## 1 Introduction
The conclusion was that the spring-back increased with the increasing of loading index \(k\), so evaluating \(k\) reasonably can improve the precision of prediction. In order to avoid the excessive error caused by the assumptions in the theoretical analysis and reduce the difficulty of solving analytical models, many researchers use the numerical simulation method to obtain the engineering solution of the rebound problem. [PERSON] et al. [26] investigated the geometry-dependent spring-back behaviors of thin-walled tube upon cold bending. They aimed at two geometry parameters--tube diameter \(D\) and wall thickness \(t\). [PERSON] et al. [27] predicted spring-back by combining explicit and implicit schema. They carried out the influence of numerical parameters such as element type, number of elements through thickness, and damping factor on prediction accuracy and simulation efficiency. [PERSON] and [PERSON] [28] established a simulation model to define the relationships between process parameters and spring-back angle. Controlling functions for plastic elongation and spring-back angle are also given. The existing research objects about the rebound of multi-layer composite components are strip, plate, and heterogeneous bellows. [PERSON] et al. [29] studied the effects of sheet thickness and position on spring-back of a stainless-steel clad aluminum sheet's V-bending though the nonlinear FEM. Their research addressed three material models--isotropic, cyclic, and Johnson-Cook hardening. [PERSON] and [PERSON] [30] derived a simplified analytical model to calculate the bending moments of sandwich sheets, and the model was applied to predict the spring-back after bending. The spring-back angle is mainly determined by the skin sheet's mechanical properties. [PERSON] et al. [31] conducted a comparative study on the profile shape spring-back of bi-layered nonhomogeneous bellows. Their results included the degree of U-shape deformation and the spring-back tendency with the variation of some parameters like layer number, material properties, etc. As for bimetallic tubes, because of the complex section characteristics, new boundary conditions are added to their spring-back on the base of geometrical and material nonlinearity. It is harder to solve the rebound problem. The spring-back theory, prediction model, and compensation method of bi-layered metallic tube are all lacking. The resolution of tube bending spring-back needs to transfer external forces into internal stress. The neutral layers are the geometrical zero points of stress and strain, the researches of whose positions make sense in the bending problems. Under pure bending, the transient stress and strain neutral layers all move toward bending center as the bending curvature increases. The transient stress of the neutral layer's shifting amount is greater than transient strain of the neutral layer if the elastic deformation can be neglected, which was mentioned by [PERSON] [32]. To reduce the calculative difficulties and obtain the stress-strain relationship easily, it is generally assumed that the neutral layers coincide with the center layer of the tube blank. However, due to the high complexity caused by the coupling deformation of the two layers, the neutral layer invariance assumption may lead to more obvious errors in bimetallic tube bending spring-back. In this paper, it was proved that the strain neural layers of outer layer and inner layer are almost coincident in the effective bending range. The neural layer shifting can be expressed by a composite strain neutral layer (\(D_{\varepsilon}\)). A novel neutral layer shifting extraction (NLSE) method was firstly proposed to ascertain the position of \(D_{\varepsilon}\). Via the NLSE method applied to simulation results as well as regression analysis, the function of \(D_{\varepsilon}\) about the parameters such as bending radius, bending angle, tube size, etc. was derived. In addition, a composite elastic modulus (\(E_{\varepsilon}\)) was proposed to describe the spring-back behaviors of bimetallics.