⋅ ⋅ ⎛⎝ ⎜ ⋅ ⋅ ⎛⎝ ⎜ Thermal Modeling The thermal-pseudo-mechanical model (TPM) for different pin profiles such as TR, SQ, PEN, and HEX is developed using the heat transfer module in Comsol 4.4. The model geometry is symmetric around the weld; hence, only one aluminum plate is modeled. The aluminum Alloy AA 2014-T6 plate dimensions are 320 × 80 × 5 mm, surrounded by two infinite domains in the x direction. The shoulder and pin diameters were kept constant for all tools at 12 and 6 mm. For different geometries, the tool rotational speed at 1000 rev/min and weld speed at 600 mm/min were kept constant. The values of axial force were 9.09 kN for TR, 8.97 kN for SQ, 6.98 kN for PEN, and 6 kN for the HEX pin profile (Ref. 17). The temperature distribution is obtained by solving the energy equation, expressed here as the conductive-convective, steady-state equation (Ref. 5). where is density, Cp the specific heat, u the velocity vector, k thermal conductivity, the temperature, and Q is the internal heat generation rate. Boundary Conditions and Initial Condition The model geometry is symmetric around the weld. Hence, only one aluminum plate is sufficient to model. Figure 6A shows the resulting model geometry. The temperature dependent yield stress is shown in Fig. 6B. The heat flux boundary condition for the workpiece at the tool shoulder/ workpiece interface is Qshoulder. Similarly, the heat flux boundary condition at the tool pin/workpiece interface and tool shoulder/workpiece interface is Q2 and Q3, respectively. Qshoulder, Q2, and Q3 can be calculated by respective equations for different pin profiles. The inbuilt material properties for the AA 2014-T6 aluminum alloy were considered, and for AISI H13 tool steel, are as follows: thermal conductivity – 36 W/(m·K), density – 7833 kg/m3, and heat capacity at constant pressure – 460 J/(kg·K). Mesh size for the model is as follows: maximum element size – 8.4 mm, minimum element size – 0.084, and maximum element growth rate – 1.3. The element type and amount used in this study are as follows: prism elements – 142, hexahedral elements – 1352, triangular elements – 142, quadrilateral elements – 1698, and edge elements – 374. Convection Boundary Conditions The upper and lower surfaces of the aluminum plates lose heat due to natural convection and surface to ambient radiation. The hup and hdown are heat transfer coefficients for natural convection. In the present study, it is considered as 12.25 and 6.25 W/m2K, respectively. Figure 7A–D shows temperature isotherms for different pin profiles. The peak temperature among different pin profile is monotonous. The highest peak temperature is for the SQ pin profile (789 K) and lowest for HEX pin profile (713 K), whereas the trend is increases from TR (733 K) to SQ (789 K), then decreasing from PEN pin profile (724 K) to HEX pin profile (713 K). Furthermore, the peak temperature in case of conical tool geometry from TR-HEX pin profiles was also monotonous (Ref. 17). It was reported that the HEX pin profile has the highest peak temperature and lowest for SQ pin profile. The peak temperature trend is decreases from HEX-TR-PEN-SQ pin profile. Results and Discussion The effective energy per weld length (QEff) (Ref. 22) is defined as the energy per weld length multiplied by the transfer efficiency (, ratio of the pin length HProbe to the workpiece thickness, t) and given as follows: h t For validation of the proposed model, the empirical relationship developed by Hamilton et al. (Ref. 22) between the temperature ratio and effective energy level is considered. The empirical formula is given by max 1 56 10 4 0 54 (25) It is agreed that the above expression will change for different work material and one has to find this expression by trial experiments. = ⋅ ω⋅μ⋅ υ⋅ ⋅ + π ⎞⎠ ⎟ = ⋅ ω⋅μ⋅ υ⋅ ⋅ + π ⎞⎠ ⎟ Q F R R a H or Q F R R R H Energy/length shoulder shoulder probe Energy/length shoulder shoulder probe probe 2 3 9 2 2 3 9 2 (22) 2 3 2 2 3 2 ρ ⋅∇θ=∇⋅ ∇θ ⋅ Cpu (k )+Q (23) Q = ⋅QEnergy/Length =β⋅QEnergy/Length Eff (24) T = × − × + T . Q . s Eff WELDING RESEARCH Table 1 — Summary of Different Pin Profiles Showing QEnergy/Length, and Tmax Pin Profile Q(Energy/length) Q(Energy/length), Tmax/Ts Tmax (K) Tmax(K) Tmax (K) J/mm Eff. (Analytical) (Numerical) (Ref. 17) TR 173.67 163.25 0.565 515 733 614 SQ 178.40 167.70 0.566 516 789 619 PEN 144.29 135.63 0.561 511 724 623 HEX 128.73 121.01 0.559 509 713 637 122-s WELDING JOURNAL / APRIL 2015, VOL. 94 .
Welding Journal | April 2015
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