Elasto-plastic Finite-Element Analysis of the Axisymmetric Tube-Flaring Process with Conical Punch

The incremental updated Lagrangian formulation of an elasto-plastic finite-element computer code has been incorporated into the extend rmin technique in order to handle the contact boundary condition as applied to the analysis of the axisymmetric tube-flaring process with a conical punch. A modified Cou-lomb’s friction law was also adopted to calculate the influence of friction coefficients on the tube-flaring process. Effects of the size and the mechanical properties of tubes, lubricants and the punch semi-angle on the flaring load were studied. It was found that good lubrication and tubular materials with a high strain hardening coefficient are both effective in reducing the flaring load. An optimum punch semi-angle (punch load is lower) in flaring is determined by work on frictional and bending at the punch inlet. In addition, the effect of spring-back on the tube diameter or angle of final deformation, under different friction coefficients after unloading, was also explored.     

Study on multiple-step incremental air-bending forming of sheet metal with springback model and FEM simulation

A mathematical model of springback radius was developed with dimensional analysis and orthogonal test. With this model, the punch radius could be solved for forming high-precision semiellipse-shaped workpieces. With the punch radius and other geometrical parameters of a tool, a 2D ABAQUS finite-element model (FEM) was established. Then, the forming process of sheet metal multiple-step incremental air bending was simulated with the FEM. The result showed that average errors of the simulated workpiece were +0.68/?0.65 mm, and provided the process data consisting of sheet feed rate, punch displacement and springback angle in each step. A semiellipse-shaped workpiece, whose average errors are +0.68/?0.69 mm, was made with the simulation data. These results indicate that the punch design method is feasible with the mathematical model, and the means of FEM simulation is effective. It can be taken as a new approach for sheet metal multiple-step incremental air-bending forming and tool design.     

An analysis of hemispherical punch stretching by the energy method

An approach using the energy method in which the total deforming region is divided into several sections of different geometric shapes is suggested for the analysis of axisymmetric sheet metal forming with friction boundary condition. The corresponding solutions are found through optimization of the total energy dissipation with respect to some parameters assumed in the velocity field as well as in the corresponding geometric profile. Computations are carried out for hemispherical punch stretching of normal anisotropic work-hardening materials for several lubrication conditions. The punch load vs stroke relation, geometric configuration and strain components are determined from the computation. The comparison of the computed results with finite element solutions and corresponding experiments shows good agreements of solutions in load vs stroke, deformed profiles and strain distribution for various lubrication conditions. It is thus shown that the present simple approach can be effectively employed for the analysis of axisymmetric sheet metal working processes.     

Effects of process variables on V-die bending process of steel sheet

This investigation aims to clarify the process conditions of the V-die bending operation of steel sheet. It provides a model which predicts the correct punch load for bending and the precise final shape of products after unloading, in relation to the tensile properties of the material and the geometry of tools. The process variables are punch radius (R_p), die radius (R_d), punch width (W_p), punch speed (V_p), friction coefficient (μ), strain hardening exponent (n) and normal anisotropy (R).This investigation is carried out by performing some experiments and by finite-element simulation. Experiments determine the punch for bending for various process variables, such as punch radius, punch speed and lubrication, were carried out. As a result it was found that punch load increases as punch radius and punch speed increase or lubrication decreases.An elasto-plastic incremental finite-element computer code based on an updated Lagrangian formulation was developed to simulate the V-die bending process of sheet metal under the plane-strain condition. Isotropic and normal anisotropic material behavior was considered including nonlinear work hardening. A modified Coulomb’s friction law was introduced to treat the alternation of sliding–sticking state of friction at the contact interface. Simulation results, such as the punch load of bending and the bend angle of the bent part after unloading, are compared with experimental data; satisfactory agreement was observed. The simulation clearly demonstrates that the code to simulate V-die bending process was efficient.Simulations were made to evaluate the effects of die radius, punch width, strain hardening exponent and normal anisotropy on punch load of bending. The punch load for bending is smaller for materials with a larger strain hardening exponent. The effect of punch width on punch load is limited. The punch load decreases in the early stage and increases in the final stage of the bending process as the die radius increases. The influences of all of the process variables on the final bend angle of the bent parts of sheet after unloading were also evaluated. The effects of process variables except die radius on the bend angle after unloading are also limited. The angle of spring-back is greater for tools with larger die radius.     

Finite-element simulation of hole-flanging process of circular sheets of anisotropic materials

A hole-flanging operation on a flat circular sheet with a hole in the center is simulated by an incremental elasto-plastic finite-element method, which incorporates strain-hardening and anisotropy in the direction normal to the sheet, with care taken to describe the boundary conditions of penetration, separation and the alternation of the sliding—sticking state of friction. The simulation clearly demonstrates the processes of generation of deformation shape until unloading. The calculated sheet geometries and the relationship of punch load to punch stroke are in good agreement with the experimental data.The stress at the hole periphery in the flange is assumed to a state of circumferential uniaxial tension, in order to simplify the fracture mode as a simple tension test. By making use of the instability of uniaxial tension, an approximate relationship to determine the onset of necking of the hole periphery in the hole-flanging process is derived and it is found to be influenced by the process geometry and the plastic properties of the material, such as the stress-concentration factor K, strain-hardening n and normal anisotropy R, and the estimated value, being obtained by the derived equation, agrees well with the experimental data.It is noted that the derived relationship for estimating the instability of the hole-flanging process can be combined into the developed finite-element model to simulate the critical condition of the limiting deformation of the hole-flanging process. This combined method could possibly be applied towards improving both the manufacturing process and the design of tools for the hole-flanging operation.     

An elasto-plastic finite element analysis of the sheet metal stretch flanging process

The incremental updated Lagrangian elasto-plastic finite element method (FEM) was employed in this study to analyse the stretch flanging of circular plates with a pre-determined smaller hole at the centre of the sheet metal. An extended r _min technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary condition along the tool-sheet interface. The experimental results, using a low-carbon (BA-CQ₂) sheet plate with a thickness of 1.0 mm, have been obtained and compared with the corresponding theoretical results. It was found that the flange thickness does not always decrease monotonically from the die shoulder to the flange edge. Reducing the punch diameter and increasing the flange height significantly reduced the flange thickness. Web width does not influence the thickness distribution of the flange. The tendency of flange thickness to thin decreases as punch diameter increases. The reduction of thickness at the die shoulder depends on the die shoulder radius. Simulation results of punch load of stretch flanging, the deformed geometry, and the distribution of thickness are compared with experimental data and found to satisfactorily agree.     

Influence of blank profile on the V-die bending camber process of sheet metal

The finite element simulation is now widely used in the design of stamping tools. A trial and error procedure has been replaced by a simulation in which defects associated with sheet forming processes are predicted and evaluated. This paper aims to clarify the process conditions of the V-die bending of a sheet metal. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of the products after unloading. An incremental elastic-plastic finite element computer code, based on an updated Lagrangian formulation, was developed to simulate the V-die bending of sheet metal. In particular, the assumed strain field (ASF) element was used to formulate the stiffness matrix. The r-minimum technique was used to deal with the elastic-plastic state and solve contact problems at the tool-metal interface. A series of experiments were performed to validate the formulation in the theory, leading to the development of the computer codes. The predicted punch load in the finite element model agrees closely with the experimental results. The whole history of deformation and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite element method .A unique feature of this V-die bending process is the camber after unloading. The computer code successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank on the camber process. The results in this study clearly demonstrate that the computer code efficiently simulated the camber process .     

Flaring and nosing process for composite annoy tube in circular cone tool application

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the flaring and nosing processes of a metal tube in the asisymmetric condition. The extended r _min technique was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The forming performed analysis using the finite element method and experiment. To examine the influence of the thickness ratio and the optimum punch semi-angle and friction on the forming load of the two-ply metal tubes consisting of soft aluminum, hard aluminum, and copper. The calculated tube geometries and the relationship between punch load and stroke are in good agreement with the experimental data.     

Influence of Cone Semi-Angle on the Formability Limitation of the Hole-Flanging Process

A hole-flanging process on a circular plate with a predeter-mined smaller hole in its centre has been analysed using the incremental updated Lagrangian of the elasto-plastic finite-element code. An extended r-minimum technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary conditions along the tool–metal interface. Coulomb’s friction law was adopted to solve the frictional effect of the tool–metal interface. This work aims to investigate the influence of the cone semi-angle of various truncated conical punches on the limitation of formability in the hole-flanging process. Experimental results, using a low-carbon (BA _ CO2) sheet plate with a thickness of 1.18 mm, have been obtained and compared with the corresponding theoretical results. It was found that the limitation of formability during the forming process is not affected by the cone semi-angle of the truncated conical punch but the finish shape and maximum punch load are dependent on the cone semi-angle.     

Finite element analysis on the V-die coining bend process of steel metal

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the V-die coining bend process of sheet metal under the plane-strain condition. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The r-minimum method was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. V-bends of sheet metals are classified according to the number of contact points of the sheet with the bending die, and include air bends, bottoming bends, and coining bends. The former has three contact points with the bending die at the punch top and die shoulders, and there have been many experimental and analytical research works reported on it. The latter two are in contact at a greater number of points. To clarify the bending characteristics, it is necessary to fully understand the process and stress state in the bent part. The experiment was performed to validate the theoretical formulation and to support the development of the computer code. Simulation was performed on the punch load of the coining bend and the bend angle of the bent part after unloading. Calculated sheet geometries and the forming force agree well with the experimental data. The simulation clearly demonstrates the efficiency of the code to simulate V-die coining bend processes that proceed under contact history.     

Finite element analysis of plane-strain sheet bending

Sheet bending between the die and the punch is analyzed as a bulk deformation process under the plane-strain condition by the finite-element method. The two finite-element formulations used for the analysis are the rigid-plastic analysis using the incremental theory and the elastoplastic analysis with large-stain formulation. The two solutions are compared in terms of detailed mechanics during bending. Spring-back and residual stresses upon unloading are obtained by rigid-plastic loading and elastoplastic unloading calculations as well as by the elastoplastic calculations for loading and unloading. The solutions agree with each other very well with minor differences.     

Metal flow prediction during sheet-metal punching process using the finite element method

In this study, part springback and metal flow caused by punch penetration into a sheet was investigated by punching circular test specimens with concentric circular tools. Strain gauges were bonded on the upper surface of the specimens at radial distances varying from 2 mm to 10 mm from the cutting edge of the punch. The experiments were used to validate a finite element model (FEM) valid for numerical simulation of sheet-metal punching processes. Damage and crack propagation were taken into account by means of an elastoplastic constitutive law. The main difficulty encountered in simulating this operation is describing the behaviour of the sheet continuously from the beginning of the operation up to the total rupture. The choice of a behaviour law is crucial, since each successive step in the whole process has to be described accurately. In this investigation, an elastoplastic behaviour law coupled with damage was retained to describe the progressive damage accumulation in the workpieces. During the analysis, the initiation of a crack is assumed to occur at any point in the structure where the damage reaches its critical value D _c . The crack propagation is simulated by the propagation of a completely damaged area. This is taken into account in the FEM by a decrease in the stiffness of the broken elements. The numerical results obtained by the simulation were compared with the experimental ones in order to verify the validity of the proposed FEM.     

Modeling and simulation for multiple-step incremental air-bending forming of sheet metal

Based on Hill’s yielding criterion and plane strain condition, the explicit expressions of elastoplastic constitutive model are derived in this paper which takes into account the effects of transverse stress, neutral surface shifting, and sheet thickness thinning on the sheet springback of air-bending. Then, this model is embedded into ABAQUS software platform by means of programming. Finally, 3D ABAQUS finite-element models (FEM), used to form the semiellipse-shaped workpiece with super length and large opening of sheet metal, are established, and the multiple-step incremental air-bending forming and springback processes are simulated. The simulation and experiment results show that the data predicted with the new constructed constitutive model under the plane strain condition are in much better agreement with experimental data than those predicted with the constitutive model built-in ABAQUS. It can be taken as a valuable mathematical tool used for multiple-step incremental air-bending forming simulation of large area sheet metal.     

Finite element analysis of tube inversion process with radiused dies

The extended r_min technique has been incorporated in the incremental updated Lagrangian formulation (ULF) of an elasto-plastic finite element computer code in order to handle the contact boundary condition when analyzing the axisymmetric tube inversion process with a quarter fillet die radius. A fillet die applies an axial compressional load onto a thin tube so that the inside or outside of the tube inverts totally making the central axis of the original tube the same as a new double-walled tube. This is called an inside-out or outside-in inversion process. This study employs an elasto-plastic finite element method to simulate and analyze inside-out inversion. The objective is to examine how different process factors, such as the geometry and material modulus, influence metal tube inversion. This study also simulates a quarter fillet radius of the die to analyze the tube forming condition and range that can be applied in engineering under these requirements. In addition, the axial compressional load under inside-out inversion stability to be suitable for a personal computer, so it can be effectively analyzed and evaluated on line instantaneously.     

An Analysis of Draw-Wall Wrinkling in a Stamping Die Design

Wrinkling that occurs in the stamping of tapered square cups and stepped rectangular cups is investigated. A common characteristic of these two types of wrinkling is that the wrinkles are found at the draw wall that is relatively unsup-ported. In the stamping of a tapered square cup, the effect of process parameters, such as the die gap and blank-holder force, on the occurrence of wrinkling is examined using finite-element simulations. The simulation results show that the larger the die gap, the more severe is the wrinkling, and such wrinkling cannot be suppressed by increasing the blank-holder force. In the analysis of wrinkling that occurred in the stamping of a stepped rectangular cup, an actual production part that has a similar type of geometry was examined. The wrinkles found at the draw wall are attributed to the unbalanced stretching of the sheet metal between the punch head and the step edge. An optimum die design for the purpose of eliminating the wrinkles is determined using finite-element analysis. The good agreement between the simulation results and those observed in the wrinkle-free production part validates the accuracy of the finite-element analysis, and demonstrates the advantage of using finite-element analysis for stamping die design.     

Three-dimensional finite-element method simulations of stamping processes for planar anisotropic sheet metals

A three-dimensional finite-element method (FEM) was developed to simulate forming processes with arbitrarily shaped tools for planar anisotropic sheet metals. An implicit, updated Lagrangian formulation based on an incremental deformation theory was employed along with a rigid-viscoplastic constitutive equation. Contact and friction were considered using the mesh-normal scheme which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relationships, which includes the equilibrium equation and mesh-normal geometric constraints, was appropriately linearized. Based on membrane approximation, linear triangular elements were used to describe formed sheets. The non-quadratic strain-rate potential previously developed by Barlat et al. was employed to account for the in-plane, anisotropic properties of sheets. Numerical simulations were performed for the deep drawing of a cylindrical cup and the stamping of an automotive front fender panel to test the planar anisotropic finite element code. In the cup-drawing analysis of a 2090-T3 aluminium alloy sheet sample, the predicted earing profile and cup height were compared with experiments. The predicted and experimental thickness strains were in relatively good agreement, even though thinning trends between rolling and transverse directions were reversed. In the fender stamping analyses of both the aluminum alloys and a mild steel sheet, the numerical stability, accuracy, and usefulness of the formulation were confirmed for automotive applications. In-plane, anisotropic effects on the forming limit curves are also discussed.     

Sheet stretching: A theoretical-experimental comparison

This paper presents numerical solutions of axisymmetric sheet stretching employing an experimentally determined stress-strain curve and measured overall coefficient of friction along the punch-sheet interface. Experiments have been conducted on thin sheet metals such as mild steel, aluminum and brass with a hemispherical steel punch. Predicted values of loads, deflections, strain distributions and other relevant data are favorably compared with experimental values of these same quantities.     

基于Deform-2D的薄板冲裁有限元分析

使用DEFORM-2D软件,对薄板零件精密冲压加工过程进行了有限元分析。从薄板精密冲压件的剪切面光亮带长度、塌角的宽度和深度以及毛刺等质量因素来分析凸模和凹模间隙、凹模刃口圆角、压边齿圈的位置和高度等工艺参数的优劣,获得了最佳的工艺参数。在最佳工艺参数下,薄板精密冲压件的剪切面光亮带长度提高了一倍,基本达到精密冲压的工艺要求,为薄板精冲模具设计提供了参考依据。