**1. Introduction**

Friction stir welding (FSW) is a novel solid phase bonding technique developed by The Welding Institute (TWI) in 1991 [1]. During welding, heat input generated by the friction heat between the tool and the workpiece, and the plastic deformation of the welded metal changes the welded metal into a thermoplastic state. The plastic metal generates plastic flow and forms a closed joint under the combined action of the pin and the shoulder [2]. FSW is of high quality with a low welding heat input, no filler metal, no smoke, and no weld splash during the welding process, and it is of a green, environmentally friendly nature. FSW technology is often used for welding magnesium alloy, aluminum alloy, and other light alloy materials [3–5]. More importantly, in recent years, FSW technology shows great advantage in joining dissimilar alloys such as Al–Mg–Si/Al–Zn–Mg alloy [6], Al/NiTi alloy [7], and Al/Steel [8]. However, FSW involves the changes of temperature, adhesive shear force, and metal

flow behavior, which is a complex thermal–fluid coupled process. The root of the welded joint often forms a weak connection or kissing bond of "S" line and non-penetration defects due to insufficient fluidity of plastic materials and heat input.

The weak-connection defect at the root of the weld has a great influence on the mechanical properties of the FSW welded joint. Weak connection defects will reduce the plasticity of the joint. When there is a weak connection defect at the root of the weld, the fracture mode in the tensile test will be brittle. For well-formed welded joints, the fracture mode is plastic [9–11]. Jolu [12–14] investigated the effect of root flow on the tensile and fatigue behavior. They found that the root flaw acts as a crack initiation site during the tensile test, which reduces the yield strength of the welded joint by 40% and the ultimate tensile strength by 20%. In the fatigue life test, they found that the tilting angle of the weak connection can influence the fatigue life of the welded joint. When the weak-connection defect is strongly tilted with respect to the loading direction, the fatigue life of the joint is higher. Zhou [15] studied the effect of weak connection defects on the fatigue strength of the FSW joint. They found that when the strain rate is 0.1/s, the fatigue life of intact weld seams is 21 to 43 times longer than that of the weld seams with weak connection defects at the root, which is owing to the fact that fatigue cracks can generate from the weak connection line, resulting in a great reduction of the fatigue life of the weld. Kadlec [16] found that the size of the root flaw significantly affects the fatigue life of the welded joint. When the size of root flaw is 315 um, it does not affect the fatigue strength of the connection. However, the 670 um size weak connection defect reduces the fatigue life of the joint to 91% of the base metal.

Due to the influence of root defects on the mechanical properties of FSW joints, many scholars began to pay attention to the formation mechanism of root defects and the relationship between the root defects and process parameters. Sato [10,17] and Okamura [18] studied the weak connection of the FSW welded joint of aluminum alloy. They found that "S line" defects originated from oxide film on the butt surface of the workpiece. During the FSW process, broken oxide particles form a black flow trace originated from the retreating side and extending to the advancing side. "S" shape weak connection lines distribute continuously in the welding direction, forming a weak bonding surface. Chen [19] used the numerical simulation method to quantitatively research the bonding behavior of the FSW joint. The numerical simulation results show that the weak connection defect is caused by the insufficient fluidity of the plastic material and heat input at the root of the welding seam, which leads to insufficient bonding pressure at the butt surface of the weld. Luo [20] studied material flow in the FSW process based on a computational fluid dynamic model; they found that the ratio of rotation speed to welding speed has an effect on the material flow behavior around the stirring pin, which is related to the defect formation in the FSW welded joint. Moussawi [21] studied the friction stir welding of DH36 and EH46 steels at different welding speeds and rotation speeds. They found that the high-speed movement of the stirring pin will result in insufficient fluidity of the weld material and weak connection defect at the root of the welded joint. Hou [22] and Zhou [23] found that the root flaws occur under high welding speed and low rotation speed owing to the insufficient heat input and material flow.

To eliminate the root flaw of the FSW welded joints, some scholars adopted the improved FSW method such as electricity-assisted friction stir welding (EAFSW) [24–26], bobbin tool friction stir welding (BTFSW) [27–29], and ultrasonic-assisted friction stir welding (UAFSW) [30,31], although the complex design of the stirring tool or the additional equipment induced by these methods increases the cost of the FSW process. In traditional FSW, some scholars believe that the root defects are caused by the improper selection of the pin length. Since the length of the pin has an important influence on the welding heat input, it also determines the forging behavior and extrusion pressure of the tool on the plastic material in the welding process [32]. However, if the pin is too long, its length will exceed the thickness of the base metal, which makes the backing plate adhere to the base material. If the pin is too short, a non-penetration defect will appear at the bottom surface of the workpiece [33]. Mandache [34] investigated the effect of pin length on the formation of defects at the root of the welding

seam. They found that with the increase of the pin length, the size of the non-penetration defect decreases gradually, but the size of the defect of the weak connection fluctuates in a wavy manner.

Weak connection and non-penetration defects at the root of the weld have seriously affected the quality of the weld, but the existing studies have not revealed the formation mechanism of defects at the root of the weld from the flow mechanism, and there is no in-depth study on the mechanism of eliminating defects at the root with the length of tool pin. In this paper, the metal flow behavior at the root of the weld and the formation mechanism of weak connection defects were studied by the numerical simulation method, the influence of different tool pin lengths on the plastic metal flow behavior at the root of the weld was investigated, and the optimized suitable length of the pin with a non-defects welded joint was identified.
