3.2.3. Effect of Pin Length on Stress Field

Although slight adjustment of the length of the pin can increase the temperature of the weld root, it has little effect on the improvement of material fluidity near the weld center, as outlined in Section 3.2.2. However, the shear action of stirring on plasticized metal will change as the length of the pin increases, as shown in Figure 16. At the root of the weld, the shear stress near the center of the weld is the lowest, which indicates that the plastic metal flow in this area is the weakest. When the length of the pin is increased from 5.91 mm to 5.95 mm with 0.01 mm per step, the shear effect of stirring on the plastic metal at the root of the weld would be gradually strengthened. Therefore, the fluidity of the plastic metal at the root of the weld also increases, which results in the gradual improvement of the forming quality at the root of the weld. When the length of the pin was 5.95 mm, a weld without root defects could be obtained.

**Figure 16.** Distribution of shear stress at the root of the joint at different pin lengths (1000 rpm, 120 mm/min). (**a**) 5.91 mm; (**b**) 5.92 mm; (**c**) 5.93 mm; (**d**) 5.94 mm; (**e**) 5.95 mm.

It should be noted that there is a sharp transition of the shear stress near the bottom surface of the workpiece, as shown by the black dash line in Figure 16. The sharp transition of the shear stress illustrates that the material flow behavior in zones I and II (marked in Figure 16a) is different. In fact, this can be explained by the difference of the constraint condition and the driving force of the material in zones I and II. In zone I, the material is constrained by the bottom surface of the pin and the material in zone II. The material flow in zone I is driven by the rotation of the bottom

surface of the pin, and the pressure and shear stress are all higher in zone I according to Figure 8a,b. Meanwhile, in zone II, the material is constrained by the bottom surface of the workpiece and the material in zone I. The material flow in zone II is driven by the material flow in zone I, and the pressure and shear stress are lower than that in zone I according to Figure 8a,b, resulting in a slower velocity in zone II, which is consistent with the velocity distribution in Figure 6b. Therefore, non-penetration defects easily generate near the weld center in zone II due to the poorest fluidity and no material mixing in this area. With the increase of the pin length, the thickness of the zone II reduces, and it is close to 0 near the weld center when the pin length increases to 5.95 mm, so that the non-penetration defect is eliminated.

Figure 17 shows the distribution curve of shear stress at the half depth between the bottom surface of the pin and the bottom surface of the workpiece under different pin lengths. In Figure 17a, when the pin length increases from 5.8 to 5.95 mm with 0.05 mm per step (Figure 17a), the shear stress on the RS side near the weld center (−0.5 < y < 0) significantly increases, which makes the material mixed more fully in this area where the "S line" defect appears. A similar trend can be observed as the pin length increases from 5.9 to 5.95 mm with 0.01 mm per step, as shown in Figure 17b. As the length of the pin changes, it should be some relationship between the increasing shear stress (Figure 17b) and the morphotype of the "S line" shown in Figure 11a–c. That is to say, in Figure 17b, as the shear stress gradually increases with the increase of pin length, the width and the tilting angle of "S line" gradually reduces according to Figure 11a–c, which also indicates that the shear stress plays a dominant role in eliminating the "S line" defect.

**Figure 17.** Distribution curves of shear stress at the root of joint with different pin lengths (1000 rpm, 120 mm/min). (**a**) 0.05 mm per step from 5.8 to 5.95 mm; (**b**) 0.01 mm per step from 5.91 to 5.95 mm.

External cooling was applied to the bottom of the workpiece to reduce the bottom temperature of the weld and explore the plastic metal flow behavior at the bottom of the weld at different temperatures. In order to change the temperature of the plastic metal at the bottom of the weld, five groups of simulations were carried out to cool the weld floor. The temperature change curve of the bottom of the weld is given in Figure 18. At the welding parameters of 1000 rpm and 120 mm/min, the temperature at the bottom of the weld gradually decreased from 377 to 302 ◦C, and the plastic metal flow behavior at the bottom of the weld was observed. The flow behavior of plastic metal at the bottom of the weld is shown in Figure 19. When the temperature at the bottom of the weld changes, the fluidity of the plastic metal in the weld basically does not change. Near the center of the pin bottom, plastic metal has little flow. With the increase of the distance to the end face of the pin bottom, the flow of plastic metal gradually increases. RS and AS plastic metal flow in the opposite direction and finally meet at the RS near the weld center. At the bottom of the weld, plastic metal flows from RS to AS, and the plastic metal flow basically stops near the center of the weld. Based on the above flow behavior, the plastic metal at the bottom of the weld will eventually form the "S line" weak connection defect and lack penetration at the center of the bottom of the weld.

**Figure 18.** Weld bottom temperature curve.

**Figure 19.** *Cont.*

**Figure 19.** Flow behavior of plastic metal at different temperatures (**a**) No. 1; (**b**) No. 2; (**c**) No. 3; (**d**) No. 4; (**e**) No. 5.

The flow behavior at the bottom of the weld is due to the lack of shear stress on the plastic metal by agitation. The distribution of shear stress at the bottom of the weld is illustrated in Figure 20. When the temperature at the bottom of weld decreases gradually, the shear stress of the plastic metal at the bottom of weld seam increases gradually. In the position of the weld center, the shear stress is the smallest—that is, plastic metal at the bottom of the weld is the weakest. When the temperature at the bottom of the weld decreases, the viscosity of the plastic metal increases, and the critical driving force required for its flow increases. Therefore, when the temperature at the bottom of the weld decreases, although the shear effect of agitation on the plastic metal at the bottom is enhanced, the flow of the plastic metal is not improved.

**Figure 20.** *Cont.*

**Figure 20.** Distribution of shear stress at the root of the joint at different temperatures. (**a**) No. 1; (**b**) No. 2; (**c**) No. 3; (**d**) No. 4; (**e**) No. 5.
