Prediction of Optimum Weld Tensile Strength Using Response Surface Methodology

— Metals are often subjected to various types of stresses, usually under tensile stress, quick failure of material can be encouraged especially when poor combinations of process parameters are employed in joining of the material. Tensile strength is regarded as the maximum stress that a material can sustain under tension. The aim of this study is to predict the weld tensile strength of tungsten inert gas (TIG) mild steel welds using Response Surface Methodology (RSM), with the purpose of achieving optimum results. The input parameters considered were current, voltage, and gas flow rate. The TIG welding process was used to join two pieces of mild steel plates, after which tensile test was conducted on the specimen. The experimental result was analyzed using the RSM. Weld Tensile test of 596.218MPa with a desirability value of 95.70% was observed to be the best, resulting from the optimized process parameters of current of 120.00 Amp, voltage of 20.00 volt and gas flow rate of 12.00 L/min.


I. INTRODUCTION
The importance of mild steel in our daily activity cannot be over emphasized. Usually, this materials are subjected to different form of stresses and in other to prevent sudden failure, it is imperative to determine the strength of the material through subjecting it to various forms of test [1]. According to [2], the failure of structural materials especially steel is of great concern globally. Some material properties affected due to welding includes tensile strength, hardness, macro and micro-structural features and toughness [3]. Tensile strength described as the maximum stress that a material can sustain under tension. In other words, it can be defined as the amount of applied load per cross sectional area that a material can withstand before failure. Mathematically it is calculated as the ratio of maximum tensile load to the original cross section area. Mild steel or low carbon steel offers numerous applications in fields of construction and engineering. The carbon in steel affects the material's ductility and strength; steel with higher percentage of carbon are stronger compared to low carbon steel [4]. On the other hand, high carbon steel are less ductile when compared to low carbon steel. Mild steel is the most versatile and common form of steel as it provide mechanical properties that are acceptable for many applications [5]. No doubt that mild steel has become an indispensable class for different applications like construction of large ships; oil, water and gas pipelines; drilling platforms; pressure vessels; building constructions; bridges; storage tanks etc. Welding on the other hand is a joining process of two or more metals [6]. This process usually introduce large amount of heat into the welded zone, thereby altering the microstructure around the area of the welded material [7]. If not properly controlled, it could reduce the tensile strength around the welded vicinity and alter the factor of safety initially designed for. Tungsten inert gas (TIG) welding is one of the best arc welding processes currently in used. This research work was aimed at prediction and optimization of tensile strength of mild steel specimen with the use of response surface methodology (RSM) tool.

A. Materials
Mild steel plate of 10mm and 100% argon gas were purchased locally and transferred to the Department of Welding and fabrication technology, Petroleum Training Institute (PTI), Warri, Delta State, Nigeria. The 10mm plate was cut into 200 pieces of dimension 140mm by 30mm by 10mm with a power hacksaw and welded. After welding, the specimens were trimmed with an angle grinder to take a dog bone shape, so it could fit into the tensometer. Response surface methodology (RSM) was employed to analyze the results obtained. The input ranges of parameters used for the research is presented in Table I. The selected input parameters have the upper (+) and lower limits (-). The limits of the four welding variables are shown in Table I.

B. Method
After welding, the sample was reduced to 100 pieces, prepared with the following dimensions as presented in

III. RESULTS
Twenty (20) experimental runs were carried out, each experimental run comprising the weld current, weld voltage and gas flow rate. The tensile strength test, was measured and the responses presented in Table II. The Analysis of Variance (ANOVA) obtained from Table  III with P-value of 0.0004, shows that the model source for the tensile test is statistically significant. ANOVA is a tool in statistics employed to determine whether there are any significant differences of means among two (2) or more groups. Accuracy of the mathematical model greatly depends on the numbers of individual variables (i.e., A, B, C etc.) in the model with p-values less than 0.05. Coefficient of determination (R-Squared) values of 0.9087 as observed in Table 4 which shows the strength of response surface methodology (RSM) and its ability to maximize the weld tesnsile test. Adjusted (R-Squared) values of 0.8265 as observed in Table IV   To asses the correctness of forecast and established the fitness of response surface methodology using the quadratic model, a reliability plot of the predicted and actualvalues of the weld tensile test response were obtained as presented in Fig. 2. To examine the effects of combine variables such as the weld current and voltage at constant gas flow rate of 13 L/min, on the weld tensile test, the 3D surface plots presented in Fig. 3 was employed.

Tensile Test
Color points by value of Numerical optimization was accomplished to ascertain the attractiveness of the overall model. In the numerical optimization phase, design expert was instructed to maximize the weld tensile test while also determining the optimum value for voltage, current and gas flow rate. Fig. 4 presents the interphase of the numerical optimization with maximization goal target.   From the results of Table V, it was observed that current of 120.00 Amp, voltage of 20.00 volt, and gas flow rate of 12.00 L/min produced a weld tensile test of 596.218 MPa. This solution obtained was selected by design expert as the optimal solution with a desirability value of 95.70%.
Finally, based on the optimal solution obtained, the contour plots showing the weld tensile test response variable against the optimized value of the input variable is presented in Fig.  5.

IV. DISCUSSION
The responses obtained in Table II, was employed to  develop the ANOVA table presented in Table III. The Model F-value of 11.06 was obtained which implies the model was significant, as only 0.04% could result due to noise in the system. The P-values obtained was less than 0.0500 indicating a significant model terms. From Table III, current, voltage and gas flow rate were represented with A, B and C coded symbols. A, B, C, AC, BC and A² had a p-value less than 0.05, which implies that the mathematical model formed using these combinations would produce a significant model terms with reduced prediction error. Those values greater than 0.1000 in Table III, are not significant. If there are too many insignificant model terms, it may affect the prediction accuracy of the model. In Table IV, it was observed that the Predicted R² of 0.7297 was in reasonable agreement with the Adjusted R² of 0.8265; having a difference of 0.0968 which was less than 0.2 in line with literature. Adequate Precision was used to measures the signal to noise ratio. A ratio greater than 4 was desirable, according to literature. In Table IV, a ratio of 10.930 was obtained, indicating a robust adequate precision. This model was applied to navigate the design space, and (1) was developed to predict the weld tensile test.
In establishing the correctness of the reliability for predicting the weld tensile test, a linear plot was used to fit the predicted and actual response as shown in Fig. 2, the results showed an acceptable positive slope with minimal noise along the slope. From the 3D surface plot provided in Fig. 3, it was also observed that an increase in current, greatly affect the tensile strength. The green area on the 3D mat denotes the area with good tensile strength, while the blue area shows the lowest tensile region. To maximize the tensile strength, process parameters that would result to responses in the green zone should be targeted. The interphace of numerical optimization presented in Fig. 4, defines the lower and upper limit of the response with the level of importance indicated. In other to maximize the weld tensile strength, the weight leans towards the higher limit as seen in Fig. 4. The contour plots in Fig. 5 show the predicted optimization region of weld tensile test. The red region represents the area with the strongest tensile test.Just like in Fig. 3, it was also observed that the weld current had a stronger effect on the tensile test. From the results of Table V, it was observed that current of 120.00 Amp, voltage of 20.00 volt, and gas flow rate of 12.00 L/min produced an optimal weld tensile test of 596.218 MPa with a desirability value of 95.70%.

V. CONCLUSION
In this study,prediction and optimization of weld tensile test was conducted on mild steel welded specimen using tungsten inert gas (TIG) welding process. A mathematical modelwas developed to predict the weld tensile test in (1). Weld Tensile test of 596.218 MPa with a desirability value of 95.70%was observed to be the best, resulting from the optimized process parameters of current of 120.00 Amp, voltage of 20.00 volt and gas flow rate of 12.00 L/min. This process parameters produced the most reliable weldment on the specimen, with current having the highest effect on the quality of the weldment.