Transient Heat input Model for Friction Stir welding using non-circular Tool Pin

Frictional heat source in the contact surface of a rotating tool and a stationary workpiece is used to join metal pieces along the weldline in the friction stir welding process. Temperature profile developed during welding decides the post weld properties on the joined workpieces not only along the weld line but also in the nearby layers of heat affected zone. As the heat input depends on the contact surface geometry in the tool/matrix interface, tool shape has a higher influence on peak temperature developed during the process and on the other hand it influences the post weld properties also. In this paper, a simplified analytical heat input model has been derived and validated for noncircular pin profile by introducing a new multiplication factor in the circular pin profile heat input model. Transient thermal numerical models are developed for, triangular, square and pentagonal pin profiles using analytical heat input results to analyse the change in temperature profiles with respect to the change in tool pin geometry. Furthermore, a detailed analysis is made to understand the percentage contribution of tool pin on the total heat supply.


INTRODUCTION
Friction stir welding is a plasticised solid-state metal joining process, which initially adopted to join easy oxidising materials like aluminium and further expanded now to weld other materials as it results enhanced properties on the weld joint comparing with other metal joining processes [1]. In this metal joining process, pin in the rotating tool is plunged into the firmly clamped workpiece until the shoulder contacts the top surface of the joint line and allowed to rotate for a while before translating it through the abutting edges to get weld joint. Heat required to join the edges is obtained by the friction on the tool/matrix interface, which is assisted by the heat generated through plastic deformation of the material during the process [2]. Temperature distribution during this process at various points along the workpiece decides the post weld properties and necessitates thermal modelling to optimise various physical parameters during FSW process. In thermal modelling based on relative motion between toll and workpiece the addition of heat source increases which is devided as three stages namely, plunge, dwell and welding. During plunge stage, friction between tool pin and workpiece produces heat and it does not produces major plastic deformation on the parental metal as it affects only the nearby layers [3]. In addition to this, enormous amount of heat is developed at the tool shoulder/matrix interface in dwell stage, soften workpiece material. In the welding stage, softened material undergoes huge strain due to the rotation and forward motion of tool, which results additional heat source, as plastic deformation of material produces heat [4].
Measurement of temperature during welding using contact type measuring devices is difficult in the weldment due to the severe plastic deformation, which damages measuring probes. Several analytical models have been developed to investigate temperature distribution at different points, especially, in the weldment during the process. As the major heat source in FSW process is frictional heat in the interface of tool shoulder and workpiece, several models are developed under various contact conditions in the interface. Neglecting heat generated by the pin, analytical models are developed assuming workpiece material completely sticking with tool and tool completely sliding on the material [5] and partial sticking/sliding conditions [6]. Models are developed to calculate total heat generation through the input torque based on the experimental readings, by varying process parameters like tool rotation speed and contact pressure [7,8]. Peak temperature developed during welding is predicted [9] based on the torque input and corresponding temperature distribution at various points are predicted using numerical analysis [10] and optimised to enhance material properties of the workpiece. Heat generation due to the plastic deformation is obtained by analysing deformation rate and flow stress developed by the rotating tool. Thermomechanical coupled CFD model [11,12] reveals the flow pattern and strain rate at various points in the weldment through which heat generation from viscous dissipation is calculated [13].
Apart from heat sources, temperature profile during welding is highly depends on fraction of rate of dissipation of heat through tool, backing plate, clamping device and other boundary conditions which are exposed to the atmosphere. Thermal conductivity between the workpiece and backing plate is remodified by considering thermal contact conductance [14]. A three dimensional FEM analysis is carried out to identify the amount of heat channelled through tool and other clamping systems [15]. Most of the heat transfer models were developed considering steady state conditions. However, plunge and dwell stage heat transfer steadies cannot be limited on steady state alone and several transient thermal models were developed coupled with material flow analysis on these stages [16][17][18]. Transient heat transfer in the weldment during dwell period plasticise the material under the tool shoulder and inturn assists free movement of tool pin along the weld line which improves the tool life by reducing tool wear rate [19].
Shape and dimension of tool pin have higher influence over post weld properties of the weld joint. Although its percentage contribution is limited in the total heat generation comparing with shoulder, for thick plate welding, considerable heat is produced by the tool pin [20]. In this paper, an equation is developed to identify a multiplication factor based on the number of sides in the pin profile, which is applied on the analytical heat generation model of the vertical pin surface. Further, the percentage contribution of tool pin over total heat generation and transient temperature distribution in the material during welding are analysed for different pin profiles by varying its dimensions.

ANALYTICAL MODELLING
To obtain simplified analytical equation following assumptions are made, Heat transfer through backing plate and clamp is not considered and the entire surfaces of the workpiece except tool shoulder/workpiece interface are considered to be exposed to atmosphere.
As in dwell period major heat generation [20] is through friction, internal heat generation through plastic deformation is not taken into account.
As heat generation during plunging is comparatively lesser, it is neglected.

Figure 1. Tool pin shapes
For all tool pin geometry, there are three contacting surfaces. Two in horizontal direction (tool shoulder and tool pin tip) and one in vertical direction (vertical surface of tool pin) (ref fig.1) Total heat obtained by the horizontal surface is the addition of heat generated from shoulder and pin tip and it is given by [21], Q 2 can be calculated by replacing R shoulder by radius of the tool pin R pin in the above equation Heat generated for one pulse form the vertical contact surface is, Here, R pin = 3 a for Triangular pin profile R pin = 2 a for Square pin profile R pin = 0.8506a for Pentagonal pin profile R pin = a for Hexagonal pin profile.
For the present analysis, in order to compare the effects of different pin profiles, pin side length (a) is selected in such a way to obtain uniform R pin value for all the pin shapes.

TRANSIENT THERMAL MODELLING
Transient thermal model is developed in ANSYS workbench based on the heat input value obtained from the analytical solutions for the different pin profile whose number of sides are increased from three to five. In order to compare temperature change during dwell period cut-off time is given as 12.5 seconds for all the pin profiles as the temperature cannot be raised more than 90% of the melting point of the parental metal [20]. Time taken to reach maximum temperature was also analysed for triangular, square and pentagonel pin profiles. Circular shape of the tool shoulder delivers an uniform heat supply in X and Z directions which results similar temperature change on those two directions. Change in temperature observed only in Y direction. So the model is limited with two dimensional cross section. Aluminium alloy 2024 plate is taken as workpiece. Properties workpiece and tool material and other parameters are given in Table 1&2. Heat transfer coefficient on the surfaces of the workpiece exposed to atmosphere. (W m -2 K -1 )

Initial and Boundary condition:
Heat flux at the tool shoulder and workpiece interface is given by in the range R pin ≤ X ≤ R shoulder when time t > 0 Heat flux at the tool pin tip and workpiece interface is given by in the range 0 ≤ X ≤ R pin when time t > 0 Heat flux at the tool pin vertical surface and workpiece interface is given by in the range 0 ≤ Y ≤ H pin when time t > 0 Heat loss from the workpiece surface other than the tool/matrix contact surface which is exposed directly to atmosphere is given by here h x and T x values are selected uniform for all worlpiece surfaces exposed to surounding medium. An uniform initial temperature is assumed at all the nodes of the workpiece and tool. T(x,y) = T initial = 22 o C at any point when time t > 0

RESULT AND DISCUSSION
In order to compare the temperature distribution in the dwell period among different pin profiles, constant pin radius is modelled through the selection of opt pin side length for all pin geometries. Increase in temperature with respect to time during tool rotation in dwell period on welding Al2024 is observed for different pin profiles. For the validation of proposed heat input, total heat generated is calculated and compared with the analytical relationship developed by Gadakh et al [23], in which total heat generated by the different pin profiles are calculated by, Detailed comparison of heat generated by the different pin profiles through its vertical and horizontal surfaces are given in the table.3 From the obtained values (Table.3.), it is understood that heat generated by the horizontal surface of tip of the pin remains same for all pin profiles as it is influenced only by the pin radius and not by the shape of the pin and will be equal to the heat generated by the circular pin profile. But there are considerable differences between the heat generated by the vertical surface of different pin profiles.

Figure 2. Time taken to attain Peak temperature (450 C)
Obtained results show that heat generated by the pin with hexagonal shape is equal to the heat generated by the circular pin as the increase in number of sides more than five results a shape much similar to the circular. From the fig.2, obtained from ANSYS transient analysis, it is understood time to attain peak temperature is inversely proportional to the number of sides in the pin.
When the number of sides in the ool pin inceased, although pin tip geomentries are diffeent, its contact area with workpiece is circular during rotation. So, Irrespective of heat supply surfaces, in the analytical calculation of total heat supplied by the horizontal surface of the tool depends only on shoulder diameter (ref eqn 1) and it remains same for circular and noncircular pin profiles. Variation in heat input is observed only in the vertical contact surface (Pin side). This reveals the importance of a generalised expression to calculate the heat generation by vertical surface of noncircular pin profiles and it can be written as, Here multiplication factor, where N denotes the number of sides and Y value should be restricted as maximum of 3 ( fig.3). For hexagonal shape it attains maximum value of 3 and remains same for further increase in the number of sides as it leads to a shape closer to the shape of circle and the vertical frictional contact surface area is almost same. It reveals that heat input remains same for pin sides more than five and it will be equal to the circular shape.  For the given input rotational speed, variation on heat input with respect to Y value is given in fig. 4. When Y value increases intensity of heat supply by the pin increases. It results quick plasticisation of the material beneath tool shoulder in the stir zone. It results less opposing force for the linear movement of the tool along the weld joint. So weld velocity can be increased [24]. It is understood that increase in Y value results increase in welding speed which reduces the size of the heat affected zone in which failure happens in FSW joints, because of less existence of needle shaped precipitate. High intensity heat supply not only reduces heat affected zone but also reduces the temperature gradient on the nearby zone around the vertical tool probe [25] ( fig. 5). Reduction in temperature gradient reduces residual stress significantly. shows the percentage contribution of tool pin in the total heat generation during the process. From the result, it can be concluded that major heat generation happens in the shoulder/matrix interface. Although the tool pin has a limited contribution on total heat supply, it increases with increase in pin diameter. It is observed that maximum contribution of tool pin on total heat input is achieved for pentagonal shape. From fig. 7, it is understood that the peak temperature produced during welding is directly proportional to the number of sides on the pin profile as the heat generation increases with the increase in number of sides. Previous comparative studies done on the post weld microstructure and other properties of weldment [26] justify the obtained value of heat generation through this analytical model. Higher heat generation rate during welding using pentagonal pin profile tool results better refined microstructure and higher tensile strength on the stir zone of the weldment. Increase in the heat generation on the pin/matrix interface reduces yield strength of the nearby layer of parental metal on the weld line. As a result, tool life increases as it experiences less opposing force during its transverse motion along the weld line. Reduction in yield strength not only reduces the stress on the tool pin but also it reduces flow stress among the metal layers under the shoulder in the stir zone which increases the strain rate and eases the stir joining process.

CONCLUSIONS
In this study, a transient thermal model was developed with the help of analytical heat input model for various non-circular pin profiles such as triangle, square and pentagon to estimate the time required to attain peak temperature during dwell. Developed numerical model based on analytical heat input reveals that time required to achieve peak temperature reduces with increase in the number of sides from triangle to pentagon and it was found that hexagonal pin profile gives almost similar result to the circular pin profile.
Furthermore, a new multiplication factor has been proposed to predict the dwell time, size of the heataffected zone and location of the peak temperature under the tool shoulder for various non-circular pin profiles. Percentage contribution of tool pin on the total heat supply is compared and it is observed that pentagonal shaped pin has higher value than other geometries. The reliability of the proposed model had been compared with the experimental results as the predicted values are closer to the measured values.