| The bulk metal forming process is a kind of metal working method having little or no cutting. It plays a significant role in modern manufacturing. An accurate simulation of the bulk metal forming process accurately can not only save high costs of the experiment, but also have significant theoretical guidance meaning and realistic application value for determining the reasonable forming process and ensuring die design completed at the first time successfully. With the development of calculation method and computer technology, numerical analysis method becomes a powerful tool to analyze engineering problems. Finite element method (FEM) has played an important role in the numerical simulation of bulk metal forming processes. However, when simulating large and severe deformation processes such as forging and extrusion, FEM often encounters some difficulties that meshes become severely distorted and remeshing is necessary because of complicated metal flowing and large deformation. And then the computation process can not be carried on continually and remeshing often brings excessively time-consuming and causes deterioration of computational precision especially.The meshless method is a new numerical computational method developed in recent years. Compared with FEM, the main benefit of the method is that the approximation field function is constructed entirely in terms of arbitrarily placed nodes of structures without using explicit mesh. And it shows obvious advantages in treating with large deformation problems because it gets rid of the reliance on the mesh and provides continuous and flexible field function. Many researchers have applied meshless method to solve metal forming problems in recent decade and made some achievements. And that drives the development of meshless numerical simulation technology applied for analyzing the metal forming process. But the researches on the application of meshless method in simulating three-dimensional unsteady bulk metal forming process are imperfect, and there are still many key application technologies to be further studied. Therefore, according to the characteristics of bulk metal forming process and technological requirements, the paper establishes rigid/visco-plastic element free Galerkin method and applies it for the analysis of three-dimensional unsteady bulk metal forming process. On the basis of further studies of rigid/visco-plastic element free Galerkin method and corresponding key numerical simulation techniques, a meshless method numerical analysis procedure for simulating the bulk metal forming process is developed. And a scientific, accurate, reliable, and new meshless method numerical simulation tool is provided to the actual production.Researches on the three-dimensional element free Galerkin method are carried out. Element free Galerkin method uses moving least square method to construct shapefunction, and to obtain shape function A-1 (x) should be calculated firstly. The cases about matrix A(x) appearing irreversible in three-dimensional problems are discussed,and the approaches to treat with this problem are given. The paper employs the orthogonal function with the weight function as the basis function to avoid the processof calculating the inversion of matrix A(x). The size of node influence domain hasgreat effects on computational accuracy and efficiency of element free Galerkin method. The size of node influence domain should be determined following the rule of "sufficiently large and as small as possible". The dynamic node influence domain method is utilized to obtain reasonable node influence domain size, and this method not only guarantees the computational accuracy but also improves the computational efficiency. Due to the lack of Kronecker delta properties in the element free Galerkin method shape functions, the essential boundary conditions can't be imposed directly. In order to exert the boundary conditions directly, the mixed transformation method is adopted to modify shape function, then the modified shape function has the interpolation property and the essential boundary conditions can be enforced exactly and directly. The realization process for the three-dimensional element free Galerkin is studied. The implementation method of the regular hexahedron fixed background cell quadrature technique is introduced. And programming steps for element free Galerkin method are given. Influences of basis function, weight function, Gauss quadrature order and node density on the computational accuracy and efficiency are researched, and the influence law is obtained.Combining element free Galerkin method and rigid/visco-plastic flow theory, the paper establishes the three-dimensional rigid/visco-plastic element free Galerkin method, and applies it to analyze three-dimensional bulk metal forming process. The velocity field is approximated by MLS method. Based on the expression of velocity field approximation function, the discretized formats of strain rate vector, effective strain rate and volumetric strain rate are established. By employing penalty function method to constrain incompressibility condition, and according to incomplete generalized variational principle, compositions of total energy rate functional are given. Moreover, the variations of the compositions are derived and expressed in matrix forms. The treatment method for the frictional conditions along the workpiece-die interface is studied. The arctangent frictional model is used to implement the frictional boundary conditions. Boundary condition is imposed correctly in the three-dimensional local coordinate system for simulating three-dimensional bulk metal forming process with arbitrarily geometrical shaped dies. The stiffness matrix equation of RVPEFGM is derived and assembled in the local coordinate system. The New-Raphson iterative procedure is implemented to solve stiffness matrix equation until a converged result is obtained. Basic theory research of rigid/visco-plastic element free Galerkin method is improved. Also simulation analysis steps and program flow are presented.Most bulk metal forming process in practical production belongs to three-dimensional unsteady metal plastic process with severe and complex deformation. Applying RVPEFGM to guide practical production and improving the generality and automation of the analysis program can take advantages of meshless method in treating with bulk metal forming process. According to the characteristics of bulk metal forming process and technological requirements, the related key simulation techniques for analyzing three-dimensional bulk metal forming process used by element free Galerkin method are studied. The problems, such as the description of dies, establishment of local coordinate system for contact points, the way to get initial velocity field, numerical iteration convergence and control method for velocity field, method for dealing with the rigid region, method to release the volumetric locking problem, node detachment and contact criterion, and implement of regional and boundary numerical integration, are solved.The finite elements are used to describe the mould cavity, and the interface program for reading STL data in ASCII format is developed. The method to establish the local coordinate system for contact point is proposed, and the transformation matrix between global coordinate system and local coordinate system is given. There are rigid regions during metal forming process. The method for avoiding numerical problem caused by rigid region in metal plastic forming is given. Initial velocity field determines the convergence and convergence rate of Newton-Raphson iteration. The direct iteration method is used to get initial velocity field guess for Newton-Raphson iteration. The method of "rapid drop slow ascend" is employed to search convergencedirection and the selection method of the attenuation factorβis given, thus theconvergence velocity of the Newton-Raphson iteration can be improved. Volumetric strain rate projection method is proposed to solve volumetric locking and pressure oscillation problems. A releasing algorithm is realized by modifying the volumetric strain rate in the governing 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 automatic technique for handling the contact and detachment states among the deforming material boundary and die surfaces is focused. And concrete algorithms of dynamic adjusting techniques are established. The reposition of the contact node is modified in terms of shortest distance principle from the contact node to the triangle patch, thus the "blind area of normal vector" caused by drawing vertical line to triangle patches to search perpendicular point due to scatted die surface meshes can be solved. The partition of unity method is introduced into regional numerical integration to avoid the integration precision loss because of decreasing Gauss integration points in three-dimensional metal forming process simulated by RVPEFGM.Based on the studies of rigid/visco-plastic element free Galerkin method and related key technology, an analysis program for simulating three-dimensional bulk metal forming processes is developed. And the program is capable of simulating three-dimensional unsteady bulk metal forming processes with severe deformation and arbitrarily shaped dies. The typical metal forming processes such as forging and extrusion processes are analyzed. The effectiveness and validity of the proposed methods and techniques are demonstrated by comparing with the numerical data obtained by using FEM and experimental data. The accuracy and reliability of the rigid/visco-plastic element free Galerkin method and numerical simulation program are ensured by correcting theoretical model and maintaining programs based on the experimental verification and numerical examples analysis.An equal channel angle extrusion process and a furcation hot forging process are simulated by using the program developed in this paper. Detail mechanical data are obtained. The deformation rules, distributions of the effective stress and effective strain and the load stroke curves are studied. The deforming mechanism of the equal channel angle process is better understood and reasonable forming processes of furcation hot forging are obtained. The scientific guide for optimizing process and die design for practical metal forming production is realized.
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