金属板料拉延二次成形的有限元法模拟

建立了二次拉延成形加工的有限元分析计算模型;采用一次成形-回弹计算-二次成形的连续计算过程模拟了实际加工过程;有限元计算采用动力显式计算程序MSC/DYTRAN;用主从面（master surface-slave surface)模型定义板料和模具的接触,摩擦力用库仑定律计算;利用动力松弛法对成形过程中的回弹进行了计算。模拟结果和实际零件比较,证明模型合理,自满稳定,结果可靠,具有良好的应用价值。     

Rate-dependent quasi-flow corner theory for elastic/visco-plastic materials

A rate-dependent quasi-flow plastic constitutive model with punch-speed sensitivity is proposed for the large-deformation sheet metal forming process, which is based on the quasi-flow corner theory and U–L formulation for the virtual work-rate equation. Three kinds of constitutive theories with strain rate dependence, classical flow theory, deformation theory with rate form obeying non-orthogonality rule, and the present quasi-flow corner theory, are introduced into the U–L finite element formulation to simulate the deformation localization processes of plane strain tension in order to investigate effects of strain rate sensitivity on the localizing deformation characters. Furthermore, three kinds of typical forming processes sheet metals, one being an uniaxial stretching and another being a square cup drawing with circular blank, and third being a deep drawing of an oil pan, actual industrial forming part, are also numerically simulated by the present model and compared with experimental results. Good agreement between numerical simulation and experimental ones exhibits the validity of the quasi-flow corner theory.     

Analytical derivation of earing in circular cup drawing based on simple tension properties

In the circular cylindrical cup drawing process of sheet materials, an earing profile develops, incurred by the planar anisotropic properties of sheets. Therefore, proper analysis of earing in cup drawing is important to evaluate anisotropic properties and also to control the development of earing. Even though anisotropic properties are commonly measured in the simple tension test, deformation in circular cylindrical cup drawing is in a near plane strain mode (at the flange) so that numerical simulations utilizing yield functions are common practices to analyze earing. In this work, simplified analytical derivation of earing development in circular cylindrical cup drawing is proposed, based on two simple tension anisotropic properties: the yield stress and the r-value. Good performance of the analytical derivation was verified for AA2090-T3, which has strong anisotropy and six ears in cup drawing. Since the current approach directly utilizes measured simple tension data without involving any yield functions, computational cost is significantly lower. Besides, the current derivation can handle any set of detailed anisotropic measurements in the simple tension test, unlike numerical approaches involving yield functions, which need the development of sophisticated yield functions in the first place.     

A quasi-flow constitutive model with strain-rate dependence

In this paper, the proposed is a quasi-flow constitutive model with strain-rate sensitivity for elastic plastic large deformation. The model is based on the Quasi-flow Corner theory, and is suitable for the sheet metal forming process simulation with a variable punch machine velocity. Uniaxial tensile tests and deep-drawing tests of a circular blank with square punch are carried out and numerically simulated. The consistency between the experimental and the numerically simulated results shows the validity of the present new constitutive model. The project supported by the Scientific Foundation of National Outstanding Youth of China (10125208), the National Natural Science Foundation of China (19832020), and the National Education Committee of China     

Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function

In this work, the recently proposed anisotropic yield function, Yld2004-18p [Barlat, F., Aretz, H., Yoon, J.W., Karabin, M.E., Brem, J.C., Dick, R.E., 2005. Linear transformation based anisotropic yield function, Int. J. Plasticity 21, 1009], is implemented in a finite element (FE) code for application to the cup drawing simulation of a circular blank sheet. A short review of the Yld2004-18p relevant features is provided and the stress integration scheme for its implementation in FE codes is described. The simulation of the drawing process is conducted for an aluminum alloy sheet sample (AA2090-T3). The predicted and experimental cup height profiles (earing profiles) with six ears are shown to be in excellent agreement. Additional simulations on a ficticious material are performed in order to show that the yield function Yld2004-18p can lead to the prediction of cups with eight ears. In order to achieve these results, a sufficient number of input data are required to calculate the yield function coefficients. Finally, a simplified analytical approach that relates the earing profile to the r-value directionality is also presented in this paper. It is shown that this approach can be very useful as a first approximation of the earing profile of drawn cups.     

Analysis of the sensitivity of FEM predictions to numerical parameters in deep drawing simulations

In this study, deep drawing finite element (FE) simulations are compared with experimental results. The steel grade, the geometry and the parameters of the experimental deep drawing processes are detailed in this paper. Particular attention is paid to numerical models. The main part of the article is dedicated to a broad sensitivity study. The influence of several numerical parameters on the predicted punch force and earing profile is analysed. A quadratic [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London Ser. A 193, 281–297] constitutive law is compared with more sophisticated micro-macro constitutive laws. The sensitivity of these laws to the initial data characterizing material behaviour is presented. A significant influence of the FE type and the number of FE layers is noticed. Finally, it also appears that friction parameters (penalty coefficient and Coulomb friction coefficient) have a significant influence on numerical results. The low anisotropy of the steel sheet increases the influence of several numerical parameters. That influence would not be observed with a highly anisotropic steel.     

Physics of the formation of fiber lightguides

A fiber lightguide is a fine continuous or tubular transparent filament. Fiber lightguides are formed from the liquid mass exuded through a dye or drawn from a suitable blank. Both of these processes can be considered using the equations of the hydrodynamics of an incompressible Newtonian liquid. (Polymers, which are not Newtonian liquids, are not considered here.) The drawing of a continuous glass fiber from a dye is considered in [1]. The drawing of a microcapillary from a dye is considered in [2], where a qualitative consideration is given which is insufficient for an understanding of the effect of different parameters of the process on the dimensions of the drawn microcapillary. In this paper we consider the formation of a microcapillary from a tubular blank using the approximation of an incompressible Newtonian liquid with a variable viscosity determined by the given temperature distribution. The effect of surface tension and of the excess pressure produced in the channel to counteract the surface tension are taken into account. It is assumed that the drawing process is steady, the blank has thin walls and is axisymmetrical, and the transition to a microcapillary occurs smoothly. With these assumptions the problem of obtaining the shape of the transition and the dimensions of the microcapillary obtained is reduced to a system of ordinary differential equations. The dependence of the dimensions of the microcapillary on the dimensions of the blank and the parameters of the process is established, thereby enabling the process to be optimized.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 167–174, March–April, 1976.The authors thank B. Z. Katsenelenbaum and A. D. Shatrov for useful discussions, A. I. Leonov for a number of observations, and I. V. Aleksandrov, T. V. Bukhtiarov, and A. A. Dyachenko for discussing the results at various stages.     

筒形件液压拉深过程最优压边力的研究

结合筒形件液压拉深新装置的基本工作原理，提出了筒形件拉深法兰部分切向应变更为精确的简化计算公式，进一步获得了该法兰区域板料径向及切向应力的新的数学表达式。应用能量法重新建立了筒形件拉深时法兰区板料不起皱的最小压边力的数学表达式。明确指出液压拉深时拉深中的危险断面在板料凹模圆角区和筒壁区相交处，建立了相应的拉深力的计算公式，并获得了拉深破裂临界状态时极限拉深力及径向应力表达式。推导出了拉深破裂最大压边力的公式．指出实际拉深时最佳压边力应在防皱最小压边力和拉破最大压边力之间选取，同时根据该结果也能计算液体压力与最小拉深系数的关系。计算结果表明，该液压拉深方法可大幅度提高拉深变形程度，值得在工业实际中推广应用。     

A MODIFIED ALGORITHM FOR DEALING WITH HOLDER FRICTION BOUNDARY CONDITION IN SIMULATION OF SHEET METAL FORMING

I. INTRODUCTIONSheet metal forming is an important metal forming technology, which has found wide applicationin automobile body, especially car body production[1]. With the constantly increasing demand forshape, quality and dimension precision of stamped products, engineers are urged to keep improvingand perfecting the forming process, which also makes the numerical simulation technology for sheetmetal forming based on elasto-plastic large deformation FEM theory[2??6] employed more exten…     

板材冲压翻边的解析理论模型

基于全量塑性理论及膜应变假设,给出两种新的冲压板材内曲拉伸／外曲收缩翻边坯料尺寸预示解析数学模型。引入板材冲压成形性分析软件KMAS系统中,对铁路客车牵引架实际冲压件的翻边成形坯料尺寸进行了预示,并与其它解析模型的预示结果以及实验及实测数据进行了对比。讨论了板材的面内各向异性对翻边高度的影响。     

Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function

Squeezed air film between two closely spaced vibrating microstructures is the important source of energy dissipation and has profound effects on the dynamics of microelectromechanical systems (MEMS). Perforations in the design are one of the methods to model these damping effects. The literature reveals that the analytical modeling of squeeze film damping of perforated circular microplates is less explored; however, these microplates are also an imperative part of the numerous MEMS devices. Here, we derive an analytical model of transverse and rocking motions of a perforated circular microplate. A modified Reynolds equation that incorporates compressibility and rarefaction effects is utilized in the analysis. Pressure distribution under the vibrating microplate is derived by using Green’s function and also derived by finite element method (FEM) to visualize the pressure distribution under perforated and non-perforated areas of the microplate. The analytical damping results are validated with previous renowned analytical models and also with the FEM results. The outcomes confirm the potential of the present analytical model to accurately predict the squeeze film damping parameters.     

Analog-discrete approach for the solution of a class of rigid-contact problems

This investigation consists in finding stresses and displacements produced by a rigid footing (or punch) at the plane boundary of a semi-infinite elastic solid. The proposed method is a combined application of electrical analog and finite-difference technique and can be applied to any arbitrary shape of rigid footing (or punch). The experimental setup is very simple and the numerical-analysis part is easily amenable to computer programming. The method has been exemplified by 3 cases: (1) rigid strip footing (or punch); (2) rigid circular footing (or punch); and (3) rigid square footing (or punch) on a three-dimensional semi-infinite solid. The results, wherever possible, have been compared with exact solutions and have been found to be in close agreement.     

Effective approach to the contact problem for a stratum

A novel effective algorithm for the problem of the circular punch in contact with a stratum rested on a rigid base is suggested in this paper. The problem is reduced to the Fredholm integral equations of the second kind. In contrast to the Cooke–Lebedev method and the moments method, which are traditionally employed, the operators of these integral equations are strictly positive definite even in the limiting case of the zero thickness. The latter provides efficient applications of numerical methods. It is also shown that a special approximation enables to obtain an approximate solution via a finite system of linear algebraic equations. As example, the well-known problem for a homogeneous layer is studied. An approximate analytical solution is found with a certain iterative method for a flat punch. This solution is remarkable accurate and possesses the right asymptotic behavior for both a very thin and a very thick layers. Asymptotic formulas for the thin inhomogeneous stratum indented by an indenter of arbitrary profile are pointed out.     

Some polynomial solutions for the non-axisymmetric Boussinesq problem

Solutions to the Boussinesq problem for the circular punch without axial symmetry can be obtained from corresponding axisymmetric solutions by parametric differentiation. The method is applied to the problem of the tilted flat punch, originally solved by Green, and to the indentation of a cylindrical surface by a flat circular punch.     

Effect of intermediate principal stress on flat-ended punch problems

The intermediate principal stress has certain effects on the yield strength of metallic materials under complex stress states. The flat-ended punch problem is a classical and fundamental problem in plasticity theory and mechanical engineering in which the metal beneath a flat-ended punch is under complex stress states. Using the finite difference codes, fast Lagrangian analysis of continua and Unified Strength Theory, the effect of the intermediate principal stress on the flat-ended punch problem is analyzed in this paper. First, the limit pressures of strip and circular punches pressed into an elastoplastic and homogeneous metallic medium are calculated by the two-dimensional finite difference method. The problems of square and rectangular punches are analyzed by the three-dimensional finite difference method. Finally, the effect of the intermediate principal stress on flat-ended punch problems with different punch geometries is analyzed.     

A generalized velocity field for plane strain backward extrusion through punches of any shape

In this paper, the process of plane strain backward extrusion process through arbitrarily curved punches, by means of the upper bound method and the finite element method is investigated. A generalized velocity field is developed and by calculating of the internal, shear and frictional powers, the extrusion force is estimated. Then, by using the developed analytical model, optimum punch lengths which minimize the required extrusion forces, are determined for a wedge shaped punch and a streamlined punch shape. The corresponding results for those two punch shapes are also determined by using a finite element code and compared with the upper bound results. This comparison shows that the upper bound predictions are in good agreement with the FE results.     

Adiabatic shear localization in the dynamic punch test,part II: numerical simulations

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during the dynamic punch test is investigated using the finite element method. Specifically, the possibility and effects of adiabatic shear localization and its role in burr formation are examined, and comparisons to experimental tests in the first part of this two part study are made. A maximum stress criterion involving strain and strain rate hardening and thermal softening is used to determine the occurrence of shear localization in the simulations. It is observed that adiabatic shear localization occurs in the simulations of the titanium alloy. This material exhibits narrow regions of concentrated shear strain during the deformation, and the shear localization criterion is satisfied in these regions. The strain is more widely distributed in the other two metals, and the same criterion is not satisfied. In the calculations of the shear localization criterion it is seen that strain rate hardening has a significant effect when compared to strain hardening and thermal softening. Also, contact between specimen and punch is lost around the center of the punch during operation. This loss of contact is important as it leads to higher stress concentrations at the punch corner and dishing of the blank.     

Inclined circular flat punch on a transversely isotropic piezoelectric half-space

Summary Utilizing the general solution of transversely isotropic piezoelectricity, the paper analyzes the problem of an inclined rigid circular flat punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to take into account the effect of the electric field in piezoelectric materials. Assuming that the punch is maintained at a constant electric potential, exact expressions for the elastoelectric field are derived in terms of elementary functions. It is noted that the solution corresponding to a flat circular punch centrally loaded by a concentrated force can be obtained as a special case. Received 15 December 1998; accepted for publication 9 March 1999     

Adhesive Frictionless Contact Between an Elastic Isotropic Half-Space and a Rigid Axi-Symmetric Punch

In this paper we consider the problem of adhesive frictionless contact of an elastic half-space by an axi-symmetric punch. We obtain integral equations that define the tractions and displacements normal to the surface of the half-space, as well as the size of the contact regions, for the cases of circular and annular contact regions. The novelty of our approach resides in the use of Betti’s reciprocity theorem to impose equilibrium, and of Abel transforms to either solve or substantially simplify the resulting integral equations. Additionally, the radii that define the annular or circular contact region are defined as local minimizers of the function obtained by evaluating the potential energy at the equilibrium solutions for each pair of radii. With this approach, we rather easily recover Sneddon’s formulas (Sneddon, Int. J. Eng. Sci., 3(1):47–57, 1965) for circular contact regions. For the annular contact region, we obtain a new integral equation that defines the inverse Abel transform of the surface normal displacement. We solve this equation numerically for two particular punches: a flat annular punch, and a concave punch.     

Analytical Solution for Sliding Rounded-Edge Contact

Reliable analysis of the local stress fields in the vicinity of sliding frictional contacts of engineering components is a pre-requisite for the reliable assessment of structural integrity. In this paper we present the use of Muskhelishvili potentials to derive an analytical solution for a semi-infinite punch with a rounded edge pressed against a half-pane substrate, and a general numerical solution for a kind of Cauchy integral involved in the analytical contact solution. Using these solutions, the effect of the friction coefficient on the normal traction distribution is investigated. Numerical results show that the peak normal traction value is altered in comparison with the frictionless case solution, but this variation is mild (less than 5%), provided the friction coefficient does not exceed about 0.6. Finally, the adaptation of the analytical result to the solution of practical contact problems is addressed.