EFFECT OF WALL SLIP ON SQUEEZE FLOW OF RIGID-PLASTIC MEDIA BETWEEN PARALLEL DISK

The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium with the following four diferent slip boundary conditions are obtained. (1) The Coulombic friction condition is applied, and the stress distribution on the wall is derived, which is linear or exponential distribution in the no-slip area or slip area. (2) It is assumed that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, with the stress distribution and the squeeze force gained. (3) The assumption that the slip velocity at the disks is related to the shear stress component is used, with the stress distribution and the squeeze force obtained, which is equivalent to the result given in (2). (4) Rational velocity components are introduced, and the stress distribution is satisfed.

Three-Dimensional Rigid-Plastic FEM Simulation of Bulk Forming Processes with New Contact and Remeshing Techniques

Some techniques such as die surface description, contact judgement algorithm and remeshing are proposed to improve the robustness of the numerical solution. Based on these techniques, a three-dimensional rigid-plastic FEM code has been developed. Isothermal forging process of a cylindrical housing has been simulated. The simulation results show that the given techniques and the FEM code are reasonable and feasible for three-dimensional bulk forming processes.

ADAPTIVE RIGID-PLASTIC MESHLESS GALERKIN METHOD AND ITS APPLICATION IN ANALYSIS OF EXTRUSION PROCESSES

Under the hypothesis of the rigid-plastic material, specific efforts are placed on the developments of the key simulation techniques of the meshless Galerkin method because of the complexity of the deformation process as well as the generality and atomization of the simulation procedures for non-steady state large deformation plastic processes, therefore, an adaptive rigid meshless Galerkin method is developed. The influence domain control method is used in the least square approximation by dynamic evaluation of the magnitude of the influence domain and the effective control of the amount and the positions of the points in the least square approximation in order to improve approximation precision. The amount of the Gauss integration points in the discrete domain is maintained in a considerable magnitude in order to ensure the integration precision in the discrete domain. The length of the frictional boundary of the plastic deformation process may be getting longer when its deforma- tion is getting severe. Thus, the densities of the boundary points of some places get lower. The adaptive boundary points setting method is employed to improve the approximation precision of the boundary points and enhance the constraint of the boundary condition by adaptive control of boundary point density. Some typical extrusion processes are analyzed, detail simulation results such as the deformation field, velocity field, effective strain field, effective strain rate field, the volume loss curve and load-stroke curve are obtained. The effectiveness of the method developed is demonstrated and the precision of the meshless simulation is proved by overall comparison with the results obtained by using the commercial software deform.

A Numerical Method for Rigid-plastic FEM Analysis Basing on Mathematical Programming

The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm is used to solve this formulation, which distinguishes the integration points of the rigid zones and the plastic zones and solves a series of the quadratic programming to overcome the difficulties caused by the nonsmoothness and the nonlinearity of the objective function. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method.

Study on Remeshing Technique for Three-Dimensional Rigid-plastic Finite Element Simulation

A new method of three-dimensional remeshing is proposed for rigid-plastic finiteelement analysis of a complicated forging process.The forging process of a cylindricalhousing has been simulated to show the effectiveness of the scheme.The result ofsimulation shows that the computation can be effectively carried out by using the des-cribed remeshing scheme.

RIGID-PLASTIC/RIGID-VISCOPLASTIC FEM BASED ON LINEAR PROGRAMMING-THEORETICAL MODELING AND APPLICATION FOR PLANE-STRAIN PROBLEMS

A new rigid-plastic/rigid-viscoplastic (RP/RVP) FEM based on linearprogramming (LP) for plane-strain metal forming simulation is proposed. Compared with thetraditional RP/RVP FEM based on iteration solution, it has some remarkable advantages, such a it'sfree of convergence problem and its convenience in contact, incompressibility constraint and rigidzone treatment. Two solution examples are provided to validate its accuracy and efficiency.

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC RESPONSE OF RIGID-PLASTIC CIRCULAR PLATE RESTING ON FLUID

A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this interaction problem is reduced to a problem of dynamic plastic response of the plate in vacuum.The closed-form solutions are derived for both middle and high pressure loads by solving the equations of motion with the large deflection in the range where both bending moments and membrane forces are important.Some numerical results are given.

DEEP-DRAWING PROCESS ANALYSIS OF ELLIPTIC CUPS BY RIGID-PLASTIC FEM

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A NOVEL APPROACH FOR THE PREDICTION OF SURFACE PROFILE OF OUTGOING WORKPIECE AND THE CALCULATION OF MEAN ROLL RADIUS IN ALLOY BAR ROLLING

In alloy bar rolling process, the component of alloyed steel influenced the spread coefficient greatly, therefore, the component influence coefficient m of different alloyed steel has been determined firstly to calculate the maximum spread. Then the curvature radius of stress free surface and the ＂critical point on the contact boundary＂ have been solved, the surface profile of outgoing workpiece has been obtained. Furthermore, the formula of the equivalent contact section area has been proposed and the mean roll radius has been calculated. The bar rolling experiment and the rigid-plastic FEM （finite element method） simulation have been carried out to verify the novel approach. Compared with experimental data and simulation results, the novel approach can be used in setting processing parameter and design of finishing groove.

A Numerical-analytic Method for Quickly Predicting Springback of Numerical Control Bending of Thin-walled Tube

Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.

FEM Simulation of Effect of Process Parameters on Static Recrystallization in 60SiMnA Spring Steel

Two-dimensional rigid-plastic finite element method (FEM) was used for simulation of the effect of process parameterson the static recrystallization of 60SiMnA spring steel using MARC/AutoForge 3.1 software. A thermo-mechanicalcoupled analysis was conducted considering the heat transfer between the workpiece, the roll and the environment,and the heat generation due to plastic work. The static recrystallization laws under different processing conditionsand the predicted distribution of the static recrystallization volume fraction on the deformation cross section arepresented.

Constitutive model of disturbed soil-structure interface within mining subsidence areas

The characteristics of a disturbed soil-structure interface were studied based on the variation regularities of the disturbed soil within its mining subsidence area using direct shear tests.The effects of the initial moisture content on the shear strength parameters of the soil-structure interfaces were analyzed.The results indicate that the cohesion of the interface initially increased and then decreased as the initial moisture content increased.In addition,the friction angle of the interface decreased as the initial moisture content increased.A constitutive model of the disturbed soil-structure interface,a rigid-plastic model based on the initial void ratio and saturability(VSRP) model,was established based on the results.In order to validate this model,a finite element analysis of DRS-1 direct shear tests was conducted.The finite element model calculations coincided with the results of the DRS-1 direct shear tests.The proposed model also reflected the nonlinear features of the soil-structure interface.

FEM Analysis of Effect of Die Angle on Tube Inversion Forming Process under Conical Die

Tube inversion including free deformation under conical die is an advanced forming process for manufacturing complicated thin-walled parts with high strength/weight ratio, high efficiency, and good flexibility for size changing.However, the successful reality of forming process, the change of deforming mode and shape and size of part formedare mainly on the die angle. Based on the analysis of the forming process, the model of rigid-plastic FEM (finiteelement method) is established and a numerical simulation system is developed. The effect of die angle on the tubeinversion forming process is investigated with the code developed. The results of the effect of half die angle on shapeof free deformation zone and on deforming load are obtained. There is an optimal die angle (about 75 deg), whichmakes the forming load minimum.

Plastic variational principle based on the least work consumption principle

Plastic variational principles are foundation to solve the boundary-value problems of plastic mechanics with the variational method(or energy method) and finite element method.The most convenient way of establishing different kinds of variational principles is to set up the extreme principle related to the studied problem.Based on a general new extreme principle-the Least work consumption principle,the variational principles of the rigid-plastic and rigid-viscoplastic material were derived.In comparison with existing methods,the method in this paper is more clear and direct,and the physical meaning is clear-cut.This method can offer a new way for establishing other kinds of variational principles.

Simulation and Analysis of Ring Compression Using RP/RVP Meshless Method

To avoid mesh distortion and iterative remeshing in mesh-based numerical analysis,a meshless approach based on element free Galerkin (EFG) method is applied to the metal forming analysis of ring compression. Discrete equations are formulated upon the moving least-squares (MLS) approximation and modified Markov variational principles for rigid-plastic/ rigid-viscoplastic (RP/RVP) material models. The penalty function is used for the incompressible condition without volumetric locking. Based on the axisymmetric mechanical model,ring tests with different friction coefficients are studied. The deformed nodal configurations and shaded contours of equivalent strains are shown by developed meshless post processor. The comparison of meshless and finite element (FE) results validates the feasibility and accuracy for meshless method to simulate metal forming process.

Metal-forming problems with combined hardening

A class of quasisteady metalforming problems under nonlocal contact and Coulomb＇s friction boundary conditions is considered with an incompressible, rigid plastic, strainrate dependent, isotropic, and kinematic hardening material model. A coupled variational formulation is derived, the convergence of a variable stiffness parame ter method with time retardation is proved, and the existence and uniqueness results are obtained.

Dynamic Plastic Response of Circular Plates Resting on Fluid with Finite Deformation

This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.

MULTI-PARAMETER ACCELERATED MODIFIED NEWTON-RAPHSON METHODS FOR RIGIDPLASTIC FE ANALYSIS

Applications of certain multi-parameter acceleration techniques used with themodified New-ton-Raphson (mN-R) methods to solve the nonlinear equations arising from rigid-plasticfinite element analysis are investigated. New modified multi-parameter techniques, developed fromCrisfield's multi-parameter methods, are utilized to solve these nonlinear equations. The numericalperformance of these techniques is compared with the standard Newton-Raphson method (sN-R),Crisfield's single parameter method (C1), Crisfield's two parameter method (C2) and Crisfield'sthree parameter method (C3). The new techniques do not involve additional residual force calculationand require little extra computational effort. In addition, they are more robust and efficient thanother existing acceleration techniques.

Development of simulation system of strip flatness for hot tandem mill

Using three-dimensional rigid-plastic finite element method base on Lagrange multiplier to analyze the deformation of strip,influence function method to calculate the elastic deflection of rolls and three-dimensionalelastic FEM to analyze the flattening deformation between work roll and strip,a coupled model was established with a iteration way.The effect of various kinds flatness control method such as bending force,rolls shift and cross angle and also various kind of influence factors such as friction coefficient,strip crown,rolls wear and thermo-crown on strip flatness can be analyzed using this coupled model.A great deal of information for example outlet crown of the strip,front and back tension,rolling force distribution for per length,rolls elastic deformation and forward slip can be obtained.In order to improve computational efficiency,the average change of rolling force for per unit length was added into the criterion to determine if the coupled process is end,which can save 30 percent computing time for one pass but the changes of strip thickness is not large than 5μm.The exploration has certain conductive significance for improving efficiency of other type of mill.