型材拉弯的力学与回弹分析

回弹是弯曲成形中普遍存在的现象,是由卸载过程中内力重新分布引起的,回弹的存在直接影响弯曲件的成形精度.本文针对转台拉弯成形过程,对等边型材等曲率拉弯进行了应力-应变分析,并按照卸载预拉力与不卸载预拉力两种情况对工件回弹进行了研究与探讨,得到两组半径回弹率理论曲线.通过与试验结果对比,不卸载拉力计算的结果与试验值比较吻合.     

Investigation of Non‐Linear Springback for High Strength Steel Sheets by ESPI

Abstract: The springback of the sheet metals after large deformations during deep drawing is not a strongly linear process with a constant Young’s modulus, but the stress–strain behaviour during the unloading phases shows considerably non‐linear and inelastic effects. Unloading of two types of steel sheets for cold forming, a cold‐rolled high‐strength microalloyed steel and a low‐carbon steel sheet, has been analysed using the method of electronic speckle pattern interferometry (ESPI). The specimens were investigated by uniaxial tension tests, and the influences of different testing parameters upon springback were analysed. The experimental measurements showed that the stress–strain curve during unloading is non‐linear, the influence of the prestrain path upon unloading is minor, and the secant moduli of unloading curves decrease with increasing prestrain. When the prestrain value becomes high enough, a saturated value for the secant modulus is approached. An empirical relation was found to describe the changes in the unloading modulus in accordance with the prestrain value.     

Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.     

On the identification of an effective cross section for a cruciform specimen

Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm² for the considered specimen.     

Experimental prediction of sheet metal formability of AW-5754 for non-linear strain paths by using a cruciform specimen and a blank holder with adjustable draw beads on a sheet metal testing machine

The main objective to guarantee a high efficiency in the press shop is to produce sheet metal parts without failure. The feasibility of sheet metal parts is nowadays ensured during the development process by a comparison of the occurring strains in the simulation with the Forming Limit Diagram (FLD). The principle of the experimental procedure to determine the FLD is standardized in ISO 12004–2 [1]. This procedure is only valid with high accuracy for proportional unbroken strain paths. However, in most industrial forming operations non-linear strain paths occur. To resolve this problem, a phenomenological approach was introduced by Volk [2], the so-called Generalized Forming Limit Concept (GFLC). Localized necking and the remaining formability for any arbitrary non-linear strain path can be predicted with the GFLC. Furthermore, experimental investigation of multi-linear strain paths appears highly complex in practice and involves a range of testing equipment, e.g. different specimens, testing machines and tools. In this paper an alternative method is introduced by using a cruciform specimen and a draw bead tool on a sheet metal testing machine. The different draw bead heights allow the creation of arbitrary strain states, which can be changed at different height of the punch. Conventionally cruciform specimens are used to determine the yield loci in the first quadrant of the stress space at low strain values. To enable a cruciform specimen for the evaluation of strain limits comparable to the conventional Nakajima test, an optimization of the geometry regarding the maximum achievable strains in the specimen center takes place. The developed specimen and tool allow testing of materials under multi-axial strain states with a reduced testing effort.     

An analytical model for bending and springback of bimetallic sheets

Springback is an inevitable phenomenon due to elastic redistribution of internal stresses occurring in sheet metal forming operations. Most of the research reported in this area has been concerned with the components formed from single metal. This article deals with the analytical solution for prediction of springback in bending of bimetallic sheets. A mathematical model is derived based on Woo and Marshall's constitutive equation, considering logarithmic strain (nonlinear) distribution across the thickness and thickness change during bending. Analytical modeling, based on logarithmic strain distribution across the thickness, can be used for accurate springback predictions in the case of smaller bend radius to the thickness ratio. The results of the springback and thickness change are validated using experimental results for the aluminum sheet layered with steel. Further, springback variation in bimetallic sheets is studied, with a change in material properties and thickness of each layer.     

Finite element modelling and experimental investigation of single point incremental forming process of aluminum sheets: influence of process parameters on punch force monitoring and on mechanical and geometrical quality of parts

New trends in sheet metal forming are rapidly developing and several new forming processes have been proposed to accomplish the goals of flexibility and cost reduction. Among them, Incremental CNC sheet forming operations (ISF) are a relatively new sheet metal forming processes for small batch production and prototyping. In single point incremental forming (SPIF), the final shape of the component is obtained by the CNC relative movements of a simple and small punch which deform a clamped blank into the desired shape and which appear quite promising. No other dies are required than the ones used in any conventional sheet metal forming processes. As it is well known, the design of a mechanical component requires some decisions about the mechanical resistance and geometrical quality of the parts and the product has to be manufactured with a careful definition of the process set up. The use of computers in manufacturing has enabled the development of several new sheet metal forming processes, which are based upon older technologies. Although standard sheet metal forming processes are strongly controlled, new processes like single point incremental sheet forming can be improved. The SPIF concept allows to increase flexibility and to reduce set up costs. Such a process has a negative effect on the shape accuracy by initiating undesired rigid movement and sheet thinning. In the paper, the applicability of the numerical technique and the experimental test program to incremental forming of sheet metal is examined. Concerning the numerical simulation, a static implicit finite element code ABAQUS/Standard is used. These two techniques emphasize the necessity to control some process parameters to improve the final product quality. The reported approaches were mainly focused on the influence of four process parameters on the punch force trends generated in this forming process, the thickness and the equivalent plastic deformation distribution within the whole volume of the workpiece: the initial sheet thickness, the wall angle, the workpiece geometry and the nature of tool path contours controlled through CNC programming. The tool forces required to deform plastically the sheet around the contact area are discussed. The effect of the blank thickness and the tool path on the punch load and the deformation behaviour is also examined with respect to several tool paths. Furthermore, the force acting on the traveling tool is also evaluated. Similar to the sheet thickness, the effect of wall angle and part geometry on the load evolution, the distribution of calculated equivalent plastic strain and the variation of sheet thickness strain are also discussed. Experimental and numerical results obtained allow having a better knowledge of mechanical and geometrical responses from different parts manufactured by SPIF with the aim to improve their accuracy. It is also concluded that the numerical simulation might be exploited for optimization of the incremental forming process of sheet metal.     

Evaluation of yield criteria for forming simulations based on residual stress measurement

Process induced anisotropy in sheet metal is accounted for in analytical modeling by anisotropic yield criteria. The suitability of a yield criterion for predicting sheet metal forming process is generally validated by way of its ability to predict surface strains. However, the sensitivity of surface strains to yield criteria is dependent upon strain modes, with plane strain mode exhibiting higher sensitivity. To eliminate dependency on strain modes, stresses are used to evaluate yield criteria, since forming stresses are less sensitive to strain modes. In the study, the residual stresses remaining in a hemispherical cup formed in plain strain mode is predicted using Hill48 and Barlat89 criteria. The residual stresses are experimentally characterized by using X-Ray diffraction method. Suitable yield criterion for forming simulation is validated based on the correlation of theoretical predictions with experimental residual stress values.     

Thinning as a failure criterion during sheet metal forming

Thinning during forming is often considered a failure criterion in the metal forming industry. It is believed that a critical amount of thinning takes place in a sheet metal before failure. In this study, varying widths of low-carbon steel sheets were punch stretched under laboratory conditions. Thinning during punch stretching was measured at various locations along the steel sheets. These measurements demonstrated that thinning during forming is not constant, but that it is a function of the strain path followed by the sheet. Hence, thinning should not be used as a failure criterion during forming of sheet metals.     

Semi-analytical approach for plane strain sheet metal forming using a bending-under-tension numerical model

In this paper, we revisit the plane strain deep-drawing process. We show that a detailed analysis of the physical process may result in a dramatic reduction of computing time when the problem is split into several regions undergoing well-defined loading paths. The proposed approach allows us to assess the springback of the formed sheet in a quasi-instant time and is thus suitable in the initial design phase and provides a fast and economical way to determine the influence of the numerous parameters involved in sheet metal forming. We present a semi-analytical model that has been developed for sheet metal forming mainly subjected to plane strain bending-under-tension and involving large strains. The sheet is considered to be an assembly of regions where the loading is considered homogeneous in the length direction. A handful of finite elements or even a single element is sufficient to compute the loading path followed by each region. The contact is circumvented by constraining the kinematics with appropriate boundary conditions and the approach is valid for any material behavior law. The semi-analytical model is applied to standard test cases and then compared with full-scale simulations.     

Modelling the correlation between the geometrical features and the forming limit strains of perforated Al 8011 sheets using artificial neural network

In the recent years, sheet metals are produced with perforations in various shapes and patterns to improve the appearance of sheet and to save weight of components. As in conventional metal sheets, it is important to form the perforated sheet metals also within their safe strain regions to avoid the forming failures like necking, fracture and wrinkling. The Forming Limit Diagram (FLD) is an appropriate tool to determine the forming limit strains. The limiting strains of perforated sheet metals mainly depend on the geometry of the perforations and forming variables. This leads to large increase in number of test to be conducted with various geometry and forming variables for determining the forming limit strain for perforated sheets. Aiming to reduce the number of experiments needed, in this work, an Artificial Neural Network (ANN) model has been developed for forming limit diagram of perforated Al 8011 sheets based on experimental results and correlated with the geometrical features of the perforated sheets. This model is a feed forward back propagation neural network (BPNN) with a set of geometrical variables as its inputs and the safe true strains as its output. This ANN model can be applied for prediction of FLD of perforated sheet having any geometry.     

Full-field measurement technique and its application to the analysis of materials behaviour under plane strain mode

The purpose of the paper is to provide a comprehensive experimental and numerical analysis of one of the encountered and critical state modes in sheet metal forming processes. The study is carried out with the help of the full-field measurement techniques. In order to confer some generality to the proposed work, several materials and different specimen shapes are considered that exhibit more or less homogeneous strain field. The proposed experimental study of the plane strain test is completed by a preliminary identification of the material parameters for non-linear behaviour at finite strains, using heterogeneous strain field.     

利用高速振动降低零件回弹及蒙皮件制造——电磁成形技术的新应用

目的 为了解决传统大型蒙皮成形需要大型装备及零件回弹大的问题,提出带弹性垫的蒙皮件电磁渐进成形新方法.方法 通过电磁线圈放电,材料在磁压力和弹性垫的反弹力作用下出现高速振动,消除零件回弹.采用ANSYS和ABAQUS有限元分析软件分别进行电磁场和结构场模拟,分析有无弹性垫、线圈结构和放电位置对蒙皮成形质量的影响规律.结果 在无弹性垫的条件下对板料进行冲击,板料上的塑性应变几乎没有变化.如果采用螺旋方形线圈和带弹性垫的成形工艺,虽然板料上的塑性应变增加,但是线圈正对板料区域出现1.5 mm的鼓包.采用电磁屏蔽方法调整板料上的电磁力分布和材料流动,当线圈在6个位置多次放电后,板料回弹明显减低,并且零件表面光滑.结论 在模拟得到的最佳工艺参数下,建立了实验装置,实验结果与模拟一致.     

Overview and comparison of various test methods to determine formability of a sheet metal cut‐edge and approaches to the test results application in forming analysis

This paper presents an overview of published test methods for determination of formability of a sheet metal cut‐edge. The presented test methods were developed to evaluate formability of a sheet metal edge that was produced by shear cutting. Due to high local strains, hardening, or even microcracks, the cut‐edge might have less formability than the base material. The presentation of the tests is structured according to the three steps each test can be divided into: cutting, forming and evaluation. Similarities and differences concerning these steps were worked out. Additionally, a classification of the tests is made regarding their strain gradients in the vicinity of the cut‐edge. For this, finite element models of exemplary tests were built up using LS‐DYNA explicit and analyzed accordingly. Evaluation approaches that go beyond the common hole expansion ratio (HER) from the hole expansion test (HET) standardized in the ISO 16630 are also described. The tests can be used not only for a quantitative comparison of materials and cutting processes with regard to the cut‐edge formability but to determine input data for the finite element analysis (FEA) of forming processes to allow a simulation based cut‐edge failure prediction. The paper also presents appropriate procedures on the transfer of the test results into the FEA of forming of a workpiece with a cut‐edge.     

利用最小厚度准则预测高强热轧钢板的FLC曲线

为更便捷地获得成形极限图(FLD)中的成形极限曲线(FLC),用最小厚度准则,通过少量成形极限试验结合数值模拟来预测FLC.采用Barlat1989屈服准则对QStE340TM、SAPH370、ZStE260P三种高强度热轧钢板进行成形极限模拟,并以最小厚度准则作为极限判据,根据数值模拟结果绘制FLC图.计算结果表明,采用平面应变路径下的成形极限实验数据作为最小厚度准则的已知参数时,数值预测结果与实验结果能较好吻合.故采用平面应变路径下的成形极限实验数据,结合最小厚度准则和数值模拟,即可得到材料完整的FLC曲线.     

Effect of reverse and cyclic shear on the work-hardening of AISI 430 stainless steel

Sheet metal forming commonly involves various processing steps leading to complex strain paths. The work hardening of the metal under these circumstances is different from that observed for monotonic straining. The effect of the strain path on the hardening of materials is usually studied through sequences of standard mechanical tests, and the shear test is especially well adapted to such studies in sheet forming. Shear straining covering Bauschinger and cyclic strain paths were used in the analysis of the hardening of AISI 430 stainless steel sheets. The tests were conducted at 0°RD, 45°RD, and 90°RD (Rolling Direction) and for three effective strain amplitudes. The results indicate that the material presents Bauschinger effects and strain hardening transients that are sensitive to the testing direction. In addition, the cyclic straining leads to an oscillating stress pattern for the forward and reverse shearing cycles, which depends on the deformation amplitude.     

Effect of reverse dome stretching on dome height and forming limits of sheet materials

Reverse bending and stretching of sheet materials is often employed in press forming of complex automotive components. In this work, hemispherical dome stretching tests were followed by reverse dome tests on automotive aluminum sheet specimens to assess the influence of the strain and shape on dome height at neck formation and limit strains. The above test scheme offers a means of subjecting the sheet material to reverse bending and stretching and thereby changing its strain path during the process. The results indicate significant improvements in dome height as a function of pre-strain (or initial dome height) compared to the simple dome stretching process. The forming limit strains, on the other hand, are lowered. The reason is attributed to the redistribution of strain (more uniform deformation) through the punch/specimen contact during the reverse bending and stretching process.     

Shell element formulation of multi‐step inverse analysis for axisymmetric deep drawing process

Inverse analysis today is generally performed with membrane models in analysing sheet metal forming processes. Given the final desired configuration, it usually estimates the deformation in a one‐step calculation. However, for some practical problems where the bending effect is significant and the strain history departs from a linear path, this calculation becomes not good enough to provide the optimal design values. In this paper, an axisymmetric shell element for the multi‐step inverse analysis is developed for more accurate prediction of design variables such as the initial blank shape, strain distributions, and intermediate shapes, etc.The algorithm has been applied to deep drawing processes for both thin and relatively thick sheet metal. Numerical examples demonstrate that the proposed combination of shell element and multi‐step inverse analysis can provide more precise results than the previous algorithms used in inverse analysis. Copyright © 2001 John Wiley & Sons, Ltd.     

A new anisotropic elasto-plastic model with degradation of elastic modulus for accurate springback simulations

Springback, a phenomenon that is governed by elastic strain recovery after the removal of forming loads, is of great concern in sheet metal forming. There is no doubt that in this regard, physically reliable numerical modelling of the forming process and predictions of springback obtained by respective computer simulations are crucial for controlling this problem. Unfortunately, by currently available approaches, springback still cannot be adequately predicted in general. In this paper, a new constitutive model is proposed which considers simultaneously sheet anisotropy, damage evolution and strain path-dependent stiffness degradation during sheet metal forming. For parameter identification of the built constitutive model, a particular experimental procedure is developed and an optimization procedure is employed to solve the inverse problem that arises. The proposed approach to constitutive modelling is validated in the end by a simulation of the springback in the formed HSS steel sheet. The simulation results, which prove to be in good agreement with the experimental ones, lead to the conclusion that accurate modelling only of anisotropic yielding is not enough to accurately predict the springback phenomenon; the constitutive model should also include the strain path-dependent change of the elastic moduli.     

双相钢冲压成形应变路径影响规律研究

设计特征盒形件,使其包含双拉、拉-压、平面应变以及双线性应变路径,反映了覆盖件成形中常见的应变路径状态。通过正交试验方法,分析了工艺参数（压边力、摩擦系数、板厚）对其成形过程中特征区域应变路径影响的显著性,并得出了显著因素对应变路径的影响趋势。初步取得了控制DP600高强钢成形过程中特征区域应变路径的方法,为控制DP高强钢成形质量提供了有力的指导。