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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.

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 [

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 [

It was suggested by [

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.

the TIG machine.

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.

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

The model summary which shows the factors and their lowest and highest values including the mean and standard deviation is presented as shown in

Result of

Analysis of the model standard error was employed to assess the suitability of response surface methodology using the quadratic model to minimize the aspect

Parameters | Unit | Symbol | Coded value | |
---|---|---|---|---|

Low (−1) | High (+1) | |||

Current | Amp | A | 120 | 190 |

Gas flow rate | Lit/min | G | 10 | 17 |

Voltage | Volt | V | 20 | 27 |

ratio. The computed standard errors for the selected responses are presented in

From the results of

error ranging from 0.27 for the individual terms, 0.35 for the combine effects and 0.26 for the quadratic terms. Standard errors should be similar within type of coefficient; smaller is better. The Variance inflation factor (VIF) of approximately 1.0 as observed in

Leverages of 0.6698 and 0.6073 calculated for the factorial and axial points coupled with 0.1663 for the center point as observed in

In assessing the strength of the quadratic model towards minimizing the aspect ratio, one way analysis of variance (ANOVA) was done for each response variable and result is presented in

From the result of

To validate the adequacy of the model based on its ability to minimize the aspect ratio, the goodness of fit statistics presented in

To obtain the optimal solution, we first consider the coefficient statistics and the corresponding standard errors. The computed standard error measures the difference between the experimental terms and the corresponding predicted

terms. Coefficient statistics for aspect ratio is presented in

Variance inflation factor (VIF) value of 1.00 for the individual and combine

terms, 1.02 for the quadratic terms as observed in

The optimal equation which shows the individual effects and combine interactions of the selected input variables (Current, Voltage and Gas flow rate) against the mesured responses (Aspect ratio), is presented the actual factors as shown in

The diagnostics case statistics which shows the observed values of each respones variable (Aspect ratio) against their predicted values is presented in

Lower residual values resulting to lower leverages as observed in Tables are indicators of a well fitted model. To asses the accuracy of prediction and established the suitability of response surface methodology using the quadratic model, a reliability plot of the observed and predicted values of aspect ratio is presented in

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

To study the effects of combine variables on each response (Aspect ratio, 3D surface plots presented in

The 3D surface plot as observed in

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

The numerical optimization produces about twenty two (22) optimal solutions which are presented as shown in

From the results of

It can be deduce from the result that the model developed based on response surface methodology and optimized using numerical optimization method,

Aspect ratio with an accuracy of 96.67%.

One of the uniqueness of Response Surface Methodology (RSM) is its ability to carry out predictions based on the numerical optimal solution or models it developed. RSM displays this strenght by generation of contur plots which shows the response varaible of interest and the coresponding input factors. Hence, based on the optimal solution, the contour plots showing aspect ratio response variable against the optimized value of the input variable is presented in

In this study, the response surface methodology was used to optimize the aspect

ratio of tungsten inert gas mild steel welds. A model was developed using RSM. Result of

The 3D surface plot as observed in

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.

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.

The authors declare no conflicts of interest regarding the publication of this paper.

Odoemelam, C., Achebo, J.I., Ehiorobo, J.O. and Osaremwinda, J.O. (2018) Simulation-Based Optimization of Aspect Ratio in Tungsten Inert Gas Welding. Engineering, 10, 876-890. https://doi.org/10.4236/eng.2018.1012061