Subregion Based Prediction of Residual States in Friction Stir Welding of Dissimilar Metals

Abstract

Mechanical property changes in friction stir welding can directly affect the rebalance of the stress field in friction stir welding. This means that it reveals a high relevance with the residual states of friction stir welding. Here, we propose a subregion model in which the mechanical property changes are considered to predict the residual states in friction stir welding of dissimilar metals. Results indicate that the accuracy of the predicted distortion can be greatly increased when the different mechanical properties are considered in friction stir welding of 2024-T3 and 6061-T6. The final mechanical property is determined by the mixture of the materials at retreating and advancing sides. The final mechanical property in the stirring zone can be increased to 171 MPa for yield strength and 194 MPa for tensile strength when the strength of the advancing side material is higher. The shrinkage of material in the stirring zone during the cooling stage is the key reason for the formation of the tensile residual stress and the V-shape distortion on the cross-section in the as-weld state.

1. Introduction

Friction stir welding (FSW), as a solid-state joining technology, offers several advantages when it comes to joining dissimilar metals [1,2,3,4,5], including Al/Cu [6,7,8], Al/Ti [9,10,11], Al/Al [12,13,14], Al/Mg [15,16,17], and Al/Steel [18,19,20]. Due to the formation of intermetallic compounds and element diffusions, the mechanical properties can differ significantly from the parent metals after FSW. This change can further affect the structural performance of friction stir welds, including residual stresses, distortions, and fatigue-induced stress and crack propagations. The challenge in FSW of dissimilar metals lies in correlating the mechanical property changes with the subsequent structural performance.

Mechanical properties in the welding region can be changed by the selected welding technologies, especially when dissimilar materials are involved [21,22,23,24,25]. The mechanical properties, mainly yield strength and tensile strength, generally decrease due to precipitate dissolutions in FSW of aluminum alloys [26,27,28,29]. In FSW of dissimilar metals, changes in mechanical properties becomes more complex [30]. They are influenced not only by precipitate evolutions but also by the mixture fractions of advancing and retreating materials, presenting a significant challenge in describing and controlling the changes in mechanical properties.

Numerical simulation is an efficient tool for unravelling the process-structure-property relationship [31,32,33,34,35]. In simulations of temperature distribution during FSW of Al 6061 and AZ31 Mg [36], the maximum temperature on the advancing side (Al) is markedly higher than that on the retreating side (Mg). This difference is attributed to the higher thermal diffusivity in Al, determined by the ratio of thermal conductivity to specific heat capacity. In the FSW of Al and Cu dissimilar alloy [37], temperature distribution is not symmetrical across the welding line due to the different thermally physical properties between Al and Cu. The use of water cooling in FSW can enhance the properties of the weld by reducing temperature and promoting the formation of IMCs, including Al₂Cu, Al₃Cu, and Cu₉A_l4. Different temperature profiles on the advancing and retreating sides lead to different residual stresses. Measurements using diffraction methods [38] reveal higher longitudinal residual stress on the 7075 side compared to 2024 side in FSW of dissimilar metals. Tensional stress can be found in the 7075 side and compressive stress can be found in the 2024 side for transverse and normal stresses. Molecular dynamic simulation [39] reveals that the diffusion coefficient of Al is 59% higher than that of Cu in FSW of Al and Cu alloys. The diffusion of Al and Cu at the interface leads to the formation of the γ-Al₄Cu₉ phase. FSW of 2017A-T451 and 5083-H111 [40] reveals that 2017A dominates the nugget zone, regardless of its position in FSW of dissimilar metals. The high dislocation density on both sides shows that the recrystallization occurring in FSW is incomplete. In FSW of Al and Cu [41], copper reveals higher viscosity than aluminum, which leads to Al 1050 displacing copper on the advancing side and the shifting of Al-Cu interface towards the advancing side.

The change in mechanical properties caused by the mixing of materials in the stirring zone can play a crucial role in determining the formation of residual states in FSW of dissimilar metals. The resulting stresses are highly relevant to the process parameters and tool geometries in FSW of dissimilar metals [42]. Recrystallization plays a key role in this process [43]. The tensional stress can be reduced by applying a rolling effect after FSW [44]. The formation of residual stress and its relevance to microstructures can be investigated through a sequentially coupled thermomechanical model. The sequentially coupled thermomechanical model has been revealed to be successful in simulating the residual stresses in FSW [45,46,47]. The influence of material mixtures and changes in mechanical properties in the stirring zone remain unknown in FSW of dissimilar metals, which is the motivation of this work. A subregion model is proposed to show the changes in mechanical properties in the stirring zone, which is further combined with the sequentially coupled thermomechanical model to accurately predict residual states in FSW of dissimilar metals.

In Section 2, the main experimental procedure and the numerical model are introduced. In Section 3, the obtained results are compared with experimental data to validate the proposed subregion model. Then, different cases with different advancing and retreating materials are compared to show how the selection of advancing and retreating materials affects mechanical properties and, subsequently, the final residual states in FSW of dissimilar metals.

2. Experiment and Numerical Model

2.1. Experiment

The HT-JM16 × 8/1 type FSW machine is used to join 6061-T6 and 2024-T3 aluminum alloys. The diameter of the shoulder is 12 mm. The pin is in conical shape, with diameters ranging from 3.5 mm to 5 mm. AA2024-T3 aluminum alloy is selected as the advancing material, while AA6061-T6 is the retreating material. The sizes of the welding plates are 200 × 110 × 4 mm. This case is compared with one in which AA6061-T6 aluminum alloy is selected as the advancing material and AA2024-T3 as the retreating material. The rotation speed is set at 800 rev/min, and the transverse speed is 150 mm/min, in accordance with previous experiments on FSW [14,48,49]. A Flir TG297 type infrared thermometer is used to capture the temperatures in the FSW experiment. A WDW-100 type machine is used to obtain stress-strain curves of FSW specimens in tension. The chemical compositions of the 6061-T6 and 2024-T3 alloys used are shown in

Table 1. Chemical composition of aluminum alloy 2024-T3.

Material	Percentage of Ingredients (%)
2024-T3	Ti	Si	Mn	Mg	Fe	Cr	Zn	Cu
	0.15	0.50	0.30–0.90	1.2–1.8	0.50	0.10	0.25	3.8–4.9

and

Table 2. Chemical composition of aluminum alloy 6061-T6.

Material	Percentage of Ingredients (%)
6061-T6	Ti	Si	Mn	Mg	Fe	Ni	Zn	Cu
	0.034	0.414	0.074	0.966	0.397	0.004	0.046	0.228

.

2.2. Numerical Model

The authors have developed a moving heat source model for the prediction of thermal histories in FSW and a sequentially coupled thermo-mechanical model for the prediction of residual states in FSW. However, the simulation of the FSW with dissimilar metals is still challenging. The main difficulty lies in the complexity of defining the constitutive model for material mixing in the stirring zone. The constitutive model for this element cannot be pre-defined before actual mixture occurs. Moreover, the traditional Arbitrary Lagrangian Eulerian model does not support material transportation between different mesh domains. To solve this problem, we conducted experiments to measure stress-strain curves, and the measured data are then applied to the subregions in the model for the accurate description of the constitutive model in FSW of dissimilar metals.

The schematic to the FSW process of dissimilar metals is shown in Figure 1. In Figure 1a, 2024-T3 is selected as the material on the advancing side, and 6061-T6 is the retreating material. In Figure 1b, 6061-T6 is selected as the material on the advancing side, with 2024-T3 as the retreating material. The sizes of the welding plates are 200 × 110 × 4 mm, which are exactly the same as the experimental specimens. The thermally physical properties are considered to be functions of temperature for both 2024-T3 and 6061-T6, as shown in Figure 2. The mechanical properties are also considered to be functions of temperatures, as shown in Figure 3.

The surface heat source model [52] is used to simulate temperature variations in FSW of dissimilar metals. The heat input power is mainly caused by the frictional dissipations between the welding plates and tool:

$$q_{\mathrm{shoulder}}=\frac{W_{\mathrm{shoulder}}}{A_{\mathrm{s}}}=\frac{2\left(r_{\mathrm{s}}^3-r_{\mathrm{p}}^3\right)\tau \delta \omega }{3\left(r_{\mathrm{s}}^2-r_{\mathrm{p}}^2\right)}$$

(1)

where W is the powder, and q is the heat flux. r_s and r_p are the radii of the shoulder and pin. τ is the frictional stress. δ is the slipping coefficient and ω is the rotating speed.

Thermal convection boundary conditions are applied to all the free surfaces of the welding plates [53]:

$$k\frac{\partial T}{\partial n}=h\left(T-T_a\right)$$

(2)

where h is the convection coefficient and T_a is the ambient temperature.

Room temperature is selected to be 25 °C and is applied to the front surface of the welding plates:

$$T=T_{\mathrm{a}}.$$

(3)

The geometrical model for predicting temperature variations in FSW of dissimilar metals is shown in Figure 4. When 2024-T3 is selected as the advancing side, 234,165 elements and 185,600 nodes are used for meshing in this model. Similarly, when 6061-T6 is selected as the advancing side, 234,165 elements and 185,600 nodes are used for meshing in this model. A thinning of 0.5 mm caused by FSW is considered.

The materials on the advancing and retreating sides can be mixed together [54]. The final mechanical strength, mainly including yield strength and tensile strength, is determined by the volume fractions of the advancing and retreating materials entering the stirring zone:

$${\sigma }_{\mathrm{Y}}=f_{\mathrm{adv}}{\sigma }_{\mathrm{Y},\mathrm{adv}}+f_{\mathrm{ret}}{\sigma }_{\mathrm{Y},\mathrm{ret}}$$

(4)

where σ_Y is the yield strength (tensile strength) of the material in the stirring zone. σ_Y,adv is the yield strength (tensile strength) of the FSWed material on the advancing side. σ_Y,ret is the yield strength (tensile strength) of the FSWed material on the retreating side. f_adv is the volume fraction of advancing material. f_ret is the volume fraction of retreating material. Optical microscope can be used to determine the volume fractions of materials entering the stirring zone on both advancing and retreating sides.

After the determination of yield strength in the mixture region (stirring zone) through tensile testing at room temperature, the yield strength can be further treated as a function of temperature and strain rates as follows [55]:

$${\sigma }_{\mathrm{Y}}\left(T\right)={\sigma }_Y\left\{1-\frac{T}{T_{\mathrm{m}}}\exp \left[{\theta }_{\mathrm{g}}\left(1-\frac{T_{\mathrm{m}}}{T}\right)\right]\right\}{\left\{1-{\left[\frac{RT}{\Delta G}\ln \left(\frac{{\dot{\epsilon }}_0}{{\dot{\epsilon }}_p}\right)\right]}^{1/q}\right\}}^{1/p}$$

(5)

where T_m is the melt temperature of the material. ΔG is the activation energy for dislocation and precipitate interaction [56,57,58].

The welded plates are divided into different regions, and different material properties are applied to these regions to establish the subregion model, as shown in Figure 5. The mechanical property changes are measured in our experiment. The obtained stress-strain curves are then applied to the mixed regions in the subregion model. The yield strength in the stirring zone is determined by the definition of Equation (5), and σ_Y at room temperature is determined through experimental tensional test.

Sequentially coupled thermomechanical model is then used to predict the residual states in friction stir welding of dissimilar metals. Detailed information about this model can be found in Refs. [59,60,61].

The computational procedure for the proposed numerical model is summarized in Figure 6.

3. Results and Discussions

3.1. Temperature Variations

The temperature distributions around the welding tool obtained in the numerical model are compared to the experimental observations made with an infrared thermometer, as shown in Figure 7 and Figure 8. The maximum temperature is very similar when the advancing/retreating materials are changed from 2024/6061 to 6061/2024. This similarity is because the contact conditions are not changed in both cases. However, the temperature field is asymmetrical with respect to the welding line. As revealed in Figure 2, the differences in thermally physical properties are the fundamental reason for the formation of asymmetrical temperature distributions in FSW of dissimilar metals. The maximum temperature is 423.3 °C in the numerical model and 428 °C in the experiment when the advancing side material is 2024-T3. The error between the experimental and numerical data is 1.1%. The maximum temperature is 423.3 °C in the numerical model and 420 °C in the experiment when the advancing side material is 6061-T6. The error between the experimental and numerical data is 0.8%. The comparison of temperatures between the experiment and the numerical model can show the validity of the used moving heat source model.

The temperature variations with time are depicted in Figure 9. Points on the borders of the shoulder and pin are selected to show the temperature history. It can be seen that the temperature on the top surface is higher than on the bottom surface. The difference between the temperatures on the top and bottom surfaces at the 2024-T3 side is 24.5 °C when the advancing side material is 2024-T3. The difference between the temperatures on the top and bottom surfaces at the 6061-T6 side is 19.9 °C when the advancing side material is 6061-T6.

3.2. Mechanical Properties

Figure 10 reveals the stress-strain curves for FSW of dissimilar metals. Tensile tests on the specimens obtained from FSW of dissimilar metals show that the yield strength and tensile strength are 171 MPa and 194 MPa, respectively, when the advancing side material is 2024-T3. When the advancing side material is changed to 6061-T6 and the retreating side material is changed to 2024-T3, the yield strength and tensile strength decreased to 166 MPa and 186 MPa. According to Figure 2, the tensile strength and yield strength of 2024-T3 are higher than those of 6061-T6. This means that the final mechanical properties can be increased when a higher-strength material is selected for the advancing side.

By utilizing Equation (5), the variations of yield strength with temperature and strain rate can be obtained, as shown in Figure 11. With an increase in temperature, the yield strength decreases. The differences between the two cases decrease from 5 MPa at room temperature (25 °C) to 0.2 MPa at 482 °C. With an increase in strain rate, the yield strength increases. The yield strength differences between the two cases are 4.69 MPa at a strain rate of 0.0001, 4.72 MPa at a strain rate of 0.001, and 4.74 MPa at a strain rate of 0.01.

3.3. Residual States

The residual distortions in FSW of dissimilar metals can be obtained by the subregion model, as shown in Figure 12. The maximum residual distortion is 1.2 mm when the advancing material is 2024-T3 and 1.3 mm when the advancing material is 6061-T6. The residual distortion takes on a classical V-shape. When the subregion model is not applied, the predicted residual distortion becomes higher, as shown in Figure 13. The maximum residual distortion is 1.7 mm when the advancing material is 2024-T3 and 1.5 mm when the advancing material is 6061-T6. Further details can be discerned in Figure 14. The comparison shows that considering the mechanical properties changes in the subregion model can increase computational accuracy in predicting residual distortions in FSW. The final geometrical shape is formed by the shrinkage of the material inside the stirring zone during the cooling stage. Due to temperature differences between the top and bottom surfaces, the material on the top surface experiences greater shrinkage than the material on the bottom surface. This leads to a bending deformation in the stirring zone. The local curvature is determined by $1/\rho =M/EI$, where M is determined by the stresses caused from the shrinkage of the material in the stirring zone. As a result, the specimen exhibits a V-shape in the cross-section. Although the cutting of such specimens can release longitudinal residual stresses, transverse residual stresses are not obviously affected. The comparison between experimental and numerical results validates the proposed subregion model for predicting residual distortions in FSW of dissimilar metals.

Figure 15 shows the residual vertical distortions in FSW of dissimilar metals. The vertical distortion is 0.67 mm on the advancing side and 0.68 mm on the retreating side when the advancing material is 2024-T3. Conversely, when the advancing material is 6061-T6, the vertical distortion is 0.79 mm on the advancing side and 0.58 mm on the retreating side. The obtained numerical data fit well with the experimental data on the cross-section of the friction stir welded specimens.

Figure 16 shows the residual stress distributions in FSW of dissimilar metals. Tensile stresses can be found for both the longitudinal and transverse residual stresses near the welding line. However, compressive residual stresses can be found near the borders of the FSWed specimens. The longitudinal residual stress is significantly higher than the transverse residual stress. This phenomenon is consistent with what is observed in FSW with single material [62,63]. The longitudinal residual stress near the welding line reveals a W-shape, as shown in Figure 17. The maximum longitudinal residual stress is 292.4 MPa when the advancing material is 2024-T3, while the maximum transverse residual stress is 203.7 MPa in the same case. However, when the advancing side material is changed to 6061-T6, the maximum longitudinal residual stress increases to 339.6 MPa, and the maximum transverse residual stress reaches 211.3 MPa.

4. Conclusions

(1)

Selecting a high-strength material for the advancing side significantly improves the final mechanical properties in friction stir welding of dissimilar metals. The yield strength and tensile strength can be increased from 166 MPa and 186 MPa to 171 MPa and 194 MPa, respectively, when the advancing material is changed from 6061-T6 to 2024-T3.

(2)

The residual distortion of the friction stir weld exhibits a V-shape, resulting from the material shrinking in the stirring zone during the cooling stage. The maximum residual distortion is 1.2 mm when the advancing material is 2024-T3 and 1.3 mm when the advancing material is 6061-T6.

(3)

The longitudinal residual stress is significantly higher than transverse residual stress. The longitudinal residual stress on the cross-section forms a W-shape, with peak values occurring at the borders of the stirring zone on the top surface.