Titanium alloys are peculiar in characteristics such as high strength, temperature, and corrosion resistance. Therefore, titanium alloys are widely-adopted in aircraft engines, fuselages, and landing gears. However, the aerospace fuselage requires thin-walled structures, involving thin curved surfaces, complicated structures, and poor rigidity. So, bending or twisting during the manufacturing process is very obvious. The failure to meet the design requirements and assembly accuracy severely affect production efficiency and cost of the product. Therefore, it is imperative to determine the bending deformation precisely. With the rapid development in the aviation industry, demand for plates, beam, and shafts for aerospace structural parts is increasing, which has promoted the development of the theory of bending correction. The straightening process of thin-walled structures is a typical elastic-plastic bending deformation process. The elastic-plastic mechanical properties of the workpiece material under the external force are directly related to the success of the straightening.
According to elastic-plastic mechanics, elastic-plastic deformation of materials is a complex non-linear problem, and the stress-strain relationship no longer follows Hook’s law. With the progress of the straightening process, the amount of plastic deformation continues to increase, the metal rheological strength also increases, and the yield limit may increase in one direction and decrease in the opposite direction. The stress and strain in the process are incredibly complicated. For this reason, many scholars have done much research on the mechanical properties of materials in the process of straightening. Megharbel et al introduced an analytical analysis of the elastic-plastic bending of tubes and sections with different shapes. Analytical methods are given in the form of equations to provide a quantitative method for predicting the moment for forming the section of the tube to a specific radius of curvature. The results obtained show that the present analysis is more realistic to represent the material behavior since the applied constitutive equation is in the form of a power-law equation. Al-Qureshi presented a theoretical analysis of the elastic-plastic bending of the tube.
Analytical methods are given whereby approximate equations are derived from providing a quantitative method for predicting the springback behavior and residual stress distributions. Experiments were performed on materials with different work hardening characteristics. Chakrabarty et al have studied the theoretical for the elastic or plastic bending of sheet metal 57 exhibiting a state of normal anisotropy. The relationship between the bending couple and the curvature of the bent sheet is in a graphical form that reveals the influence of anisotropy and strain-hardening on the bending characteristic of the sheet metal. The results indicate that the elementary bending theory significantly overestimates the magnitude of the bending couple to produce a given elastic or plastic curvature of the bent sheet. Zhao carried out cyclic three-point bending tests on two types of sheet metals. Strain hardening and Bauschinger effecs for both materials were detected. The three finite element models are presented to numerically simulate the three-point bending. The different hardening laws were applied with a simplified non-contact finite element model. The cyclic stress-strain curves are generated based on the identified material parameters.
It is difficult to establish a unified analytical model between the straightening curvature, the straightening bending moment, and the straightening stroke due to the non-linearity of the workpiece material properties and the contact relationship, and even the difference in the 70 cross-sectional structure. Numerous research studies have targeted specific research on elastic-plastic mechanics and experiment data. They have established related straightening theory models. Regarding the straightening theory, especially the relationship between the straightening curvature and the straightening moment, analytical models have the utmost significance, which significantly promotes the straightening theory. For the analytical solution, Song et al studied the springback in T-section rails after lateral bending, considering the work-hardening materials. The authors have established the analytical formulas for the springback and residual curvatures. The numerical results indicate that the material hardening directly affects the accuracy of spring-back prediction compared with the experimental results. Johnson and Yu have determined the elastic springback in elastic work-hardening beams and plates under elastic-plastic pure bending and determined the mathematical model for the final curvatures.
Kosel et al have investigated a repeated elastic-plastic pure plane bending/unbending process of beams made of a material with an elastic-linear hardening rheological model. The attentions are devoted to beams having cross-sections that have at least one axis of symmetry and are initially straight or have a constant radius of curvature. Boris et al have considered the deflection analysis of beams with rectangular cross-section under specific loading conditions, resulting in at most quadratic bending moment distribution and assuming elastic-plastic behavior with no hardening. Within the framework of small strain and small displacement approach, analytical solutions are derived, which enable elastic-plastic analyses of beams to be performed in a closed analytical form. It is challenging to find the straighten-strokes precisely for automatic straightening machines. The existing calculation method of straightening stroke is based on a straightening curvature equation. Because the initial curvature is obtained by the curve fitting method, the method is inconvenient to use and not very accurate. Li et al put forward a method to calculate straighten-stroke based on the straightening model. The straightening process model for shafts is developed according to the elastic-plastic mechanic’s theory.
By using the model, the straightening stroke can be calculated directly according to the initial deflection of the bent part. Zhai has studied the effect of elastic region ratio on precise straightening of sheets. The m ξ β euation is presented and is used in an automatic straightening technique. In a nutshell, the bending correction of titanium alloy is usually heat treatment correction. Unlike the usual cold correction, the high-temperature correction has different behavior. The correction process becomes very complicated due to stress relaxation. This study is a novel in nature that establishes the constitutive relationship between materials properties and the true stress-strain model of Ti6Al4V material, which can be more accurately describe the true stress-strain relationship of materials. In order to grasp the inherent mechanism of high-temperature spring-back and quantitatively predict the spring-back amount, this paper is based on the theory of elastic-plastic mechanics and combined with the mechanism of stress relaxation to establish the spring-back and residual relative curvature equations of spring-back at different bending degrees, respectively. The law of straightening spring-back is further explored, and the spring-back and residual deflection equations are provided.