The Extrusion Process Grid Numerical Simulation Study

With the development of computer technology and computational methods, the finite element method (FEM) gained great achievement and was applied wildly in many engineering fields. Although great success in the metal forming process numerical simulation is achieved by FEM, the mesh distortion will be inevitable for the accumulation of the metal deformation. Compared with FEM, the meshless approximation based on discrete point information has advantages in the simulation of large deformation problems with mesh distortion for getting rid of the reliance on the mesh. But there are still many key techniques, which need more attention for the complexity of the metal deformation in unsteady metal forming process. Especially when the deformation is more severe or metal flow is more complex, the approximation precision of the velocity field and integration precision of deformation domain will be deteriorated for the severe un-uniformity of the metal flow and complexity of the deformation zone. Thus simulation error will be occurred. So, the study focused on the development of the rigid-visco plastic meshless Galerkin method and its key techniques for unsteady large deformation metal forming process.Under the hypothesis of the rigid-visco plastic material, a rigid-visco plastic meshless Galerkin method is developed. An arctangent frictional model is used to describe the frictional boundary condition. For the metal forming processes with arbitrarily shaped dies, the frictional boundary conditions are imposed under the local coordinate system in order to impose mixed boundary conditions directly. The coordinate transform matrix is given for the transformation of the stiffness matrix equation from the global coordinate system to the local coordinate system. Therefore, the stiffness matrix equation is established. The direct iteration method is used to get the initial velocity field for the simulation, the Newton-Raphson iteration method is used to solve the stiffness matrix equation in order to achieve a faster convergence, and the procedures are given for the simulation of the isothermal metal forming problems.For non-steady plastic processes, specific efforts are placed on the modifications of simulation model and developments the key simulation techniques for the meshless Galerkin method based on rigid-visco plastic material hypothesis for the complexity of the deformation process, difficulties of mathematic treatments and the deficiencies in the establishment of the simulation model and the generality of the simulation procedures. The problems, such as the description of dies or workpieces with arbitrarily shaped boundary, iteration convergence criterions and detachment and contact criterion, are solved, the meshless analysis of the non-steady plastic deformation processes with arbitrarily shaped dies is realized, the generality of the analysis programs is improved. The releasing of the volume locking problems encountered in the analysis of the metal plastic forming problems is focused. A releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent constraint equations.The automation of the meshless analysis program is low for necessary artificial modification of the simulation coefficient in meshless simulation for the deterioration of analysis precision and efficiency in metal forming processes with severe deformation or complex metal flow. Therefore a variety of adaptive meshless analysis processing methods are established which enhance the automation of analysis. The velocity field is approximated by compactly supported functions such as MLS and RKPM, so the influence domain of the weighted function or kernel function has important influence on the approximation precision. So a modified adaptive influence domain is introduced in the approximation of velocity filed in order to improve approximation precision. An adaptive background cell partition method is established in order to improve the integration precision by maintaining the amount of the Guass integration points. So, an adaptive boundary points control method is adopted to enhance the frictional boundary condition constrain by adaptive inputting points to the place with less boundary points.Through detail comparisons of simulation data with those obtained by using corresponding rigid visco-plastic finite element method and experimental data, the distribution laws and numerical values of the velocity field, temperature filed and stress and strain distributions obtained by using these two methods are in good agreements, thus the effectiveness of the mathematic model and related key techniques established in this paper are demonstrated.