Formability of Sheet Metal Under Non-Coaxial and Zig Zag Strain Paths

Abstract

The aim of this thesis is to provide a wider conception of the formability of sheet metal to cover a wider range of sheet metal products. In circular cup drawing, the deformation in the work-piece is coaxial owing to axial symmetry; in other words, during the forming operation, the principal axes of stress and strain coincide with each other and are fixed with respect to the material. The directions of the principal axes are along the meridional tangential and the circumferential directions all the time during the forming operation. In non-axisymmetrical forming, however, non—coaxial deformation is involved in the forming operation owing to the lack of axial symmetry. The principal axes of stress and strain do not coincide with each other and they both rotate with respect to the material. To widen the meaning of formability, it is defined on the one hand to mean the forming limits of sheet metal, which is represented by the forming limit curve; on the other hand, to mean the drawability of sheet metal in a drawing process. The forming limits of sheet metal under coaxial simple and coaxial zigzag strain paths as well as the drawability of sheet metal in a circular cup drawing have been investigated by many sheet metal forming research scientists hitherto. There has not been, however, any investigation on the forming limits of sheet metal under non-coaxial strain paths. This omission is no doubt due to the lack of theoretical analysis of non-coaxial strains, as can be seen in the usual incomplete representation for a state of strain by only the three principal strains. Although there are some investigations on non-circular cup drawing, they are all empirical studies, The drawability of sheet metal is up to now limited to ™ circular cup drawing and the definition of drawability is restricted to mean the ratio of the blank diameter to the punch diameter, as defined in the Swift test. In this thesis, a fundamental analysis of non-coaxial strains is pursued, A state of strain is completely represented by the three principal strains and the directions of the principal axes of strain with respect to the material. With the complete representation of a state of strain, a non-coaxial strain path can be represented graphically and is plotted for the first time in this thesis. The relation between the rotation of the principal axis of stress with respect to the material and that of the principal axis of strain is investigated. The non-coaxiality of the principal axes of stress and strain results in a type of zigzag strain path, and such zigzag strain path is also investigated both theoretically and experimentally. At the same time, the definition of drawability is generalised to be the largest draw-in at the completion of the drawing operation so that it is applicable to any shape of cup drawing. An index of non-symmetry is proposed to specify the characteristics of a non-circular forming process. The large volume of useful experimental work which these investigations can lead to is discussed in a separate chapter on suggestions for future work. The achievements of this project are as follows: 1. The investigation of non-coaxial deformations on both theoretical and experimental bases. 2. The generalisation of the definition of drawability and the drawability test to cover all shapes of cup. 3. The provision of a theoretical link between the partial view of stretch ability in the Forming Limit Curve and Swift's Limiting Drawing Ratio to form a more nearly complete view of sheet metal formability.