## 6 Results and Comparison
### Spring-Back  
Through the FE analysis, the stress distributions of bimetallic bending tubes under different bending angles were shown in Figure 16. In this figure, the uploading states were illustrated in (a1)-(a6) and the spring-back states illustrated in (b1)-(b6). The stress neutral layer displayed clearly on the cloud chart. The ultimate stress on the bimetallic tubes under the uploading process appears at the bending start. Meanwhile, the largest residual stress after unloading occurs near the neutral layer. There were some tiny shape defects on the cloud chart, such as wrinkling waves and point separation between double layers. Because it is hard to measure these tiny defects in the empirical experiments, they were neglected in this paper. Figure 17 illustrates the spring-back angles of bimetallic tubes under increasing bending angle. This figure contains four kinds of spring-back results. They are the spring-back angles from experiments, FE simulation analysis, theoretical calculation neglecting neutral layer shifting and theoretical calculation considering NLSE. In the calculation process, the interlaminar friction coefficient is 0.2 and the same as the simulation. While calculating the unloading moment, referring to E and Zhou [34], the cross-section takes the model that the short axis change rate of bending outside is 0.05, and the wall-thickness is invariable. It can be found that the spring-back angles from FE analysis are almost greater than others. That is because the spring-back in the simulation environment can be affected by many special factors, such as the unloading method, meshing, contacts, friction between the tube and dies, the position of dies, etc. It is difficult to consider all these factors in the theoretical models. This may conduce to the difference between the results from FE analysis and theoretical models. The pure theoretical spring-back angles have a positive linear correlation with the bending angle. Compared with the theoretical results neglecting neutral layer shifting, the theoretical results considering NLSE are closer to the experimental results. Generally, the spring-back angle increases with the bending angle increasing. The angle differences between the theoretical results considering NLSE and experimental results are less than 0.0766\({}^{\circ}\). Under 30-90\({}^{\circ}\) bending, the relative errors of theoretical spring-back angles to experimental spring-back angles are less than 18.68%. The relative errors between the forming angles after spring-back are less than 0.1258%. Under 15\({}^{\circ}\) bending, the largest error of the forming angles is 0.3159%. It is demonstrated that the accuracy of the theoretical model is acceptable. Figure 15: Response value of neutral layer shifting to significant factors. Figure 16: _Cont._  
Figure 16: Uploading and spring-back states under 15-90\({}^{\circ}\) bending: **(a1)** Uploading states under 15\({}^{\circ}\); **(a2)** Spring-back states under 15\({}^{\circ}\); **(b1)** Uploading states under 30\({}^{\circ}\); **(b2)** Spring-back states under 30\({}^{\circ}\); **(c1)** Uploading states under 45\({}^{\circ}\); **(c2)** Spring-back states under 45\({}^{\circ}\); **(d1)** Uploading states under 60\({}^{\circ}\); **(d2)** Spring-back states under 60\({}^{\circ}\); **(e1)** Uploading states under 75\({}^{\circ}\); **(f1)** Uploading states under 90\({}^{\circ}\); **(f2)** Spring-back states under 90\({}^{\circ}\). Figure 17: Spring-back angles under 15–90\({}^{\circ}\) bending. To investigate the coupling between the two layers, the change of spring-back angles with the increasing of interlaminar friction coefficient is illustrated in Figure 18. The values of other factors are constant. It can be obvious from the diagram that the impact of interlaminar friction coefficient to bimetallic tubes' spring-back is not monotonic. In the unloading spring-back process, the potential energy in the elastic deformation region of the bimetallic tube transfers to the kinetic energy and work caused by interlaminar friction.