A C Fig. 7 — Temperature contours for the following: A — TR; B — SQ; C — PEN; and D — HEX pin profile. Fig. 8 — Variation in peak temperature with the number of polygon sides. • No heat flows into the workpiece if the local temperature reaches the material melting temperature. Due to friction interface conditions, the frictional shear stress friction is considered. The shear stress estimates for a sliding condition is as contact = friction = p (where p = F/Area under shoulder). Analytical Modeling Analytical Heat Generation Equation for Triangular Pin Profile During the FSW process, due to complex geometries of the tool (Fig. 1), the estimation of heat generated at the contact surfaces is quite complex. In the analytical estimation, a simplified tool design with a flat shoulder surface, a vertical SQ prism probe side surface, and a flat probe tip surface is assumed. The simplified tool design for the TR pin is presented in Fig. 2, where Q1 is the heat generated under the tool shoulder, Q2 at the tool SQ probe side, and Q3 at the tool probe tip, hence the total heat generation, Qtotal = Q1 + Q2 + Q3. To derive the different quantities, the surface under examination is characterized by either being a vertical or horizontal surface. The expressions for each surface orientation are different but are based on the same equation for heat generation: dQ=ω⋅dM =ω⋅x ⋅dF =ω⋅x ⋅τcontact ⋅dA (1) Heat generation from shoulder surface is calculated by subtracting the heat generated due to probe tip (Q3) from the heat generated due to shoulder (QShoulder) where a = Rprobe • 3 is the side of the TR pin profile. Thus, heat generated due to the shoulder is given by Frigaard et al. (Refs. 20, 21) as 2 3 3 (2) Qshoulder = ⋅π⋅ω⋅τcontact ⋅R shoulder Therefore, Q1 is calculated as Qshoulder – Q3, i.e., Equations 2–5 = ⋅π⋅ω⋅τ ⋅ − ⋅π⋅ω⋅τ ⋅ 2 contact 3 1 (3) Q R a contact shoulder 2 9 3 3 3 WELDING RESEARCH 118-s WELDING JOURNAL / APRIL 2015, VOL. 94 B D
Welding Journal | April 2015
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