## 4.2 Mechanical properties in different positions

Mechanical properties of different positions of single-curvature "S" shaped lap joint is shown in Fig. 7(a). At position Ⅲ (Z-axis positive curvature position), the tensile load of the joint is minimum which is 1.5kN. In Fig. 6(a), there are defects in advancing side of upper plate and interface at the Z-axis positive curvature position (position Ⅰ-Ⅲ). Besides there is bending deformation in edge of upper plate. These phenomenon cause the decrease of tensile load. At the Z-axis negative curvature position (position Ⅴ-Ⅶ), as shown in Fig. 6(c), there are less defects and the tensile loads are great whose value can increase to more than 2.4kN. Figure 8(a) ~ Fig. 8(c) show the fracture morphology of different positions of single-curvature "S" shaped weld. In Position Ⅲ and Ⅳ, the fracture shows cleavage river pattern and tearing ridge which is dissociative rupture. But In Position Ⅵ, the fracture shows a lot of dimples and tearing ridge which is quasi-dissociation rupture.

Mechanical properties of different positions of double-curvature "S" shaped lap joint is shown in Fig. 7(b). At position Ⅱ (Z-axis positive and Y-axis positive curvature position), the tensile load of the joint is minimum which is 1.7kN. And from position Ⅱ to Ⅶ, the tensile load of the joint increases gradually. In Fig. 6(d), there is bending deformation in edge of upper plate at the positive Ⅱ which may be the reason of the minimum tensile load. The tensile loads of different positions of the weld are different, indicating that the welding process is unstable. The tensile load can get a maximum to 3.0 kN. Figure 8(d) ~ Fig. 8(f) show the fracture morphology of different positions of double-curvature "S" shaped weld. In Position Ⅱ, Ⅳ and Ⅵ, the fracture all shows some dimples and tearing ridge which is quasi-dissociation rupture.

Comprehensively analyze the above joints morphology and mechanical properties, it shows that curvature of the Z-axis and Y-axis have a great influence on the mechanical properties of the weld joint. In single-curvature "S" shaped weld, the edge of the upper plate of the joint tends to warp towards Z positive at the Z-axis positive curvature position, resulting in reduced tensile load of the lap joint. This is related to the stress state of the lap joint to be welded when the axial force is loading. In double-curvature "S" shaped weld, the tensile loads of different positions of the weld are different. This is affected by the combined action of Z-axis and Y-axis curvature. Because the Y-axis curvature is realized by the change of axial force motion state during welding. So it is necessary to further study the axial force loading process of FSW equipment and it’s influence on the lap joint.

## 4.3 Axial force loading process analysis

Figure 9(a) ~ Fig. 9(c) show simulated stress field of single-curvature lap joint during axial force loading process. When the axial force is loaded, the shape of the stress concentration zone near weld area of three selected positions have little difference, but the peak value of the stress shows a gradually increasing trend from position Ⅲ to position Ⅵ. The peak stress is 353.5 MPa, 360.6 MPa and 490 MPa, respectively. Figure 10(a) shows the cross section of simulated stress field. The white dotted line indicates the stress concentration distribution of the final nugget zone (NZ). As shown by the black arrow position in the figure, the stress level in the interface also gradually increases, from about 250 MPa (position Ⅲ) to about 275 MPa (position Ⅳ), and then to about 300 MPa (position Ⅵ).

Figure 11(a) shows simulated deformation field of single-curvature lap joint during axial force loading process. The white dotted line indicates the shape of the NZ. It can be seen from the figure that the blue area in the weld center gradually increases from position Ⅲ to position Ⅵ, indicating that the pressing depth of the weld position gradually increases when the axial force is loaded. At the interface position, as shown in the black dotted boxes 1 to 3, it’s color changes from orange to yellow and then to green, indicating that the deformation along the Z positive direction gradually decreases. Which is corresponding to the phenomenon in Fig. 6(a) ~ Fig. 6(c), the amount of edges bending deformation forwards Z positive direction of upper plate gradually decreases.

Figure 11(b) shows simulated deformation field of double-curvature lap joint during axial force loading process. The white dotted line indicates the shape of the NZ. From position Ⅱ to position Ⅵ, the pressing depth of the weld position also gradually increases. At the interface position, as shown by the black arrow position, it’s color changes from green (position Ⅱ, the value is positive) to cyan (position Ⅳ and Ⅵ, the value is negative), indicating that the deformation along the Z direction changing from positive to negative. Which also explains the phenomenon in Fig. 6(d) ~ Fig. 6(f), the bending deformation of interface showing in position Ⅱ but disappearing in position Ⅳ and Ⅵ.

These phenomenon means the axial force FN of same value has different effects because the lap joint curvature. The force state of single-curvature joint in axial force loading process is analyzed in Fig. 12(a). In Position Ⅰ-Ⅲ with Z-axis positive curvature, the thermal action in the welding process causes the expansion of the lap joint, which produce the force F1 and F2 with the restraint of the pressing block 1 and 2. This will lead to the generation of the upward force F’ which is opposite to the axial force FN. The resultant force FR (FR=FN-F’) which is the actual axial compressive force will be smaller than FN. Thus the interface stress of the lap joint will be smaller than other positions. And this eventually leads to the edges of the upper plate bending towards Z positive (As shown in Fig. 6(a)). In Position Ⅳ with Z-axis no curvature, the force F1 and F2 are in opposite direction and offset their effects to lap joint which means the F’=0. The resultant force FR (FR=FN) is the actual axial compressive force. Thus the interface stress of the lap joint will be a little bigger than position Ⅰ-Ⅲ. And this eventually leads to the edges of the upper plate bending towards Z positive but the bending deformation getting a little smaller (As shown in Fig. 6(b)). In Position Ⅴ-Ⅵ with Z-axis negative curvature, the force F1 and F2 with the restraint will lead to the generation of the downward force F’ which has same direction as the axial force FN. The resultant force FR (FR=FN+F’) which is the actual axial compressive force will be greater than FN. Thus the interface stress of the lap joint will be more bigger. And this eventually leads to the edges of the upper plate bending deformation disappearing (As shown in Fig. 6(c)).

The force state of double-curvature joint axial force loading process is analyzed in Fig. 12(b). In Position Ⅰ-Ⅲ with Z-axis positive & Y-axis positive curvature, the force F’ which points to the Z positive direction occurs because of material thermal expansion, restraint and Z-axis positive curvature. Due to Y-axis positive curvature, the axial force FN deflects a certain angle towards the Y positive direction during welding. This means an included angle between the axial force FN and F’ will be greater than 90°. So the direction of the actual resultant force FR will lie between Y positive direction and Z negative direction, and its value will be smaller than FN. Thus, the stress at retreating side of the weld will be higher than advancing side. And this eventually leads to the edges of the upper plate bending towards Z positive and causes the edge bending deformation of retreating side bigger than advancing side (As shown in Fig. 6(d)). In Position Ⅳ with Z-axis no curvature & Y-axis negative curvature, the force F’ is 0 because of Z-axis no curvature. Due to Y-axis negative curvature, the axial force FN deflects a certain angle towards the Y negative direction during welding. The direction of the actual resultant force FR (FR=FN) will lie between Y negative direction and Z negative direction. Thus, the stress at advancing side of the weld will be higher than retreating side. And this eventually leads to the interface bending deformation disappearing (As shown in Fig. 6(e)). In Position Ⅴ-Ⅵ with Z-axis negative & Y-axis positive curvature, the force F’ which points to the Z negative direction occurs because of material thermal expansion, restraint and Z-axis negative curvature. Due to Y-axis positive curvature, the axial force FN deflects a certain angle towards the Y positive direction during welding. This means an included angle between the axial force FN and F’ will be smaller than 90°. So The direction of the actual resultant force FR will lie between Y positive direction and Z negative direction, and its value will be greater than FN. Thus, the stress at retreating side of the weld will be higher than advancing side. And this eventually leads to the interface bending deformation disappearing (As shown in Fig. 6(f)).

It can be seen from the above that Z-axis curvature direction has important influence on joint forming. By split type pressing blocks fixture, the material thermal expansion causes upward force F’ in Z-axis positive curvature position, but causes downward force F’ in Z-axis negative curvature position. So the actual axial compressive force FR is smaller than the device input FN in Z-axis positive curvature position. It will cause the interface stress of the lap joint decreasing. Then it will cause the tendency of upper plate edges bending deformation and the probability of interface defects increasing. While FR is greater than FN in Z-axis negative curvature position, which will cause the interface stress of the lap joint increasing. Then it will cause the tendency of upper plate edges bending deformation decreasing and the interface defects disappearing.

For Y-axis curvature direction, its impact is mainly shown in changing the direction of resultant force FR. In Y-axis positive curvature position, the force FR lies between Y positive direction and Z negative direction. This inclination of force FR is helpful to eliminate the interface defects of the joint. At the same time, it will cause the interface stress of retreating side bigger than advancing side. When cooperating with Z-axis positive curvature, the value of force FR is less than FN, resulting in the edge bending deformation of retreating side bigger than advancing side. When cooperating with Z-axis negative curvature, the value of force FR is greater than FN, resulting in the edge bending deformation disappearing. In Y-axis negative curvature position, the force FR lies between Y negative direction and Z negative direction. This inclination of force FR is also helpful to eliminate the interface defects of the joint. And it will cause the interface stress of advancing side bigger than retreating side. When cooperating with Z-axis no curvature, the value of force FR is equal to FN, resulting in the edge bending deformation disappearing. The changing direction of FR causes inconsistent stress between the advancing side and the retreating side of the joint interface, which is the reason that the double-curvature lap joint welding process is unstable.