| Sheet metal forming processes are among the most important metal-working operations. These processes account for a sizable proportion of manufactured goods made in industrialized countries each year. Furthermore, to reduce the cost and increase the performance of manufactured products, in addition to the environmental concern, more and more light weight and high strength materials have been used as a substitute to the conventional steel. These materials usually have limited formability, thus, a thorough understanding of the deformation processes and the factors limiting the forming of sound parts is important, not only from a scientific or engineering viewpoint, but also from an economic point of view.; An extensive review of previous studies pertaining to theoretical analyses of Forming Limit Diagrams (FLDs) is contained in Chapter I. A numerical model to analyze the neck evolution process is outlined in Chapter II. With the use of strain gradient theory, the effect of initial defect profile on the necking process is analyzed.; In the third chapter, the method proposed by Storen and Rice is adopted to analyze the initiation of localized neck and predict the corresponding FLDs. In view of the fact that the width of the localized neck is narrow, the deformation inside the neck region is constrained by the material in the neighboring homogeneous region. The relative rotation effect may then be assumed to be small and is thus neglected.; In Chapter IV, Hill's 1948 yield criterion and strain gradient theory are employed to obtain FLDs, for planar anisotropic sheet materials by using bifurcation analysis. The effects of the strain gradient coefficient c and the material anisotropic parameters R's on the orientation of the neck and FLDs are analyzed in a systematic manner and compared with experiments. In Chapter V, Hill's 79 non-quadratic yield criterion with a deformation theory of plasticity is used along with bifurcation analyses to derive a general analytical expression for calculating FLDs.; In the final chapter, a method is proposed to construct forming limit diagrams for sheet metals under different deformation histories. This analysis employs Hill's 79 anisotropic yield function and uses strain gradient theory to describe the constitutive equation for the flow stress. In order to utilize an analytical method developed earlier for proportional loading, the concept of “virtual deformation” is introduced. The actual deformation path is divided into a sequence of linear paths and an effective “virtual deformation” path is defined having a strain ratio identical to that of the linear part in the final deformation stage, and a plastic work identical to that of the prior actual deformation it is replacing. (Abstract shortened by UMI.)... |
