This research work was conducted at the Department of Welding and fabrication technology, Petroleum Training Institute (PTI), Warri, Delta State, Nigeria. The Tungsten Inert Gas (TIG) welding method was adopted, thereafter, the samples from the welding process were subjected to impact test. Table 1 presents the process parameters employed for the research. The selected input parameters have the upper (+) and lower limits (−). All the materials used in this research were purchased from a local vendor.

The 10 mm mild steel plate was cut into 200 piecescouponsmeasuring 27.5 × 10 × 10 mm for the experiment, after welding of the piece, 100 specimens of 55 × 10 × 10 mm were produced, the experiment was performed twenty (20) times as presented in Table 2, using five (5) specimens per run. The welded specimen fits into the Charpy impact tester. The welded specimen was a rectangular shaped mild steel plate with measured dimension of 55 × 10 × 10 mm with a V-shaped notch, 2 mm deep, with 45 angle and 0.25 mm radius along the base cut in one side. The notch allows for a predetermined crack initiation location as shown in Figure 1.

The study produced twenty experimental runs, each experimental run comprising the current, voltage and gas flow rate, used to join two pieces of mild steel plates measuring 55 mm × 10 mm × 10 mm. The impact test strength, was measured. The responses are shown in Table 2.

According to literature, the difference between the predicted and adjusted R² must be less than 0.2. In this research, a difference of 0.131 which is less than 0.2 was obtained in Table 3. The adequate Precision of 12.8046 which is used to measures the signal to noise ratio was obtained in our study. Literature states that the ratio should be greater than 4 to be desirable. Since the required condition for the fit statistics has been meet, the model can now be used to navigate the design space.

Table 4 presents the sum of squares which is a Type III―Partial, 16.10 was obtained as the Model F-value which describe a significant model. This means that there is only a 0.01% chance that an F-value this large manifest due to noise. The P-values less than 0.0500 shows that the model terms are significant. In this case A, B, C, AC, AB, BC, A² and C² obtained a P-val less than 0.05. This would increase the accuracy of our mathematical model in predicting the responses.

Based on the P-value obtained in Table 4, Equation (1) was mathematically modelled in terms of coded factors for predicting the impact test (IT). For minimal prediction error, more factors with P-value less than 5% should be included in the equation.

IT = 230.91 − 8.00 A − 5.93 B − 5.93 C + 3.98 AB + 6.52 AC     + 8.16 BC + 12.90 A 2 + 2.74 B 2 + 4.54 C 2 (1)

where, A = voltage, B = current, C = gas flow rate.

The plot in Figure 2 was used to examine the reliability of future prediction based on the response obtained from the actual vs predicted impact. The blue square dots indicates the lowest limits of 219.128 joules while the red square dots, shows the maximum impact of 278.096 joules absorbed by the specimen.

The 3D surface plot was employed to examine the effect of the welding voltage and current on the impact absorption of mild steel specimen. At a gas flow rate of 13 L/min, the current and voltage could be varied to obtain the 3D surface plot architect presented in Figure 3. To target above the known predicted value, aim at the wine dot above the 3D mat while to predict below the known prediction value, aim at the dotted peach below.

The interphase in Figure 4 with the maximization target for the impact test, was employed to optimize the response. In the numerical optimization phase, design expert was instructed to maximize the impact test, while also determining the optimum value of voltage, current and gas flow rate.

Table 5 shows five (5) out of the eighteen (18) optimal solutions obtained from the settings made in Figure 4.

Finally, from the optimal solution, the contour plots showing the impact response variable of voltage and current at a gas flow rate of 12 L/min, against the optimized value of the input variable is presented in Figure 5.

The Fit Statistics for the Impact Test in Table 3, shows that The R² value of 0.9354, Predicted R² of 0.7463 and an Adjusted R² of 0.8773 were obtained. The difference between the predicted and adjusted R² of less than 0.2 was recorded, indicating a significant model. With an adequate Precision of 12.805, demonstrating a significant model. It meant that the mathematical model in Equation (1), can be employed to navigate the design space. In Figure 2, the reliability plotdeveloped was employed to compare the predicted response values obtained from using Equation (1) to that of the actual response. Based on the plot, it was observed that a positive linear relationship existed between the predicted and the actual response, with majority of the points clustering along the stright line. This indicates a good prediction model which can be employed for unknown prediction of the impact test. Figure 3 shows the 3D surface plot for the impact test with the lower impact test area denoted by the blue region and the green region representing the area with the highest impact strength. The 3D surface plot was used to determine the effect of current and voltage at a gas flow rate of 13 L/min on the impact test responses. From Figure 3, it was noticed that only current had a very strong effect on the response. Optimization was initiated using the interphase presented in Figure 4 with the lowest and highest impact of 219.128 and 278.096 being the optimization boundary space. Five (5) optimal results were selected as shown in Table 5 with the best having a current of 120.00 Amp, voltage of 20.00 volt and gas flow rate of 12.00 L/min, to produce a weld material with impact test of 275.514 joules at a desirability value of 95.6%. To further understand better, the effect of the process parameters on the response, Figure 5 was employed. This plot also known as the contour plot, shows that at a constant gas flow rate of 12 L/mm, quality weld can be achieved with voltage ranging between 20 - 25 volts, and a current range of about 120 - 125 amp, represented the red area on the plot in Figure 5. It shows that current has a significant effect on either increasing or reducing the material toughness. From the contour plot, it was noticed that lower current between 120 - 125 amp produced better impact test as compared with higher current input of 170 amp.