Towards An Advanced 14-Node Brick Element For Sheet Metal Forming
Sheet metal forming is used in a wide range of industrial processes ranging from tube manufacturing to automobile and aviation industry. It includes processes like stamping, bending, stretching, drawing and wheeling. In the past few years materials for sheet metal forming and, technology have improved a lot. The improved materials have higher strength and more ductility than conventional sheet steel and therefore they have to be worked differently. For such steels conventional methods can not be applied totally. So there is a need for constant improvement in technology. Trial and error method currently in use increases lead time and is not economic also. To overcome the problems, use of simulation software in metal forming processes has increased significantly. The rapid development of software technology accompanied with lower cost computer hardware have enabled many manufacturing operations to be modeled cost-effectively that only a few years ago would have been considered impractical. However there are some difficulties in simulation of sheet metal forming process. For example it is never an easy task to select the correct software for a particular process. Various authors ascribe different causes for the difficulties. Among them the prominent ones are lacunae in elasto-plastic modeling, material behaviour, involved complexities and a lack of good elements. Apart from that the demands of sheet metal processes are increasing both with respect to the tolerance requirements of the finished part and with regard to geometric complexity of the part to be formed. A few years ago finite elements have been developed using Papcovitch-Neuber solutions of the Navier equation for the displacement function. Among these elements PN5X1 has the abilities to predict both displacements and stresses accurately. And recently the element is extended to include material nonlinearity and is working well for the small deformation range. To use this element for sheet metal forming it is necessary that the element should predict correct results for large deformations. In the present work we have further extended this element for large displacements and large rotation. In the literature there are various algorithms recommended for use with large deformation. Among them we have selected a suitable algorithm and verified its usefulness. First we have taken a simple truss and applied loads to cause large deflection. We observe adequate convergence with the chosen algorithm and then we extend it to PN5X1. in large deformation analysis, equilibrium is computed about the deformed shape. In the chosen algorithm we apply incremental loading and within each load step loop we iterate for equilibrium. We ensure error free solution (equilibrium) before additional loading is introduced. With the help of flowchart these processes have been depicted. A computer program in C, based on the above incremental method and equilibrium check has been written. For the purpose of verification of the program, we have solved some benchmark tests. We start with linear cases and then attempt a number of geometric nonlinear problems like- cantilever subjected to end shear, pinched cylinder with open end etc. We have also included the classical benchmark problem of the cantilever subjected to end moment. The present algorithm gives solutions which are in excellent agreement with those reported in the literature. Finally, we look at some aspects of the problem which require further investigation.