Simulation-Based Optimization of Aspect Ratio in Tungsten Inert Gas Welding

The shape of the fusion zone after weld in terms of its width-to-depth ratio is known as the aspect ratio, large aspect ratios in welded joints usually results in cracks formation during solidification of the weld; it also results in tensile residual stresses at the fusion zone. In this study, central composite design matrix was employed using Design Expert 7.01 software to optimize the aspect ratio of mild steel welded joint. A total of 20 sets of experiments were produced; the weld specimen was mild steel plate measuring 60 mm × 40 mm × 10 mm. TIG welding machine with 100% Argon Shielding Gas was used for this experiment and at the end of the experiment, an optimum weld aspect ratio of 0.646 was achieved using current of 140 amp, voltage of 25 volt and gas flow rate of 15 L/min. This value of 0.646 is expected to contain the minimum adequate molten metal just enough to make the desired bead penetration to form good aspect ratio at a minimum cost with appropriate weld quality and productivity. This would help minimize the formation of cracks after weld.


Introduction
Premature failure of welded structures had resulted in great loss of life and properties; it had also been a huge engineering problem, huge source of concern cutting across all strata of engineering [1] failures that often results from welded joint can sometimes be linked to poor combinations of process parameters which often manifest in the form of cracks [2]. Their work proved that some of these failures originate at welded joints; this area is very critical to the overall lifespan of the weld is determined by the welded joint. Engineering Visual defects appearance in welds compromises the quality of weldment and can manifest in forms such as deformation, excessive undercut, porosity, and cracks. Crack defects are regarded as the worst since even a minute crack can grow and lead to failure [3] that is why a good weld aspect ratio is required for quality welded joints. [4] showed that metal structures at their welded joints, do not have the same strength characteristics as the parent material; this means to optimize the strength enhancing properties at the welded joint; optimum process parameters are required. And to further minimize the cost of try and error approach, a robust design of experiment would be imperative [5].
It was suggested by [6] that one of the proven ways of enhancing the strength and lifespan of structural material at welded joints is to optimize its aspect ratio where, the optimum weld parameter is geared towards ensuring quality weld all the time. Over the years, the desired process parameters of welded joints have been gleamed out by applying various multi criteria optimization tools and statistical models in an attempt to broaden the scope, and increase the options open to researchers and developers in arriving at optimum process parameters to meet specific needs [7] and [8]. According to [9] and [10], the preferred welding parameters are selected based on knowledge or from a welding handbook. It should be noted that, this does not ensure that the selected welding parameters can make the best or near best weld bead profile for that particular welding process and environment. It is therefore desirous to produce welded joints and metal products that are of high quality, but with more precision, less energy, and time constraints by careful selection of the various process control parameters through some established guidelines or models.

Materials
One hundred (100) pieces of mild steel coupons, measuring 60 mm × 40 mm × 10 mm were used for the experiments, the experiment was performed 20 times using, 5 specimen for each run. Figure 1 shows the weld torch. Figure 2 shows  the TIG machine. Figure 3 shows the argon gas cylinder and regulator for varying the gas flow rate while. Figure 4 shows the mild steel weld sample. The range of values of the process parameters was obtained from the open literature accessed and each parameter has two levels which comprise the high and low as expressed in Table 1.

Methods
The Central Composite Design matrix with 6 central points, 6 axial points and 8 factorial points was developed using the Design Expert 7.01 software, which produced 20 experimental runs. The input parameters and output parameters made-up the experimental matrix and the responses recorded from the weld samples were used as the data. Figure 5 shows the Central Composite Design matrix.

Results
The optimization objective was to reduce the aspect ratio of welded joint, the randomized design matrix comprising of three input variables (current, voltage and gas flow rate) and their ranges in real values is presented in Figure 6, the response variable of interest is circled in orange colour.         the Ri-squared value was observed to be between 0.0000 to 0.0179 which is good.
The correlation matrix of regression coefficient is presented in Figure 9. Lower values of the off diagonal matrix as observed in Figure 9 indicates a well fitted model that is strong enough to navigate the design space and adequately optim- To validate the adequacy of the model based on its ability to minimize the aspect ratio, the goodness of fit statistics presented in Figure 11 were employed.
To obtain the optimal solution, we first consider the coefficient statistics and    terms. Coefficient statistics for aspect ratio is presented in Figure 12. To accept any model, its satisfactoriness must be checked by an appropriate statistical analysis. To diagnose the statistical properties of the model, the normal probability plot of residual of aspect ratio is presented in Figure 16.
To study the effects of combine variables on each response (Aspect ratio, 3D surface plots presented in Figure 17. The 3D surface plot as observed in Figure 17 shows the relationship between the input variables (current, voltage and gas flow rate) and the response variables (Aspect ratio) to the work piece. It is a 3-dimensional surface plot which was employed to give a clearer concept of the response surface. As the colour of the curved surface gets darker, the aspect ratio decreases.
Finally, numerical optimization was performed to ascertain the desirability of the overall model. In the numerical optimization phase, we ask Design Expert to minimize the aspect ratio, also determining the optimum value of current,   voltage and gas flow rate. The interphase of the numerical optimization is presented as shown in Figure 18.
The numerical optimization produces about twenty two (22) optimal solutions which are presented as shown in Figure 18.
From the results of Figure 19 it was observed that a current of 140.00 Amp, voltage of 25.00 volt and a gas flow rate of 15.00 L/min will produce a weld material with aspect ratio of (0.646234). This solution was selected by Design Expert as the optimal solution with a desirability value of 96.70%.
It can be deduce from the result that the model developed based on response surface methodology and optimized using numerical optimization method,

Discussion
In this study, the response surface methodology was used to optimize the aspect   and predicted values of each response was obtained as presented in Figure 15.
The 3D surface plot as observed in Figure 17 shows the relationship between the input variables (voltage, current and gas flow rate) and the response variables (aspect ratio). It is a 3 dimensional surface plot which was employed to give a clearer concept of the response surface in terms of the strength of the interactions between the input variables and the respective selected responses. Similarly, based on the optimal solution the expert system generated contour plots as observed in Figure 20 showing several predicted responses and their respective input variables, all within the boundaries of experimental design.
Finally, numerical optimization was performed to ascertain the desirability of the overall model. In the numerical optimization phase, Design Expert was asked to minimize the aspect ratio, while also determining the optimum value of voltage, current and gas flow rate.

Conclusion
The aspect ratio is a very important factor considered in assessing the quality of welds. The models developed possess a variance inflation factor of 1.0 and P-values < 0.05 indicating that the model is significant; the model also possessed a high goodness of fit with R 2 (Coefficient of determination) values of 94% for aspect ratio. Adeq Precision measures the signal to noise ratio; a ratio greater than 4.0 is desirable. Adequate precision values of 12.79 were observed for the Aspect ratio. The model produced numerical optimal solution of Current 140.0 Amp, Voltage of 25 Volt and a Gas flow rate of 15 L/min will produce a welded material having aspect ratio of 0.646234 at a desirability value of 96.7%. Therefore, the aspect ratio was minimized, optimized within a controlled range. In this research, the following has been established. An approach using the Response Surface Methodology to determine the optimum aspect ratio which translates into better weld quality has been successfully demonstrated. It has been shown that the optimization and prediction of aspect ratio have a significant effect on the quality and integrity of welded joints. It is, therefore, recommended that welding and fabrication industries should endeavor to use the optimum welding process parameters achieved in this study to produce high quality welds in Tungsten inert gas welding process.