Research On Linearization Analytical Method Of Metal Plastic Forming Forces And Its Applications

Metal forming technology plays an important role in the manufacturing industry. It has the merits of high productivity, stable quality and effective utilization of raw material. The mechanical properties of the metal are also improved in the forming processes. However, fulfilling the metal plastic deformation, external forces must be exerted and forming parameters must be optimized. The purpose is to achieve energy saving and emission reduction more effectively, reduce production cost and enhance market competitiveness. When the plasticity processing products are used, parameter design and strength check for structural parts are required to ensure the usage safety. Analytical method and numerical method are the main computational methods of solving metal plastic forming force parameters. For most metal forming problems, the existing methods can provide valuable analysis and understanding for simplified actual process and idealized material status; but they are powerless if the problems influenced by many influencing factors and complex boundary equations. At this time, just discrete numerical results can be presented with the help of computer. However, analytical solutions have irreplaceable theoretical value. They play very important roles in understanding essence of the problems, in analyzing physical relationship of different variables as well as in checking numerical methods. In this dissertation, because of the problems of physical equation nonlinearity, geometrical equation nonlinearity as well as the boundary condition complexity in the analysis of forming force for rolling and drawing as well as ultimate bearing capacity for circular plate and steel pipeline, research on linearization analytical method and its applications was carried out. The main works and progresses included are as follows:(1) For the nonlinearity of synchronous rolling (or called symmetrical rolling) power functional, two effective linearization ways for internal deformation power were proposed, one was the strain vector inner product method by linearizing the nonlinear specific plastic work rate of Mises criterion directly. The other was the method via replacing the nonlinear specific plastic work rate of Mises criterion with linear specific plastic work rate approximately. As for the shear and friction powers, the co-line vector inner product method was used. Starting with the analysis of deformation characteristic of heavy plate rolling, the stream function velocity field and global weighted velocity field were proposed, and the analytical solutions of rolling force and torque were first derived, and the effects of friction factor and geometry factor on the location of neutral point were also presented. It is found that the calculated results of rolling forces and rolling torques are consistent with measured ones, change rules of parameters obtained are tally with actual situation, which are complements for this field at home and abroad. The above linearization methods afford enlightenment for power functional analyses of extrusion, drawing, forging, and so on.(2) In allusion to the shortage of the traditional slab method for neglecting vertical shear stress of each slab in the analysis of asymmetrical rolling force, the linear distribution and its quantitative expression of vertical shear stresses in the forward slip zone, cross shear zone and backward slip zone were provided, and the analytical solution of asymmetrical rolling force and torque was obtained by introducing the net shear stress into force equilibrium equation. Compared with the traditional method, it is shown that the new method has improved prediction precision. The proposed analytical solutions of asymmetrical rolling force and torque can exactly reflect the "cross shear" effect. The new method provides a scientific means for the calculation of multivariable coupling, and plays crucial roles for the development and optimization of various traditional methods.(3) With the purpose of simplifying nonlinear power functional integral of crack closing, the upper bound triangular velocity field with central micro crack was constructed, and the critical mechanical criterion for micro crack closing was attained, i.e. when l/h>0.518 the closing of micro crack occurred. Compared with the traditional criteria, the proposed criterion just falls within the allowed experimental range by TapHOBCKHH, and is also concise and convenient to be used relative to that of Kiuchi. Besides, for the current situation of isolated analysis of crack closing and healing, the present dissertation linked them with the local temperature rise of micro crack, and an combined criterion for closing and synchronously healing the central micro crack was first established. The direct dependency between micro crack closing and healing was clearly revealed. The impacts of main rolling parameters on the crack healing were also discussed. The pre-placement crack rolling experiment and field application show that the present combined criterion is reasonable, and has the practical significance of realizing reduction rolling and improving central internal quality for heavy plate.(4) In order to further investigate the characteristic of linearization analytical method and to expand its application scope, a velocity field for conical die drawing in cylindrical coordinate system and the other velocity field for twin parabolic die drawing were established, and the linearization analyses of their internal deformation powers were conducted. Research shows that both the strain vector inner product method and the method of replacing the nonlinear Mises specific plastic work rate by MY (Mean Yield) specific plastic work rate are also applicable to the analysis of drawing force. Calculation of drawing forces shows that the calculated results using strain vector inner product method for conical die are coincide with Avitzur’s upper bound results according to spherical coordinate velocity field; the calculated results for twin parabolic die are in agreement with FEM simulated results. In addition, since the stream function condition of the twin parabolic die is satisfied, the die does not dissipate shear power. This leads to the advantages of decreasing drawing force evidently, improving stress concentration, reducing wear of die, and increasing yield when the proposed die is used. Since the die accords with the requirement of modern production, it has broad application prospect. The above two linearization ways provide a new idea for effective integral of power functional for complex curve die.(5) In view of the problems of traditional analytical methods in solving the limit loads of simply supported circular plate, two linearization methods, defined as power linearization method and stress linearization method, were proposed respectively. These two methods are obviously different. The former starts from principle of energy balance, and is based on kinematically admissible velocity field; and the latter starts from principle of force balance, and is based on statically admissible stress field. Both the above two methods have solved the problems of wasting material due to conservative prediction by Tresca criterion and obtaining numerical results only owing to the analysis difficulty from nonlinearity of Mises criterion in the analysis of limit load of circular plate. It is demonstrated that the present EA (Equal Area) and GM (Geometrical Midline) results of limit loads lie between those based on Tresca and TSS (Twin Shear Stress) criteria, and are closed to the numerical results based on Mises criterion. The two proposed solutions have high prediction precision. The calculated results of limit loads are well with FEM simulated results, which has further validated the feasibility and effectiveness of the two linearization methods. The above methods will play very important reference values for the analytical solutions of other engineering structure components.(6) According to the need of linearization analysis, an equal perimeter (called EP for short) yield criterion with definite geometrical meaning was first developed and its expression of specific plastic work rate was also deduced. The yield locus of this criterion on the π plane is an equilateral but non-equiangular dodecagon, which has high approximation degree to Mises circle. Considering the deformation characteristic and development tendency of pipeline steel, the limitation of rigid-plastic material hypothesis adopted in traditional methods has been overcome. In the application of MY and EP yield criteria to burst pressures of straight pipe and pipe elbow, the superiority of calculus of variation for the ability to obtain strain field has been incorporated effectively. The combined analysis by the two methods played complementary advantage role, and the results obtained have given full consideration of the strain hardening exponent. Research finds that taking (?)p/(?)ε=0 as the burst failure criterion is reasonable, and the geometrical size, engineering tensile strength, strain hardening exponent as well as the curvature influencing factor of pipeline are the key factors to the burst pressure. Experimental data has verified the correctness of the analytical results. The MY and EP solutions of burst pressures obtained have significant meaning to material selection, design and safety assessment for pressure pipeline.