as shown by Rosenthal's 3D equation, the weld pool becomes more elongated as Q and V are both increased. As shown in Figure 2.22, the pool shape in GTAW of a Ni‐base alloy IN718 does become more elongated when Q and V are both doubled [38]. In fact, the weld pool becomes teardrop‐shaped at higher Q and V. Figure 2.23 shows the end of a teardrop‐shaped weld pool in GTAW of 309 stainless steel, which was revealed by Kou and Le by quenching the weld pool during welding [39]. Although Rosenthal's equation can correctly predict that the weld pool becomes more elongated at higher Q and V, it cannot calculate a teardrop‐shaped weld pool because it neglects, among other things, heat of fusion and the presence of the liquid phase. A very sharp end of the weld pool like that in Figure 2.22 or 2.23 is likely caused by undercooling at high travel speed (i.e. high cooling rate).
Figure 2.22 Weld pool shapes in GTAW of IN718 sheets.
Source: Hunziker, Dye, and Reed [38]. © Elsevier.
Figure 2.23 Sharp pool end in GTAW of 309 stainless steel revealed by ice quenching during welding.
Source: Kou and Le [39]. © TMS.
The calculated results of Rosenthal's equation in Figures 2.20 and 2.21 show that the cooling rate is higher at a lower Q/V ratio. The thermal cycle at the centerline (y = 0 mm) of the fusion zone is steeper (i.e. higher cooling rate) in Figure 2.21, where Q/V = 806 J/mm, than in Figure 2.20, where Q/V = 1333 J/mm. Lee et al. [40] measured the cooling rate in GTAW of 2024 aluminum by sticking a thermocouple into the weld pool. They showed that decreasing Q/V increased the cooling rate (the slope). Kihara et al. [41] showed that the cooling rate increased with decreasing Q/V and preheating. Liu et al. [42] showed that the cooling rate in electroslag welding (ESW), which is known to have a very high Q/V, is much smaller than that in arc welding. Thus, the prediction of a higher cooling rate at a lower Q/V based on Rosenthal's equation is consistent with experimental results.
Kihara et al. [41] showed that the cooling rate increases with the thickness of the workpiece. This is because a thicker workpiece acts as a better heat sink to cool the weld down. Inagaki and Sekiguchi [43] showed that, under the same heat input and plate thickness, the cooling time is shorter for fillet welding (Figure 1.6d) than for bead‐on‐plate welding because of the greater heat sink effect in the former.
2.4 Computer Simulation
Many computer models have been developed to study 2D heat flow [44–49] and 3D heat flow [24, 50–61] during welding. Kou and Le [24] developed a 3D (x, y, z) finite‐difference computer model to study heat flow and solidification in welding. All Rosenthal's assumptions were dropped. Figure 2.24 shows the calculated results of Kou and Le [24] for the GTAW of 3.2‐mm‐thick sheets of 6061 aluminum alloy. The agreement with observed fusion boundaries and thermal cycles is good.
Figure 2.24 Computer simulation of GTAW of 3.2‐mm‐thick 6061 Al, 110 A, 10 V, and 4.23 mm/s: (a) fusion boundaries and isotherms; (b) thermal cycles.
Source: Kou and Le [24]. © TMS.
Figure 2.25 shows the results of computer simulation of Kou and Le [24] on the effect of the power density distribution of the heat source on the weld shape. Under the same heat input and welding speed, weld penetration decreases with decreasing power density of the heat source. In the computer simulation, the power density distribution at the workpiece surface is approximated by the following Gaussian distribution:
(2.12)
where q is the power density, Q the rate of heat transfer from the heat source to the workpiece, r is the radial distance at the workpiece surface from the centerline of the heat source, and a is the effective radius of the heat source. As shown previously in Figure 2.13, the measured power density distribution is close to a Gaussian distribution.
Figure 2.25 Effect of power density distribution on weld shape in GTAW of 3.2‐mm 6061 aluminum with 880 W and 4.23 mm/s.
Source: Kou and Le [24]. © TMS.
2.5 Weld Thermal Simulator
2.5.1 The Equipment
The thermal cycles experienced by the workpiece during welding can be duplicated in small specimens using a weld thermal simulator called Gleeble. These simulators evolved from an original device developed by Nippes and Savage in 1949 [62]. Figure 2.26 shows a specimen being resistance heated by the electric current passing through the specimen and the water‐cooled jaws holding it [63]. A thermocouple spot welded to the middle of the specimen surface is connected to a feedback control system that controls the amount of electric current passing through the specimen such that a specific thermal cycle can be duplicated. A heating rate as high as 10 000 °C/s can be achieved.
Figure 2.26 The thermal cycle at any location in a weld can be duplicated in the specimen with the help of a thermocouple and the thermal simulator.
Source: Courtesy of Dynamic Systems Inc.
2.5.2 Applications
There are many applications for weld thermal simulators. For instance, a weld thermal simulator
