Study on experimental approaches of forming limit curve for tube hydroforming

This paper proposes a set of experimental approaches to establish the forming limit curve (FLC) in different forming modes for tube hydroforming. In tension–compression strain state, analytical models are constructed to determine the linear strain paths at the pole of the hydroformed tube, and a self-designed free hydroforming apparatus with axial feeding and internal pressure are used to carry out the bulge tests. In plane strain state, the difference is that both ends of the tube are fixed with different punches. In tension–tension strain state, a novel hydroforming apparatus are designed. The novel device requires the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. The linear strain paths for the right hand side of FLC by finite element method simulation are calculated. The linear strain paths in different strain states are verified and the FLC of roll-formed QSTE340 seamed tube is constructed through the proposed experimental approaches. Comparison between simulation and experimental results for hydroforming process of front crossmember shows that the experimental FLC is accurate and valid for tube hydroforming.     

Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.     

Bursting failure prediction in tube hydroforming using FLSD

In tube hydroforming, circular components are hydrobulged or hydroformed from tubular blanks with internal pressure and simultaneous axial loading. Thus the tube can be fed into the deformation zone during the bulge operation allowing more expansion and less thinning without any defects such as wrinkling, buckling, and bursting. By contrast with the buckling and the wrinkling, the bursting is generally classified as an irrecoverable failure mode. Hence in order to obtain the sound hydroformed products, it is necessary to predict the bursting behavior and to analyze the effects of process parameters on this failure condition in hydroforming processes. In this study, a forming limit stress diagram (FLSD) is constructed by plotting the calculated principal stresses based on the local necking criterion. Using the theoretical FLSD, we carry out the numerical prediction of bursting failure in a hydroforming process, which usually has non-linear strain path. Finite element analyses are carried out to find out the state of stresses during simple hydroforming operation, in which the FLSD is utilized as the forming limit criterion for assessment of the initiation of necking, and influences of the material parameters on the formability are investigated. In addition, the numerical results obtained from the FEM combined with the FLSD are confirmed with a series of bulge tests in view of bursting pressure and show a good agreement. Consequently, it is shown that the theoretical and numerical approach to bursting failure prediction proposed in this paper will provide a feasible method to satisfy the increasing practical demands for assessment of the forming severity in hydroforming processes.     

Effects of sheet thickness and anisotropy on forming limit curves of AA2024-T4

In this study, the effects of sheet thickness and anisotropy of AA2024-T4 on forming limit curve (FLC) are experimentally investigated according to ISO 12004-2 standard. A new limit strain measurement method is proposed by using the grid analysis method so as to determine limit strains conveniently and reliably. In addition to the regular test specimens, various widths are added to enhance the FLC’s accuracy at the plane strain condition (PSC). The accuracy and reliability of the proposed method are verified for different materials. Results illustrate that an increase in the sheet thickness increases the FLC level. The additional experiments for additional widths improve the accuracy of the FLC at the PSC, and the position of the lowest major strain value differs from the literature. However, the effect of anisotropy on the FLC is found to be insignificant. Finally, experimental and numerical case studies are carried out for conventional deep drawing, stretch drawing, and hydraulic bulge processes. Results reveal that different FLCs are necessary for different thicknesses for accurate predictions.     

A general forming limit criterion for sheet metal forming

The forming limit of sheet metal is defined to be the state at which a localized thinning of the sheet initiates during forming, ultimately leading to a split in the sheet. The forming limit is conventionally described as a curve in a plot of major strain vs. minor strain. This curve was originally proposed to characterize the general forming limit of sheet metal, but it has been subsequently observed that this criterion is valid only for the case of proportional loading. Nevertheless, due to the convenience of measuring strain and the lack of a better criterion, the strain- based forming limit curve continues to play a primary role in judging forming severity. In this paper it is shown that the forming limit for both proportional loading and non-proportional loading can be explained from a single criterion which is based on the state of stress rather than the state of strain. This proposed criteria is validated using data from several non-proportional loading paths previously reported in the literature for both aluminum and steel alloys. In addition to significantly improving the gauging of forming severity, the new stress-based criterion is as easy to use as the strain-based criterion in the validation of die designs by the finite element method. However, it presents a challenge to the experimentalist and the stamping plant because the state of stress cannot be directly measured. This paper will also discuss several methods to deal with this challenge so that the more general measure of forming severity, as determined by the state of stress, can be determined in the stamping plant.     

Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic-nonlinear kinematic hardening

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic-nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.     

FMEA for the reliability of hydroformed flanged part for automotive application

Tube hydroforming technology is widely used in the automotive industries due to its advantages such as weight reduction, increased strength, improved quality, and reduced tooling cost compared to conventional manufacturing technology. The hydroformed parts often have to be structurally joined at some point. Therefore, the hydroformed automotive parts which have a localized attachment flange are useful. In many cases, the parts formed by hydroforming process are directly related with structural safety, reliability of hydroformed parts must be considered. In this study, hydroforming process of flanged rectangular parts was designed and process reliability was investigated. Finite element analysis was performed to optimize tool geometry considering process parameters such as die aspect ratio and pressure conditions with Dynaform 5.5. Hydroforming experiments to fabricate a flanged rectangular part were performed with optimized tool geometry. The relationship between process parameters and defect was analyzed by FMEA (failure modes and effects analysis). The result shows that process condition was optimized and reliability of rectangular part was increased.     

铝板数控单点渐进成形的成形极限曲线研究

对薄壁复杂构件进行数控单点渐进成形时,板料易发生破裂、起皱等缺陷,且材料变形机制演化复杂,对加载条件极为敏感,使得板料在数控单点渐进成形时的破裂预测和控制变得极难。为此,选取1060铝板作为研究材料,通过试验研究了数控单点渐进成形技术中板料的成形性能,以实现对破裂的预测和控制。利用拓印法将制件的空间变形问题转化为平面变形问题,采用数码显微镜对拓印的制件网格数据进行测量和提取,选用插值法和多项式拟合法对数据进行拟合处理,最终得到了1060铝板料在数控单点渐进成形技术下的成形极限曲线（FLC）。通过对FLC进行分析研究,得到了制件破裂区和安全区域的应变分布,实现了制件破裂的预测和控制。为进一步提高1060铝板的成形极限,将超声振动引入到单点渐进成形中,通过试验对比研究了超声振动辅助渐进成形的FLC和传统渐进成形的FLC,试验结果表明：当振动功率为120 W、振动频率为25 kHz时,1060铝板料的成形极限提高了11%。     

考虑可靠度的成形极限曲线建立方法

实验获得板材成形极限的方法是通过对不同加载路径下获得的极限应变点进行拟合,从而得到成形极限曲线。将百分回归分析理论应用到成形极限实验数据点的曲线拟合方法中,利用该方法可以对成形极限曲线的百分位值进行分析和预测,可以在给定的实验可靠度和置信度下,根据实际需要调节曲线的位置,同时为给定极限应变点分布带的上下限的确定提供理论依据。     

Statistical evaluation of forming limit in hydroforming process using plastic instability combined with FORM

Deviation of raw material parameters, such as work hardening, anisotropy, yield stress, etc., leads to an uncertainty to the position of the forming limit curve (FLC). This paper presents a novel approach to statistically evaluate the forming limit in hydroforming processes when taking into account the variations in the material parameters. First, plastic instability based on the Hill’s quadratic plastic potential is employed to construct the deterministic FLC. Then, with using the assumption that all material parameters are normally distributed random variables, stochastic modeling of the FLC with a confidence level is carried out, and statistical evaluation of the FLC is performed. In this work, a first-order reliability method is adopted for the reliability assessment of the FLC, and this is verified with the Monte-Carlo simulation method.     

Forming limit investigation of friction stir welded sheets: influence of shoulder diameter and plunge depth

The main aim of the present work is to analyze the influence of shoulder diameter and plunge depth on the formability of friction stir welded sheets. The base material used for welding and forming was AA6061-T6. Formability evaluation was performed through limiting dome height tests. The forming limit curve, FLC (only in the stretching region), thickness distribution, and strain hardening exponent of the weld region were monitored during formability studies. It is found from the work that the forming limit of friction stir welded sheets is better than unwelded sheets. In general, with an increase in shoulder diameter and plunge depth, the forming limit is found to improve considerably. With a decrease in thickness gradient severity and an increase in strain hardening exponent (n) of the weld region, the forming limit is found to increase. The increase in n value of the weld region is believed to occur because of the reduction in dislocation density. The maximum thickness difference is higher in the retreating side, rather than in the advancing side, of the weld. This is due to the differential straining and hardness levels attained by both sides during friction stir welding.     

Comparison of plastic strains on AA5052 by single point incremental forming process using digital image processing

In this study, a surface based strain measurement was used to determine the formability of the sheet metal. A strain measurement may employ manual calculation of plastic strains based on the reference circle and the deformed circle. The manual calculation method has a greater margin of error in the practical applications. In this paper, an attempt has been made to compare the formability by implementing three different theoretical approaches: Namely conventional method, least square method and digital based strain measurements. As the sheet metal was formed by a single point incremental process the etched circles get deformed into elliptical shapes approximately, image acquisition has been done before and after forming. The plastic strains of the deformed circle grids are calculated based on the nondeformed reference. The coordinates of the deformed circles are measured by various image processing steps. Finally the strains obtained from the deformed circle are used to plot the forming limit diagram. To evaluate the accuracy of the system, the conventional, least square and digital based method of prediction of the forming limit diagram was compared. Conventional method and least square method have marginal error when compared with digital based processing method. Measurement of strain based on image processing agrees well and can be used to improve the accuracy and to reduce the measurement error in prediction of forming limit diagram.

     

采用可移动凹模的板材液压成形技术

提出一种改进的板材液压成形新工艺,即采用可移动凹模,实现拉深与胀形的复合液压成形。在整个变形过程中,板材初始变形部分始终与可移动凹模接触,从而抑制已变形区进一步变形,使变形更加均匀,实现变形的顺序控制,板材成形极限得到提高。从试验和数值模拟两方面对可移动凹模板材液压成形技术进行了研究,分析各种工艺参数,如摩擦因数等对板材成形性的影响,并且分析了可移动凹模对板材成形极限的影响。     

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.     

Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet

Forming limit curves at neck and at fracture have been experimentally determined, and surfaces of fractured dome specimens have been observed optically and in the SEM, for an automotive AA6111-T4 sheet material. Various continuum ductile fracture criteria from the literature along with the assumptions of power law hardening, Hill’s quadratic yield criterion, and proportionality of stress and strain paths have been utilized for prediction of forming limit curve at fracture and compared with the experimental curve to assess the applicability of the different fracture criteria. The maximum shear stress criterion by Tresca predicts reasonably well the fracture limits of AA6111-T4 sheet material for a range of strain ratios, and is consistent with the microstructural observations. The criterion can be used to predict fracture limit curves from uniaxial tensile data and plane strain limit at fracture. A methodology for incorporating such a ductile fracture criterion into FE simulations of sheet stampings for prediction of fracture is discussed.     

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This article studies tubular hydroforming of high strength low alloy (HSLA) and dual phase (DP600) straight tubes under the action of end feeding loads. Experiments demonstrate that higher end feed loads enhance the formability of the tubes and increase the internal fluid pressure for onset of necking and bursting. Because of the action of the internal pressure and the axial compressive load, the onset of localization (necking) is due to a complex three-dimensional state of stress. Using free expansion experiments, approximate upper and lower bound strain-based forming limit curves are determined for the tube materials. These limit curves, in turn, are used to derive upper and lower bound extended stress-based forming limit curves [Simha et al., Prediction of necking in tubular hydroforming using an extended stress-based FLC. Transactions of the ASME Journal of Engineering Materials and Technology 2007;129(1): 36-47]. In conjunction with finite element computations that use solid elements to model the tube, these stress-based limit curves are used to predict upper and lower bound necking pressures under the action of end feed loading. These predictions of necking pressures, when an appropriate coefficient of tube-die friction is used, are found to bracket the experimentally measured necking pressures. Computations using plane stress shell elements to model the tubes are shown to give erroneous results, since the plane stress approximation is not valid when tubes are hydroformed in a die.     

基于成形应力极限的管材液压成形缺陷预测

基于塑性应力应变关系及Hill79屈服准则,推导出极限应力与极限应变间转化关系,进而建立2008T4铝合金的成形应力极限图(Forming limit stress diagram,FLSD)。采用LS-DYNA软件对三通管液压胀形过程进行模拟,应用FLSD预测胀形过程中破裂的发生及成形压力极限,并与传统成形极限图(Forming limit diagram,FLD)结果进行了对比。研究表明,FLD与FLSD预测结果中破裂缺陷位置相同,但极限内压力值存在很大差别,而FLSD预测结果与物理试验结果较吻合。考虑到FLD受应变路径影响显著的因素,将FLSD作为管材液压成形等复杂应变路径下的成形极限的判据更加方便可靠。     

Analytical model for planar tube hydroforming: Prediction of formed shape, corner fill, wall thinning, and forming pressure

An analytical model for planar tube hydroforming based on deformation theory has been developed. This analytical model can be used to predict hydroformed shape, corner fill, wall thinning, and forming pressure. As the model is based on a mechanistic approach with bending effects included, local strain and stress distribution across the wall thickness can be determined. This includes strain and stress distributions for the outer layer, inside layer, and middle layer. The model is validated using finite element analysis and tube hydroforming experiments on irregular triangular, irregular quadrilateral, and pentagonal hydroformed shapes.     

Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology

In a sheet forming process, drawbead plays an important role on the control of the material flow. In this paper, a numerical procedure for the design of forming processes is described. It is based on the coupling of an optimization technique and the simplified one step finite element method (also called inverse approach). The optimization technique allows adjustment of the process parameters so that specified criteria are fulfilled. Response surface methodology (RSM) is a global approximation method, which is ideally suited for solving highly nonlinear optimization problems. The finite element method, in addition to predicting the response of the process to certain parameters, allows assessment of the effect of a variation in these parameters on this response. The authors utilize the one step method at the preliminary design stage to supply stress or strain information for the following optimization using RSM. The procedure for this optimization process is fully described. The front fender for Numisheet 2002 is presented and the real defect free workpiece is produced to demonstrate the usefulness of the proposed optimization procedure. A comparison between the two forming limit curves (FLC) before and after optimization and results obtained using the precise incremental commercial software DYNAFORM based on the explicit dynamic approach verify that the optimization design method of drawbead could be successfully applied in designing actual tools of auto body cover panels.     

板料成形极限预测新判据

从控制塑性变形能的角度出发,基于总塑性功的积分形式,建立板料的成形极限预测判据.这种板料成形极限预测判据考虑应变路径变化、材料的硬化指数、各向异性系数及材料的初始厚度等对成形极限的影响.判据中的参数可由常用的单向拉伸极限应变试验确定.由此通过数值模拟可以预测板料在各种不同应变路径下的成形极限,适用于成形极限图的拉-压和拉-拉应变区,从而建立完整的成形极限曲线,可大大减少试验工作量.试验验证表明,这种成形极限预测判据对于钢板和铝合金板的成形极限可做出较为准确的预测.实现了只进行单拉试验即可预测板料在不同应变路径下的成形极限.