Analysis of Springback Characteristics of Bending Unloading for Stainless Steel tubes

Stainless steel tubes are widely used in piping systems in aviation, aerospace and other high-tech fields because of their high strength, excellent corrosion and high-pressure resistance, and good resistance to high-temperature oxidation. This paper takes 304 stainless steel pipe as the research object, based on ABAQUS finite element platform, the springback behaviour of stainless steel pipe in the process of precise bending and forming has been studied in depth. The results show that: pipe bending unloading bending springback angle increases with the increase of the bending angle. The results of the study have important theoretical and practical significance for improving the accurate forming and springback of stainless steel tube bending.


Introduction
With the continuous development of modern industry, the traditional stainless steel tube has been unable to meet the high performance as the goal of aerospace on the requirements of high strength and pressure resistance, and high strength, corrosion resistance, high temperature and high pressure resistance and oxidation resistance of stainless steel tubing will be widely used.The accurate bending forming and springback behavior of stainless steel tube are mainly manifested in the distribution of stress and strain and springback after unloading.The bending angle affects the stress-strain response of the elbow under complex loading conditions [1] .
At present, scholars at home and abroad have conducted a large number of in-depth studies on the factors affecting the quality of pipe bending and forming.Wang et al. [2] studied the variation of stress field, strain field and free bending force of formed parts through tensile tests at different temperatures and different tensile rates.Fang et al. [3] studied the influence of cross-section distortion of tube bending under the condition of elastic modulus change.The results show that the change trend of the influence of process parameters on the cross-section distortion of the elbow is similar whether the change of elastic modulus is considered or not.Fang et al. [4] studied the influence of process parameters on the wall thickness reduction of 21-6-9 high strength stainless steel tube in numerical control bending.Most of the above studies are about the process parameters on the quality of pipe bending and forming, while there are relatively few studies about the bending angle on the pipe bending resilience behavior, therefore, this paper takes 304 stainless steel pipe Ф20×t 1.5mm as the research object, and establishes a stainless steel pipe accurate bending and forming finite element model based on ABUQUS finite element platform to study the influence law of the bending angle on the unloaded springback.

Establishment and Validation of Finite Element Model of Stainless Steel Tube
Finite element numerical simulation for the systematic and in-depth study of stainless steel pipe plastic bending problems to provide a scientific theoretical basis and guidance, has become a very effective method to study the law of stainless steel pipe plastic bending and forming process [5] .

Establishment of Finite Element Model
According to the pipe bending process, a stainless steel pipe accurate bending and springback finite element model is established, which can take into account the nonlinear dynamic contact conditions in the bending process, and can realize the whole process simulation.
Figure 1 show a finite element model for accurate bending of stainless steel pipe, the material is 304 stainless steel.In order to simplify the finite element model, the mold surface in direct contact with the pipe is used to represent a variety of forming mold shape.

Selection of units
A 4-node hyperbolic shell cell S4R is selected to describe the bending deformation behavior of the pipe, which has reduced integration and hourglass control.For the finite element model, five integration points are selected in the direction of the cell thickness, and the discrete rigid shell cell R3D4 is selected to describe the contact surface of the mold on the pipe.

Selection of mesh size
The mesh size of the finite element model in this paper is 1 mm×1 mm.selecting the optimal mesh size can improve the computational efficiency of the finite element model and ensure the accuracy of the finite element model simulation.

Selection of material model
In the process of establishing the finite element model, the selection of the material model is critical to the stability of the finite element simulation.The material used in the simulation is stainless steel pipe, the Mises yield criterion is used to describe the plastic deformation behavior of the pipe [6] .The material parameters used in the finite element model for accurate bending and forming and springback of stainless steel tubes mainly include the modulus of elasticity E, strength coefficient K, hardening index n, yield strength σ0.2, and Poisson's ratio μ.Based on the unidirectional tensile experiments of stainless steel tubing in the literature [7] , the material of stainless steel tubing is determined with the specification of 304 stainless steel tubing of Ф20mm×t 1.5mm as the object.Performance parameters (see Table 1).

Friction modeling
In this paper, the classical Coulomb friction model is chosen to describe the contact between the pipe and the mold [8] .Stainless steel tube accurate bending and forming process, friction on the bending and forming performance is more important.Pipe bending is dependent on the pipe and mold contact and friction between the mold and forming, the friction between the various contact interfaces play a key role in pipe bending and forming.

Finite Element Model Stability Verification
Stainless steel pipe accurate bending and forming and springback behavior is mainly manifested in the distribution of stress-strain and springback after unloading and other phenomena, selected mesh size of 1mm × 1mm and the quality of the amplification factor of 3000, through the energy curve to verify the stability of the built finite element model.Simulated energy curves by examining the ratio of kinetic energy to internal energy with bending time are the most commonly used method for theoretical evaluation of finite element models.If the ratio of kinetic energy to internal energy is less than 10%, the finite element model does not introduce significant dynamic effects, which in turn indicates that the model is stable.In addition, if the ratio of the pseudo-strain energy to the internal energy is less than 2%, then there is no hourglass problem in the model.From Figure .2 it can be seen that the model is stable and has no hourglass problem.

Analysis of the Results of the Bending Angle on the Springback Angle of Stainless Steel Tubes after Unloading
For Ф20mm×t 1.5mm stainless steel tubes, change the bending angle θ so that θ={20°, 40°, 60°, 80°, 90°}, respectively, to study the effect of the bending angle θ on the springback angle of stainless steel tubes for precise bending and molding.The springback characteristics of stainless steel tube are analyzed by the distribution of stress and strain in the springback process of accurate bending unloading of stainless steel tube.

Distribution of Stress and Strain of Stainless Steel Pipe after Unloading Springback
Figure 3 shows the stress-strain distribution cloud diagram of the precise bending unloading springback process of stainless steel tube.As can be seen from Figure 3, the tangential stress of the bent pipe increases rapidly, the maximum value of the tangential stress is located in the region near the bending plane, and with the bending process, the shape and location of the bending deformation zone basically does not change.Meanwhile, the distribution of tangential plastic strain along the bending direction is more uniform and continuous, the tangential plastic strain in the middle part of the bending section is larger, the tangential plastic strain at the two ends is smaller, and the plastic strain in the middle part is characterized by a plateau change.

Effect of Bending Angle on Springback Angle of Stainless Steel Tube in Accurate Bending
Figure. 4 shows the variation curve of the springback angle of the stainless steel tube with the bending angle.From Fig. 4, it can be seen that the bending angle is in the range of 0° to 90°, and the springback angle increases with the bending angle, this is mainly due to the fact that, all other things being equal, one is that as the bending angle increases, the amount of material involved in the plastic deformation of the pipe bending increases; secondly, as the bending angle increases, the bending deformation region becomes larger, the more thoroughly the pipe bending section is bent, and the accumulated elastic strain energy increases, making the springback angle of stainless steel pipe increase after unloading [9] .

Experimental Verification of Finite Element Models
In order to further verify the reliability of the established finite element model, accurate bending and forming experiments and finite element simulation studies were carried out for the stainless steel pipe with specifications of Ф20mm ×t 1.5mm.Then the reliability of the established finite element model is verified from the aspect of bending pipe springback angle.
As shown in Figure 5 the experiment was carried out on a profile bending machine, a universal angle ruler was selected as the measuring tool, and the forming conditions used in the simulation were identical to the experimental conditions.The bending angles θ were 20°, 40°, 60°, 80° and 90°.
Figure 6 shows the shape of the experimentally obtained bent fittings, and Table 3 shows the angle of springback of the pipe after bending and unloading the springback.From figure 7, it can be seen that the simulation results of the bent tubing profile are more similar to the experimental results.7 Angle of springback of pipe after unloading springback The above comparison found that there is still a certain deviation between the simulation results and the experimental results, which is mainly caused by the fact that there is still a certain deviation between the experimental boundary conditions and the simulation boundary conditions, which is specifically manifested in the following aspects: (1) The finite element simulation loading conditions and experimental loading conditions are not completely consistent.In the finite element simulation, the motion of the mold is loaded through the smooth step amplitude curve, so that the motion of the mold is completely smooth and stable, while the experimental loading conditions by the bending equipment, precision and rigidity and the control mechanism will be fluctuations or delays in the phenomenon.
(2) Measurement error.The accuracy of the measuring instrument itself and the error introduced by improper measurement operation.Such as the use of universal angle ruler to measure the springback angle, due to the concave characteristics of the inner side of the pipe, so that the universal angle ruler cannot contact the actual surface of the pipe bending and lead to errors in the readings.

Conclusion
The influence of bending angle on the springback angle of stainless steel tube in the process of bending unloading springback was studied by means of experiment and finite element numerical simulation.The conclusions are as follows: (1) Based on the ABAQUS finite element platform, the finite element model of the whole process (2) The springback angle of the bent pipe after pipe bending and unloading increases with the increase of the bending angle.

Figure. 5 Figure. 6
Figure.5 (a)Profile bending machine (b)Universal Angle Ruler .1088/1742-6596/2706/1/012004 6 of precision bending and springback of stainless steel tube was established.The key technologies involved in the modeling process were processed, and the reliability of the model was verified by experiments.

Table . 1
Material Performance Parameters of High Strength Stainless Steel Tubes