Development of Thermo Mechanical Model for Prediction of Temperature Diffusion in Different FSW Tool Pin Geometries During Joining of AZ80A Mg Alloys

Heat generated during the friction stir welding (FSW) process is of complex nature and plays a vital role in influencing the quality of the fabricated joints. In this experimental research, an thermo mechanical process model was formulated to estimate the values of peak temperatures generated during the employment of FSW tools with four different pin geometries (namely cylindrical, taper cylindrical, square and triangle) for joining of AZ80A Mg alloy flat plates, to understand their significant role in influencing the size of the grains, their mechanical strength and in the quality of the joints. The peak temperature values of the formulated thermo mechanical process model are found to be consistent with that of the actual experimental results and exhibited relatively very small variation It was observed that the joints fabricated by taper cylindrical pin geometry was found to possess very fine sized grains, due to the generation of ideal peak temperature (i.e., 348 °C which is nearly 81–82% of the melting temperature of AZ80A Workpiece).


Introduction
In the recent years, alloys of Magnesium (Mg) are continuously earning great attraction and significance under the category of easy to machine metals together with exceptional strength to weight ratio, for various sectors including automotive, aerospace and structural applications. In addition to these applications, AZ80A Mg alloys are also preferred over polymer and composite materials in electronic sectors, due to their unique electromagnetic intervention shielding and heat conduction properties [1][2][3]. At the same time, the HCP (hexagonally close packed) feature and larger thermal conductivity of this AZ80A Mg alloys hinders their fabrication by various conventional joining techniques and employment of fusion joining methodologies are found to generate joints with coarse microstructures, severe fracture, porosity, high residual stresses etc. [4,5]. Hence, there exists a need for identifying a reliable and optimal joining technique to obtain unique and quality AZ80A joints with mechanical preponderance [6,7] Categorized under joining techniques of solid state, friction stir welding (FSW) has been found to be most effective in generating sound quality weldments with equiaxed and fine sized grains. Joints of some series of alloy of Mg including AZ31B, AZ91C etc. have been reported to be successfully obtained by employing this solid state technique of joining namely, FSW in which the frictional heat gets produced because of the continuous rotation of the shoulder of non-expendable FSW tool over the connecting regions of the work piece surfaces to be joined [8][9][10].
The tool employed for carrying out FSW comprises of a unique shoulder and a pin with a particular geometry, which will be employed to obtain joints of the two flat metal plates. This tool will be made to rotate at high speed and then it will be forced to infiltrate into the connecting regions of the joining region of the two workpieces, until the shoulder of tool contacts top surface of these flat metal plates. Then, this tool is made to travel along the line of joint. The face of the workpiece, where rotation of tool harmonizes with the direction of joining is indicated as the AS (advancing side) and other face of the workpiece is indicated as RS [11,12].
The frictional heat generated by virtue of the contact betwixt the shoulder of employed tool and the surface of flat metal plates softens their material and plastic deformation of the plasticized material occurs, without melting the metal plates [13]. The softened and plasticized materials on both sides of the workpieces are stirred around the region of the FSW tool pin (with unique geometrical shape), by the impact of the rotational and translational movements of pin of the tool, which happens along the entire line of travel of the tool pin [14]. Once the pin of the FSW tool is retrieved from the surfaces of the flat metal plates, the plasticized material flows across the metal plates stops, then the cooling of the plasticized material takes place and the welding gets completed successfully [15][16][17].
Thus, it can be understood that, the technique of FSW joins materials in their solid state itself and due to this reason, it has various added merits like less input of energy, reduced volume of residual stresses, greater strength of weld etc. when compared to that of the numerous fusion welding techniques [18,19]. But, inspite of the simple and user friendly principle of joining, there seems to exist various unexplored areas and research complications arising due to the anomalies occurring internal flow of plasticized materials due to the exhilarating action of the FSW tool pin geometry and by the generated heat arising from friction between shoulder and workpiece surface [20][21][22][23] Detailed illustration of the thermo mechanical anomaly occurring between the flat metal plates to be joined and the employed FSW tool pin will enable optimization of welding parameters, perfect design of FSW tool, extending the application of the FSW to various new dimensions [24][25][26]. For better and perfect understanding of the FSW process, especially w.r.t to the tool temperatures and flow of heat, there exist the need of employing both mathematically developed simulation models and real experimentation methods [27][28][29][30][31].
It was revealed by various experimental researchers [32][33][34][35][36] that, the joining parameters of FSW, the flow of plasticized material, interface anomaly of FSW tool and workpiece surface etc. have been proven to significantly influence the volume of heat generation during of joining of Al alloys using FSW. As majority of these experimental research works have concentrated their research towards the measurement of the temperature over distinct and limited regions of the workpiece surface, there exists a vital and unavoidable need for analysing and understanding the temperatures, flow of generated around the FSW tool pin profile, to derive a mathematical model to predict the flow of temperature for various FSW tool pin profiles, the role of the geometrical design of the various pin profiles in regulating the flow of generated frictional heat and to compare these model results with that of the actual experimental data.
In this numerical and experimental research work, a thermo mechanical model for was formulated and developed using the COSMOL software to predict the temperature diffusion around the FSW tool with 4 unique profile geometries (namely cylindrical, taper cylindrical, square and triangle) and to understand the role, impact of these pin geometries in regulating the generated frictional heat. The predicated results (i.e., simulated peak temperature) of the formulated mathematical model are then compared and validated with that of the actual experimental results and analysed.

Material, Machine and Tool Pin Geometries
In this experimental research, wrought AZ80A Mg alloy was investigated and a uniquely developed and fabricated FSW machine (semi-automatic category) was employed to fabricate joints for the flat AZ80A Mg work pieces with the dimension of 50 mm width and 100 mm length together with a thickness of 5 mm. The employed FSW machine comprised of a spindle motor with 5 kW capacity, working table measuring 810 mm in length and 400 mm in width.
Several experimental investigations [37][38][39] have proven that High-Speed Steel graded M35 metal is an ideal material for fabricating FSW tools, due to their excellent resistance to wear, superior toughness and this material possesses a larger resistance to softening, especially at peak temperatures around 500-550 ℃, making it more desirable for employment for higher operational speeds. Based on these reasons, in this experimental research, High-Speed Steel graded M35 material was used to fabricate the various required FSW tools. FSW tools having four distinctly unique pin geometries, including cylindrical, taper cylindrical, square and triangle as seen in the Fig. 1 were designed and fabricated.
Except the geometry of the tool pin, all other dimensions namely tool outer and inner shoulder diameter, pin length, shoulder lengths etc. remains the same for all the four FSW tools. All the four FSW tools have a 20 mm outer shoulder diameter (for 50 mm length), 15 mm diameter for inner shoulder (for 10 mm length) and a pin length of 4.85 mm.

Tool and Workpiece Temperature Measurement Setup
In this numerical and experimental research, the temperature on the surface of investigational workpiece (AZ80A Mg) were measured by the employment of thermocouples fabricated out of Cr-Al wires. Figure 2 graphically illustrates the arrangement and location of the employed thermocouples on various regions of the AZ80A Mg alloy flat plates both on AS and RS.
Three different categories under which measurement of temperature was carried out includes (a) Line of axis along the bottom side (b) axis of transverse on the top side and (c) at an offset of 10 mm on the top side from the axial line. Measurement of temperature on the FSW tool side was employed for determining the temperature of the FSW process, as the temperature of the FSW tool will be in stable position and state, when compared with that of the other regions during the joining of the AZ80A Mg plates. The arrangements of the thermocouples in the interior regions of the employed FSW tools are graphically represented in the Fig. 3. The various interior locations of the placement of the thermocouples inside the FSW tool include the tip of the tool pin geometry, inner shoulder region and root of the FSW tool pin geometry.
All the thermocouples were placed in their respective above mentioned positions arrangements of the thermocouples in the interior regions of the employed FSW tools at a distance of around 1 mm from the surfaces of the FSW tool to calibrate the temperature as nearer to the temperature at the workpiece/tool interface, as far as possible. The various conditions of the proposed experimental research are mentioned in Table 1.

Formulation of Thermo Mechanical Model
Several modelling based experimental investigations [40][41][42] reveals us that, the issues related with differential equations can be dealt by approaching the enario by means of a mathematical strategy. In this experimental research, the formulated process model for fabricating AZ80A Mg alloy joints through employment of FSW tools (with four unique Pin geometries namely cylindrical, square, triangle, taper cylindrical) was devised with the help of COMSOL Multiphysics transfer of heat component.
A thermo mechanical based process modelling is the distribution and bisection of a geometric sector into restricted number of fundamental points and primitive volumes. In this formulated thermo mechanical process model, a definite assessment of the overseeing limit prerequisite regulating each nodal point and its neighbouring focuses are also characterized. Observational conclusions are also acquired for the above mentioned equational structures, emerging from those definite assessments. As it is evident that, the numerical dominion is well-proportioned along the line of weld, it is sufficient to consider only half of the flat plate of investigational workpiece, in the course of formulation of the process model [43,44]. The generated computational domain for the joining of AZ80A mg alloy by FSW technique is shown in the Fig. 4 and it can be visualized that, the surface of the workpiece is attached with two absolute dominion along the direction of x-axis.
Apart from this, the below mentioned elemental presumptions were considered in formulating the thermo mechanical process model: • Angle of inclination of the FSW tool is neglected • The various cycles of weld including 1st and 2nd dwell, cycles of retraction etc. are excluded • The numerical assessment based on the general presumption of the consistent contact shear stress τ con has been taken into account It was also assumed that, flow of heat into the workpiece will not take place, when the regional temperature attains the melting temperature of the workpiece.

Heat Transfer in the AZ80A Mg Alloy Surface
Volume of transmission of heat happening above the surface of investigational workpiece during FSW in a movable system of coordinate is governed by the equation: In the above equation, T represents the generated temperature, Cp is the quantity of heat, ρ represents the density, the conductivity of heat being denoted by k and u represents the traversing speed of the FSW tool.

Generation of Heat from Tool Shoulder
Similarly, the various equations governing the generation of heat in between the region of interface of the FSW tool shoulder and AZ80A Mg (workpiece) for the employed FSW tools with 4 different pin geometries are as follows [45,46]: In the above equations, Q shou represents the heat generated around each of the employed FSW tools, the angular speed of rotation of the FSW tools are denoted by ω, the shear stress of contact by means of τ con , R shou denotes the employed tool shoulder's radius, the radius of the pin of employed FSW tools are indicated by R pin and S indicates the side length of the square and triangle pin profiles of the FSW tools.

Generation of Heat from Pin of FSW tool
The equations governing the generation of heat by the pins of the various employed FSW tools are as follows [45,46]:  In the above equations, the quantity of heat generated by the pin of employed tools is denoted by Q pin , the height of the pin of employed tools by H pin , and in the case of a taper cylindrical pin, R pin,min denotes the bottom radius of the taper pin and R pin,max denotes the top radius of the taper pin.

Heat Loss
The convection taking place in a natural manner and radiation prevailing due to surface to element scenarios are the two most important criterions, due to which the AZ80A Mg alloy workpieces lose the heat on their lower and upper regions. The relevant equations of flow of heat corresponding to the above mentioned regions of the workpiece are as follows:   Table 2 describes the various temperature reliant characteristics of workpiece (AZ80A Mg) and Table 3 describes the properties of the employed tool, i.e., M35 grade high speed steel (FSW tool) which are considered during the framing of the established thermo mechanical process model.

Irregular Mesh
From various experimental observations [47][48][49], it is proven that, there exists a need for placing greater number of nodes of grid along the circumference of the FSW tool This arises because of the reality that, the extent and proportion of the FSW tool pin is very smaller, comparing it with that of the surface of workpiece. Figure 5 graphically portrays the position of the countless, infinite nodes of grid placed around the entire circumferential region of the pin geometries (namely cylindrical, square, triangle and taper cylindrical) of the employed FSW tools. Table 4 provides the complete description of the important criterions taken into account for the generation of the mesh in the established thermo mechanical modelling process.

Analytical Modelling Scheme
The analytical and numerical models pertinent to transmission of heat resulting from conduction, radiation and convection are established by employing the steady-state heat transmission, established on solids interface theory [50]. The thermo mechanical process model has been formulated in such a way that, when the temperature (peak) reaches the melting temperature of the workpiece, the heat input generating from the tool pin will get adjusted to zero automatically. In this experimental research, the temperature of melting of the workpiece (AZ80A Mg) is less, when comparing it with that of the experimentally generated heat by friction. So, on occasions, when the simulated peak temperature approaches value equal to the melting temperature of AZ80A Mg, the generated heat by friction will get adjusted to value of zero immediately. In better mathematical words, it can be understood as, Figure 6 graphically illustrates the differences in peak temperatures between the actual experimental values and the mathematical model simulation values for the four different types of the pin geometries (namely cylindrical, taper cylindrical, square and triangle) of the FSW tools.

Experimental Validation of T max
The peak temperature values of the formulated thermo mechanical process model are found to be consistent with that of the actual experimental results and exhibited relatively very small variation and completely unbiased. The percentage difference between the experimental and mathematical model simulation values obtained for the maximum temperature are 1.42%, 0.96%, 1.18% and 0.98% respectively for FSW tools with cylindrical, taper cylindrical, square and triangle pin geometries.

Comparison of Anticipated and Experimental T max
In this experimental research, anticipated peak temperature T max was validated against experimentally measured temperature values and found to coincide with one another.
Results of experimental runs carried out at the optimised process parameter conditions (i.e., tool rotational speed = 818 rpm; force applied on the FSW tool axially = 3.64 kN; rate of traversing of tool over workpiece = 1.48 mm/s) were taken as the inputs for generating line plots and contours [3,44]. The variations of temperature on the surface of the workpiece w.r.t the offset lines and bonding lines, when the tool approaches the workpiece centre part, for the various employed FSW tools with the different pin geometries are illustrated in the Fig. 7a, b. Figure 8 describes in detail, the generated temperature contour graphs on the top surfce of the work piece and on the bonding surfaces for tools with different pin geometries. Figure 9 illustrates the generated temperature distribution on the tool contact area w.r.t work piece surface and on the different tool pin geometries of the FSW tools. From these various temperature distribution graphs, it can be understood that, the peak value of the generated temperature occurs around the portions of the work piece, which are dominated by exhilarating action of rotating shoulder of tool.

Analysis of Temperature Distribution
It can be realized that, tool with cylindrical pin geometry has generated maximum value of peak temperature (i.e., 634 K) and the FSW tool with the triangular pin geometry has generated minimum value of peak temperature (i.e., 601 K). The FSW tool with the square pin geometry has generated a peak temperature of 608 K.
The ideal peak temperature value of 621 K was found to be generated by tool with taper cylindrical pin geometry, which is nearly 81-82% (348 °C) of the melting temperature (427 °C) of the work piece (i.e., AZ80A Mg alloy). Figure 10 describes the optical microstructrual images of joints fabricated employing tools with four different pin geometries under optimized process parameter conditions. From these microstructural images, it can be observed that, there exists some variations in size of the grains in the fabricated joints and this variations in grain size is due to the employment of the four different pin geometries, as the tool material and other operating conditions were kept completely constant for the entire set of experimental runs.

Examination of the Micro Structural Images
By inspecting these microstructures, it can be presumed that, the welded specimen obtained by employing tool with taper cylindrical pin geometry (with other process parameters being constant) is found to possess very exceptional sized grains, distributed consistently and homogenously, in comparison with remaining three welded joint's microstructures. This unique transformation of grain structures is a direct evident to the fact that, the ideal peak temperature (ie., 348 °C which is nearly 81-82% of the melting temperature of AZ80A Workpiece) has been generated due to the employment of the FSW tool with optimal pin geometry (i.e., taper cylindrical pin geometry). This ideal peak temperature generation have led to superplasticity, which has contributed for plastically deformed material flow in an orderly manner, coupled together with dynamic recyrstallization of the grain structures [18,23,38,47]. Further detailed examination of these microstructures also helps us to understand that, generation of the peak temperature in ideal volumes plays a crucial part in deciding grain size and their refinement. For example, the peak temperature generated during the employment of the FSW tool with Triangle Pin geometry is 601 K, which is nearly 75% of the melting temperature of our investigational workpiece (i.e., AZ80A Mg). But this generated peak temperature is not sufficient and ideal enough to recrystallize the grain structures into fine grains. At the same time, generation of high levels of peak temperature is also not preferred, as seen in the case of employment of FSW tools with cylindrical  pin geometry, which has resulted in the generation of 634 K peak temperature (i.e., nearly 85% of the melting temperature of our investigational workpiece). This peak temperature is beyond the ideal level and the size of the refined grains of these welded joints are found to be larger in size, in comparison with the size of the grains of the joints fabricated by tool with taper cylindrical pin geometry, where a ideal peak temperature of 621 K has been obtained. Thus, it can be understood that, the generation of ideal peak temperature plays a momentous part in determining grain size and this refinement of grains are found to have a lineal impact on improving the strength of the fabricated weldments. Bigger the grain size, smaller the mechanical strength of joints, which means that, generation of finely refined small sized grains in centre zone of stir, contributes directly for the increased strength of the FSW joints [51]

Interpretation of the SEM Images
The above implicated experimental result, that the employment of tool with taper cylindrical pin geometry have resulted in ideal peak temperature, which have contributed to the fabrication of good quality welded specimen possessing fine sized grains can be further justified by investigating the SEM images of these fabricated welded joint. Figure 11a illustrates us the SEM image of meeting portion of AZ80A Mg alloy and the region which are dominated by exhilarating action of rotating shoulder of tool. It can be seen that at this junction, the grains have started disintegrating due to the turbulent stirring action of the rotating FSW tool along with the suitable amount of stirring force exerted due to the adoption of ideal amount of axial force and in the zone of stir, the elements of the AZ80A Mg alloy have diffused and the grains seems to be disintegrated completely, due to the dynamic recrystallization process. Figure 11b reveals us the generation of peak temperature (in ideal volumes) in the thermo mechanically transformed region, due to which the precipitates were fragmented and the flow of the plasticized materials have been directed along the vertical direction, by the impact of the rotation taper cylindrical pin of the FSW tool. In the Fig. 11c, which is the centre of the zone of stir, we can observe the existence of the secondary particles of AZ80A Mg alloy, which have dissolved fully, due to the production of peak temperature

Justification from Tensile Test Fractography Images
Examining the manner in which the fracture of the joints fabricated using these tools with four different pin geometries have occurred, will helps us to gain more knowledge and to understand the role of peak temperature in increasing the mechanical strength and quality of joints. The fractographs of the fractured tensile specimen obtained during the employment of FSW tools with cylindrical, taper cylindrical, square and triangle pin geometries are illustrated in the Fig. 12a-d respectively. Various zones of the SEM fractographic image of the tensile specimen obtained by using FSW tool with triangle pin geometry, i.e., Fig. 12d, shows the presence of cleavages and improperly deformed grains. This is mainly due to the lack of fusion of the constituents of grain with one another, as the generated peak temperature (601 K) was not sufficient enough to fuse the grains constituents completely. Similarly, the SEM fractographic image of the tensile specimen obtained by using FSW tool with square pin geometry, i.e., Fig. 12c, is found to possess large sized inter granular cavity which probably deteriorates the mechanical strength of these joints. The formation of these large sized inter granular cavity in these joints is due to the lack of generation of sufficient amount of peak temperature, which could not fuse the grains together. At the same time, the SEM fractographic image of the tensile specimen obtained by using FSW tool with cylindrical pin geometry, i.e., Fig. 12a, reveals us the fact that, generation of surplus of amount of frictional heat resulting in large peak value temperatures (634 K) will be able to fuse the grains together, but it will also lead to the formation of voids, large crests and troughs, which will gradually reduce the mechanical strength of these joints.
And this ideal peak temperature plays a momentous part in improving the mechanical properties of joints, leading to high quality weldments. Further, we can observe that, this tensile specimen has undergone a cone and cup fracture mode. This mode of fracture takes place only when the joints have experienced uniform flow of plasticized material in their centre zone of nugget and uniform flow of plasticized material during FSW happens whenever the nugget zone is defect free [52][53][54]. Thus, it can be inferred that, the peak temperature generated (621 K, nearly 81-82% of the melting temperature of employed workpiece) in the time of employment of tool with taper cylindrical pin geometry is ideal enough to fabricate high quality AZ80A Mg weldments.

Conclusions
In FSW technique, the geometry of pin of employed tool plays a momentous part in influencing the plasticized material flow, temperature generation, grain refinement, mechanical properties of fabricated joints etc. For better and perfect understanding of the FSW process, especially w.r.t to the tool temperatures and flow of heat, there exist the need of employing both mathematically developed simulation models and real experimentation methods. Majority of the previously carried out experimental research works have concentrated their research towards the measurement of the temperature over distinct and limited regions of the workpiece surface, there exists a vital and unavoidable need for analysing and understanding the temperatures, flow of generated around the FSW tool pin profile, to derive a mathematical model to predict the flow of temperature for various FSW tool pin profiles, the role of the geometrical design of the various pin profiles in regulating the flow of generated frictional heat and to compare these model results with that of the actual experimental data. Based on these aspects, this experimental research focuses to investigate the reasons behind generation of varying temperature values during the employment of tools with different pin geometries, leading to variations in microstructural characterisation and properties of the fabricated joints. In this research, an thermo mechanical process model was formulated to estimate and determine the values of peak temperatures generated during the employment of tools with four distinct pin geometries (including cylindrical, taper cylindrical, square and triangle) for welding AZ80A Mg, to understand their indicative part in influencing the grain size, their mechanical strength and quality of the joints. The generated numerical values are compared with that of the actual experimental values and the following results were inferred: • A thermo mechanical process model was formulated successfully and the numerically simulated temperature distribution clearly illustrates the variation in temperature on the workpiece, tool pin contact area, shoulder area and tool pin region. • The percentage difference between the experimental and mathematical model simulation values obtained for the maximum temperature are 1.42%, 0.96%, 1.18% and 0.98% respectively for FSW tools with cylindrical, taper cylindrical, square and triangle pin geometries. • FSW tool with triangular pin geometry generated minimum value of peak temperature (601 K) and maximum peak temperature (634 K) was found to be generated by cylindrical pin. • Taper cylindrical pin generated 621 K peak temperature which is nearly 81-82% of the melting temperature of the material of investigation, i.e., AZ80A Mg and square pin generated a peak temperature of 608 K. • The joints obtained by employing tool with taper cylindrical pin geometry was found to possess very exceptional sized grains, distributed consistently and homogenously, in comparison with remaining three welded joint's microstructures. • The discrepancies of the anticipated values from that of the real experiential outcomes are within ± 1%, which reveals us that, the established mathematical model is very much fit to the actual experimental results. Moreover, the established quadratic regression model was found not to be over fitted and it is evident that, only less than 1-2 per cent of the total variations are not interpreted by this model. • Seven AZ80A Mg joints were obtained using the optimized input parameters of FSW technique. All the seven weldments were found to be absolutely defect free and the tensile strength of these seven joints were found to be in the range of 245 MPa to 249 Mpa, which exhibits that their exquisite compliance with the predicted values.