Materials Processing
Simulation and Experimental Study on Temperature and Flow Field in Friction Stir Welding of TC4 Titanium Alloy Process
2020 Volume 61 Issue 12 Pages 2378-2385
Details
2020 Volume 61 Issue 12 Pages 2378-2385
In this study, numerical simulation method was used to investigate the temperature field and the flow field of FSW for TC4 titanium alloy. According to the contact condition between the tool surface and the weld piece, a scientific heat source calculation method was built and its reliability has been verified by experiments. The temperature distribution characteristics of welding zone were investigated. The simulation results shows that the welding materials around the friction head flows like funnel-shape in a whole, similar to the shape of the friction head. The flow condition of welding materials is asymmetric with respect to the weld line, and the flow velocity increases with the greater distance from the center of the weld. As the depth of the weld increases, the flow capacity of the material gradually becomes weaker.
Friction Stir Welding (FSW) is a solid phase welding technique invented by the British Welding Institute (TWI) in 1991.1) There was no melting during the welding process compared to the conventional welding method. Therefore, defects such as pores and cracks could be avoided to some extent.2) FSW is mostly used for the connection of metals such as copper, titanium, steel and their alloys and dissimilar metals. During the welding process, the stirring pin was inserted into the plate with a certain rotating speed, and the friction-heat generation between the friction head and the plate made the material in the weld area plasticized. As the tool moves, the plastic material in the weld was squeezed and connected together.
Titanium alloy was widely used in aviation, aerospace and medical field. The research on FSW of titanium alloys were mainly focuses on the optimization of welding parameters, analysis of weld microstructure and mechanical properties. In recent years, people began to pay more attention to the numerical simulation of FSW of titanium alloy. For example, McClure et al.3) proposed the Rosenthal model that considered the work-piece as an infinite object, and treated the problem as a common heat conduction problem. And it used a moving point heat source and a line heat source to describe the heat input of the friction stir welding. Gould et al.4) also proposed a similar analytical model and verified it with experimental results. The model only considered that the heat generated by the shoulder, and controlled the temperature by adjusting the friction coefficient and the pressure. They also found significant dynamic recrystallization and grain growth in the weld nugget zone, indicated that the material in the zone didn’t melt. Frigaard et al.5) used the finite element method to study the FSW process of TC4 alloy. In the simulation process, only the frictional heat generation of the shoulder was considered, and the heat generation of the stirring pin was neglected. The study results indicated that there was a relatively large temperature gradient in the joints. Schmidt et al.6,7) proposed an analytical model for the heat generation of FSW, which described the contact conditions as viscous, sliding or partially sliding partially viscous. The correctness of the model was confirmed by the FSW test on 2024 aluminum alloy. It was found that the heat production was not directly proportional to the force. Therefore, they believed that the viscous contact must be taken into consideration, which was important for further research on the FSW. Zhang et al.8,9) have researched that the heat in the welding process mainly came from the friction between the tool and the workpiece. The faster the welding speed and the weaker the stirring effect of the welding tool. This research also pointed out that the temperature field was basically symmetrical about the center of the weld, and the rotation of the shoulder could accelerate the flowing of the surface material and the deformation of the material.
In this study, we explored the temperature field and material flow characteristics of TC4 titanium alloy sheet during friction stir welding by means of experiments and numerical simulations, and proposed a formula for generating heat of stirring pin, and gave a detailed calculation method. Using the results of numerical simulation, the mechanism of material flow was studied. The defect area is proposed, and the formation mechanism of the defect area is explained by studying the flow characteristics of the material.
Compared to traditional experimental methods, numerical simulation has great advantages. The flow of material and the change in temperature during the FSW process can be observed very intuitively. In this research, it established the heat source model of FSW of TC4 plate, and set reasonable welding parameters to study the heat generation, temperature distribution and material flow mechanism. The software of Marc and Fluent were selected as finite element simulation software in this study.
The heat generation in the FSW process is a complex process that a coupling process of friction heat generation and phase change latent heat. It is very difficult to analyze the influence of various influencing factors in together. So this study established a heat generation model that ignored the latent heat of phase change during the welding process. Thus the heat in the welding process is considered that the heat was only generated by friction between the tool and workpiece.10–12)
Table 1 and Table 2 are the thermal conductivity and specific heat capacity of TC4 titanium alloy respectively. The software will automatically use these data during the simulation. The measurement environment of these data is consistent with the experimental environment.
The geometric model used to study the FSW of TC4 plate is showing in Fig. 1. The workpiece are TC4 plates with 2 mm thickness. The tool rotating speed is 800 r/min and welding speed is 30 mm/min. The axial pressure of friction head is 12 MPa. The selection of all these parameters was based on the preliminary experimental studies of research group.13) It defined that the plate surface where the workpiece was in contact with the tool as a heat source. So as showing in Fig. 2, the heat source contained three parts: tool shoulder surface (SS), pin side surface (PSS) and pin tip surface (PTS). In the actual welding process, the tool shoulder has a certain penetration amount, so a part of the shoulder side in contact with the workpiece, but the heat contribution in this contact area was small. So in this study, the heat generated in the shoulder side area was ignored. The tool sizes were presented in Table 3.
FSW model illustration.
Schematic diagram of the friction tool.
According to the heat source formula proposed by Hamilton et al.,14) the heat generation could be calculated by the following:
| \begin{equation} \mathrm{Q}_{\text{total}} = \delta \mathrm{Q}_{\text{sticking}} + (1 - \delta) \mathrm{Q}_{\text{sliding}} \end{equation} | (1) |
As showing in Fig. 2, according to study of the FSW of 2024 aluminum alloy by Schmidt,6,7) it believed that the viscous contact must be considered, so the basic condition of the shoulder and the workpiece was the partial sliding part. According to the study by Zhang et al.,14) the heat generated at the shoulder surface (QSS) can be expressed as:
| \begin{equation} \mathrm{Q}_{\text{SS}} = \omega [\delta_{\text{SS}} (\tau_{b} - \mu \mathrm{P}) + \mu \mathrm{P}] \int_{\mathrm{R}_{2}}^{\mathrm{R}_{1}} 2\pi r^{2}\text{dr} \end{equation} | (2) |
| \begin{align} \mathrm{q}_{\text{SS}} & = \frac{\mathrm{Q}_{\text{SS}}}{\pi\mathrm{R}_{1}{}^{2} - \pi\mathrm{R}_{2}{}^{2}}\\ & = \frac{2[\omega\delta_{\text{SS}}\tau_{b} + \omega(1 - \Delta_{\text{SS}})\mu\mathrm{P}]*(\mathrm{R}_{1}{}^{3} - \mathrm{R}_{2}{}^{3})}{3(\mathrm{R}_{1}{}^{2} - \mathrm{R}_{2}{}^{2})} \end{align} | (3) |
The heat generated at the pin side surface (QPSS) is expressed as
| \begin{align} \mathrm{Q}_{\text{PSS}} & = 2\pi\delta_{\text{PSS}}\omega\tau_{b}\int_{0}^{\text{H}}(\mathrm{R}_{3} + \mathrm{h}\tan\alpha)^{2}{\text{dh}} \\ &\quad + \frac{2\pi\mu \mathrm{P}_{1}\omega * (1 - \delta_{\text{PSS}})}{\cos\alpha}\int_{0}^{\text{H}}(\mathrm{R}_{3} + \mathrm{h}\tan\alpha)^{2}\text{dh}\\ & = \frac{2\omega\pi(\mathrm{R}_{2}{}^{3} - \mathrm{R}_{3}{}^{3})}{3\sin\alpha}[\delta_{\text{PSS}}\tau_{b}\cos\alpha + (1 - \delta_{\text{PSS}})\mu\mathrm{P}_{1}] \end{align} | (4) |
The surface heat flux density of the pin side surface (qPSS) is:
| \begin{align} \mathrm{q}_{\text{PSS}} & = \cfrac{\mathrm{Q}_{\text{PSS}}}{\displaystyle\int_{0}^{\text{H}} \cfrac{2\pi(\mathrm{R}_{3} + \mathrm{h}\tan\alpha)}{\cos\alpha}{\text{dh}}}\\ & = \frac{2\omega(\mathrm{R}_{2}{}^{2} + \mathrm{R}_{3}{}^{2} + \mathrm{R}_{2}\mathrm{R}_{3})}{3(\mathrm{R}_{2} + \mathrm{R}_{3})}\\ &\quad\times [\delta_{\text{PSS}}(\tau_{b}\cos\alpha - \mu\mathrm{P}_{1}) + \mu\mathrm{P}_{1}] \end{align} | (5) |
The heat generated at the pin bottom surface (PBS) is expressed as:
| \begin{align} \mathrm{Q}_{\text{PBS}} & = \delta_{\text{PBS}}\omega\int_{0}^{\mathrm{R}_{3}}(\tau_{b} - \mu\mathrm{P}) * 2\pi\mathrm{r}^{2}{\text{dr}} + \mu\mathrm{P}\omega\int_{0}^{\mathrm{R}_{3}}2\pi\mathrm{r}^{2}\text{dr}\\ & = \frac{2\pi\omega\mathrm{R}_{3}{}^{3}}{3}[\delta_{\text{PBS}}\tau_{b} + \mu\mathrm{P}(1 - \delta_{\text{PBS}})] \end{align} | (6) |
| \begin{equation} \mathrm{q}_{\text{PBS}} = \frac{2\omega\mathrm{R}_{3}}{3}[\delta_{\text{PBS}}(\tau_{b} - \mu\mathrm{P}) + \mu\mathrm{P}] \end{equation} | (7) |
It also should be considered that the heat exchange was between the workpiece and the external environment. The way of the heat exchanged between the surface of workpiece and the external environment was mainly convective heat transfer mode. The convection heat transfer formula is:
| \begin{equation} k\frac{\partial\mathrm{T}}{\partial\mathrm{z}}\bigg|_{\text{top}} = \mathrm{h}_{\text{t}}(\mathrm{T} - \mathrm{T}_{0}) \end{equation} | (8) |
The boundary conditions at the bottom of the workpiece are formulated as:
| \begin{equation} \mathrm{k}\frac{\partial\mathrm{T}}{\partial\mathrm{z}}\bigg|_{\text{bottom}} = \mathrm{h}_{\text{b}}(\mathrm{T} - \mathrm{T}_{0}) \end{equation} | (9) |
The thermal energy conservation equation is given as:16)
| \begin{equation} \rho\mathrm{C}_{\text{p}}\frac{\partial(\mathrm{u}_{\text{i}}\mathrm{T})}{\partial\mathrm{x}_{\text{i}}} = -\rho\mathrm{C}_{\text{p}}\mu_{\text{weld}}\frac{\partial\mathrm{T}}{\partial\mathrm{x}_{\text{i}}} + \frac{\partial}{\partial\mathrm{x}_{\text{i}}}\left(\mathrm{k}\frac{\partial\mathrm{T}}{\partial\mathrm{x}_{\text{i}}}\right) + \mathrm{Q}_{\text{v}} \end{equation} | (10) |
| \begin{equation} \mathrm{Q}_{\text{v}} = \frac{\mathrm{Q}_{\text{PSS}} + \mathrm{Q}_{\text{PBS}}}{\mathrm{V}_{\text{pin}}} \end{equation} | (11) |
The fluidity of the material is also an important parameter in this study. The governing continuity equations for the material flow can be expressed as:17)
| \begin{equation} \frac{\partial\mathrm{u}_{\text{i}}}{\partial\mathrm{x}_{\text{i}}} = 0 \end{equation} | (12) |
| \begin{equation} \rho\frac{\partial\mathrm{u}_{\text{i}}\partial\mathrm{u}_{\text{j}}}{\partial\mathrm{x}_{\text{i}}} = -\frac{\partial\mathrm{P}}{\partial \mathrm{x}_{\text{i}}} + \frac{\partial}{\partial\mathrm{x}_{\text{i}}}\left(\eta\frac{\partial\mathrm{u}_{\text{j}}}{\partial\mathrm{x}_{\text{i}}} + \eta\frac{\partial\mathrm{u}_{\text{i}}}{\partial\mathrm{x}_{\text{j}}}\right) - \rho\mu_{\text{weld}}\frac{\partial\mathrm{u}_{\text{j}}}{\partial\mathrm{x}_{\text{i}}} \end{equation} | (13) |
The non-Newtonian viscosity η can be expressed as:
| \begin{equation} \eta = \frac{\sigma(\mathrm{T},\bar{\varepsilon})}{3\bar{\varepsilon}} \end{equation} | (14) |
According to a study by Sheppard T et al.,18,19) the flow stress can be expressed as:
| \begin{align} \eta& = \frac{1}{3\bar{\varepsilon}\alpha}\ln\left\{\left[\cfrac{\bar{\varepsilon}\exp\biggl(\cfrac{\mathrm{Q}}{\text{RT}}\biggr)}{\text{A}}\right]^{-1/\mathrm{n}} {}\right.\\ &\quad \left. {} + \left[1 + \left(\cfrac{\bar{\varepsilon}\exp\biggl(\cfrac{\mathrm{Q}}{\text{RT}}\biggr)}{\text{A}}\right)^{2/\mathrm{n}}\right]^{1/2}\right\} \end{align} | (15) |
At different stages of welding, the overall distribution of the temperature field is the same, and the peak temperature will change. The main purpose of this study is to qualitatively analyze the distribution characteristics of the temperature field. Therefore, the temperature field at the stable stage of welding is selected for research. Figure 3 is the temperature field distribution diagram under three process parameters. Except for the difference in peak temperature, the temperature distribution under different process parameters is roughly the same. Since the thermal conductivity of TC4 is relatively poor, the temperature gradient around the friction head is difference. Behind the pin, the workpiece material is affected by heat conduction and heat input. So the high temperature area is relatively large in this area, and the temperature is relatively lower due to the influence of the thermal conductivity. After the tool passed, the temperature decreased slowly and the temperature gradient is relatively decreased too. The material in front of the tool was only affected by the friction, the temperature rises rapidly in a short time, and the temperature gradient is also relatively larger. The two sides of the tool are transitional zones, showing a distinct asymmetric temperature profile between the AS and RS. This is because the material flow direction of AS is opposite to the direction of tool rotation. These results were also in well agree with the literature.22,23)
Distribution of the simulated temperature: (a) 800 r/min, 30 mm/min, (b) 600 r/min, 30 mm/min, (c) 400 r/min, 30 mm/min.
In order to explore the temperature distribution of the welding zone in the welding process and verify the effectiveness of the model, a series of characteristic points were selected to test the temperature change in the actual FSW trials and simulation model. As shown in Fig. 4, a series of points are taken along line a and line b on the lower surface of the workpiece, line a is 1 mm from the center of the pin, line b is 6 mm from the center of the pin. In the FSW experiment, the temperature for these points was measured by thermocouple thermometers. The temperature change test results are shown in Fig. 5. From this picture we can see that the actual temperature on the retreating side is slightly higher than the temperature of the simulation experiment. The cause of this difference may be that the material on the retreating side is heated by extrusion, which is ignored in the simulation experiment. The experimental results are well agreements with the numerical results, which indicate that this model could be used to predict the temperature profiles in real FSW process. As can be seen from the Fig. 6, the surface temperature of the workpiece is characterized by rising firstly and then falling from the forward side to the backward side. Clearly, the peak temperature of line a is not at the center of the weld, but at a distance of about 4 mm from the weld line. This is because of the farther away from the center of shoulder, the greater the line speed of the shoulder, so the more heat generated by the friction. Thus the heat generated at the edge of the shoulder is larger than that of the center of weld. But the heat lost is also larger at the edge of tool, so the highest temperature point isn’t at the edge line of weld but between the center weld line and the edge line. The heat input at the midpoint of line b is relatively more, the peak temperature of line b is higher than the peak temperature of line a, and the position of the peak temperature is closer to the soldering surface.
Schematic diagram of the lower surface feature points of the workpiece.
Comparison between calculated and experimental temperature of the measured points: (a) ai points, (b) bi points.
Temperature of characteristic point of workpiece bottom surface.
In order to fully understand the temperature change in the workpiece during the welding process, some of the feature points are taken for analysis. As shown in Fig. 7(a), some points on the upper surface with a distance of 4 mm from the center of the weld were selected to investigate the temperature characteristic. The interval between each point was 5 mm. It can be seen from the Fig. 7(b) that the temperature curves at different points are roughly with the same trend, and the rate of temperature rise is greater than that of temperature decrease. This is due to the thermal conductivity of the TC4 is relatively poor, so the decrease of temperature is relatively slow and the temperature curve is relatively smooth.
Schematic diagram of simulation result of temperature: (a) characteristic point distribution, (b) profile of temperature over time of characteristic point.
Figure 8 is a simulation model for the flow field of FSW of TC4. In this model, the flowable area (FCR) represents the welding area. The width of the FCR is set to be 1 mm wider than the shoulder and the depth of the FCR is 0.5 mm deeper than the weld. The groove region (GR) of workpiece means not welded. So there is almost no material flow in this area, thus the GR has the function of transferring heat and maintaining the plasticized material.
Model of the flow characteristics of FSW.
In this experiment, it assumed that heat generation and material flow were stable in the welding. And the elastic deformation of the material was neglected, and the plasticized material was regarded as an incompressible viscoplastic material. It was also considered that only plastic deformation and fluid flow occurred during the welding process.
The materials in the FCR and GR regions are the same during the welding process and are considered viscoplastic fluids in this study, the difference being the difference in viscosity. For FCR, viscosity is primarily dependent on temperature and strain rate. The GR material did not flow and was set to a very large value in the experiment.
During the FSW process, the material flows plastically under the influence of the tool, and the flow velocity of the material is affected by the contact conditions of the tool and the workpiece. Figure 9 is the simulation result of the FSW of TC4 plate with a given tool. As can be seen from Fig. 9(a), the entire material stream is funnel-shaped, similar in shape to the surface in contact with the agitating head and the workpiece. As can be seen from Fig. 9(b), the materials near the tool surface have a higher flow velocity, and the velocity near the outer circle of tool is greater than that of inside. The velocity value generally shows the variation tendency. As the depth increases and the distance from the axis of the stirring head decreases, the flow velocity of the material gradually decreases. This is because the linear velocity of the tool surface increases as the diameter increases, and the flow of materials is driven by the tool, so the velocity of the nodes of materials also exhibits the same characteristics. So it could be concluded that the friction tool is the main source of material momentum in the FSW process.
Material flow velocity in the weld zone (a) overall distribution of velocity vectors (b) material flow velocity of weld cross section.
Figure 10 is the two-dimensional material flow behavior of the weld zone under three process parameters. In the Fig. 10(a), it indicates that the material in the front of the tool flows to the RS side of the tool as the tool rotating, and that finally deposits behind the tool. This process consists of three parts: (1) the material is softened by the heat conduction before it comes into contact with the rotating tool; (2) the softened material sticks to the surface of the tool and flows with the rotation of the tool before final deposition; (3) with the tool continuous move forward, the material that behind the tool is split, and form a moon-like cavity. When the flowing material passes through the region A, it may be accumulated and overflow in the region A, which is the main reason for the formation of the welding flash during the friction stir welding process.8) As shown in Fig. 10(c), the fluidity of the region B is poor, and defects such as grooves and voids were generated usually in this region. This region is called a defect-prone area (DPR). Thus the cause of defects such as grooves and voids was insufficient fluidity of the plastic materials. As can be seen from Fig. 10(a) and Fig. 10(b), as the rotational speed increases, the fluidity of the material in the B region becomes better. Figure 11 is the joint morphology under three process parameters. It can be seen from Fig. 11(c) that there is a tunnel defect on the AS aside and some flash on the RS aside, which is well agree with the simulate result that the groove defect usually generates in DPR region. At a rotation speed of 800 rpm, the results of numerical simulation show that the flow field lines in area A are very dense. It can be seen from Fig. 11(a) that a large number of flashes appeared; At a rotation speed of 600 rpm, a welded joint with good surface formation was obtained. So it means that this simulation model for FSW of TC4 alloy is valid.
Material flow behavior: (a) 800 r/min, 30 mm/min, (b) 600 r/min, 30 mm/min, (c) 400 r/min, 30 mm/min.
Surface morphology of welding sample: (a) 800 r/min, 30 mm/min, (b) 600 r/min, 30 mm/min, (c) 400 r/min, 30 mm/min.
A detailed calculation model for the heat generation of the FSW of TC4 was developed. Combined with numerical simulation and welding experiment results, the temperature field distribution and flow characteristics during the friction stir welding process were analyzed, and the following conclusions could be drawn:
