**1. Introduction**

Friction stir welding (FSW) has achieved great success in joining aluminum alloys since its invention. Due to the characteristics of a high joint quality, small welding deformation, green welding process and no pollution, FSW technology is often applied to the welding of aluminum, magnesium and other light alloy materials [1–3]. High-strength aluminum alloys are used in the welding of aerospace products. Because of its good strength and hardness, 2XXX aluminum alloy is used for the welding of rocket storage tanks and aircraft wings [4,5]. However, FSW is a complicated thermal-mechanical coupling process, and the forming quality is mainly affected by the tool shape, rotation speed, welding speed and other process parameters [6–8]. If it is not properly controlled, it is easy to change the physical quantities, such as the heat generation and plastic flow state of the weld materials, which will lead to welding defects [9]. The material flow has an important influence on the quality of the weld forming. Studying the material flow will help to understand the welding process and prevent welding defects.

In FSW, there is a close contact between the tool and the material to be welded, so there is severe friction between the tool and the workpiece. During the welding process, the intense friction between the tool and the workpiece generates a large amount of heat. This heat causes the temperature of the material to rise, and the material softens at high temperatures [10–12]. The softened material undergoes severe plastic flow under the drive of the tool. At the same time, the shear deformation of the material also generates a part of the heat [13]. Along with the plastic flow of the material at a high temperature, the heat transfer inside the material is convective and conductive. The severe plastic flow of the material under the drive of external force causes heat convection, and the temperature distribution also affects the plastic flow of the material [14,15].

Franke et al. [16] examines the intermittent flow of material and its relation to defect formation. In addition, advances have been made in a force-based defect detection model that links changes in process forces to the formation and size of defects. Gratecap et al. [17] placed a steel powder mark on the butt to study the material flow. The results show that the material in the weld zone extrudes around the retreating side (RS) of the tool pin as it moves from the leading side to the trailing side. Huang et al. [18] observed the vertical flow behavior of the material by observing the distribution of Cu foil fragments and Al-Cu intermetallic compounds. The downward and upward flows encounter each other at the advancing side (AS) in the material depositing process, changing the morphology of the weld nugget zone. Dialami et al. [19] used the fourth-order Runge-Kutta (Rk4) integration method to calculate the particle trajectory. The effect of the input process parameters and pin shape on the weld quality was studied by a particle tracking method.

Li et al. [20] added a 0.1 mm thick bronze foil to the 7075-T651 aluminum alloy welding interface. The distribution characteristics of the horizontal and vertical cross-section bronze foil were analyzed by X-ray. They measured that the shear force at the front of the tool was stronger than the shear at the back of the tool pin. The metal is mainly sheared from the advancing side in front of the tool to the retreating side. Then, under the squeezing force of the rotary tool, the plastic material is pushed back to the advancing side at a slow speed. As a result, a temporary cavity is formed on the advancing side. The plasticized material is extruded into a cavity and filled therein. Figure 1 shows a schematic of the flow of material around the tool. Shanavas and Dhas [21] discussed the development of fuzzy models for predicting the weld quality. The effects of welding parameters, such as the tool geometry, tool rotation speed, welding speed and tool inclination angle, on the welding quality are studied. De Filippis et al. [22] established a simulation model to monitor, control and optimize the friction stir welding process. The correlation between the process parameters and mechanical properties can be identified. In order to improve the welding performance, the parameters of the joint are controlled in real time through experiments. Cisko et al. [23] conducted a large number of experiments and calculations on the fatigue behavior of aluminum-lithium alloy (AA2099) friction stir welding (FSW). The effect of the friction stir welding process on the fatigue life was studied by using a microstructure sensitive fatigue model.

Zhang et al. [24] proposed a conceptual model describing weld formation to study the effect of the Alclad layer on material flow and defect formation. He found that the top Alclad assembled at the shoulder/workpiece interface, thereby weakening the material flow in the shoulder-driven zone and favoring the formation of a void defect at high traveling speeds. Zhu et al. [25] established a three-dimensional coupled finite element model of friction stir welding defects based on the Euler-Lagrange coupling method. The results show that smaller gaps will be generated at higher welding speeds.

**Figure 1.** Schematic of the material movement around the friction stir welding (FWS) tool.

Although some scholars have conducted some research on material flow [26–28], the numerical model is still in the initial stage, and there are still many problems to be studied. According to the author's knowledge, there is no report about the process from the plunging process to the material staying behind the weld. This paper understands the frictional heat generation of the tool and the material by establishing the heat input model. A finite element model was constructed to simulate the AA2A14-T6 friction stir welding process. The axial force and torque of the welding process were collected by electromagnetic coupling technology and compared with the simulation data. The results verified the correctness of the finite element model.

The contribution of this article is to establish the thermogenic physical model of the FSW process and to establish the finite element model of FSW. The material flow and temperature fields of the welding process are studied by a numerical simulation. The numerical simulation results are further verified by using the microstructure of the weld. Through the stratified analysis of the temperature of the weld zone, it was found that the advancing side and the retreating side above the material showed obvious temperature differences, and this phenomenon was also found in the test [29]. A material flow analysis was carried out on the inside of the stirring pin via particle tracking technology. It was found that a small part of the internal material of the pin was extruded to the bottom of the weld and that most of the materials moved upward with the pin. A material flow analysis was performed on the advancing side and the retreating side of the welded area, respectively. The material flow exhibits different flow conditions on the advancing and retreating sides. At the same time, a similar situation was found through the microstructure of the joint. The analysis of the flow trend of the microstructure confirmed the correctness of the finite element analysis. Since the material flow is closely related to the weld formation, this paper can predict or provide a reference for future welding experiments by analyzing the defects of the finite element model.

## **2. Modeling and Acquisition Methods**

#### *2.1. Friction Stir Welding Heat Input Model*

The heat input of friction stir welding makes the plastic flow of materials a complex process, which is accompanied by the coupling and interaction of the friction heat generation, metal plastic flow and structural transformation. Therefore, it is very difficult or even impossible to carry out a comprehensive analysis of all factors in the friction stir processing (FSP) [30]. Therefore, the heat input during the friction stir welding is studied.

It is difficult to establish the model within actual conditions, so the model studies the main factors of the heat production process and makes an ideal treatment for the less influential factors. Therefore, this model is an ideal model based on these assumptions. The following assumptions are made: (1) Ignoring latent heat of the phase change during the tissue structure transformation; (2) The thread

on the surface of the tool pin is not considered; (3) Ignoring the welding inclination to simplify the model; (4) It is assumed that the friction work is all converted into friction heat.

The tool pin and tool shoulder dimensions are shown in Figure 2. The main variables used in this article are shown in Table 1. Assuming that the tool shoulder forging force acts evenly on the shoulder area, the frictional force received on the *dA* area is:

$$df = \frac{\mu F}{\pi r\_1^2} r dr d\theta \,, \tag{1}$$

where *F* is the axial force, *r*<sup>1</sup> is the radius of the outer circumference of the tool, and μ is the coefficient of friction. The torque and power generated on the *dA* area are:

$$dM = \frac{\mu F}{\pi r\_1^2} r^2 dr d\theta,\tag{2}$$

*dp*, (4)

$$dp = dM\omega = \frac{\mu F}{\pi r\_1^2} r^2 dr d\theta \omega,\tag{3}$$

where ω is the rotational angular speed. For the integration of both sides of Equation (3), the total heat production power of the shoulder zone is:

> <sup>2</sup><sup>π</sup> 0

*P*<sup>1</sup> = *<sup>r</sup>*<sup>1</sup> *r*2

**Figure 2.** Schematic diagram of the pin and tool shoulder size.

**Table 1.** Variables used in this article.


Therefore, the surface heat flux density of the tool shoulder area is:

$$q\_1 = \frac{P\_1}{\pi (r\_1^2 - r\_2^2)},\tag{5}$$

The friction force on the pin side *dl* is:

$$df\_2 = 2\pi\tau(r\_3 + h\tan\gamma)dh,\tag{6}$$

$$
\pi = \frac{\sigma\_s}{\sqrt{3}} \,\prime \tag{7}
$$

where *r*<sup>3</sup> is the radius of the end of the tool pin, γ is the taper angle of the tool pin, τ is the ultimate shear strength of the material, and σ<sup>s</sup> is the yield stress of the material. The torque and power of *dl* are:

$$dM\_2 = \frac{2\pi\sigma\_s (r\_3 + l\tan\chi)^2 dl}{\sqrt{3}},\tag{8}$$

$$dp\_2 = \frac{2\pi\sigma\_8\omega(r\_3 + l\tan\gamma)^2 dl}{\sqrt{3}},\tag{9}$$

By integrating Equation (9), the heat production power on the side of the pin is obtained.

$$P\_2 = \int\_0^L dp = \frac{4\pi^2 n \sigma\_s L}{3\sqrt{3}} (3r\_3^2 + 3r\_3 L \tan\chi + L^2 \tan^2\chi),\tag{10}$$

where *L* is the length of the tool pin. The heat generation at the bottom surface of the pin is similar to that at the tool shoulder. The heat generation is as follows:

$$P\_3 = \int\_0^{r\_3} \frac{\mu F}{\pi r\_1^2} 2\pi r dr \times \omega r = \frac{4\mu F \pi r r\_3^3}{3r\_1^2},\tag{11}$$

The body heat flux density of the tool pin is:

$$
\eta\_2 = \frac{P\_2 + P\_3}{V},
\tag{12}
$$

$$V = \frac{\pi L(r\_2^2 + r\_2 r\_3 + r\_3^2)}{3},\tag{13}$$
