled and optimized. The quality measure of a resistance spot welding joint is estimated from thetensile–shear strength. Furthermore, four important process parameters, namely welding current(WC), welding time (WT), electrode force (EF), and holding time (HT) are considered as the factors influ-encing the quality of the joints. In order to develop an accurate relationship between the process inputs(4-component vectors) and the response output (tensile–shears strength) at first a linear regressionmodel was utilized but the residuals analysis revealed a non-linear behavior. Therefore, an artificial neu-ral network (ANN) was proposed because the ANNs are capable of mapping the non-linear systems. Aback propagation neural network model was developed to analyze RSW process and the interactioneffects of the parameters. In the second phase of this research, Genetic Algorithm with the fitness func-tion based on an ANN model was employed as an optimization procedure for determining a set of processparameters; as a result, the maximum joint strength was obtained. Optimization results showed highcompatibility with the actual experimental data.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction industrial applications. Structures employing RSW joints are usu-

Resistance spot welding (RSW) is an efficient joining processwidely used for the fabrication of sheet metal assemblies. RSWhas excellent techno-economic benefits such as low cost, highspeed and suitability for automation which make it an attractivechoice for auto-body assemblies, truck cabins, rail vehicles andhome appliances [1]. Due to the large number of spot welds in aparticular application (for example 3000–7000 in a car body), theprocess parameters of RSW need to be fine tuned [2]. Moreover,the weldability of galvanized steel sheet is more demanding thanthat of ordinary steel sheets for the existence of spatter generatingand electrode pollution during the spot welding. This limits theapplication of galvanized steel sheets and the large-scale auto-matic fabrication of automotive products [3].

Like any other welding process, the quality of the joint in RSW isdirectly influenced by welding input parameters. A commonproblem faced by manufacturer is the control the process inputparameters to obtain a well welded joint with required strength[4]. Thus, finding the relationships between the strength of spotweld and process parameters is of great interest in related

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: +98 2166912981.idi.mahdi@Gmail.com (S.M.

ally designed so that these joints are loaded in shear even if theparts are exposed to tension or compression loading [5]. Therefore,the tensile–shear strength of spot weld is an important index towelding quality [6]. Static tensile shear test is the most commonlaboratory test used to determine weld strength because of its sim-plicity [7].

In recent years, analytical and numerical methods have beenemployed to model welding processes and to establish the rela-tionships between different weld quality indicators and processparameters. Specifically, several research works are reported onusing artificial neural networks (ANNs) to model various weldingtechniques. ANNs are mathematical models that imitate the behav-ior of the biological nervous system. They have parallel, distributedand adaptive processing capable of mapping non-linear and com-plex systems in which the regression methods have their limita-tions [8,9]. Ates [10] presented a technique based on artificialneural networks (ANNs) to model gas metal arc welding parame-ters. The proposed ANN predicts mechanical properties of theweldment such as tensile strength, impact strength, elongationand weld metal hardness. Fratini et al. [11] linked ANN to a finiteelement model (FEM) to estimate average grain size values in thefriction stir welding (FSW) process. Based on experimental results,Cevika et al. [12] proposed an ANN to determine the ultimatecapacity of arc spot welding. The ultimate capacity of arc spot

760 S.M. Hamidinejad et al. / Materials and Design 34 (2012) 759–767

welding is modeled in terms of weld strength, average weldingthickness and diameter. Martín et al. [2] developed an ANN tointerpret ultrasonic oscillograms and to classify the respective spotweld in a certain quality level. In another study, Martín et al. [13]proposed an ANN to predict the tensile shear strength of the 304austenitic stainless steel RSW welded joints. They investigatedthe effect of three process parameters namely welding time, weld-ing current and electrode force, on the tensile shear strength.

With regard to the points mentioned, in this study at first a lin-ear regression model has been proposed, but the residuals analysisrevealed the inherent nonlinearity behavior of the RSW process.Therefore, an artificial neural network (ANN) is developed to pre-dict spot weld quality measure (tensile–shear strength). The pres-ent study differ from the existing research in the sense that wehave considered two different materials; namely galvanized inter-stitial free (IF) and galvanized bake hardenable (BF) steel sheets.Moreover, the interaction effects of RSW parameters are analyzed.The important process parameters considered here include weld-ing current, welding time, electrode force and holding time. Next,a Genetic Algorithmic (GA) procedure has been employed to deter-mine optimal process parameter values for desired tensile–shearstrength. The optimization results are then verified against actualexperimental data which revealed that they are satisfactory.

Table 4Experimental variable levels.

Experimentalvariables

Lowlevel(�1)

�0.5 0 0.5 Highlevel(+1)

WC Welding current (kA) 10 10.5 11 11.5 12EF Electrode force (kgf) 195 200 210 220 225WT Welding time (cycle(1/50 s)) 8 9 10 11 12HT Holding time (cycle(1/50 s)) 8 9 10 11 12

2. Experimental procedure

2.1. Materials and equipment

The materials used in experiments are commercially availablegalvanized steel sheet widely used in car fabrication. Interstitialfree (IF) and bake hardenable (BH) steel sheets are lately developedmaterials with superior properties. Due to the presence of alloyingelements such as Mn and Si, they have excellent formability andmechanical properties. They are appropriate for galvanizing andannealing to produce specialized sheets of steel, which is requiredfor automotive body manufacturing [14]. The chemical composi-tion of the IF and BH sheets is shown in Tables 1 and 2.

The mechanical properties of the IF and BH sheets is shown inTable 3. The sheets thickness is 0.67 mm.

Table 1Chemical composition of the interstitial free (IF) steel sheets (wt%).

C Si S P Mn Ni Cr

0.003 0.006 0.005 0.018 0.173 0.011 0.031

Mo V Cu Al Nb Zn Ti

0.001 0.002 0.017 0.035 0.001 0.004 0.05

Table 2Chemical composition of the bake hardenable (BH) steel sheets (wt%).

C Si S P Mn Ni Cr

0.002 0.005 0.006 0.018 0.162 0.022 0.021

Mo V Cu Al Nb Zn Ti

0.0006 0.001 0.015 0.044 0.005 0.008 0.005

Table 3Mechanical properties of the IF and BH steel sheets.

Yield strength (Mpa) Ultimate strength (Mpa)

Before baking After baking Before baking After baking

IF 164.6 164.9 309.8 310.2BH 186.4 218.1 310.1 310.2

IF and BH sheets are welded in a single-phase AC 50 Hz equip-ment by using water cooled type B (Dome) RWMA electrodes [15]with 7 mm face diameter.

2.2. RSW process parameters

Experimental data were gathered using Design of Experiment(DOE) approach. The full factorial and central composite design ta-bles were combined together which resulted in 124 different weld-ing tests. To determine the feasible working limits of weldingconditions, several trial tests were carried out. Different combina-tions of RSW parameters were used in the trial runs. The weld pen-etration and nugget appearance were inspected to identify theappropriate ranges of the welding parameters. In this regard, itwas observed that if the welding times are less than 8 cycles, therewould be lack of fusion and incomplete penetration. Actually, suchcycles produced very small nuggets. On the other hand, weldingtimes greater than 12 cycles resulted in weld splash and spatter aswell as penetration of the electrodes into the workpiece and work-piece crushing. Also, the welding currents less than 10 kA resultedin incomplete penetration and lack of fusion. For currentsgreater than 12 kA, weld splash and spatter would occur. The limitsfor electrode force and holding time were determined in similarfashion.

The considered process parameters and their ranges are shownin Table 4.

Fig. 1. The tensile–shear strength definition and calculation from laboratory test. Dis eccentricity and d is thickness.

Fig. 2. Dimensions of spot welded tensile shear test specimens.

Table 5Model summery.

S R square Adjusted R square

130.321 70.10% 69.00%

Table 6ANOVA.

df Sum of squares Mean of square F Significant

Regression 4 4,728,340 1,182,085 69.6 0.000Residual Error 119 2,021,045 16,984

Total 123 6,749,385

Table 7Coefficients.

Coefficients SE coefficients T Significant

Constant 799.7 295.7 2.7 0.008

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2.3. Tensile shear test

Tensile–shear strength is an important measure of weldingquality in RAW [3]. Therefore, in this research tensile–shearstrength has been selected to describe the mechanical propertiesof spot weld. Referring to Fig. 1, there is an eccentricity D betweentwo tensile axes of the overlap joints. The tensile stress and shearstress are both playing a role during tension test to spot weld be-cause of the eccentricity [3].

A tensile shear test specimen was spot welded for each of the124 welding conditions mentioned above. The specimens wereprepared according to ISO 14273 [16] (Fig. 2).

In order to increase the accuracy and the confidence level, theexperiment related to each of the parameters combinations wascarried out three times and their average value reported as thestrength related to this parameters combination. The tensile–sheartests were carried out at a crosshead of 20 mm/min with a Zwick(Z050) universal testing machine. During the tests, three types ofbreaking failure were observed: (1) separation; (2) knotting; (3)tearing. Samples of them are shown in Fig. 3.

EF �1.758 1.025 �1.71 0.089WC 212.84 15.47 13.76 0.000WT 71.226 7.733 9.21 0.000HT 8.637 7.733 1.12 0.266

3. Results and discussion

3.1. Linear regression model

A linear regression model was developed to relate the tensile–shear strength of the RSW joints to the four welding parameters;WT, WC, EF and HT. For regression analysis Minitab14.12.0.0 wasused.

Tables 5–7 illustrate the results of the regression analysis. Table7 shows that the regression is significant at the 95% confidence le-

Fig. 3. Breaking types observed in tensile–shear test; (A): separation type breaking;(B): knotting type breaking; (C): tearing type breaking.

Fig. 4. Residual plot.

vel (p = 0.000). Table 6 shows that EF (p = 0.089) and HT (p = 0.266)are not significant. Nevertheless, the coefficient of determination(R2 = 70%) and the residuals analysis (Fig. 4) for this model revealnon-linear behavior of the process. Hence, in the next section anANN model is proposed.

762 S.M. Hamidinejad et al. / Materials and Design 34 (2012) 759–767

3.2. The proposed ANN model

Traditional modeling methods are mostly relied on assumptionsfor model simplifications, and consequently may lead to inaccurateresults. The ANN captures the underlying trend of the data setpresented to it, in the form of a complex non-linear relationshipbetween the input parameters and the output variable [9]. Thecharacteristics of the ANNs make them suitable for modeling thestrength of a resistance spot welding joint, and therefore it wasused as the modeling tool in this research.

3.2.1. The artificial neural network architectureIn this paper, a multilayer back propagation feed forward ANN,

implemented and trained using the Neural Network Toolbox in theMATLAB� 7.4 package, has been used. While BPNs can have manylayers, but all pattern recognition and classification tasks can beperformed with a three-layer BPN [17].The Bayesian regularizationalgorithm (called trainbr in MATLAB�) was used for training the

Table 8Assessment of the ability to generalize of the ANN.

Input Output

EF(kgf)

WC(kA)

WT(cycle)

HT(cycle)

Experimentvalue

Predictedvalue

225 10 12 8 3512.64 3501.19210 10 12 8 3639.16 3552.37195 12 8 12 3697.39 3701.05225 11 12 8 3735.52 3748.81225 12 12 12 3638.91 3662.2210 12 12 8 3709.21 3688.26195 12 12 12 3796.56 3782.68225 10 8 10 2981.93 2922.28195 10 8 8 3153.57 3171.22210 10 8 12 3081.86 3101.72225 11 8 8 3489.89 3384.3225 10 12 8 3519.35 3501.19195 12 8 10 3718.1 3685.94210 11 10 10 3698.36 3710.34210 10 10 8 3284.74 3279.23225 10 8 8 2893.07 2895.65225 12 12 10 3626.17 3636225 12 8 8 3672.18 3620.5210 12 12 12 3729.65 3734.5195 12 8 8 3655.95 3670.43

Fig. 5. Plot of ANN outputs vs. experimental outputs.

ANN. Bayesian regularization is a network training function thatupdates the weight and bias values according to Levenberg–Mar-quardt optimization. It minimizes a combination of squared errorsand weights, and then determines the correct combination so as toproduce a network that generalizes well.

An ANN learns by means of training the same as a biologicalnervous system does. In this research, a supervised learning mech-anism was utilized in training of the ANN; thus each input shouldcome with its respective desired output. The inputs are 4-compo-nent vectors, a component for each of the welding parameters,WT, WC, EF and HT. Each target is the tensile–shear strength ofthe RSW joint obtained with the respective input.

The overfitting phenomenon may occur in the training whenthe ANN memorizes the training data instead of building an in-put–output mapping for the problem in question. Consequently,the overfitting problem results in drop of the ability to generalizethe ANN. The data were organized in input/output pairs. The totaldata set had 124 pairs and was randomly divided into two subsets[18–20]:

� Training subset: With 104 input/target pairs for training theANN. In the training, the synaptic weights are repetitivelyupdated to decrease an error function.

Fig. 6. Interaction between welding current and welding time, electrode force is225 kgf and holding time is 12 cycles.

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� Validation subset: With 20 input/target pairs for evading overfit-ting and attaining good generalization by means of cross valida-tion. Training stops if the error with regards to validation subsetstarts to increase (early stopping).

The performance of the ANNs depends on the number of hiddenlayers and number of neurons in them. So, many trials need to bemade to find the optimum structure for the neural network bychanging the number of hidden layers and also the number of neu-rons in each of them. The proper neural network structure for pre-dicting the tensile–shear strength of the RSW joint was chosen bytrial-and-error method. In this paper, the number of neurons in theinput and output layers of the ANN are four and one respectively.There is a hidden layer with 10 neurons. The transfer function forthe hidden layer is the Log-sigmoid transfer function, called logsigin MATLAB�; the transfer function for the output layer is the iden-tity function, called purelin in MATLAB�.

The 20 input/target pairs used for cross validation were alsoemployed as well for estimating the ability to generalize the previ-ously trained ANN. The 20 inputs were presented to the ANN andan experimental output was attained for each input, Table 8. AsFig. 5 depicts, the network outputs (ANN-output) are plotted ver-sus the experimental outputs (E-output) as open circles. The bestlinear fit is indicated by a dashed line. The perfect fit (network out-puts equal to experimental outputs) is indicated by the solid line. It

Fig. 7. Interaction between welding current and electrode force, welding time is12 cycles and holding time is 12 cycles.

is difficult to distinguish the best linear fit line from the perfect onebecause the fit is so good. In this model, the correlation coefficient(R-value), which is a measure of how well the variation in the net-work output is explained by the experimental output, is 0.991. Theresult indicates that the ANN has a high performance, and it canaccurately map the relationship between the tensile–shearstrength of the RSW joint and the process parameters.

3.3. Analysis of process parameters

A major advantage of ANN is that it can take into account theinteraction effects of process parameters. Due to the complicatedeffects of interactions, it is important to pay more attention tothe marching of process variables during the welding process de-sign [3]. In this regard, the ANN model has high capability to pre-dict the tensile–shear strength in RSW joints and hence isemployed in this study to evaluate the interaction effects of param-eters. For this purpose, the mathematical function developed bythe ANN was extracted and the effect of the process parametersand their interactions on the tensile–shear strength was illustratedby 3D surfaces and their contours. The effects of six interactionswere shown in Figs. 6–12. The surfaces and their contours reveal

Fig. 8. Interaction between welding current and electrode force, welding time is8 cycles and holding time is 12 cycles.

764 S.M. Hamidinejad et al. / Materials and Design 34 (2012) 759–767

the variations in the tensile–shear strength by the actions of twovariables (two out of the four parameters remained constant).

The physical weld attributes such as fusion zone size (FZS), weldpenetration and electrode indentation are the most importantparameters governing the mechanical performance of resistancespot welds. It has been shown that welding current and weldingtime significantly affect these characteristics [21]. For instance,volume of melted metal is a function of heat input which is gov-erned by the welding parameters including welding current andwelding time. Fig. 6 demonstrates the interaction effect of weldingcurrent and welding time (EF is 225 kgf and HT is 12 cycles). Asillustrated, within the range of 8–10 cycles, by increasing the weld-ing current the strength increases at a sharp ascending rate andthen remains constant in the 11.5–12.5 kA welding current range.On the other hand, at higher welding times (10–12 cycles), byincreasing the welding current to 11 kA the strength increasesand then decreases. This happens due to the fact that more resis-tance heat is generated by increasing the welding current and time.Moreover, the liquid metal during nugget forming is crushed toturn into a spatter under the action of the excessive resistance heatgenerated by the large welding current and electrode force, there-by decreasing the nugget size. In fact, the input heat melts andsoftens the welding sheets and, if the electrode force remains

Fig. 9. Interaction between welding time and electrode force, welding current is12 kA and holding time is 12 cycles.

constant, a deeper imprint is created. A spike in electrical currentresults in a large imprint and a potential burn-through effect onthin metal plates [22]. Also, the appearance of the welds is impor-tant, particularly on the high condition where the spatter is exces-sive [23]. Furthermore, because of significant resistance heat theoverheating microstructure is generated in the heat affected zone(HAZ) and then the mechanical properties of the spot weld de-creases as a result [3].

Fig. 7 demonstrates the interaction effect of welding currentand electrode force (WT and HT are 12 cycles). The role of the elec-trode force in forming nuggets in the RSW process is crucial, espe-cially regarding the galvanized steel sheets. As can be seen, ingeneral, by increasing the welding current, at first the strength in-creases and after reaching a maximum amount, it decreases. Athigher electrode force there is a further decrease in strength be-cause of excessive electrode force leading to zinc coat with lowmelting point to melt and to accumulate around the electrode toenlarge the contact area between workpieces and electrodes. Thus,the resistant heat decreases because of lower current density withthis phenomenon, and then the nugget size decreases with this ef-fect, which is also disadvantageous to the quality of RSW becauseof the decreasing of effective area to load and mechanical proper-ties of spot weld. Another important reason for the increase in

Fig. 10. Interaction between welding current and holding time, welding time is12 cycles and electrode force is 225 kgf.

Fig. 11. Interaction between electrode force and holding time, welding current is10 kA and welding time is 12 cycles.

Fig. 12. Interaction between welding time and holding time, welding current is12 kA and electrode force is 210 kgf.

S.M. Hamidinejad et al. / Materials and Design 34 (2012) 759–767 765

strength at higher welding currents is the excessive resistance heatgenerated and the liquid metal spattering. Under these circum-stances, due to the penetration of the electrodes into the workpieceand the workpiece crushing, the strength decreases.

In order to investigate the interaction effect of EF and WC moreaccurately, Fig. 9 is presented. By comparing Fig. 7 with Fig. 8, itcan be concluded that the effect of the electrode force at higherwelding currents depends greatly on the welding time because atthe higher welding time (12 cycles) the increase in the electrodeforce contributes to a decrease in strength. This is also due to thepenetration of the electrodes into the workpiece and the workpiececrushing. However, by decreasing the welding time (8 cycles-Fig. 8) the decrease in strength is not observed any more. In otherwords, by decreasing the welding time the electrode force param-eter causes much fewer variations in the strength. Fig. 9, whichillustrates the interaction effect between WT and EF (WC is 12 kAand WT is 12 cycles), also confirms this fact.

Fig. 10 demonstrates the interaction effect of welding currentand holding time (EF is 225 kgf and WT is 12 cycles). As can beseen, by increasing the current from the lowest level, the strengthincreases and after reaching a maximum amount, it decreases. Thisis because of the overheating microstructure which is generated inthe heat affected zone (HAZ). However, as can be seen in thisfigure, the holding time has little impact on the quality index. Sincethe alloys used in this research are low-carbon steels, the holding

time, which is regarded as heat treatment, does not make notice-able changes to the microstructure of the nuggets and HAZ. There-fore, lack of considerable dependence of strength on the holdingtime is reasonable.

Figs. 11 and 12 show the interaction effect of electrode forceand holding time (WC is 10 kA and WT is 12 cycles) and theinteraction effect of welding time and holding time (EF is210 kgf and welding current is 12 kA), respectively. They also ex-hibit lack of intense dependence of mechanical properties on theholding time.

In spite of the analyses and investigations conducted on theproposed ANN, it is still impossible to find out how to adjust theprocess parameters to reach the highest strength level. In otherwords, due to the existence of various parameters and their inter-action effects in the defined boundary restrictions, the estimationof the optimized combination of the process parameters to achievethe highest strength level of the RSW joints is a demanding task.Thus, it is essential that a capable tool for obtaining the optimizedcombination of the process parameters be utilized. For this pur-pose, in this research a Genetic Algorithm (GA) approach has beendevised to obtain the optimum combination of the process param-eters to reach the highest strength level.

Table 9GA parameters.

GA parameters

No. of generations for evolution 200Population size 50Type of selection Stochastic uniformProbability of cross over 0.95

Table 10Predicted tensile–shear strength of the RSW joint under optimum process parametersand experiment value.

EF(kgf)

WC(kA)

WT(cycle)

HT(cycle)

Predicted value byGA

Experimentvalue

201 11.3 12 12 3858.62 3802.21

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3.4. Process parameters optimization using combined ANN/GA method

Genetic Algorithm is a capable, general-purpose optimizationtool which is widely used for solving optimization problems inthe mathematics, engineering, etc. In this research, Genetic Algo-rithm is employed to optimize the RSW process parameters toobtain a set of desired values for tensile–shear strength duringRSW welding experiments.

The aim of the process optimization is to find the optimal con-trol variables in RSW under certain given constraints, in order toobtain the best RSW joint quality. The fitness function used inthe optimization procedure is based on the proposed ANN model.

In this research, the ANN model has been implemented as theobjective function of the optimization problem. The process win-dow for each variable, as given below, was used as the boundaryconstraints.

10 kA 6Welding Current (WC) 6 12 kA195 kgf 6 Electrode Force (EF) 6 225 kgf8 cycle 6Welding Time (WT) 6 12 cycle8 cycle 6 Holding Time (WT) 6 12 cycle

Table 9 lists GA parameters used to optimize the processparameters. The objective functions were the maximum values ofthe strength of the RSW joints; therefore, the reciprocal of theobjective functions were used as the fitness functions.

The proposed ANN model presented in Section 3.2.1 was opti-mized by GA code. The neural network prediction of the tensile–shear strength of the RSW joint, under the optimized process con-ditions, was 3858.62 N. This value is higher than all of the train andtest samples. This indicates that the optimization procedure per-forms satisfactory.

In order to evaluate the correctitude of the value predicted bythe proposed GA, an actual experiment was carried out based onthe optimized process parameters. The obtained experimental va-lue was then compared with that predicted by the Genetic Algo-rithm. The results given in Table 10, show that the modelingapproach presented in this study can accurately predict thestrength values of RSW joints. Additionally, the developed optimi-zation approach had a desired performance in determining theoptimal set of process parameters.

4. Conclusions

From the present work the following conclusions can be drawn:

(1) The regression analysis reveals that there is a non-linearrelationship between the welding parameters and the ten-sile–shear strength of the RSW joints.

(2) The proposed ANN, 4-10-1 was an effective tool for model-ing the complex relationship between the process parame-ters and the quality index (the tensile–shear strength) ofthe RSW.

(3) The effects of welding parameters and their interactions onthe tensile–shear strength were analyzed on the basis ofthe ANN model. This can provide a beneficial referencefor the RSW process of galvanized interstitial free (IF) steelsheets and galvanized bake hardenable (BH) steel sheets.

(4) The combined ANN / GA optimization procedure proposed inthis paper provides reasonable results for the optimization ofthe RSW process. The optimized results, obtained by GA, weresuccessfully verified against the actual experimental data.

Acknowledgements

The authors would like to express their gratitude to Sapco Com-pany for providing foundations for this research. They would alsolike to thank Iran Khodro Company (Iran’s largest car manufacturer)for providing spot welding machine for this research. The authorswould also like to acknowledge Mr. Mohammad Hossein Hasannia,for his help and considerable support in experimental work.

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