Optimization of parameters and formulation of numerical model employing GRA–PCA and RSM approach for friction stir welded Ti–6Al–4V alloy joints

In this work, an endeavour was made to determine the impact of the tool’s shoulder diameter, pin profile, rotational and traverse speeds on the mechanical properties of the friction stir welded namely Ti–6Al–4 V alloy joints. A total of 21 experiments were carried out based on the central composite design (CCD) concept of response surface methodology (RSM). A quadratic regression based numerical model was formulated to ascertain the relationship amidst the parameters of FSW process and the mechanical properties of the fabricated Ti alloy joints. Analysis of variance (ANOVA) was employed to confirm the importance of parameters and their interactive impacts. Optimized process parameter combinations were ascertained by grey relation based analysis (GRA) was coupled together with principal component analysis (PCA), a hybrid based approach. Single score of GRG based response was determined and GRG scores were ranked for all experiments. 1st rank was attained by the experiment no. 20 possessing a GRG score of 2.9989. Optimized values of 25 mm shoulder diameter having a taper cylindrical pin geometry employed at a tool traverse speed of 40 mm min−1, rotational speed of 1400 rpm resulted in the generation of flaw free Ti alloy joint possessing a largest tensile strength of 809.8 MPa, yield strength of 778.7 MPa and percentage of elongation of 6.9%. SEM based fractography of Ti alloy joint specimens announced that taper cylindrical pin geometry along with 25 m shoulder diameter of employed tool have an inevitable part in generating frictional heat in ideal volumes and a perfect stirring action during FSW process.


Introduction
Titanium (Ti) and alloys of Ti have been employed widely in the aerospace sectors owing to their superior specific strength, exemplary resistance against corrosion and higher heat withstanding capability.Moreover, in the recent years alloys of Ti have also been proven to be an efficient biocompatible material due to their reduced allergy based risk to the human body [1].During the employment of Ti and its alloys as structural and architecture relevant materials, these alloys of Ti were usually considered to be joinable by the employment of fusion based welding techniques including gas, arc welding etc.At the same time, distortion of the welded Ti alloys by employment of fusion welding methodologies normally occur owing to the low thermal based conductivity of the Ti [2,3].In addition to this, Ti and its alloys are extremely reactive in their molten condition and the generation of Ti based oxides, porosities, inclusions etc, in the nugget of the weld zone will certainly result in the fabrication of inferior quality Ti joints possessing degraded mechanical properties [4].
After the invention of the technique of friction stir welding (FSW) by TWI (The Welding Institute), United Kingdom, joining together several low melting point metals such as aluminum, copper, magnesium etc, have been possible using this FSW process.In the recent years, several experimental attempts investigating the possibility of joining together high melting point metals including stainless steel, carbon steel, cast iron etc, employing the technique of FSW have been made and joints have been attained successfully [5][6][7].On the other hand, so far only few attempts were made by researchers regarding the FSW of Ti and its alloys.Major reason behind these fewer attempts exploring the weldability of Ti using the FSW process is that when compared with that of steel, Ti possesses larger melting point and there prevails a vital need for employing optimized values of FSW process parameters so as to control the volume of heat being generated and also to regulate the input of frictional heat during the FSW of Ti alloys [8][9][10].
Even though several researchers [11][12][13][14][15] have focused their experimental works on FSW towards optimizing the process parameters.For instance, Senthil et al [12] in his experimental investiagtion devised a RSM based numerical model involving desirability approach for optimizing the two important parameters of FSW process, namely tool traverse speed and rotational speed during the joining of Al alloy.Tool rotational speed was taken in the range of 1800 rpm, 2000 rpm and 2200 rpm, followed by tool traverse speed in the range of 0.4 mm sec −1 , 0.6 mm sec −1 and 0.8 mm sec −1 respectively.In this experimental work, a regression numerical model having a 95% confidence level was devised to forecast the mechanical strength of the friction stir welded Al alloy joint.Likewise, Goyal et al [14] employed RSM to create a numerical rapport between the various parameters of FSW process and the mechanical attributes of the AA5086-H32 alloy joints attained using the FSW process.The process parameters taken into consideration during this investigation were tool's rotational speed, traverse speed, tilt angle, shoulder & pin diameter, hardness of the tool.For example, 724 rpm to 1675 rpm, traverse speed ranging from 37 to 132 mm min −1 , 7.8 mm to 22.1 mm shoulder diameter etc In this work, the established numerical model's competency was verified by employing analysis of variance (i.e., ANOVA).
Investigations on FSW taking into considerations the impact of tool based dimensions including shoulder diameter of the tool, geometry of the employed tool pin during FSW of Ti alloys are very scarce.The major reason for taking into account these tool dimension based parameters in this experimental investigation is that the shoulder diameter of the employed tool and its pin geometry have an inevitable role in influencing the volume of frictional based heat input and quantum of heat generated during the FSW of alloys of several metals [16].Moreover, the highest melting point of alloys of Ti also demands for optimizing tool dimension based parameters along with tool rotational speed and rate of traverse of the tool.
As a result, in this experimental work investigating the FSW of Ti alloys, an attempt was put forward to establish a relationship amidst the input parameters of FSW process (namely tool's rotational speed, rate of tool traverse, tool's shoulder diameter and its pin geometry) and the outputs namely ultimate tensile strength, elongation percentage and yield strength.This was accomplished by formulating a quadratic regression based numerical model employing two distinctive approaches namely GRA-PCA i.e., Grey Relational Analysis (GRA) coupled with Principle Component Analysis (PCA) and RSM (Response surface methodology).

Metals of research
In this experimental work, 5 mm thick plates of Ti alloy (namely Ti-6Al-4 V alloy) possessing a dimensional width of 55 mm and a length of 110 mm was taken as the metal of investigation.Table 1 describes in detail, the several chemical based constituents of this metal of investigation, i.e., Ti-6Al-4 V alloy.The 5 mm thick flat plate of Ti-6Al-4 V alloy possessed a tensile strength of 970 MPa, 890 MPa yield strength and its elongation was 13%.

Experiments
In this experimental work, the tool was fabricated out of tungsten carbide (WC) based alloy and tools possessing three distinctive pin profiles namely taper cylindrical, straight cylindrical and straight square were employed during this FSW of Ti alloy flat plates.Photographs describing these three distinctive pin geometries are illustrated in the figure 1.
In addition to these three distinctive pin geometries, tools possessing three different shoulder diameters (20 mm, 25 mm and 30 mm respectively) were also employed during this FSW of Ti alloy flat plates.The tool profiles of all the pin geometries used in this work possessed a length of 4.85 mm.Complete set of Ti alloy flat plate joints were attained by employing a semi-automatic category FSW machine possessing a 410 ×805 mm work table and this table was movable in the 3 different axis, namely vertical, longitudinal and horizontal axes.  2 describes in detail the several parameters being taken into consideration in this experimental work along with their corresponding levels, respective units and notations.

RSM
RSM (i.e., response surface methodology) based approach was employed in this investigation for evaluating the proposed experimental research scenario and for formulating a suitable numerical model for the FSW of Ti alloys.
During 1951, Wilson and Box formulated this schematics to establish the intermediary relationship amidst the parameters of FSW process and the responses, in an efficient manner.It was proven by various researchers that a well formulated regression based numerical model can perfectly figure out the behavior of the system [17,18].A quadratic based numerical model of 2nd order polynomial can be expressed as: Where y represents the preferred response of output, xi indicates the variables of the FSW process, k denotes the number of variables of design, regression coefficient was indicated by β i and the error (i.e., the noise) being observed during the response was denoted by ε.

GRA-PCA
The theory of multiple components employing GRA (i.e., grey relation analysis) was put forward by Dang for the purpose of optimizing the parameters of a process whenever an insufficient data or evident was identified [19,20].In the models based on GRA, the interrelationship amidst the components in a system was calculated and then quantified with the outcomes of the experiment together with a relational based system of grade for distinctive distribution.If the interrelationship amidst the two components of a system is stronger, then it will contribute for a larger value of GRG (i.e., grey relation grade) [21,22].Each and every output and input variable possess distinctive range and corresponding units.This discrepancy will lead to generation of imprecise results, during the evaluation process of GRG.As a result, there prevails a need for normalizing the actual data [23,24].The contribution percentage of each and every response can be determined by employing PCA (i.e., principal  component analysis) and then used in GRG based calculation.The various step by step procedures and several formulas for the three outcomes of this experimental investigation, namely tensile strength (TS), yield strength (YS) and percentage of elongation (PE), in the manner of which are 'larger is the better' are illustrated in the figure 2.

Investigational results and discussions
Table 3 elaborates the entire set of experimental runs designed as per the approach of central composite design (CCD) and the respective results of the mechanical properties of the Ti alloy joints attained during every experimental run.Three trial runs for every experiment were performed to document the value of every mechanical property based response, namely TS, YS and PE.The mean of these 3 attained values have been described in the table 3.As it a well proven fact that the efficiency, effectiveness and quality of the joints attained during the employment of the FSW process were dependent on the choice of parameters of FSW process and their corresponding values (i.e., levels), in this experimental investigation, an endeavor was put forward to optimize the process parameters for mechanical based properties.To determine the competency and effectiveness of the formulated quadratic regression model, ANOVA was employed to carry out the analysis and a numerical model was also established for each and every response.Figure 3 portrays the photographs of a set of friction stir welded Ti alloy joints fabrciated during the trial runs.Tensile specimens were obtained from the mid length of each fabricated joint.ASTM (i.e., American society for testing and materials) guideline namely ASTM: B557M-10 was followed for preparing the tensile specimens, in order to study and understand the properties of the fabricated joints.

ANOVA based results
Major objective of employing ANOVA is to ascertain the impact of the parameters of the FSW process for responses based variation.ANOVA based results for the TS, YS and PE are described in the tables 4-6 respectively.The source based list in these tables demonstrate the model, the interactive, individual and square based terms of the input FSW parameters, whose P based values are lower than 0.05, announcing that the importance of the above mentioned terms at a 95% level of confidence.The coefficients possessing value of F larger than 0.05 are not taken into consideration for the analysis.F based test was carried out to ascertain the importance of parameters impacting the process based responses [25].Models possessing F values of 18.53, 37.19, 9.71 announces that all the three mathematical models are numerically compassionate and the data were found to be fitted more competently.For all the three formulated model p values was 0.392 (TS), 0.342 (YS) and 0.958 (PE) for the component lack of fit, which announces them as a non-significant term in the context of the pure error.The component R2 being termed as determination coefficient is yet another important coefficient in ANOVA and the formulated model leads to the best illustration of the investigational data, whenever the R2 value approaches unity.
The calculated values of R 2 namely 0.9774, 0.9886 and 0.9577 in these tables announces that the formulated model elucidates 97.74%, 98.86% and 95.77% variability of TS, YS and PE respectively.To validate whether the formulated model have depicted the fine interrelationship amidst the parameters of FSW process and the measured responses, the anticipated R 2 and adjusted R 2 have been validated.For TS, YS and PE, the values of adjusted R 2 and anticipated R 2 were 0.9246 and 0.851; 0.9620 and 0.868; and 0.8591 and 0.847, respectively.
The S/N ratio (i.e., signal to noise ratio) is exhibited by means of the adequate precision element.The model was formulated in such a way that it will be fit enough to continue further, if the value of the same exceeds 4. The values 15.54, 12.18 and 10.49 confirms acceptable indication of all the 3 formulated numerical models.The fraction of the SD (i.e., standard deviation) to the mean is termed as CV (i.e., coefficient of variance) which explicates the relative based variance.For TS, YS and PE, the CV values were 1.37%, 0.88% and 12.96%  respectively, which again demonstrates the perfect accuracy and reliability of the investigation being performed.The numerical regression based numerical equations were formulated by employing the RSM based approach for various responses of the FSW process.Regression based equations in coded values of the parameters of the FSW process were described as equations (2) to (4) for TS, YS and PE, respectively.Backward based eradication was employed for the annihilation of the non-significant variables.

Impact of parameters of FSW process on TS
From the ANOVA based outcome, it was revealed that almost all the four process parameters were found to have a dominant role in impacting the tensile strength of the friction stir welded Ti alloy joints.Schematics of variation in TS with the modification in the values of the process parameters are illustrated in the form of perturbation curve as seen in the figure 4(a).The shoulder diameter and geometry of the employed tool's pin determine the area of contact of the material and tool, thereby ascertain the volume of frictional heat to be generated during the FSW process.So, lower the area of contact with the work piece surface leads to generation of heat in reduced volumes and higher area of contact with work piece results in generation of heat in surplus volumes [26].Both of these scenarios, i.e., lower and higher volume of heat generation leads to inappropriate plasticization and grain coarsening in the heat impacted zone (HIZ) respectively.Tensile strength of the friction stir welded joints was found to decline with the increment in the shoulder diameter of the employed tool from 20 mm to 30 mm.TS can be found to escalate with the increase in the rate of traverse of the tool from 30 mm min −1 to 40 mm min −1 , but then it starts declining at 50 mm min −1 .
In FSW, the rotational speed of the employed tool impacts the deformation of plasticized metal by influencing the volume of generated frictional heat.Slower tool rotational speeds will generate lower volumes of heat input and insufficient reaction temperature, thereby hindering the pertinent deformation of the plasticized metal in the nugget zone [27,28], leading to the generation of defects namely channel defects and macro sized  cracks in the friction stir welded joints, thereby reducing the tensile strength of the fabricated joint.At the same time, larger tool rotational speeds will lead to exaggerated stirring by the tool pin, leading to detachment of huge number of Ti particles, which will be too huge in size to get distributed evenly in the nugget zone, thereby leading to several flaws (including cracks, voids etc,) thereby degrading the strength of the fabricated joint [29].From the figure 4(a), it can be visualized that the TS increases with the escalation in the tool's rotational speed from 1200 rpm and reaches its maximum value at 1600 rpm.Similar trend was also observed during the employment of distinctive tool pin profiles and highest value of tensile strength was attained during the employment of taper cylindrical pin profiled tool.The interactive impacts of the input parameters of the FSW process are portrayed in the figure 4(b)-(f) in the form of 3 dimensional surface based plots.The combined impact of the FSW process variables, namely shoulder diameter and pin profile of the employed tool on the tensile strength of the fabricated Ti alloy joints is illustrated in the figure 4(b).The shoulder diameter affirms the area of contact surface of the tool and the flat plates during employment of consistent tool pin profile, which in turn determines the volume of heat being generated due to friction during the FSW.A lower volume generated heat will not be sufficient to plasticize the metal, and at the same time, higher volume of heat will lead to the growth of grain structures in an inappropriate in the HIZ [7,30].These two scenarios will lower down the values of tensile strength.When the employed tool's pin geometry impacts the flow of plasticized metal during welding, these two inputs, i.e., flow of plasticized metal and input of heat will determine the strength of the attained joints [5,31].As a result, from the figure 3(b), it can be visualized that both the combinations, namely moderate value of tool shoulder diameter together with a taper cylindrical pin profile have contributed for larger value of tensile strength.If the volume of heat generated during FSW process is determined by the shoulder diameter of the tool, then the input of heat per unit length of the flat plate to be welded using FSW process will be determined by the traverse speed of the tool [6,10].Figure 4(c) demonstrates highest value of tensile strength at moderate values of tool traverse speed and shoulder diameter, which announces that moderate volume of heat input is needed for attaining superior joint quality.From figure 4(d) which illustrate the interactive impact of pin geometry and rotational speed, we can observe that the tensile strength seems to be maximum when the heat input is moderate around 1250 rpm and during employment of taper cylindrical pin profiled tool.Interactive impact of tool traverse speed and rotational speed is illustrated in the figure 4(e), which reveals us that the combination of tool traverse speed of 45 mm min −1 and rotational speed of 1250 rpm, can contribute towards attainment of Ti alloy joints possessing larger values of tensile strength.Interactive impacts of tool pin geometry with that of the tool's rotational speed and traverse speed are illustrated in the figures 4(f) and (g) respectively.

Impact of parameters of FSW process on YS
Similar to tensile strength, yield strength was also found to be impacted by all the four employed parameters of FSW. Figure 5(a) illustrates how the modifications in these input parameters of FSW impacts the yield strength of the fabricated Ti alloy joints.From this curve, it can be visualized that the escalation in the values of the shoulder diameter after 25 mm, leads to a decline in the yield strength of the fabricated Ti alloy joints.We can also visualize an escalation in the yield strength of the Ti alloy joints when the tool's traverse speed was raised from 30 mm min −1 to 50 mm min −1 .In addition to this, a linear rise in yield strength can also be observed when the pin profile is changed from straight square to straight cylindrical and from straight cylindrical to taper cylindrical pin geometry.This was mainly due to the proven fact that the taper cylindrical pin profile has played an inevitable role in enabling perfect mixing of the plasticized metal and uniform distribution of the secondary category precipitates [19,32].
Interactive impacts amidst the two employed parameters of the FSW process are illustrated in the figures 5(b)-(e).For instance, figure 5(b) portrays the interactive impact amidst the shoulder diameter and rotational speed of the employed tool on the attained Ti alloy joints.It can be observed form this graph that higher values of yield strength have been attained during the employment of rotational speed of 1250 rpm to 1350 rpm, together for a shoulder diameter of 22 mm to 24 mm.The interactive impacts amidst the tool's pin geometry and its rotational speed are portrayed in the figure 5(c) and the figure 5(d) illustrate the interactive impacts of tool's traverse speed and rotational speed on the yield strength of the friction stir welded Ti alloy joints.
From these 3D surface plots, it can be understood that the volume of heat generated during the optimized parameters (i.e., optimized tool rotational speed, traverse speed and shoulder diameter) have increased the yield strength of the Ti alloy joints [15,33].Using a taper cylindrical pin profiled tool have enabled appropriate mixing of the plasticized metal and homogeneous dispersion of the secondary category precipitates in the nugget zone and as a result, the yield strength of the friction stir welded Ti alloy have increased further.

Inferences from confirmation tests
Real time experiments, i.e., friction stir welding of Ti alloy flat plates were carried out to affirm the competency of the formulated numerical models for each and every response.The levels of combination of distinctive parameters of the FSW process other that in the design of experiments matrix was preferred for the test of confirmation.Table7 summarizes the outcomes of these tests and from this table it can be visualized that the formulated numerical models are competent enough to anticipate the responses.

Inferences from GRA-PCA tests
To absolutely initiate the correlative significance of every response in GRA, PCA was specifically bestowed to figure out the corresponding values of weightage for every response.Equivalent eigen based value for every response together with its respective proportion in the data based clarification is described in the table 8.
Predominant components were evaluated such that the 1st predominant component's square equivalent to the highest eigen based value represents the contribution of that appropriate response.As a result, the contribution of TS, YS, PE were determined as 33.49%, 33.49% and 33.02% respectively, as described in the table 9.
Table 9 describes in detail, the coefficients of deviation and their normalized data for every response.The single category score of every response GRG was determined using GRC (i.e., grey relation coefficient) and PCA and the sequence of deviation for every response is mentioned in the table 10.
Larger GRG indicates higher optimum values for all responses for this experimental investigation.Scores of GRG were ranked for all the experimental investigations and are being described in the last column of the  3.6.Analysis of SEM images SEM (i.e., scanning electron microscope) images of the base metal of investigation, namely, Ti-6Al-4 V alloy is illustrated in the figure 6(a).From this figure, it can be visualized that the metal of investigation inherits the presence of large sized lengthened primary alpha (α) grains and altered beta (β) grains, scattered in an uneven manner.Figures 6(b)-(e) illustrates the various regions of the friction stir welded, flaw free Ti alloy joint attained during the experiment no.20.For instance, figure 5(b) illustrates the SEM images of the three distinctive zones of the friction stir welded Ti alloy joint, namely: heat impacted zone (HIZ), thermo-mechanically impacted zone (TMIZ) and nugget zone (NZ).SEM image of the heat impacted zone is portrayed in the figure 6(c) and it can be visualized that there is no major change in the size of the grains of the parent metal and HIZ have experienced thermal heat impact only which have resulted in the twining of the lamellar alpha (α) and prior beta (β) grains in the HIZ.Grain growth of the lamellar α particles and prior β particles can also be observed in this zone.TMIZ of the friction stir welded Ti alloy joint attained during the experiment no.20 is illustrated in the figure 6(d) and we can visualize the presence of nugget zone with fragmented particles of Ti in the upper portion.In the middle portion, we can observe some precipitated β particles and lower portion exhibits the presence of grain orientation of the twinned lamellar α grains.Figure 6(e) portrays the nugget zone of the Ti alloy joint and the parallel flow of fragmented grains can be seen along the direction of the tool shoulder.Generation of frictional heat in ideal volumes and perfect stirring action caused by the employment of the taper cylindrical pin tool geometry and its shoulder have led to the fragmentation of the grains of lamellar α, prior β particles and these particles have undergone perfect dynamic re-crystallization, resulting in the generation of finely refined, uniformly distributed, fragmented particles of α and β grain precipitates [5,16].This nugget zone exhibits the substantial grain flow towards upward direction and orientation of the fragmented grains along the direction of stirring.
From the SEM images illustrated in the figures 6(a) and (e), i.e., SEM images of the parent metal and nugget zone of the flaw free Ti alloy joint attained during experiment no.20, it can be inferred that the large sized lengthened primary alpha (α) grains and altered beta (β) grains of the parent metal being scattered in an uneven manner have been transformed into finely refined, homogeneous uniformly distributed lamellar α and prior β grains.This was attained due to the generation of frictional heat in ideal volumes and perfect stirring action caused by the employment of the taper cylindrical pin tool geometry and its shoulder [11,34].These finely refined grains distributed in a uniform manner in the nugget zone have in turn contributed for the fabrication of flaw free Ti alloy joints [22,28].

Inferences from tensile fractography
With the objective of understanding the manner in which the friction stir welded Ti alloy joints undergo fracture, the specimen extracted from the Ti alloy joints were subjected to tensile tests.Tensile test results revealed Ti alloy joints possessing larger values of tensile strength and ductility encountered fracture in the region of interface of TMIZ and NZ.The grains of the nugget zone were found to have undergone dynamic recrystallization and possessed finely refined, equally spaced grain structures.At the same time, the grains present in the TMIZ were found to have undergone strain hardening and possessed coarser grain structures, thereby making this TMIZ, a weaker region of the Ti alloy joint [15,35].Whenever the input of heat was reduced, it makes the NZ smaller, thereby decreasing the distance of location of fracture from the centre of the joint [36,37] and similar scenario was observed in the tensile fractured specimen of the Ti alloy joint attained during the experiment no.19.At the same time, the tensile fractured specimen of the Ti alloy joint attained during the experiment no.20 have experienced sufficient heat input and the tensile test specimen extracted from this joint have exhibited fracture at the interface of the NZ and TMIZ.
Tensile test specimen extracted from the Ti alloy joints attained during the experiment no.19 and 20 were chosen for comparing the fracture mechanism and for analysing the surfaces of fracture.The reason for choosing these two joints was that the experiment no.20 possesses highest GRG value (i.e., 29989) and  Figure 7(a) demonstrates that the surface of the fractured surface is flat and slightly inclined towards the axis of loading.Figures 7(b) and (c) are magnified views of that fractured surface and these images reveals us the existence of laterally contracted area, which is a direct evident for the reasonable necking at the region of plasticized instability, where strain hardening have failed to compensate for the reduction in the area, before the fracture based failure [38,39].
From the figure 7(c), we can observe the existence of cup like depressions and dimples, which proves us that the flaw free Ti alloy joint attained during the experiment no.20 have undergone a ductile category of fracture during the tensile test.Even though, similar laterally contracted area was found in the Ti alloy joint attained during the experiment no.19 as seen in the figure 7(d), from its magnified SEM images being illustrated in the figures 7(e) and (f), we can observe honey comb like surfaces having several dents and huge depressions, revealing us the failure of this joint have undergone a brittle-ductile category of fracture.This mode of failure usually occurs in friction stir welded joints, when the heat input was lower [17,27].It was proven fact that whenever the heat input was lower during the FSW process, it leads to improper forging of plasticized metal and will result in generation of coarsened, strengthened precipitates of secondary phase.These secondary phase precipitates encounter fracture in foremost manner during tensile test.This was mainly due to the fact that these secondary phase precipitates promote the formation of micro dents and deep hole depressions in the TMIZ, leading to the failure of the joint in the TMIZ [18,23,32].

Conclusions
In this experimental investigation, an attempt was put forward to formulate a relationship amidst various parameters of FSW process and mechanical strength related outputs, by establishing a quadratic numerical model employing two distinctive approaches GRA-PCA coupled with PCA and RSM during friction stir welding of Ti alloys.From this experimental investigation, below mentioned inferences were made: • All the considered process parameters, namely tool's rotational speed, rate of tool traverse, tool's shoulder diameter and its pin geometry were found to have an inevitable contribution in varying the mechanical related properties including tensile strength, yield strength and percentage of elongation.
• Formulated quadratic regression based numerical models for every mechanical strength based outcomes were validated for their competency by conduction of confirmatory experiments and the generated results were observed to be within 5% agreement error with the anticipated values of the model.
• It was determined by GRA-PCA that the 25 mm shoulder diameter having a taper cylindrical pin geometry employed at a tool traverse speed of 40 mm min −1 , rotational speed of 1400 rpm were the optimized values during this friction stir welding of Ti alloys.
• Experiments carried out during the employment of these optimized process parameter values resulted in the generation of flaw free Ti alloy joints possessing a largest tensile strength of 809.8 MPa, yield strength of 778.7 MPa and percentage of elongation of 6.9%.
• To ascertain the correlative importance of every response in GRA, PCA was employed to determine the weightage values of every response and the single score of every GRG based response was determined using GRC & PCA and the scores of GRG were ranked for all experiments.1st rank was attained by the experiment no.20 possessing a GRG score of 2.9989.
• SEM images of the parent metal and nugget zone of the Ti alloy joint attained during experiment no.20 revealed that the large sized lengthened primary alpha (α) and beta (β) grains scattered in an uneven manner have been transformed into finely refined, uniformly distributed lamellar α and prior β grains, due to the generation of frictional heat in ideal volumes and perfect stirring action.
• Tensile test results revealed Ti alloy joints possessing larger values of tensile strength and ductility encountered fracture in the region of interface of TMIZ and NZ.SEM fractography images of the flaw free Ti alloy joint revealed the existence of cup like depressions and dimples, announced that the Ti alloy joint attained during the experiment no.20 have undergone a ductile category of fracture during the tensile test.

Figure 1 .
Figure 1.Three distinctive pin profiles used in this experimental work.

Figure 2 .
Figure 2. Illustration of the procedure employed during the approach of GRA-PCA.

Figure 3 .
Figure 3. Photographs of the friction stir welded Ti alloy joints.

Figure 4 .
Figure 4. (a) Perturbation and (b)-(g) 3 Dimensional surface plots illustrating the interactive impact of various parameters of FSW process on tensile strength.

Figure 5 .
Figure 5. (a) Perturbation and (b)-(d) 3 Dimensional surface plots illustrating the interactive impact of various parameters of FSW process on yield strength.
experiment no.19 possesses lowest GRG value (i.e., 1).SEM images of the fractured surface of the tensile test specimen attained during the experiment no.20 are illustrated in the figures 6(a)-(b) respectively.Similarly, SEM images of the fractured surface of the tensile test specimen attained during the experiment no.21 are illustrated in the figures 6(d)-(f) respectively.

Figure 6 .
Figure 6.SEM images of (a) Parent metal (b) three distinctive zones of the friction stir welded Ti alloy joint attained during experiment no.20 (c) heat impacted zone (d) thermo-mechanically impacted zone (TMIZ) and (e) nugget zone (NZ) of the flaw free Ti alloy joint attained during experiment no.20.

Figure 7 .
Figure 7. SEM images of the fractured surface of friction stir welded tensile specimen of the Ti alloy joint attained during (a) experiment no.20, (b) and (c) its magnified images and (d) experiment no.19, (e) and (f) its magnified images.

Table 1 .
Several chemical ingredients of the metal of investigation in wt%.

Table 2 .
Description of various FSW process parameters and their corresponding levels considered in this investigation.

Table 3 .
Experimental runs and results for mechanical properties of friction stir welded Ti alloy joints.

Table 6 .
ANOVA based table for 3rd response: percentage of elongation (PE).

Table 7 .
Outcomes of the test of confirmation.

table 11 .
1st rank was attained by the experiment no.20 possessing a GRG score of 2.9989 along with the response based values of 809.8 MPa, 778.7 MPa and 6.9% of TS, YS and PE respectively.

Table 8 .
Eigen values of responses.

Table 9 .
Predominant components and their response contribution.

Table 10 .
Predominant components and their response contribution.

Table 11 .
Determined GRG and GRC values with ranking for every experiment.