چكيده به لاتين
Metal forming involves obtaining desired shape and size by subjecting the material to large plastic deformation and is one of the most important steps in manufacturing a large variety of products. Metal forming processes are divided into two categories i.e. sheet metal forming and bulk-forming. Bulk-forming is a controlled plastic flow of material into useful shapes and refers to processes like extrusion, forging etc. Sheet metal is one of the fundamental forms used in manufacturing and it can be changed into a variety of shapes by an industrial process into thin, flat pieces. The sheet metal forming has a wide domain with innovative techniques that the manufacture of complex pieces with simple tools and low costs can be realized. In Sheet metal forming, thin sheet metal blanks through Mechanisms like plasticity and dynamic recrystallization are converted into parts of desired shapes with the processes like deep drawing, bending, cutting etc., for the manufacture of components in automobile and aerospace applications. Sheet metals divided into two categories subjected to their Thicknesses. So that, thin sheets are considered as foils, and pieces with thicker thickness are considered as plates. Mechanical behavior of metal is important to understand in sheet metal products and manufacturing processes. The necking of sheet metal is the main problem in forming processes that cause unacceptable thickness decreasing and leads to stop the process. Generally, a desirable property for metals is a large plastic deformation before necking. The remaining problems to solve are the applicability and the accuracy of the methods for determining forming limits for various strain paths encountered in industrial processes. The modeling of necking occurrence in sheet metal forming is a real challenge for the engineer concerned with the processing of new geometries and materials. Regard that a high total elongation of the material before the fracture is also desirable for sheet metal forming, Forming limit diagram is used in sheet metal forming for predicting the forming behavior of sheet metal. Failure prediction in sheet metal forming is presently mainly based on experimentally measured Forming Limit diagrams. The Forming Limit Diagram or “Forming Principal Strain Map” is the plot of principal true strains in the sheet metal occurring at critical points which provides a graphical description of material failure in formability tests or in the fabrication processes. Mathematical models for theoretical determination of these curves have been developed such as Marciniak and Kuczynski method which is known as the M-K approach. In this study, the investigations on sheet metal forming based on strain gradient plasticity join with conventional M-k approach has been presented. This method considered the effects of deformation inhomogeneity by introducing new constitutive equations. Finite difference method has been used to solve second order nonlinear differential equations of thickness variation and finally, the desired forming limit results obtained. The numerical solution for necking evolution has been presented which has good convergence and rapid time of calculations.
