成形极限曲线的新概念

失稳理论是成形极限曲线（ＦＬＣ）的理论基础。本文论述了ＦＬＣ理论研究中存在的问题。研究指出：一般出厂板的表面状况不会影响板料的集中失稳；板内损伤平面应变时最严重；双拉时，板内损伤的积累、发展，导致应力状态向平面应变漂移；拉压时，载荷失稳后引起的双拉，也会导致平面应变。因此平面应变状态的出现是板料集中失稳的共同原因。在此基础上，建立了ＦＬＣ左右两半部统一的模型。新模型与试验结果符合良好，优于Ｍ－Ｋ理论。     

Finite element simulation of springback for a channel draw process with drawbead using different hardening models

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong-Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress-strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.     

Error analysis of FLC experimental data at warm/hot stamping conditions

Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250℃. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.     

An analysis of localized necking in aluminium alloy tubes during hydroforming using a continuum damage model

In this work, localized necking in aluminium alloy tubes subjected to free hydroforming is analyzed. The main objective is to study the influence of loading conditions, such as prescribed fluid pressure or volume flow rate in conjunction with axial end feed, on the nature of the forming limit curve (FLC). To this end, the strain histories experienced at the tube mid-length, which were computed in an earlier investigation [14] [Varma NSP, Narasimhan R. A numerical study of the effect of loading conditions on tubular hydroforming, Journal of Materials Processing Technology 2005; [Submitted for publication]], are analyzed using the Marciniak–Kuczynski (M–K) method along with an anisotropic version of the Gurson model. The Gurson constitutive parameters are determined following an inverse approach using the sheet FLC for the chosen alloy. The predicted FLC for combined pressure and axial contraction corroborates well with the experimental data obtained in [12] [Kulkarni A, Biswas P, Narasimhan R, Luo A, Stoughton T, Mishra R, Sachdev AK. An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming. International Journal of Mechanical Sciences 46:2004;1727–46] and is almost flat, whereas it is akin to the sheet FLC and increases with negative minor strain when fluid volume is specified. The forming limit strains for loading with specified fluid volume are in general higher when compared to those with prescribed fluid pressure. Finally, it is demonstrated that a transition from axial to circumferential necking occurs when high ratios of axial extension to volume flow rate are applied to the tube.     

Effect of Plastic Anisotropy on the Formability of Aluminum 6016-T4 Sheet Material

Sheet metal formed of lightweight materials such as aluminum sheeting has received great attention related to the reduction of vehicle emissions. This paper evaluates the anisotropic yield locus using Kuwabara’s biaxial tensile tester and stretches formability using Hecker’s hemispherical punch stretching test for aluminum 6016-T4 sheet material. The anisotropic yield locus of the Al6016-T4 sheet measured is fitted well by the modified Drucker yield function. Moreover the best fitting to the experimental stress-strain curve from the tensile test was obtained by taking an appropriate hardening model. Analytical study to predict the stretch formability by using Hora’s Modified Maximum Force Criterion (MMFC) was performed. The predicted forming limit curves (FLC) based on various yield functions were compared with the experiments and discussed.     

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.     

不同硬化模型对铝合金板冲压成形模拟结果的影响

研究不同塑性变形硬化模型对汽车5182-O铝合金板材冲压成形模拟结果的影响。采用材料单向拉伸试验得到应力应变关系曲线,基于Hollomom、Krupskowsky与Power方程对曲线进行拟合,建立材料室温下塑性变形硬化模型,对厚度为1.5 mm和0.85 mm的5182板材进行冲压试验和有限元模拟分析,对比分析冲压试验与模拟结果。试验与模拟结果显示,当板料厚度为1.5 mm时,板料冲压试验的成形力最大为42.95 kN,板料拉深深度为30.58 mm,基于Power方程计算得到的最大成形力为41.5kN与试验结果比较接近,Hollomom方程计算得到的拉深深度为30.546 mm,板材成形厚度分布与试验结果比较接近;当板料厚度为0.85 mm时,板料冲压试验的成形力最大为34.47kN,板料拉深深度为33.792 mm,基于Power方程计算得到的最大成形力为34.27 kN与试验结果比较接近,Hollomom方程计算得到的拉深深度为33.636 mm,板材成形厚度分布与试验结果比较接近。基于三种硬化模型铝合金冲压成形过程的计算模拟分析结果,并通过与试验对比得到不同硬化模型对铝合金板材冲压成形计算模拟的影响,进一步为汽车铝合金覆盖件在成形工艺的研究分析提供理论指导。     

A practical method to evaluate the forming severity of tubular hydroformed parts

In view of the prevalence of non-linear strain paths that develop in parts that are formed in multiple stages, such as bent and hydroformed structural components, the conventional forming limit curve (FLC) cannot be used to assess the forming severity of this manufacturing process. A path-independent stress-based forming limit criterion has been shown to be far more suitable to evaluate such parts, and this paper shows how this failure criterion can be effectively used to evaluate tubular hydroformed parts “on the shop floor”. Knowing the strain history in a given location of a part, a shifted FLC can be computed from the stress-FLC and used to determine the safety margin at this location. This methodology was used to evaluate the forming severity of an automotive instrument panel beam. It was found that this approach is user-friendly and provides a significant improvement in the ability to assess process robustness and product quality compared to the conventional method. The FLCs obtained using the proposed method were found to be in good agreement with those predicted with an MK-based calculation code. Finally, it is shown that a numerical simulation of the entire forming process is recommended to confirm the estimated strain path in critical locations and improve the accuracy of the method.     

利用激光局部硬化效应提高2B06铝合金板材拉深成形性研究

针对2B06铝合金复杂零件成形困难问题,提出了利用激光热处理局部硬化提高板材成形性的思路。在通过激光热处理试验研究了铝合金板的激光硬化效应的基础上,采用数值模拟计算了铝合金板激光热处理过程中激光光斑路径和其周边热影响区域的峰值温度场,并通过实际测温验证了其准确性。提出并构建了耦合性能梯度的差性坯料模型,对激光局部硬化的杯形件拉深成形性进行了模拟和试验研究。结果表明,激光扫描方式可以形成稳定的梯度温度场并对周边非加热区影响较小,且可以通过多道次扫描方式设计不同宽度范围的大梯度差性板材坯料。力学性能试验表明激光热处理可以有效地提高铝合金的局部加工硬化能力,这种效应可以有效抑制杯形件拉深时圆角大变形区的减薄,从而提升了板材的拉深性能。在上述基础上,将激光局部热处理用于2B06铝合金航空复杂口框零件的成形,通过设计激光处理路径和参数,获得合理的局部硬化区域,可有效地避免在加强筋处出现过度减薄导致的破裂,大大提高复杂零件的成形性。     

基于M-K模型的相变诱发塑性钢板的成形极限研究

在M-K模型的基础上，将描述相变诱发塑性的硬化方程引入到成形极限的推导中，通过考虑板料冲压成形过程中硬化性能的变化对TRIP钢极限变形能力的影响，建立了适合于TRIP钢板的成形极限预测模型。预测结果与试验结果吻合较好，表明提出的考虑相变诱发塑性效应的成形极限预测模型较准确地预测了相变诱发塑性钢的极限变形能力，有利于指导相变诱发塑性钢板成形工艺。     

A simplified type-2 fuzzy logic controller for real-time control

Increasingly, genetic algorithms (GAs) are used to optimize the parameters of fuzzy logic controllers (FLCs). Although GAs provide a systematic design approach, the optimization process is generally performed off-line using a plant model. Differences between the model and physical plant may result in unsatisfactory control performance when the FLCs are deployed in practice. Type-2 FLCs are an attractive alternative because they can better cope with modeling uncertainties. Unfortunately, type-2 FLCs are computationally intensive. This paper presents a simplified type-2 FLC that is suitable for real-time applications. The key idea is to only replace some critical type-1 fuzzy sets by type-2 sets. Experimental results indicate that the proposed simplified type-2 FLC is as robust as a conventional type-2 FLC, while lowering the computational cost.     

Earing predictions for strongly textured aluminum sheets

Metallic alloy sheets develop crystallographic texture and plastic anisotropy during rolling. Deep drawing of a cylindrical cup from a rolled sheet is one of the typical forming operations where the effect of this anisotropy is most evident. Generally, in the finite element analyses of this process, the evolution of anisotropy during forming is neglected. In this paper, results of an experimental program carried out to quantify the anisotropy of aluminum alloy AA5042-H2 are reported. In addition to tensile tests along seven directions in the plane of the sheet, cup-drawing tests were conducted. It was observed that the material displays eight ears. The effects of the evolution in anisotropy and the directionality in hardening on the predictions of the earing profile for this material are investigated using a new methodology that incorporates multiple hardening curves corresponding to uniaxial tension along several orientations with respect to the rolling direction, and to biaxial tension. Yielding is described using the anisotropic yield function Yld2000-2D [1] and a form of CPB06ex2 yield function [2], which is tailored for metals with no tension–compression asymmetry. It is shown that even if distortional hardening is neglected, the latter yield function predicts a cup with eight ears as was observed experimentally. Consideration of distortional only leads to improved accuracy in prediction of the non-uniformity of the cup height profile.     

Calculation of forming limit diagrams using Hill's 1993 yield criterion

Based on the analysis proposed by Jones and Gillis (JG), forming limit diagrams (FLDs) are calculated from idealization of sheet deformation into three stages: (I) homogeneous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with precipitous drop in load. In the calculation, Hill's 1993 yield criterion is used. Using this yield criterion and the JG model, effects of materials parameters such as ratio of uniaxial to equi-biaxial yield stress, strain hardening, strain rate sensitivity and plastic anisotropy on the shape and level of forming limit curves are studied. In addition, the capability of the JG model to predict limit strains is demonstrated through comparison of calculated results with experimental data for the interstitial free (IF) steel and aluminum alloys 3003-O and 8014-O. It is concluded that although the model predicts the effect of material parameters reasonably well, the calculated limit strains are higher than the experimental FLDs. The observed discrepancy may be attributed to the assumption of planar isotropy, cavitation and the nature of texture present in the sheets. Due to the overestimation of the predictions, care must be taken when using this approach for industrial purposes.     

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。     

Large deformation compression–torsion behaviour of a titanium alloy and its modelling

A range of sequential and compound compression-torsion tests has been carried out on titanium alloy IMI834 at 1000°C and nominal true strain rate 5 × 10⁻³ s⁻¹, typical of forging conditions. The tests were used to investigate initial and subsequent yield and flow behaviour, the nature of the material hardening and the effect of flow softening on subsequent deformation. In addition, a material model with isotropic or directional hardening has been used to predict the material behaviour.The results show that the material behaviour at large strains is reasonably isotropic, although a directional hardening model provides slightly better quantitative agreement with the experimental results. Large pre-strains (0.4), either axial or torsional, are found not to change significantly subsequent material behaviour. A stress state dependence of flow softening is observed to exist.The material model presented is shown to give good quantitative agreement of predicted and experimental results.     

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.     

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.     

Anisotropic plasticity with application to sheet metals

Hill’s 1948 anisotropic theory of plasticity is extended to include the concept of isotropic–kinematic hardening. The “anomalous” effect can be accounted for by kinematic hardening. It is shown that the quadratic yield function can be used for sheet metals irrespective of its plastic strain ratio R. It is further shown that effects of thickness reduction due to further rolling may be accounted for by kinematic hardening.     

不同强化模型下的板料成形极限

介绍Hill48屈服准则下基于不同强化模型的屈服方程。推导出能够用来确定随动强化模型和混合强化模型中参数的方程。采用单向拉伸曲线上所取得的数据,对所得方程进行拟合,得到参数值,并使用所得参数值得出三种强化模型下的单向拉伸曲线。结果表明采用上述方法能够准确地确定强化模型中的参数。给出随动强化模型和混合强化模型下成形极限的计算方法。基于三种强化模型,针对分散性失稳准则、Hill集中性失稳准则、凹槽失稳准则和平面应变漂移失稳准则,得到简单加载路径下的成形极限图和成形极限应力图。从这些图中可以看出,强化模型对成形极限图和成形极限应力图影响明显。因此应当确定板料在成形过程中的强化规律,选择合适的强化模型进行成形极限预测。     

两种强化模型在拉伸筋阻力计算中的比较

将等向强化模型与运动中化模型分别引入逐级更新Ｌａｇｒａｎｇｅ有限元列式,采用八节点平面 应变单元,对拉伸筋阻力进行了数值计算,并将两种模型的计算结果进行了比较与讨论,运动强化模型更好地反映了板料在拉伸筋处的弯曲反弯过程,可以更准确地预测拉伸筋阻力。