Establishment of empirical relations amidst mechanical attributes of friction stir welded distinctive alloys of Mg and optimized process parameters

This experimental investigation aims to formulate quadratic regression based empirical model taking into account the parameters of friction stir welding (FSW) process for predicting the optimized process parameters to maximize the response (i.e., ultimate tensile strength) of the distinctive alloys of Mg joints. Parameters of FSW process taken into consideration includes tool’s traverse speed, axial force and rotational speed of tool and response being the fabricated joint’s tensile strength. A central composite rotatable category 3–factor, 5 level design based matrix was formulated and response surface methodology was used to obtain regression based models, to generate contour plots and to visualize the interactive impacts of parameters on the joint’s tensile strength. Formulated quadratic regression based model was validated employing analysis of variance. Comparison amidst the realistic and anticipated values of the response announced the superior fitting accuracy of the formulated quadratic model. For a constant tool’s rotational speed (of 1000 rpm to 1250 rpm), the tensile strength was observed to be highly sensitive to the axial force values than the tool traverse speed values. Mean tensile strength of the friction stir welded AZ31B, AZ80A, AZ91C, AM50A and ZK51A-T5 Mg joints during the employment of optimized process parameters were found to be 217.5 MPa, 251.4 MPa, 231.9 MPa, 192.1 MPa and 173.2 MPa respectively, thereby exhibiting perfect agreement with the anticipated values.


Introduction
Owing to superior strength-to-mass ratio, easy degree of castability, lower density, excellent damping relevant capacity and larger specific stiffness, alloys of magnesium (Mg) were found to be potential candidates for replacing alloys of steel and aluminium, in the aeronautical and automobile relevant sectors [1,2]. AZ31B is one of the most popular and easily available wrought alloy of Mg possessing low mass density, high degree of machinability, superior strength, ductility etc, and is widely employed in manufacture of several aircraft components including aircraft fuselages, transmission castings [3]. AZ80A is a heat treatable, wrought alloy of Mg, recommended for forgings and extrusions requiring extreme creep resistance and good fatigue strength. Forgings in AZ80A Mg alloy finds application in superior strength components and parts like gear boxes and rotor hubs of helicopters, inter-stage fairings and frames of missiles, landing type gear struts, components of superchargers and satellites [4].
AZ91C is a popular sand casting Mg alloy possessing superior ductility, pressure related tightness and strength, exemplary resistance against corrosion. This Mg alloy can be forged, formed and cast easily and hence preferred widely in sectors of automotive for fabricating brake and clutch related pedals, transfer cases for 4wheel drives, drive brackets, rear-link arms, steering column brackets etc [5]. AM50A is a cast Mg alloy possessing excellent ductility, superior energy absorbing relevant properties, high strength and good castability. This AM50A Mg based cast alloy is mainly used in the manufacture of several automobile components including frames of seat, brackets, instrument panels, steering wheels [6]. ZK51A-T5 alloy of Mg possessing superior room-temperature related strength, larger yield strength and excellent ductility is widely applied in military and aerospace sectors for manufacturing highly stressed aerospace castings and military relevant castings of uniform cross-section [7].
Even though alloys of Mg are widely preferred for automotive and aerospace sectors, joining of alloys of Mg employing traditional fusion based techniques is a quite complex task, owing to the very severe affinity of Mg alloys for oxygen and other chemical based oxidants. In addition to this, Mg alloys will get readily oxidized in the joint portions during fusion based joining methodologies, owing to their superior-chemical reactivity at larger temperatures [8,9]. Moreover, usage of these fusion based joining techniques for welding together Mg alloys have led to the generation of several flaws that have generated during solidification including partial melting, hot based cracking, porosity etc, which diminishes the mechanical strength of the joints. So, there prevails a vital need for identifying a reliable welding technique to join the alloys of Mg for enhancing its degree of usage in automotive and aerospace sectors [10][11][12].
Friction stir welding (i.e., FSW) belonging to the category of solid state joining techniques was proven to eliminate flaws and problems relevant to solidification, as during this FSW process, the bulk melting of materials is avoided. Moreover, the residual type stresses and relevant distortions was also found to be reduced reasonably as the joining temperatures are reasonably lower when compared with that of the traditional fusion joining techniques [13,14]. Flaw free joints with superior mechanical properties were obtained for a wide variety of alloys of Aluminium, which were regarded as not weldable by traditional fusion welding methodologies. In addition to this, FSW process does not generate flaws like segregation of materials, porosity, hot cracks etc, as the metal, being welded does not melt during the FSW process. As the melting of parent metal does not occur during this process, FSW process possesses various merits over fusion joining techniques [15][16][17].
Fabricating sound quality joints is of considerable significance for several engineering sectors. Even though, FSW process possesses several merits, fabrication of superior quality joints by employing FSW process is a quite challenging task, as the FSW process is very sensitive to the joining parameters. Due to this, pertinent welding parameters selection is very crucial during FSW process in order to attain sound quality joints [18]. Conventionally, a time exhausting trial and error based methodology was used to obtain suitable welding parameters. In those scenarios, optimized welding parameters may not be attained owing to the large number of welding parameter combinations [19]. To solve these issues and to forecast the joining parameters precisely without exhausting time, materials and effort of labors, optimization based methodologies can be applied to ascertain ideal, optimized parameter combinations and one of the well-known optimization methodology is the RSM (i.e., response surface methodology) [20].
For instance, Palanivel et al [21] put forward a systematic concept to formulate the empirical based model for forecasting the strength of the AA5083-H111 Al alloy joints, fabricated employing FSW process. In this work, FSW process was selected, taking into consideration 3-factor and 5-level based central composite category design technique and RSM was applied for generating linear regression type models for demonstrating the relationship amidst the tensile strength and parameters of FSW process. Similarly, in the experimental work carried out by Senthil et al [22], a multi-objective based technique of optimization involving RSM based function of desirability type approach was used in optimizing the parameters of FSW process for joining pipes of AA6063-T6 alloy. Rotational speed and traverse speed of the tool were optimized for attaining joints possessing enhanced mechanical properties. A regression based model having a 95% level of confidence was formulated using RSM to anticipate the mechanical strength of the welded joints. Goyal et al [23] friction stir welded AA5086-H32 alloy by varying 6 distinctive parameters including tool's traverse speed, rotational speed, tool's hardness, its angle of tilt, its pin diameter and shoulder diameter. RSM was employed to establish numerical relationship amidst these input parameters and the performance parameters namely tensile elongation and strength and the competency of the formulated model was verified using ANOVA (i.e., analysis of variance).
From these literature review [20][21][22][23][24][25], it can be understood that, it is significant to examine the mechanical relevant attributes of the joints so as to characterize its efficiency. Usually, a joint attained employing FSW process is characterized by being comprising of three distinctive zones namely, heat impacted zone, thermomechanically impacted zone and nugget zone, also sometimes termed as dynamically recrystallized zone. Generation of these three zones are influenced by the behavior of flow of the plasticized metal under the impact of the spinning tool. On the other hand, this flow behavior was found to be essentially influenced by the mechanical related attributes (including elongation percentage, yield strength, tensile strength etc,) of the parent metal, geometry of the tool, several parameters of the FSW process etc As a result, in this experimental work, one of the main objective is to employ RSM to establish empirical relations amidst the various parameters of the FSW process (including tool's traverse and rotational speed, axial force) and tensile strength of the fabricated weldment as the output response. Another objective is to determine the ideal and optimized combination of parameters of FSW that will result in the fabrication of joints possessing highest tensile strength values.

Description of base Mg alloys
Flat plates of five distinctive grades of Mg alloys including AZ31B Mg alloy, AZ80A Mg alloy, AZ91C Mg alloy, AM50A Mg alloy and ZK51A-T5 Alloy, (in the size of 100 mm × 50 mm × 6 mm) were taken as the parent metals in this investigation. The chemical related constituents and mechanical related attributes of these parent metals are described in the tables 1 and 2 respectively. The chemical based constituents of the base alloys of Mg were ascertained using the metallography related tests and Energy Dispersive x-ray Spectrometry (i.e., EDS) based analysis.

FSW machine setup
Plates of these Mg alloys were welded as butt joints at 90 degree angles to their rolling direction and an indigenously designed and manufactured semi-automatic in category, FSW machine was used in this investigation to friction stir weld the alloys of Mg. This FSW machine is displayed in the figure 1(a) and this machine comprises an exclusively manufactured work holding fixture, using which the Mg alloy plates were held rigidly during the FSW process. A tool fabricated from M42 grade HSS (i.e., high speed steel) material possessing a taper cylindrical pin as seen in the figure 1(b) was used to friction stir weld the Mg alloy plates and the diagrammtic illustration of the dimensions of the tool is illustrated in the figure 1(c).

Experimental trial runs
Initially, trial runs were performed to determine the suitable working related limits of the parameters of the FSW process. Spectrum of working of each and every parameter of the FSW process was fixed and determined by examining the cross sectional portion of the joint (i.e., macrostructure) for any detectable flaws including kissing bond, pinhole, tunnel defects etc By examining the macrostructure of the attained Mg alloy joints, some significant observations were made and are described in the table 3.

Determination of significant parameters
Selected level of significant parameters for FSW of distinctive Mg alloys together with their notations and units are described in the table 4. Above mentioned process parameter values were taken into account and the expedient limits of the process parameters of the FSW process were selected such that all the Mg alloys of our investigation, i.e., AZ31B, AZ80A, AZ91C, AM50A, and ZK51A-T5 Mg alloys can be welded without flaws.
As the spectrum of the respective factors are broad, a central composite based rotatable category 3-factor, 5 stage pattern based matrix was chosen. 2nd order central composite based rotatable pattern was proven to be remarkably effective tool of RSM to demonstrate the statistical relationship of the surface of response by means of least possible number of runs without comprising the relevant accuracy [4]. The formulated matrix of design comprised of 20 sets of codified scenarios and encompassed a complete duplication of 3-factorial 8-points, 6 star points and 6 center points pattern. As the matrix of design was comprised of 5 levels, the lower and upper boundaries were coded as -1.682 and +1.682 respectively and remaining 3 were equivalent hiatus of lower and upper values. Reasons for choosing a rotatable type central compoiste design is that it allows for the estimation of the response surface curvature easily, which plays a vital part in determining the optimal values of the independent variables. Moreover, an alpha value of 1.682 is preferred in this type of rotatable design based central composite, because it has the advantage of being able to fit a second-order response surface model without bias. This means that due to this alpha value, we can accurately estimate the response variables, even when the true response surface is not known or is difficult to estimate.
The coded values for the in-between levels were determined from the relation mentioned below: where X i is the prescribed codified value for the X variable and X can be of any ranging from X min to X max . As recommended by the matrix of design, a total of 20 joints for each Mg alloy were welded and altogether 120 joints were friction stir welded in this investigational work. Photographs of some of those 120 fabricated Mg alloy joints were displayed in the figure 2. For every experimental scenario, 3 specimen from each welded Mg alloy joints were examined and the average of these 3 results were tabulated in the table 5.

Formulation of regression equations
Portraying tensile strength of Mg alloy joints by TS, the outcome (i.e., response) was characterized as a behavior of rotational speed of the tool (R), axial force (A) and tool's traverse speed (T) and are specified as 2nd order regression (i.e., polynomial) based equation used to describe the surface of response 'Y' was given by [26,27] å å å and for five based factors, the chosen regression (i.e., polynomial) was specified as = + + + Where b0 is the mean of outcomes and b1, b2, K., b33 are the concomitants that rely on corresponding major and interactive impacts of the parameters. The values of these concomitants were estimated using the below mentioned equations [28,29]:- Entire set of concomitants were evaluated for their weightage at 95% degree of certainty employing Minitab software package. Determination of these significant coefficients were followed by formulation of the finalized models and employing the determined significant coefficients. Finalized numerical relationships to assess the tensile strength of the fabricated distinctive Mg alloy joints were formulated using the above described procedure and are mentioned below:-FSW of AZ31B Mg alloy:

Verification of the competency of the formulated model
The competency of the formulated relationships were evaluated employing the technique of analysis of variance (i.e., ANOVA) and the outcomes of the 2nd order related surface based response model being fitted in the pattern of analysis of variance are described in the table 6. The concomitants determinant (i.e., R 2 ) announces the perfect fitness of the established model and in this scenario, values of R 2 also announces that the formulated model deviates in explaining the total variations by less than 7% only [30,31]. Values of the modified coefficient determinant (i.e., modified R 2 ) were also reasonably high, which announces the large significance of the formulated model. Anticipated values of R 2 were in perfect agreement with the modified R 2 values. Satisfactory precision correlated the spectrum of the anticipated values at the points of design w.r.t the mean prediction error [32] and a graphical comparison amidst the realistic and anticipated values of the response variable (namely tensile strength) are illustrated as figures 3(a)-(e) for all the distinctive alloys of Mg and these graphs also announces the marginally superior fitting accuracy of the formulated tensile strength based model. From these graphs, it can be understood that the R 2 values for the formulated relationships prevails in the range of 96%-99%, announcing the perfect correlation amidst the predicted and realistic values.

Interactive impacts of process parameters
In this investigational work, the parameters of the FSW process interrelated to the maximized tensile strength of the fabricated Mg alloy joints were taken into consideration as optimal after evaluating the contour type graphs generated using the Minitab software. It is a known fact that the contour type plots are illustrated as peculiar  Model  9  9  9  9  9  Linear interaction  3  3  3  3  3  Square interaction  3  3  3  3  3  2-Way interaction  3  3  3  3  3  Error  10  10  circular shaped plots representing the possible interdependency of input parameters with the responses of output. Especially for the 2nd order response based surfaces, these plots are more convolute when compared with that of the elementary side by side line series which are generated based on 1st order models. Contour plots was found to play an inevitable part in the analysis of the response surfaces and examination of the generated     contour plots helps to understand that the specific static point was a minimum or maximum response or a point of saddle [33]. Contour type graphs for AZ80A Mg alloy are illustrated in the figures 4(a)-(c). It can be observed that figure 4(a) exhibits more or less a circular type contour suggesting the independency of the factors. From these contour graphs, it can be apprehended that the tensile strength of the fabricated joints have been greatly influenced by the rotational speed when compared with that of the axial force and traverse speed of the tool.
It can also be visualized from figures 4(a) and (b) that for a constant tool rotational speed (of 1000 rpm to 1250 rpm), the tensile strength of the joints have been highly sensitive to the axial force values than the tool traverse speed values. Interactive impacts amidst these three factors on the tensile strength of the joint also prevails which can be visualized from these contour graphs. Moreover, the escalation in the tool rotational speed with simultaneous increase in the axial force have declined the tensile strength of the joints. Interactive impact amidst the rotational speed and axial force have influenced the Mg alloy joints when compared with that of the interactive impact amidst the traverse and rotational speed. And this interactive impact amidst the rotational speed and axial force have also contributed for the highest value of the tensile strength of 253.6 MPa for the AZ80A Mg alloy joints, as seen in the figure 4(c).
Likewise, this interactive impact amidst the axial force and rotational speed have also contributed for the highest value of the tensile strength in other Mg alloy joints and the contour graphs corresponding to the interactive impact amidst the rotational speed and axial force illustrating the attainment of highest value of tensile strength for other Mg alloys namely AZ31B, AZ91C, AM50A and ZK51A-T5 Mg alloy joints are illustrated in the figures 5(a)-(d) respectively. Table 8. Micro-structural images of the parent metals and fabricated joints and SEM images of the nugget zone of the Mg alloy joints.

Optimization of process parameters
The optimized values of the tensile strength attained during the fabrication of the distinctive alloys of Mg can be ascertained from these contour graphs [34]. For instance, the highest value of tensile strength being estimated from these contour plots for the AZ80A Mg alloy joints was 253.6 MPa and was found to be attained during the optimized process parameters conditions of rotational speed of 1172.22 rpm, speed of tool traverse of 2.24 mm sec −1 and a 4.25 kN axial force respectively. Table 7 describes the optimized values of parameters of the FSW process for attaining highest values of tensile strength during the joining of distinctive alloys of Mg.
Distinctive Mg alloy joints were fabricated employing the optimized values of the above mentioned parameters and the micro-structural images of the parent metals (i.e., the distinctive alloys of Mg), together with the fabricated joints micro-structural and SEM images of the nugget zone are displayed in the table 8. From these micro-structural images of the parent metals (i.e., distinctive alloys of Mg), it can be observed that basically all these Mg alloys possesses enormous cast sporadic boundaries distributed in an uneven manner over the entire surface.
At the same time, from the micro-structural images and SEM images of the Mg alloy joints, it can be visualized that during the usage of optimized process parameters of the FSW process, the large sized, irregular shaped grain boundaries have transformed into finely refined, homogeneous, uniformly distributed, small sized grains. It can also be observed that the tool's stirring action under the optimized process parameters, have elongated and fragmented the plastically deformed grains, along the direction of rotation of the tool and have contributed for fabrication of flaw free Mg alloy joints [35,36].
With the objective of examining the tensile strength of these Mg alloy joints attained during the optimized process parameters, specimen were extracted from the Mg alloy joints, machined to the required specifications as prescribed by the ASTM-E8 standard guidelines and are being subjected to tensile test [37]. Photographs of the specimen before being subjected to tensile test are illustrated in figure 6.
Mean tensile strength of AZ31B, AZ80A, AZ91C, AM50A and ZK51A-T5 Mg alloy joints were found to be 217. 5  Moreover, these tensile strength values exhibited by the Mg alloy joints were found to around 84% to 87% of the strength of their parent Mg alloys. The major reason for enhancement of the strength in the fabricated Mg alloy joints which was found to eb superior when compared with the Mg joints attained during other joining techiques is that during FSW process, the engagement of optimized values of parameters have played a vital part in refining the size of the grains in the nugget region of the joints [26,32]. As a result, the grains in these regions have undergone transition into small sized, homogeneous, equally spaced,uniaxial grain structures, as portrayed in the table 8. In addition to this, the stirring action of the FSW tool have also contributed for improving the tensile strength of the Mg alloy joints by elongating the plastically deformed, fragmented grains towards the tool's rotational direction [25,36]. Out of these fabricated Mg alloy joints, AZ80A Mg alloy joints have exhibited 86.69% of the strength of its parent metal.
Similarly, the highest values of other mechanical related attributes including yield strength, elongation percentage for distinctive alloys of Mg attained during these optimized process parameters (mentioned in the table 7) are graphically illustrated in the figures 7(b) and (c), along with the tensile strength in the figure 7(a).

Conclusions
In this experimental investigation, an effort was put forward to establish the empirical relationships amidst the various parameters of the FSW process (including tool's traverse and rotational speed, axial force) and tensile strength of the fabricated joint of distinctive alloys of Mg namely AZ31B, AZ80A, AZ91C, AM509A and ZK51A-T5 Mg alloys, employing response surface methodology (RSM). Following important inferences were made from this experimental investigation: • Empirical relationships and Regression based quadratic equations were formulated and the formulated model was proven to be effective in ascertaining the response (i.e., ultimate tensile strength) for the friction stir welded five distinctive alloys of Mg, in the range of ±10% of their realistic investigational values at a confidence level of 95% • RSM was used to optimize the parameters of FSW process to fabricate joints possessing highest tensile strength values. Contour graphs have been generated to visualize the interactive impacts of the parameters on the tensile strength of the distinctive Mg alloy joints • For a constant tool rotational speed (of 1000 rpm to 1250 rpm), the tensile strength was observed to be highly sensitive to the axial force values than the tool traverse speed values. Moreover, the escalation in the tool rotational speed with simultaneous increase in the axial force have declined the tensile strength of the joints.
• Highest value of tensile strength was estimated from the generated contour plots for the distinctive Mg alloy joints and for instance, for AZ80A Mg alloy it was found to be 253.6 MPa and was attained during the optimized process parameters conditions of rotational speed of 1172.22 rpm, tool traverse speed of 2.24 mm sec −1 and a 4.25 kN axial force respectively.
• Mean tensile strength of the AZ31B, AZ80A, AZ91C, AM50A and ZK51A-T5Mg alloy joints fabricated during these optimized process parameters were found to be 217.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).