Bending Deformation And Stress Of Skew Metal Sheets

Techniques of punching sheets have advantages of high material utilization, high production efficiency, high production accuracy and stability, simple production procedures, easy automations. Hence, the techniques of punching sheets are widely used in fields of automobile, airplanes, Electronics, instruments, and various civil products. Bending sheets is one of punching sheet processes. The bending processes of sheets are related to shapes, sizes, thickness, and material properties of sheets. The mould structures also influence the bending processes of sheets. Material properties of sheets are the most important and complicated factors in bending process. When the rolling, transverse, and normal directions of metal sheets are coincident with three axis x_i(i= 1,2,3) of a fixed Cartesian coordinate system respectively, the metal sheets are orthorhombic. When the orthorhombic metal sheets have rotation angleφaround x₃, the rolling and transverse directions of the orthorhombic metal sheets are not coincident with axis x₁, and x₂ respectively of the fixed Cartesian coordinate system yet and the orthorhombic metal sheets become the skew metal sheets. Here we study relations between bending deformation and stress of skew sheets. Our maincontributions in this thesis include:(1) People already give cubic crystallites yield function of orthorhombic sheets, and relationships between deformation and stress in orthorhombic sheets. In this thesis, we derive Hexagonal crystallites yield function of orthorhombic sheets, and yield function which is suitable to the skew metal sheets. We derive the relation betweenbending deformation and stress when the skew metal sheets are bended around x₂,where the metal sheets are aggregates of cubic crystallites or aggregates of hexagonal crystallites. We give the relations among bending stress, texture coefficients, and bending deformation for skew sheets.(2) During bending a metal sheet there exists elastic and plastic deformation in the sheet. After unloading, the elastic deformation will be recovered, which is called springback. Springback is an important factor influencing the forming quality of bending sheets. Hence, in the procedures of bending sheets, we have to consider the effect of sheet springback. People have studied springback problems of bending orthorhombic sheets. Here, we will give expressions of springback on bending skew sheets.(3) Yielding of metals is related to stress components. Hill assumed that yield functions on metals depend on quadratic terms of stress components and derived Hill's yield function. People often use Mises' yield function to solve plastic problems on isotropic metals and use Hill's yield function for orthorhombic sheets. If plastic properties of some metals (such as aluminum) can not be described very well by Hill's yield function, then yield functions should contain effects of cubic terms on stress components. In this thesis we employ a yield function which is given by Man. The yield function is more general than Hill's yield function and includes effect of stress up to cubic terms of stress components. By means of the yield function, we derive the stress field in bending sheets.