Temperature Distribution And Mechanical Properties of FSW Medium Thickness 2219 Aluminum Alloy

Friction stir welding (FSW) is a solid-state jointing technology, which has the advantages of high joint strength, low residual stress aXnd small deformation after welding. During the process of FSW, the welding temperature has an important effect on the quality of the weldment. Therefore, the heat generation model of FSW of medium thickness 2219 aluminum alloy is established based on the friction heat generation at the interface between the tool and the workpiece and the plastic deformation heat generation of the weldment material near the tool. The heat transfer model is set under the premise of considering heat conduction, thermal convection, and thermal radiation. Using JMatPro technology, the temperature-related material parameters of 2219 aluminum alloy are calculated based on the material composition, and the heat generation model is imported into the ABAQUS simulation software based on the DFLUX subroutine, and the establishment of the FSW thermodynamic model is realized. The effectiveness of the model is verified by FSW experiments. The thermodynamic model takes into account both heat generation (friction heat generation and plastic deformation heat generation) and heat transfer (heat conduction, thermal convection and thermal radiation), so it has a high prediction accuracy. Based on the FSW thermodynamic model, the influence of welding parameters on temperature distribution is explored, subsequently the influence of welding temperature on mechanical properties of welded joint are also studied. The research can provide guidance for predicting and characterizing the temperature distribution and the improvement of mechanical performance of FSW.


Introduction
To promote promote the leapfrog sustainable development of space technology and promote the study of major scientific issues such as the origin and evolution of life, manned moon landing and deep space exploration have become the responsibility of all countries to promote sustainable development.
Manned moon landing and deep-space exploration have been included in the medium and long-term development plans of various countries, and the heavy launch vehicle is the basic vehicle. A certain heavy-lift launch vehicle storage tank has a diameter of 10 meters and a wall thickness of 18 mm. It is the main load-bearing structure of the rocket and has extremely high requirements for manufacturing quality and reliability. Friction stir welding (FSW) has become the main joining process for tank assembly due to its advantages such as pollution-free, smoke-free, no radiation, high welding efficiency, small product deformation after welding, and excellent weld mechanical properties [1].
FSW is a new type of solid-state jointing technology invented by the British Welding Research Institute in 1991 [2], which can realize flat seams, cylindrical circular seams, and spatial curved seams, and can complete butt joints, lap joints, T-joints, double Face welding and other welding methods, but to ensure that the connection coefficient is not less than 0.7, it is still a challenge for FSW to weld 2219 aluminum alloy with a thickness of 18mm. The welding heat input is large, the welding high temperature time is long and the upper and lower temperature difference is large, the strengthening phase redissolution and the microstructure and properties of the weld are different in the thickness direction, which makes it difficult to obtain a high connection strength. It can be seen that the temperature distribution in the FSW process has a great influence on the welding quality [3]. In order to improve the connection strength of the weld, it is urgent to study the temperature distribution in the welding process.
At present, the research on FSW temperature field has mainly included experimental method, simulation method and analytical method. In the FSW process, it is difficult to directly obtain the temperature distribution over the weldment through experimental methods during the welding process due to the rotation of the tool, the shielding of the shoulder, the flow of the weldment material, and the severe plastic deformation. Using the finite element simulation method to study the temperature field has become an important means of analyzing the FSW process, but it cannot reveal the heat generation mechanism of the welding process. The analytical method can not only quickly obtain the temperature distribution of the weldment, but also reveal the heat generation mechanism of the FSW process.
Therefore, the analytical method is used in this paper to study the FSW temperature field and further explore the influence of the temperature distribution on the mechanical properties of the FSW process.
Relevant experts and scholars have conducted a lot of research on the modeling of FSW temperature using analytical methods. The heat source model of the FSW process was first described by the similar to Rosenthal analytical method of a uniformly moving point heat source or a linear heat source [4][5].
McClure et al. [4] used Rosenthal analysis method in 1998 to conduct a preliminary analysis of heat transfer in the FSW process. Since the weldment is assumed to be the heat conduction problem of a semiinfinite object, the accuracy of the simulation results is not high, but the proposal of this method opens up a new way for the study of the FSW temperature field. Later, Song and Kovacevic [6] also established the FSW heat source model based on the Rosenthal analytical method, but ignored the heat generation by plastic deformation. With the in-depth study of the analytical FSW heat source model, Chang et al. [7] established a heat source model considering the frictional heat generation of the tool shoulder, the tool pin, and the weldment, simulated the temperature field of the 4mm thick 6061-T6 aluminum alloy FSW, and studied the effect of welding speed on the microhardness and tensile strength of welded joints.
Frigaard et al. [8] established a heat source model based on the frictional heat generation of torque, used MATLAB code to simulate the temperature distribution of 6mm thick AA6082-T6 and AA7108-T79 weldments and analyzed the microhardness of the weldment material according to the prediction model, but the heat source model ignored the heat generated by plastic deformation. Kiral et al. [9] used the same torque heat source model as Frigaard et al. and used ANSYS and HyperXtrude software to simulate the temperature field of the 3.1mm thick 6061-T6 aluminum alloy FSW, and investigated the effect of different rotational speed, welding speed, and dwell time on the peak temperature of the weldments.
Schmidt et al. [10] considered the different contact conditions between the tool and the weldment, the concave angle of the shoulder and the cone angle of the tool pin, and modified the heat source model.
Gadakh [11], Yaduwanshi [12], Ghetiya [13], Liu W M [14], Bonifaz [15], Liu X Q [16] based on Schmidt's heat source model, separately studied the effects of rotational speed and welding speed, axial pressure, cone angle of the tool pin, backing plate type and welding inclination angle on the temperature distribution of thin plates. Among them, Ghetiya's research showed that the tensile strength and microhardness of joints are affected by temperature.
Analytical FSW heat source models have been studied in great depths, but some FSW heat source models have only considered the frictional heat generation of the tool, while ignoring the heat generated by the plastic deformation of the weldment material during the welding process, which leads to errors in the prediction of the temperature field. Moreover, research studies have been basically carried out around low-strength thin plates, but there are few studies on high-strength medium plates. Compared with lowstrength thin plates, the temperature and mechanical properties of high-strength medium thickness plates are more uneven in the FSW process [17], and the welding quality is difficult to guarantee. Therefore, there is an urgent need to establish an FSW heat source model that considers friction heat generation and plastic deformation heat generation, and explores the temperature distribution of the 2219 aluminum alloy plates of medium thickness, so as to provide a deeper understanding of the welding process performance and weld quality.

FSW thermodynamic model
The FSW process generates heat through friction, softens the welding material, and mixes the material through the stirring action of the tool pin. The main mechanism of the FSW process is the contact interactions between the tool6 pin and the shoulder and the weldment material. The shoulder is the main source of heat generated by friction. Another function of the shoulder is to keep the material flowing around the tool. The tool pin is located below the shoulder, and its main function is to mix the sheet materials to be welded. In fact, in the FSW process of the plate material, heat is generated by not only the friction between the tool and the sheet material, but also the plastic deformation in the stirring zone.
In the FSW process, the heat is generated by various sources and also by various types of complex heat transfer processes: namely the heat conduction, thermal convection and thermal radiation. The FSW process is a complex thermodynamic and heat transfer process.

Heat production model
The tool moves in the processing direction while rotating at a high speed. Frictional heat is generated between the tool and the welded plates due to the existence of frictional resistance. The heat during welding comes from the frictional heat between the tool and the welded plate, including the friction heat Q 1 between the shoulder and the surface of the welded plate, the friction heat Q 2 between the side of the tool pin and the welded plate, and the friction heat Q 3 between the bottom surface of the tool pin and the welded plate. The welded plate near the tool will produce plastic deformation under the action of the tool, and these plastic deformations will also generate heat Q t .
The friction heat Q 1 between the shoulder and the surface of the welded plate : Where  is the friction coefficient, p is the positive pressure,  is the rotation speed of the tool, 1 R is the shoulder radius, 2 R is the large diameter of the tool pin, 3 R is the small diameter of the tool pin, 1 dM is the micro-element torque of the shoulder, and df is the microelement friction.
The frictional heat Q 2 between the side of the tool pin and the welded plate: Where H is the length of the tool pin,  2 is the cone angle of the tool pin , and 2 dM is the micro-element torque on the side of the tool pin.
The friction heat Q 3 between the bottom surface of the tool pin and the welded plate : dM is the micro-element torque of the bottom surface of the tool pin. Plastic deformation heat Q t: Where p  is the conversion coefficient of plastic deformation energy into thermal energy,  is the equivalent stress, and p  is the equivalent strain rate.
Therefore, the total heat production Q total during the FSW process should equal the sum of the friction heat Q 1 , Q 2 , Q 3 and the plastic deformation heat Q t .

Heat transfer model
The FSW process is very complicated, and the temperature of the weldment material changes all the time, so the three-dimensional transient heat transfer problem is analyzed. Assuming that the heat conduction of the material is isotropic, in the Cartesian coordinate system, the transient temperature field in the deformed body satisfies the differential equation: Where  is the material density; c is the specific heat capacity of the material; t is the time;  is the thermal conductivity of the material; Q  is the heat source density inside the object.
The accuracy of the temperature field in the FSW process is related to heat input on one hand, and heat output on the other hand. When the tool rotates at a high speed and is pressed into the welded plate frictional heat is generated due to the friction between the tool and the welded plate. As the tool presses down to a certain position on the welded plate, tool starts to move in the welding direction. There is a great temperature gradient between the tool and welded plate, so that the heat is transferred from the high temperature area to the low temperature area. The main transfer methods are heat conduction, thermal convection, and thermal radiation.
(1) Heat conduction The temperature difference within an object or system is a necessary condition for heat conduction.
The rate of heat conduction is determined by the distribution of the temperature field in the object. Heat conduction follows Fourier's law, and its basic form is: Where q is the heat flux density,  is the thermal conductivity of the material, and x T   is the temperature gradient in the direction of heat conduction.
In the FSW process, there is heat conduction between the tool and the welded plate, the inside of the welded plate, and between the welded plate and the fixture and the backing plate as follows.
①The heat conduction between the tool and the welded plate In FSW process, a lot of heat is generated due to the frictional resistance between the tool and the welded plate. The total heat generated will have a certain distribution ratio between the tool and the welded plate, and the distribution ratio can be different, depending on the model.
②The heat conduction inside the welded plate Heat will first be generated from the area where the tool directly acts on the welded plate.
Subsequently, heat will be transferred from the high temperature area in the welded plate to the low temperature area because of the temperature difference between this area and the surrounding welded plate. The rate of heat transfer depends on the thermal conductivity of the welded plate.
③The heat conduction between welded plate and backing plate When the thermal boundary conditions are considered, the thermal conductivity of the contact area between the welded plate and the backing plate, that is, the bottom surface of the welded plate, is set to 100W/(m 2 ·K) [18].
(2) Thermal convection Usually the Newtonian cooling formula is used to describe the thermal convection: Where q is the heat flux density; h is the coefficient of heat convection, and T  is the temperature difference between solid and fluid.
In the FSW process, the coefficient of heat convection on the upper surface and the four sides of the weldment is set as 30W/(m 2 ·K) [18].
(3) Thermal radiation Thermal radiation refers to the heat exchange process in which an object absorbs electromagnetic energy emitted by other objects and converts it into heat. Thermal radiation does not require a heat transfer medium. The radiant heat flux can be calculated using the empirical correction formula of Stephen-Polzman's law.
Where Q is the heat flux, T is the absolute temperature,  is the emissivity, F is the surface area, and b  is the thermal radiation constant.

Material parameters
XRF-1800 X-ray fluorescence spectrometer is used to determine the material composition of 2219 aluminum alloy. The material composition is shown in Table 1. Use JMatPro software to import material composition calculation to obtain material parameters that change with temperature, as shown in Fig. 1.
Where σ is the flow stress; A is the plastic strain; B is the strain rate; C is the reference plastic strain rate; t is the temperature of the weldment; t m is the melting temperature of the weldment material; t r is the room temperature. A, B, C, m and n are material parameters, where A is the yield strength, B is the hardening modulus, C is the strain rate sensitivity coefficient, n is the hardening coefficient, and m is the thermal softening coefficient.
Parameters of Johnson-Cook constitutive of 2219 aluminum alloy are shown in Table 2 [19].

Coefficient of friction
When the tool pin is in contact with the weldment interface, formulas (1), (3), (5), (8) fully describe the heat generated by the FSW process, and the use of a rationality of the friction coefficient is to ensure that the heat generation model is a correct foundation. In the FSW process of aluminum alloy, the friction coefficient decreases with the increase of welding temperature. Therefore, it is necessary to adopt temperature-dependent adaptive adjustment of the friction coefficient (as shown in Table 3) to better express the heat generation model. In the numerical calculation, it is realized by adjusting the value of μ in each time step dt, so that the welding temperature will have a steady state, instead of increasing the temperature as the welding progresses.

Implementation of thermodynamic model
Based on the DFLUX subroutine, the heat generation model is imported in the ABAQUS simulation software, and the FSW thermodynamic model is completed by combining the heat transfer model, the material parameters of the 2219 aluminum alloy and the friction coefficient. When the speed is 400rpm and the welding speed is 100mm/min, the solution of the final temperature field is shown in Fig. 2.

Experimental verification of FSW thermodynamic model
The welding temperature in the FSW process is used to experimentally verify the validity of the established thermodynamic model for FSW of 2219 aluminum alloy.

FSW experimental conditions
A gantry type FSW machine tool is used to carry out the FSW experiment, as shown in Fig. 3.
The FSW temperature field test system based on K-type thermocouple is used to detect the welding temperature field. The temperature measurement range is 0-1000℃, the measurement error is 0.75%T, and the sampling frequency is 10Hz. The welding material is 2219 aluminum alloy plate of 300mm*75mm*18mm. The diameter of the shoulder of the tool is 32mm, the diameter of the large end of the tool pin is 15mm, the diameter of the small end is 7mm, and the length of the tool pin is 17.8mm, as shown in Fig. 4.

Model verification
To verify the effectiveness of the simulation model, characteristic points are selected on the 2219 aluminum alloy sheet for temperature curve comparison. Fig. 6 shows a schematic diagram of the characteristic points of the thermocouple embedded in the FSW temperature measurement experiment. The characteristic points are 15mm, 18mm, 21mm from the center of the weldment and 6mm from the surface of the weldment.   The comparison results of the simulation output and the experimentally measured welding temperature are shown in Fig. 7, 8, and 9. The characteristic temperature point temperature output by the FSW thermodynamic model based on the analytical method is close to the experimentally measured temperature. Table 4 shows that the maximum relative error of peak temperature is 2%, and the average relative error of peak temperature is 1.1%, which verifies the validity of the established 2219 aluminum alloy FSW thermodynamic model.

Results and discussion
In the FSW process, the welding speed and the rotational speed of the tool are two important process parameters. The selection of different process parameters affects the temperature distribution of the weldment, subsequently the distribution of the temperature field has a direct impact on the mechanical properties of the welded joint. Because of the existence of the tool in the FSW process, the temperature of each position of the weld cannot be obtained, the required temperature is obtained through the FSW thermodynamic model as discussed herein.

Welding temperature
At the center of the joint line and 6mm away from the upper surface of the weldment, model computations have been performed to capture the effect of different welding speeds on the temperature when rotational speed is 400rpm, and the effect of different rotational speeds on the temperature when the welding speed is 100mm/min, as shown in Fig. 10 and Fig. 11.  When the rotational speed is 400rpm and the welding speeds are 60, 80, 100, 120 and 140mm/min, the peak welding value temperature is 503.5, 501.2, 498.9, 496.4 and 494.1℃, respectively, as shown in Table 5. As shown in Fig. 10, while the welding speed increases the welding temperature gradually decreases. This is because of the fact that as the welding speed increases, the frictional heat generation time shortens, the unit heat flux density becomes smaller, and the welding temperature decreases.  When the welding speed is 100mm/min and the rotational speeds are 300, 350, 400, 450 and 500rpm respectively, the welding value temperature is 477.9, 489.8, 498.9, 506.6 and 511.9℃, as shown in Table 6. As shown in Fig. 11, the welding temperature gradually increases as the rotational speed of the welding tool increases. The physical reason could be understood as follows: with the increase of the rotational speeds, the value of  increases, the heat generation of Q 1 , Q 2 , and Q 3 in formulas (1), (3), (5) increases, so the welding temperature rises.

Mechanical properties of joints
In the FSW process, because the temperature field is not uniformly distributed, the welded joint is subjected to different temperatures, resulting in differences in microhardness. To facilitate the study of the mechanical properties of the welded joint, the heat-affected zone (HAZ), the thermomechanically affected zone (TMAZ), the nugget zone (NZ) and the [20] are evaluated. The grainlevel microstructure of each zone is shown in Fig. 13. As shown in Fig. 12 with the "0" point being the center of the joint line, where NZ is located, the microhardness of the FSW joint of 2219 aluminum alloy with 18 mm thickness is roughly "U" shape. The mean microhardness of NZ zone is 285HB, slightly higher than the mean microhardness (281HB, 284HB) of the two sides of NZ. This is because in the vertical weld direction, the welding temperature gradually decreases from the joint line center to both sides, that is, the temperature of the NZ is higher than that of the TMAZ and the HAZ, and the grain structure has undergone dynamic recrystallization, forming fine equiaxed grains (as shown in Fig. 13(a)), which may increases the microhardness. However, as heat input in the TMAZ and HAZ is lower, the crystal grains grow, the microhardness is then slightly lower than that in the NZ. As can be seen in Fig. 11, the welding temperature of FSW increases with the rotational speed, but the microhardness of the NZ microhardness is 295 HB when the rotational speed is 400 rpm (when the welding temperature is 498.9℃). This microhardness value reaches 77% of the microhardness of the matrix metal (383 HB). test [21]. The tensile strength of the welded joint of 2219 aluminum alloy is only 72.4% of the tensile strength of the base material. This is mainly due to the high strength of 2219 aluminum alloy, the large axial force required for welding, the high heat input obtained, and the uneven distribution of the welding temperature of medium plate, which leads to large differences in the internal structure and properties of the joints. These effects are evident in the "S" lines of oxide accumulation in the NZ, as shown in Fig. 16. As the grains of the NZ grow, the oxides in the "S" line hinder the migration of grain boundaries and produces stress concentration, which makes the tensile strength of the joint. The macroscopic fracture morphology of the joint is shown in Fig. 17(a). The fracture positions of the joints are all located in the NZ. The scanning electron microscope of the fracture surface of the joint is shown in Fig. 17 aluminum alloy, the fracture position is located at the junction of NZ and TMAZ [22]. The possible reason is that the internal temperature of thick 2219 aluminum alloy is not evenly distributed along the thickness direction during FSW process, which leads to the uneven distribution of the strengthening phase Al 2 Cu, therefore the overall tensile strength of the joint is not high. can be characterized as follows: the tensile strength of the crown is the highest, followed by the midplane and the root. When the rotational speed is 400rpm (the welding temperature is 498.9℃ at this time), the microhardness of the NZ is 295HB, which reaches 77% of the microhardness of the matrix metal. Similarly, when the rotational speed is 400rpm, the tensile strength of the crown weldment material reaches the maximum value of 315MPa, which is 72.4% of the matrix metal's tensile strength, and the elongation rate is 3.3%. The fracture form of the joint is observed to be ductile fracture, and Al 2 Cu is a strengthening phase particle in the dimple. The unevenness distribution of temperature, the unevenness distribution of strengthening phase Al 2 Cu and the existence of "S" line during FSW lead to the benefits in the mechanical properties of the joint. The research results could provide guides for the predicting and characterizing the temperature distribution and mechanical performance of rocket tank FSW.           Table 2 Johnson-Cook constitutive model parameters of 2219 Table 3 Friction coefficient related to temperature Table 4 Comparison of simulation output and experimental results Table 5 Peak temperature values at different welding speeds Table 6 Peak temperature values at different rotational speeds DUT20ZD204. The financial contributions are gratefully acknowledged.

Conflicts of interest/Competing interests
Not applicable. The authors declare that they have no conflict of interest.

Availability of data and material
All data generated or analysed during this study are included in this manuscript.

Code availability
The code is available on request.