The present work depicts the development of a three dimensio

The present work depicts the development of a three-dimensional heat transfer analysis of FSW process following a novel methodology to analytically estimate the rate of heat generation for tools with polygonal pins shapes. The area of contact between the flat faces of polygonal pins and the plasticized material is estimated based on the principles of orthogonal machining [22]. A three-dimensional steady state heat transfer model of FSW process is developed using finite purchase Eosin Y method to compute the temperature fields in the workpiece and the tool pin. The computed temperature distribution of the workpiece material surrounding the tool is used to analytically estimate the torque and traverse force experienced by the tool. The computed values of thermal cycle, torque and traverse force are validated with the corresponding experimentally measured results for FSW of AA2014-T6. The estimated values of the pin traverse force are used to compute the stresses on polygonal pin profiles based on the principles of solid mechanics.
Experimental study 300 mm (length) × 100 mm (width) × 5 mm (thickness) aluminum alloy (AA2014-T6) plates are welded by friction stir welding in square butt joint configuration using EN40 tools with constant shoulder diameter of 12 mm and pin length of 4.7 mm. The rotational and linear speeds, the axial pressure and the tool tilt angle are kept constant for all the welds, which are 1000 rpm, 7.73 mm/s, 90 MPa and 2°, respectively. Four different tool pins with triangular, square, pentagon and hexagon profiles are used. Since the pins are tapered along the length, the side lengths of each pin profile at the root and at the tip are different (Table 1). The circumcircle diameters of all the polygonal pins are 6 mm and 3.6 mm at the root and at the tip, respectively. Table 2 depicts the compositions of the workpiece and the tool materials [23] and [24]. Table 3 provides the thermophysical properties of the workpiece material [25]. The density, specific heat and thermal conductivity of the tool material are considered as 7850 kg/m3, 485.34 J/(kg·K)and 34.73 W/(m·K), respectively [25]. The transient thermal cycles are measured using K-type thermocouples during the actual FSW experiments with a transverse distance of 4 mm from the original weld joint interface and at a depth of 2 mm from the top surface. The torque and the traverse force are also measured during the actual FSW process.
Theoretical formulation A steady state three-dimensional heat conduction analysis of the FSW process is carried out with the governing differential equationwhere ρ, k, C and U1 refer to the density, thermal conductivity, specific heat, and the constant welding speed, respectively; and T is the temperature variable. The term accounts for the rate of internal heat generation per unit volume. The rate of the frictional heat generation per unit area () at the tool–workpiece interface is applied as a surface flux and estimated as [26,27]where is the fraction of heat transferred to workpiece; ηm depicts the fraction of mechanical work due to sticking friction converted to heat; PN is the axial pressure; τy is the temperature-dependent shear yield stress of deformed material; r is the radial distance from tool axis; is the orientation of the point from the welding direction; is the angular speed; and, δ and refer to the local variations in fractional sliding and the coefficient of friction, respectively. A symmetric analysis is undertaken considering the plane of symmetry along the original weld joint interface. The rate of heat generation along the pin – workpiece interface is applied as a volumetric heat input by multiplying by where A and V refer respectively to the surface area and volume of the i-th discrete element adjacent to the tool pin surface [26,27]. A temperature-dependent convective heat transfer coefficient as is applied along the bottom surface, where hb equals to 0.0007 W/(m2·K1.25) and T0 is the ambient temperature [28]. The mechanical heating due to the viscous dissipation of the deformed material around the pin is neglected as the velocity gradient in the shear layer could not be estimated in the conduction heat transfer model.