Development of a new model for plane strain bending and springback analysis

A new mathematical model is presented for plane strain bending and springback analysis in sheet metal forming. This model combines effects associated with bending and stretching, considers stress and strain distributions and different thickness variations in the thickness direction, and takes force equilibrium into account. An elastic-plastic material model and Hill’s nonquadratic yield function are incorporated in the model. The model is used to obtain force, bending moment, and springback curvature. A typical two-dimensional draw bending part is divided into five regions along the strip, and the forces and moments acting on each region and the deformation history of each region are examined. Three different methods are applied to the two-dimensional draw bending problems: the first using the new model, the second using the new model but also including a kinematic directional hardening material model to consider the bending and unbending deformation in the wall, and the third using membrane theory plus bending strain. Results from these methods, including those from the recent benchmark program, are compared. University of Michigan, Dept. of Mechanical Engineering and Applied Mechanics, Ann Arbor, Mi 48109, USA.     

Effect of hardening laws and yield function types on spring-back simulations of dual-phase steel automotive sheets

In order to simulate the spring-back of DP-steel automotive sheets, the effect of hardening laws and yield function types has been studied based on finite element simulations performed for 2-D draw bending and S-rail tests. Specifically, the performance of the combined isotropic-kinematic hardening based on the modified Chaboche model was compared with those of the pure isotropic hardening and kinematic hardening laws, along with the non-quadratic anisotropic yield (Yld2000-2d) and Mises yield functions. As for the 2-D draw bending test, numerical results were compared with experimental results for verification purposes.     

板料冲压成形回弹的有限元数值模拟研究

随着对冲压件的尺寸精度要求的不断提高,精确预测给定冲压件的回弹量大小及分布显得非常重要。采用无模法模拟卸载回弹过程时,需要以加载成形后的应力为基础。本文给出了加载成形中的应力计算方法,并采用无模法建立了卸载回弹的计算模型。文中提出一种不同于传统的初始单元弹性化处理的方法,提高了回弹的计算精度。研究了卸载因子的取值规律对回弹计算的影响。利用自行开发的软件SheetForm模拟分析NUMISHEET’93标准考题中U型件深冲压的回弹情况,验证了该方法的有效性。     

浅谈板料弯曲回弹

如何减小弯曲件的回弹,以控制弯曲件精度和提高弯曲件质量,一直是弯曲件生产中要解决的关键问题.本文分析了板料弯曲加工中工件发生弯曲回弹的原因,阐述了影响板料弯曲回弹的因素及常用减小回弹的方法.     

3D复杂形状板料冲压成形回弹误差补偿方法及其实验验证

针对冲压件回弹误差,建立了3D复杂形状板料冲压成形精度闭环控制系统。以回弹误差为控制目标,以线性闭环控制系统、空间Fourier变换和频域传递函数为理论基础,基于模具实验迭代,建立了模具回弹误差补偿修正算法。该算法接收模具和冲压件的激光扫描测量数据,输出模具型面修正后离散数据。利用提出的频域模具修正算法对回弹现象较为严重的弯曲和浅拉深过程,进行了回弹误差补偿的有效性验证。实验结果表明,该算法可以较好地控制板料冲压成形回弹误差,具有工程使用价值。     

Reverse effect of tensile force on sidewall curl for materials with tensile/compressive strength difference

Sidewall curl occurring by the removal of tool surfaces after forming is one adverse phenomenon that should be effectively reduced in sheet metal forming operations. Among several process parameters controlling sidewall curl, a constraint tensile force is widely used along with attainable formability by introducing blank holder and drawbead. The classic but common knowledge is that sidewall curl is suppressed for conventional sheet metals as the constraint tensile force increases. Interestingly, however, for magnesium alloy sheets that have unusual asymmetry in tension and compression it has been recently reported that springback increases as the tensile force increases within a specific range of tension. The major deformation in the sidewall usually consists of bending and unbending under tensile force. Therefore, this unique stress-strain response of sheet materials with strength-differential, including magnesium alloys, should be considered for an accurate estimation of sidewall curl. In the present study, a semi-analytical bending/unbending theory incorporating characteristic constitutive behavior of magnesium alloys was developed to evaluate the moment-curvature relationship for various levels of constraint tensile forces. The present analysis proved that the reverse effect of constraint tensile force on sidewall curl was caused by the lower resistance to plastic yielding in compression with proper combination of applied tensile force.     

Using neural networks to predict bending angle of sheet metal formed by laser

In this paper, three supervised neural networks are used to estimate bending angles formed by a laser. Inputs to these neural networks are known forming parameters such as spot diameter, scan speed, laser power, and workpiece geometries including thickness and length of sheet metal workpiece. For comparison, regression models are also used to estimate bending angle. Verification experiments are then conducted to evaluate the performance of these models. It is shown that the radial basis function neural network model is superior to other models in predicting bending angle. The volume energy model is better than the line energy model in angle prediction.     

Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets

Recent work on sheet metal formability had shown that the position of forming limit diagrams (FLDs) in punch stretching is higher than that in in-plane stretching because of a strain gradient effect resulting from bending a flat sheet into a curved sheet by punch stretching. To our knowledge, none of the developed theoretical models in the study of localized necking can be used to predict this phenomenon accurately so far. In this study, a new model, using Barlat and Lian’s new nonquadratic anisotropic yield criterion, is proposed by introducing a strain gradient term in the constitutive equation to consider the effect of the first order strain gradient (curvature), in the thickness direction resulting from bending, on the localized necking in anisotropic sheets. The developed model is used to study the effects of curvature on FLDs and to predict FLDs in punch stretching and inplane stretching for various materials. It is found that the theoretical predicted results are in good agreement with experimental data.     

A constitutive model for spring-back prediction in which the change of Young's modulus with plastic deformation is considered

In order to improve the prediction capability of spring-back in the computational analysis of sheet metal forming processes, a stress–strain constitutive formulation of non-linear combined hardening rule has been proposed in this paper according to non-linear kinematic hardening theory of Lemaitre and Chaboche and Hill's 1948 anisotropic yielding function. Traditionally, Young's modulus is considered as a constant in engineering application and numerical simulation. In fact, it decreases with plastic deformation. So the effect of the change of Young's modulus with plastic strain on spring-back is considered in the constitutive model. The algorithm of stress update is elastic prediction, plastic correcting and radial returning. Numerical results and experimental results show that the proposed constitutive model significantly improves the prediction accuracy of spring-back.     

基于ABAQUS的高强钢板弯曲成形模拟中回弹影响因素的研究

以国际板料成形数值模拟会议(Numisheet2011)上提出的第四个标准考题为研究对象,应用ABAQUS对DP780高强钢板弯曲及回弹过程进行模拟。结果表明:随着网格划分尺寸减小,回弹量逐渐增大,网格密度对板料弯曲回弹量有较大的影响;随着摩擦因数的逐渐增大,回弹量先快速增大,然后缓慢减小。将得到的与试验值相匹配的网格尺寸(2.75mm)和摩擦因数(0.1)应用于板料预变形之后再拉深弯曲过程模拟,结果发现:板料预变形之后拉深弯曲回弹量增大。将模拟值与Numisheet2011会议得到的试验值对比发现,板料弯曲模拟与试验的回弹变化趋势相同,且3个回弹表征量的模拟误差都在10%以内。     

Possibilities and limitations of geometric simplifications for calculations of residual stresses and distortions

The prediction and minimization of welding distortions and the evaluation of the residual stress state after welding using numerical methods are increasingly gaining importance. These numerical models are used to optimize welding processes with respect to distortion. However, the computational time required for a transient 3-D calculation, particularly for large components, often hinders commercial usage of these approaches. Therefore, simulations have to simplify individual aspects. Due to the fact that model verification often failed according to abundant experimental research efforts, it cannot be proven whether the deformations and residual stresses calculated by those simplified models are trustworthy. With the help of the validated simulations of the IIW round robin tests and of variational calculus, this work shows the influences of sheet geometry and model simplifications, e.g. 2-D modelling, on the calculation of distortions and residual stresses. The round robin tests were performed using steel sheets made of an austenitic steel (316 LNSPH) which was bead-on-plate welded by TIG welding. The calculations for a varied sheet geometry show for the investigated process and for large components that a reduction to minimal sheet geometry is necessary and sufficient to determine the longitudinal stresses and the distortions. The transversal stresses are in general extremely sensitive to the sheet geometry.     

单元尺寸和积分点个数对冲压回弹模拟精度的影响

冲压回弹是板料成形数值模拟领域中最难准确预测的缺陷之一,其模拟精度受多种因素的影响,如材料本构模型、单元类型与尺寸、接触摩擦模型和有限元算法等。该文采用ABAQUS有限元软件对拉弯回弹进行数值模拟研究,重点分析了壳单元的积分点个数和接触角度对回弹预测精度与模拟时间的影响。研究结果表明,随着壳单元积分点个数的增加和单元尺寸的减小,冲压回弹的预测精度总体趋于提高趋势,但模拟时间相应地增大。当接触角度取16°时,得到的回弹预测精度与接触角度为5°时比较相近;另外,在7个积分点时,得到的回弹预测精度相当于25~51个积分点之间的范围。这与传统观点认为的,积分点应取25~51个,接触角度应小于10°不同。利用这一规律,有望在模拟时,既能得到较高的模拟精度,又可大大降低模拟时间。     

Ductile fracture behavior of 5052 aluminum alloy sheet under cyclic plastic deformation at room temperature

Ductile fracture behavior of a 5052 aluminum alloy sheet undergoing cyclic plastic deformation is investigated in order to clarify the effect of cyclic plastic deformation on formability enhancement in incremental stretch sheet forming at room temperature. In the incremental forming, formability markedly increases owing to strain distribution and accumulation effects. The former effect is activated when the deformation region expands along tool paths. Thus, localization of deformation, which leads to necking or fracturing, can be prevented. On the other hand, local strain is accumulated without fracturing when a blank sheet is repeatedly subjected to out-of-plane deformation at the same position. In this paper, the effect of the strain accumulation due to cyclic deformation generated by bending and unbending is primarily focused on to discuss the effect on deformability. To apply cyclic plastic straining to the specimen, a cyclic stretch-bending test was adopted. A cyclic tensile test was also conducted for larger bending curvature. The experimental results show that cyclic bending–unbending affects the ductility of sheet metals. The fractography obtained by scanning electric microscopy also indicates that fewer and smaller voids are observed particularly on bending the inner side than on the outer side.     

Effect of prior heat treatment on cyclic endurance of sheet titanium alloys of various strength groups

Shaping operations including bending and stretching deformation are often used in producing members of thin-wall titanium structures of aircraft. At the same time published sources do not give much data on the effect of the degree of deformation on the cyclic endurance of sheet titanium alloys. In addition the problem of how much alloys of medium and high strength can be deformed without diminishing their operating capacity still remains open. The present paper is devoted to the possibility of deforming sheet titanium alloys of different strength groups by bending and stretching without reducing their cyclic life. Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 12, pp. 15–16, December, 1998.     

Use of a coupled explicit—implicit solver for calculating spring-back in automotive body panels

LS-DYNA3D, an explicit code, and LS-NIKE3D, an implicit code, have been coupled to facilitate the finite element (FE) modelling of sheet metal forming. The explicit FE code is used to model the forming process, in which the deformable blank contacts rigid tools. The implicit FE code is used to model the subsequent spring-back which occurs after the tooling is removed. In this way, the explicit code with its robust handling of contact during forming is combined with the implicit code and its large time steps during spring-back. The result is an efficient method for solving even very large (>20 000 deformable elements) sheet forming models. Three examples of the application of this method are given.     

An elasto-plastic finite-element analysis of sheet metal camber process

This study aims to clarify the process conditions of the V-die bending of a sheet metal of steel. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of products after unloading, based on the tensile properties of the material and the geometry of the tools used. An elasto-plastic incremental finite-element computer code, based on an updated Lagrangian formulation (ULF), was developed to simulate the V-die bending of sheet metal. In particular, selective reduced integration (SRI) was adopted to formulate the stiffness matrix. The extended r-minimum technique was used to deal with the elasto-plastic state and 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 value of the punch load in the finite-element model agrees closely with the results of the experiments. The whole deformation history 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 special feature of this V-die bending process is the camber after unloading. The computer program successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank and the bending angle on camber process. The effects of all process variables on the final bending angle of the bent parts of the sheet after unloading were also evaluated. Results in this study clearly demonstrated that the code for simulating the V-die bending process was efficient.     

Elasto-Plastic Springback of Beams Subjected to Repeated Bending/Unbending Histories

This contribution investigated repeated elastoplastic pure plane bending/unbending process of beams made of material with an elastic-linear hardening rheological model. The attention is focused on beams with cross sections which have at least one axis of symmetry and are initially straight or have constant radius of curvature. Elastoplastic deflection states of beams after repeated bending/unbending process are determined using the large displacement theory. Experiments were conducted to verify the theory for beams made of aluminium alloy AA 5050-H38 with rectangular cross sections. It is shown that maximal relative difference between experimental and theoretical results in the case of a largely curved beams after repeated bending/unbending process is 1.27%.     

大型船用卷板机卷板成形过程的数值模拟

首先对卷板成形过程进行了理论分析;然后用有限元分析软件ABAQUS对某大型船用卷板机板料滚弯成形及回弹的过程进行模拟,得到了成形件的应力分布与应变分布;研究了上辊不同下压量对其成形过程的影响,分析了滚弯过程中辊子和板料间的法向接触正压力,并将仿真值和理论计算值进行了比较,分析了产生误差的原因.同时,分析了辊子对板料的切...     

宽板V型自由弯曲智能化控制过程的解析定量描述

板料在弯曲卸载过程中,由于弹性变形回复,从而产生回弹。回弹的结果使弯曲件的精度降低。影响回弹的因素很多,也很复杂。根据弹塑性弯曲理论,在平面变形假设的前提下,考虑了材料的硬化、各向异性及弹性变形,对宽板V型自由弯曲应力应变进行了分析,得到了弹塑性交界处曲率半径,推导出了弯曲力及目标弯曲角随弯曲行程变化的关系式。理论计算与实验及数值模拟结果进行了比较,为宽板V型自由弯曲智能化控制中参数识别及预测模型输入层和输出层变量的确定提供了理论依据。     

宽板U形自由弯曲智能化控制过程的解析定量描述

根据板材弯曲理论,在平面变形假设的前提下,考虑了材料的硬化、各向异性及弹性变形,建立了U形件自由弯曲理论分析模型,对宽板U形件自由弯曲进行了理论分析,得出了弯曲力随弯曲行程变化规律及目标弯曲角计算公式,并对各种影响弯曲力和回弹的因素进行了分析,理论计算与实验及模拟结果进行了比较,为宽板U形件自由弯曲智能化控制中参数识别及预测模型输入层和输出层变量的确定提供了理论依据。