On the modelling of the bending-unbending behaviour for accurate springback predictions

The prediction of springback is probably the area in sheet forming simulation where the least success has been achieved in terms of solution accuracy. The springback is caused by the release of residual stresses in the workpiece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on material modeling during the forming simulation. Among the various ingredients that make up the material model, the hardening law is one of the most important ones for an accurate springback prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behaviour, and permanent softening. The complexities of existing hardening laws do of course vary within quite wide ranges. One of the purposes of the present study was to try to identify a model of reasonable complexity that at the same time can fulfill the requirements concerning accuracy. Five different hardening models have been evaluated in the present investigation. The simplest model, the isotropic hardening one, involves only one history variable, while the most advanced model involves ten history variables and four additional material parameters. In the current report, results for four different materials will be accounted for. The kinematic hardening parameters have been determined by inverse modeling of a three-point bending test. A response surface method has been used as an optimization tool, together with a finite-element model of the bending test set-up. The springback of a simple U-bend has been calculated for one of the materials, and from the results of these simulations some conclusions regarding the choice of hardening law are drawn.     

A new model for springback prediction in which the Bauschinger effect is considered

Springback prediction is an important issue for the sheet metal forming industry. Most sheet metal elements undergo a complicated cyclical deformation history during the forming process. For an accurate prediction of springback, the Bauschinger effect must be considered to determine accurately the internal stress distribution within the sheet metal after deformation. Based on the foundations for isotropic hardening and kinematic hardening, Mroz multiple surface model, plane strain assumptions, and experimental observations, a new incremental method and hardening model is proposed in this paper. This new model compares well with the experimental results for aluminum sheet metal undergoing multiple-bending processes. As is well known, aluminum is one of the most difficult sheet metals to simulate. The new hardening model proposed in this paper is not only a generic model for springback prediction but also a hardening model for sheet metal forming process simulation.     

Modeling of springback, strain rate and Bauschinger effects for two-dimensional steady state cyclic flow of sheet metal subjected to bending under tension

An elastic-plastic mathematical model is presented for plane strain flow of sheet metal subjected to strain rate effects during cyclic bending under tension. The model calculates the stress, strain, strain rate, flow profile geometry, springback and residual stresses for steady state flow of sheet metal under plane strain along the width. Stress reversals were experimentally quantified using a pure bending moment test and were included in the model through Bauschinger factors. Modeling results for two materials, mild steel and aluminum alloy, were in good agreement with experimental results from bending under tension test devices. The iterative nature of the model, associated with a representative experimental framework proved a valuable approach to improving the modeling of sheet metal forming and springback control.     

板料屈服行为及强化规律的研究进展

研究板料塑性成形的理论基础是屈服准则、强化规律以及本构模型。随着新材料、新工艺的不断出现,温度和应变速率对塑性成形过程中的影响也不容忽视,原有的塑性理论已无法满足研究和工程应用的需求。从板料屈服准则研究、包辛格效应与强化模型研究、屈服强化规律试验方法研究以及涉及应变速率和温度的板料屈服强化研究4个方面阐述板料屈服行为及强化规律的研究进展,指出常用屈服准则的特点和不足,说明各种强化模型中组合强化模型仍然是研究重点。试验方法主要从研究屈服轨迹的双向拉伸试验及确定强化模型参数试验的2个方面进行介绍。此外,指出针对板料在复杂应力状态下应力张量与应变张量之间的涉及应变率和温度的屈服准则和相应的流动准则的本构关系还有待研究。提出随着新材料、新工艺的不断出现,涉及应变速率和温度的屈服准则和强化规律、试验方法以及在有限元模拟中的应用等研究将是未来的研究热点。     

Simulation of springback

Springback, the elastically-driven change of shape of a part after forming, has been simulated with 2-D and 3-D finite element modeling. Simulations using solid and shell elements have been compared with draw-bend measurements presented in a companion paper. Plane-stress and plane-strain simulations revealed the dramatic role of numerical tolerances and procedures on the results. For example, up to 51 integration points through the sheet thickness were required for accuracy within 1%, compared with 5–9 typically acceptable for forming simulations. Improvements were also needed in the number of elements in contact with the tools, and in the numerical tolerance for satisfying equilibrium at each step. Significant plastic straining took place in some cases upon unloading; however the choice of elastic–plastic unloading scheme had little effect on the results. While 2-D simulations showed good agreement with experiments under some test conditions, springback discrepancies of hundreds of percent were noted for one alloy with sheet tension near the yield stress. 3-D simulations provided much better agreement, the major source of error being identified as the presence of persistent anticlastic curvature. Most of the remaining deviation in results can be attributed to inaccuracies of the material model. In particular, the presence of a Bauschinger effect changes the results markedly, and taking it into account provided good agreement. Shell elements were adequate to predict springback accurately for R/t greater than 5 or 6, while solid elements were required for higher curvatures. As R/t approaches 2, springback simulated with solid elements tends to disappear, in agreement with measurements presented in the companion paper and in the literature.     

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlat's 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.     

Influence of constitutive model in springback prediction using the split-ring test

The aim of this paper is to compare several plastic yield criteria to show their relevance on the prediction of springback behavior for a AA5754-0 aluminum alloy. An experimental test similar to the Demeri Benchmark Test [Demeri MY, Lou M, Saran MJ. A benchmark test for springback simulation in sheet metal forming. In: Society of Automotive Engineers, Inc., vol. 01-2657, 2000] has been developed. This test consists in cutting a ring specimen from a full drawn cup, the ring being then split longitudinally along a radial plan. The difference between the ring diameters, before and after splitting, gives a direct measure of the springback phenomenon, and indirectly, of the amount of residual stresses in the cup. The whole deep drawing process of a semi-blank and numerical splitting of the ring are performed using the finite element code Abaqus. Several material models are analyzed, all considering isotropic and kinematic hardening combined with one of the following plasticity criteria: von Mises, Hill’48 and Barlat’91. This last yield criterion has been implemented in Abaqus. Main observed data are force-displacement curves during forming, cup thickness according to material orientations and ring gap after splitting. The stress distributions in the cup, at the end of the drawing stage, and in the ring, after springback, are analyzed and some explanations concerning their influence on springback mechanisms are given.     

On springback of double-curved autobody panels

The springback of double curved autobody panels is studied theoretically and experimentally. Both steel and aluminium sheets are included in this investigation. The obtained results show that the springback is decreased with increasing binder force, increasing curvature, increasing sheet thickness and decreasing yield strength. This paper comprises also a discussion on the plastic strains and their influence on the springback.     

Calculation of a constitutive potential for isostatic powder compaction

A macroscopic constitutive potential has been developed for the deformation of a powder compact of cylindrical particles during pressure sintering. The derivation is based on finite-element simulations of the densification process that proceeds under the synergistic action of power-law creep deformation in the particles, evolution of the nonlinearly developing contact area between the particles, and interparticle and pore free-surface diffusional mass transport. Solution to this initial/boundary-value problem as deformation proceeds with time provides all necessary information for the calculation of the constitutive potential. The associated constitutive law predicts the densification rate of the powder compact at a given temperature and pressure in terms of material parameters, such as creep constants and diffusion coefficients, and reflects the role played in the densification process by various micromechanical features at the microscale such as the pore surface curvature. The model predictions are compared with the existing analytical models for plane strain densification and experimental data from sintering of copper wires by grain boundary and curvature-driven pore surface diffusion.     

Die design method for sheet springback

A new method for designing general sheet forming dies to produce a desired final part shape, taking springback into account, has been developed. The method is general in that it is not limited to operations having particular symmetry, die shapes, or magnitude of springback shape change. It is based on iteratively comparing a target part shape with a Finite Element-simulated part shape following forming and springback. The displacement vectors at each node are used to adjust the trial die design until the target part shape is achieved, hence the term “displacement adjustment method” (DA) has been applied. DA has been compared with the “springforward” method of Karafillis and Boyce (K&B), which is based on computing the constraint forces to maintain equilibrium following forming. DA was found to converge in cases when K&B does not, and in cases when both methods converge, DA is many times faster. In general, i.e. nonsymmetric parts, K&B can return inaccurate results whereas DA does not. The suitability and application of the two methods is discussed, along with the origins of the differences.     

基于包辛格效应的回弹仿真分析

金属材料在一个方向上的应变硬化降低了反方向的屈服强度,材料包辛格效应的存在对车身成形仿真精度产生了重要影响,尤其现今高强钢和铝合金的大量应用,使车身成形件的回弹问题日益突出,车身模具制造对有限元回弹预测的准确性提出更高的要求。为了提高回弹的仿真精度有必要对材料的包辛格效应进行研究,利用一套夹具对DC06和DP600两种材料的薄板进行拉伸压缩试验,获得不同预应变下的位移加载曲线,通过拉伸压缩试验结果与仿真结果的对比分析,得到能反映材料包辛格效应的非线性混合硬化模型材料参数。开展U形件成形试验,并建立试验的仿真模型,计算DC06和DP600薄板的U形件成形回弹量,分析等向强化、混合强化和随动强化本构模型对回弹预测精度的影响,针对回弹仿真结果和试验结果的差别,对影响仿真精度的材料模型因素进行分析。结果表明,DC06和DP600的包辛格效应大小存在差别,考虑包辛格效应有助于回弹仿真精度的提高,但小曲率弯曲成形回弹计算对材料本构模型的敏感性,限制了回弹仿真精度的提高。     

An experimental and theoretical analysis on the application of stress-based forming limit criterion

In this paper, a detailed study on the stress-based forming limit criterion (FLSD) during linear and complex strain paths is developed. The calculation of stress-based forming limits based on experimental strain data is performed by using the method proposed by Stoughton [A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 2000;42:1–27]. By applying several combinations of different constitutive equations on the required plastic calculation, an analysis on the experimental forming stress limits is performed. The necking phenomenon is simulated by Marciniack–Kuczinsky (M–K) model using a more general code for predicting the forming limits. The selected materials are a bake-hardened steel (BH steel) and an AA6016-T4 aluminium alloy. Several yield criteria such as Von Mises isotropic yield function, quadratic and non-quadratic criterion of Hill (A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London 1948;A193:281–97; Theoretical plasticity of textured aggregates. Mathematical Proceedings of the Cambridge Philosophical Society 1979;85:179–91) and the advanced Barlat Yld96 yield function are used to show the influence of the constitutive law incorporated in the analysis on the stress-based forming limits. The effect of the hardening model on the FLSD is analysed by using two hardening laws, namely Swift law and Voce law. The influence of work hardening coefficient, strain rate sensitivity and the balanced biaxial yield stress on the theoretical FLSD is also presented. The effect of strain path changes on the stress-based forming limits is analysed. Some relevant remarks about stress-based forming limit criterion concept are presented.     

包申格效应对板料与成品管屈服强度与屈强比的影响

探讨微合金化高强度控轧钢板在制管过程中由于塑性弯曲变形所引起的包申格效应,以及这种效应对屈服强度和屈强比的影响。试验发现包申格效应导致屈服强度降低,应变硬化指数明显分为两个阶段。板与管相比,屈强比无明显改变。这些结果对管道建设业主和制板钢厂均有参考价值。     

汽车后桥横梁拉延工艺优化与回弹分析

针对汽车轻量化趋势,对某汽车后桥横梁的拉延成形和回弹问题进行了有限元数值模拟研究.首先建立零件的拉延模型,从冲压方向、工艺补充面、压料面、坯料初始形状等方面进行设计分析.利用Dynaform实现零件的成形和回弹模拟,重点对拉延筋的布置进行优化.通过对成形效果的比较,最终得到合理的拉延模型设计.     

Unconstrained springback behavior of Al-Mg-Si sheets for different sitting times

In this work, the springback behavior of the commercial 6022 aluminum alloy in temper aging (T4) is investigated taking into account that the sheets, prior to deformation process, are initially pre-strained and then submitted to various sitting times at room temperature. The unconstrained cylindrical bending test based on the NUMISHEET2002 proceedings as presented by Yoon et al. [Yoon JW, Pourboghrat F, Chung K, Yang DY. Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method. International Journal of Mechanical Sciences 2002;44:2133-53] is selected as validation benchmark. For finite element simulations, the geometry is modeled by solid-shell finite elements using the formulation of Alves de Sousa et al. [Alves de Sousa RJ, Yoon JW, Cardoso RPR, Fontes Valente RA, Grácio JJ. On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations. International Journal of Plasticity 2007;23:490-515; Alves de Sousa RJ, Cardoso RPR, Fontes Valente RA, Yoon J-W, Natal Jorge RM, Grácio JJ. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part I—Geometrically linear applications. International Journal for Numerical Methods in Engineering 2005;62:952-77; Alves de Sousa RJ, Cardoso RPR, Fontes Valente RA, Yoon JW, Grácio JJ, Natal Jorge RM. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part II—Nonlinear applications. International Journal for Numerical Methods in Engineering 2006;67:160-88]. The material behavior is described based on the work of Correia et al. [Correia JPM, Simões F, Gracio JJ, Barlat F, Ahzi S. A simple hardening rule accounting for time-dependent behavior in Al-Mg-Si alloys. Materials Science Engineering A 2007;456:170-9]. The results of conducted experiments and numerical simulations are compared. It can be concluded about the good agreement between experiments and simulations attesting the effectiveness of the material model utilized to describe the time-dependent hardening behavior.     

试制X80输油气管线钢的包申格效应研究

研究某厂试生产的X80输油气管线钢的显微组织结构和常规力学性能。该钢板以针状铁素体组织为主 ,晶粒 12级。采用四点弯曲方法 ,模拟制管工艺进行钢板的包申格效应研究。在屈服变形阶段 ,随预变形量的增加 ,由包申格效应导致的屈服强度损失单调的增加 ,此现象与屈服过程中 ,钉扎位错的脱钉 ,形成大量有方向性的可动位错有关。按API标准 ,从试制的 610mm× 7.9mm螺旋钢管取样进行测试 ,结果发现钢管由包申格效应导致的屈服强度损失 ,除卷板头部和尾部略高外 ,沿板长平均在 5 5MPa至 75MPa之间。包申格效应的影响不可忽视     

Estimation of springback in double-curvature forming of plates: Experimental evaluation and process modeling

This paper presents the results obtained from a series of experiments on double-curvature forming of 300 mm square and 15 mm thick plates of type 316L(N) stainless steel to evaluate the inherent springback and also to validate finite element method (FEM) based process model developed for forming of multiple-curvature sectors of large size vessels. The experimental results show that twisting of the plate occurs during pressing, which is unavoidable in an actual forming setup on the shop floor. Twisting increases with increase in slope of the die cavity. Springback in the plate changes in an ascending order towards the centerline of the plate from the edges. The final radius of curvature (ROC) on the pressed plate after springback does not remain constant along a particular axis although the die and the punch had constant ROC along that axis because of varying constraint to opening up of the plate from centerlines to the edges. Springback also increases with reduction in the stiffness of the die and punch. The simulated plate profiles obtained from the FEM process model for multiple-curvature plate forming compared well with the experiments, the maximum error being within 6%. The process model used a sequential dynamic explicit formulation for the plate pressing phase and a static implicit formulation for the unloading (springback) phase in the Lagrangian framework. Reduced integration shell elements were used for the plate and the die and the punch were considered rigid. Dynamic explicit FEM for pressing and static implicit FEM for the unloading phase are adequate and economic for modeling of plate forming process by using FEM. The necessary material and frictional property data needed for the FEM process model were generated in-house. This model can be applied to design of dies and punches for forming the petals of large pressure vessels. The FEM process model predicts the final shape of the product and the residual cold work level for a given die, punch and plate configuration and this information can be used to correct the die and punch shapes for springback to manufacture the petals to the desired accuracy.     

Experimental studies and constitutive modelling of the hardening of aluminium alloy 7055 under creep age forming conditions

A test programme has been designed to characterise the creep-ageing behaviour of Aluminium Alloy 7055, commonly termed AA7055, under creep age forming (CAF) conditions. Creep ageing tests have been carried out for a range of stress levels at 120 °C for 20 h, which is the typical period for a CAF process. Interrupted creep tests have also been carried out to rationalise the effect of stress levels on age hardening. Based on experimental observations, a set of mechanism-based unified creep ageing constitutive equations has been formulated, which models creep induced evolution of precipitates, dislocation hardening, solid solution hardening and age-precipitation hardening. A multiple-step reverse process has been introduced to determine, from creep ageing test data, the values of constants arising in the constitutive equations. Close agreement between experimental data and computed results are obtained for creep and age hardening data for the stress range tested. The determined equation set has been integrated with the commercial FE code MSC.MARC via the user defined subroutine, CRPLAW, for CAF process modelling. In addition to springback, the evolution of precipitate size and creep induced precipitation hardening can be predicted.