## 1 Introduction  
Bi-layered metallic tubes and their elbow components play an important role in changing the flow direction and improving the flexibility of wiring in pipeline systems [1; 2; 3]. As related industries are developing and transforming, many new demands such as corrosion protection, wear resistance, impact resistance, thermal insulation, electric insulation, low cost, lightweight, etc. have appeared. Compared with single-metallic tubes, bimetallic tubes can meet the new requirements better and have gradually been applied for engineering [4; 5; 6; 7]. By making full use of the optimum of different materials, bimetallic tubes can reduce the use of precious metals, lighten the weight of pipes, and reduce production and transportation costs. Therefore, bimetallic tubes are in wide use in the automobile, ship, aerospace, petrochemical, nuclear power, and military industries [8; 9; 10; 11]. The elbow components are formed by cold processing of straight metallic tube blanks. The bending forming quality is directly related to the assembly accuracy, operation safety, and flow stability. Usually, three indexes are used to reflect the forming quality--wall thickness thinning [12; 13; 14], wrinkling [15; 16; 17; 18], and spring-back. At present, studies of bimetallic tube bending forming almost focus on analysis of wall thickness variation and wrinkling caused by complex bulking instability under the interaction of two or more layers. [PERSON] et al. [19] proposed a model about the wall thickness distribution of Cu-Al bi-layered tube. Their research indicated that the wall thickness distribution of bimetallic tube tended to be more uniform than single-layered tube. [PERSON] and [PERSON] [20] analyzed the inner wall thickness variation of double-layered tube in hydrobending. It was found that the maximum thickness reduction occurred at a nearby point rather than the center point of the outer arc because the point with the biggest axial stress moved toward the tube ends. Apart from the common defects such as cracking caused by wall thickness changes and wrinkling due to instability, bimetallic tubes have hidden defects compared with single-layered metallic tubes. This means that the inner layer may separate from the outer layer or collapse while the bimetallic tube looks normal on the outside. [PERSON] et al. [21] studied the buckling of offshore steel-lined pipes numerically subjected to monotonic bending. The main conclusion was that low or moderate internal pressure can improve the bending performance such as ovalization, detachment of the thin-walled inner pipe from the outer pipe, and liner buckling of lined pipes. [PERSON] et al. [22] analyzed the wrinkling behaviors of carbon steel/Al-alloy bi-layered tubes with different thickness ratios and internal pressures under hydro bending. The bifurcation instability of inner tube and the limit load instability of outer tube were also noticed. It followed that internal pressure can delay the separation and wrinkling of bimetallic tube's inner layer efficiently. The spring-back behaviors of bimetallic elbow components after computer numerically controlled (CNC) bending is an important aspect of the forming defects prevention. So far, scholars have carried out a lot of mature theoretical models and reliable experimental results about tubes' spring-back behaviors. [PERSON] et al. [23] established an analytic elastic-plastic tube bending spring-back model based on static equilibrium condition considering the variations of some parameter in the bending process. [PERSON] et al. [24] proposed a semi-analytical method for the spring-back prediction of thick-walled 3D tubes. The discretization and approximation were implemented on the tube axis to derive the deformation parameters and the relationship between parameters in bending process and those after spring-back was defined. [PERSON] et al. [25] investigated the spring-back of spatial tubes under different loading modes and hardening materials.