Comparative Enhancement of Mild Steel Weld Mechanical Properties for Better Performance Using COPRAS – ARAS Method

DOI: http://dx.doi.org/10.24018/ejers.2021.6.2.2226 Vol 6 | Issue 2 | February 2021 70 Abstract — Some machine part failures have often occurred in areas of components where the strength was lowest, especially at its weld region. Presence of voids in weldments or weld joints greatly reduces the quality of the weldment. To prevent these defects, a proper optimum selection of process parameters is highly encouraged to achieve an acceptable weld mechanical property. The Complex Proportional Assessment (COPRAS) method was applied to determine the relative significance of each alternative and the quantitative utility for each alternative. The Addition Ratio Assessment (ARAS) method was applied to optimize these parameters by utilizing the weights generated using COPRAS method. In this study, the COPRAS-ARAS method which is a multi-criteria decision making tools was applied to determine the optimum process parameters to improve the mechanical properties of the weldment. From applying these methods, it was found that weldments 7, possess the optimum input process parameters. The corresponding mechanical properties of ultimate tensile strength (UTS) of 395MPa, absorbed impact strength (CVN) of 250J, Bead height (BH) of 1.98 mm and Bead width (BW) of 4.82 mm was found to possess the best mechanical properties.


I. INTRODUCTION
In different parts of Nigeria, there have been the incessant collapse of metal materials, some of which are reported and so many are not reported. In most cases, some of these failures are castatrophic and human lives are lost, or the injury sustained could lead to permanent disability [1]. Most of these failures results from poor weldment leading to compromised UTS, CVN, BH and BW which is very critical in achieving good weld. Researchers has proven that weld input parameters have a very strong effect on the responses [2].
To improve UTS, CVN, BH and BW, it is imperative that the optimum input parameters should be achieved, this can be through experimental means either by trial and error or modelling. The trial and error method takes time and mental energy but modelling that leads to optimization process takes seconds and are usually very precise. There are some authors that have worked on the optimization, [3] worked on air conditioner selection problem with COPRAS and ARAS methods. [4] evaluated some contractors using COPRAS, [5] to reduced greenhouse gas emissions in grassland ecosystems This study uses the application of COPRAS -ARAS method to select the optimum process parameters, since it has been confirmed by researchers that selecting the appropriate input process parameters could lead to improving the welded joint quality.
In this study, the optimization of mechanical properties was looked into. The optimization was done using complex proportional assessment (COPRAS) and Addition Ratio Assessment (ARAS). It has been researched that what influences weldments quality is the welding input parameters.

B. Methods
The following steps are applied for the COPRAS method as outlined by [3]. Firstly, it is assumed that there are m alternatives and n criteria in the problem [6]: Step 1: The normalized decision matrix is acquired with linear normalization procedure using Eq. (1) [7].
where ij x and ij r are the performance of the th i alternative with respect to the th j criterion and its normalized value respectively. The values of the criteria with having different units of measurement should be normalized in order to compare them [7].
Step 2: Normalized decision making matrix (D) is weighted as: where wj is the importance weight of jth criterion. Importance weights of criteria may be derived from different weighting methods. In this paper the AHP (Analytic Hierarchy Process) method is used because of its simplicity. It was developed by [8] and it depends on pairwise comparison of criteria More detailed information about the procedure of the AHP method is to be found in the paper of [8].
Step 3: The weighted normalized values are summed for both beneficial and non-beneficial criteria.  (5) and (6).
Step 4: The relative significances or priorities of each alternative (Q) are determined using Eq. (7).
where min −

S
, is the minimum value of 1 − S ,. The relative significance value of an alternative shows the degree of satisfaction attained by that alternative. The greater the value of i Q , the higher is the priority of the alternative. The alternative with the highest relative significance value ( ) max Q is the best choice among the alternatives.
Step 5: The quantitative utility for each alternative ( ) i U is calculated. The degree of an alternative's utility which leads to a complete ranking of the alternatives is determined by comparing the priorities of all the alternatives with the most efficient one and can be denoted as presented in Eq. (8).
is the maximum relative significance value.
These utility values of the alternatives range from 0 % to 100 %. ARAS method consists of the steps as below [3].
Step 1: The decision matrix X in Eq. (9) is formed from Alternatives and criteria that are listed in the row and column of the decision matrix respectively. The decision matrix shows the performance of different alternatives with respect to various criteria.
x presents the performance value of ith alternative on jth criterion, m and n are the numbers of alternatives and criteria respectively. Then the optimal performance rating of jth x is unknown, then it is assumed as the maximum values of beneficial criteria or minimum values of non-beneficial criteria [9].
Step 2: The decision matrix is normalized. Beneficial criteria are normalized with linear normalization procedure as given in Eq. (10).
x is the normalized value. Non-beneficial criteria are normalized with two-stage procedure. In the first stage the reciprocal of each criterion with respect to all the alternatives is taken as given in Eq. (11).
Step 3: The normalized decision matrix is weighted using where j w is the weight (importance) of jth criterion.
Step 4: The optimality function (S1) is determined for each alternative using (14). Step 5: The degree of the utility (Ui) is determined for each alternative. It is calculated using Eq. (15): In this method, a utility function value determines the relative efficiency of an alternative over the best alternative [6]. The U, values of alternatives range from 0 % to 100 % and they are placed in ascending order. The alternative with the highest utility value is the best choice among the alternatives [9]. Table II shows the measured mechanical properties for the eight (8) samples, ultimate tensile strength (UTS), absorbed impact energy (CVN), Bead height (BH) and Bead width (BW) with their corresponding weights.  Table III shows the normalized decision matrix of the experimental test. The normalized decision matrix was obtained using Eq (1).  Table IV shows the weighted normalized decision matrix of the experimental test. The weighted normalized decision matrix was obtained using Eq. (2).  (8)). The calculation above were done using Eqs (3) and (4); and Eqs (7) and (8). The value of Qi and Ui are tabulated in Table  V. In the case of ARAS, Table II is revisited, with the optimal performance ratings, W0 for each criterion; for beneficial criterion, maximum values are considered and for nonbeneficial criteria, minimum values are considered as contained in Table VI.  Table VII shows the pre-normalized decision matrix.

B. Discussion of Results
This study was made in two parts, application of COPRAS for the determination of the optimum weld properties. The process is explained as follows; Table II shows the results of the weld mechanical properties obtained from tensile and impact strength tests conducted, as well as the measurements of the bisected weld geometry to obtain the bead height (BH) and bead width (BW) respectively. Table II also contains the  weight of each of the weld properties.  Table III shows the normalized value of the experimental test results. Normalization process is a reduction process that further simplifies the test result values. The value lies between 0 and 1. Table IV shows the weighted normalized values of each of the results of each of the weld property and their corresponding weights. These values also lie between 0 and 1.
The relative significances and properties of each alternative as well as the degree of utility were determined and shown in Table V. The degree of utility was used as the criteria for ranking the weld quality properties. In this study weldment 7 was found to possess the best weld properties with UTS of 395MPa, CVN of 250J, BH of 1.98mm and BW of 4.82mm.
The second part deals with using ARAS in determining the optimum weld properties. The application of ARAS starts with the content in Table VI, which contains the mechanical properties of the weldments. Table VII shows the prenormalization process subjected under the larger the value of the weld properties, the better the quality which is the referred to as maximum and the lower the values of the weld properties, the better the quality which is referred to as minimum. Table VIII shows the normalized values of the test results of the weld properties, these values normally lie between 0 and 1. Table IX shows the weighted normalized value of the weld properties. Table X shows the optimality function and the utility degree comprising of each of the mechanical properties shown in Table IX. The utility degree was again used as the criteria for ranking the weldment. In this study weldment 7 was ranked as the weldment with the best mechanical properties.
From this study the application of COPRAS and ARAS methods showed that weldment 7 has the best quality properties.

IV. CONCLUSION
In this study, the COPRAS -ARAS methods were used to select the optimum welding process parameters. The procedure involves the conduction of the welding operations according to the set out experimental matrix design and the mechanical properties of the weldments obtained. The assessment of the results of these mechanical properties by Experts were converted to weights which were used for the optimization process. Eventually, the optimized process parameters shows that weldment 7 has the best mechanical properties which were in line with the criteria for categorizing weld properties.