Prediction and Verifcation of Forming Limit Diagrams Based on a Modifed Shear Failure Criterion

The forming limit diagram plays an important role in predicting the forming limit of sheet metals.Previous studies have shown that,the method to construct the forming limit diagram based on instability theory of the original shear failure criterion is efective and simple.The original shear instability criterion can accurately predict the left area of the forming limit diagram but not the right area.In this study,in order to improve the accuracy of the original shear failure criterion,a modifed shear failure criterion was proposed based on in-depth analysis of the original shear failure criterion.The detailed improvement strategies of the shear failure criterion and the complete calculation process are given.Based on the modifed shear failure criterion and diferent constitutive equations,the theoretical forming limit of TRIP780 steel and 5754O aluminum alloy sheet metals are calculated.By comparing the theoretical and experimental results,it is shown that proposed modifed shear failure criterion can predict the right area of forming limit more reasonably than the original shear failure criterion.The efect of the pre-strain and constitutive equation on the forming limits are also analyzed in depth.The modifed shear failure criterion proposed in this study provides an alternative and reliable method to predict forming limit of sheet metals.

Theoretical prediction of forming limit diagram of AZ31 magnesium alloy sheet at warm temperatures

A theoretical prediction on forming limit diagram（FLD） of AZ31 magnesium alloy sheet was developed at warm temperatures based on the M-K theory. Two different yield criteria of von Mises and Hill＇48 were applied in this model. Mechanical properties of AZ31 magnesium alloy used in the prediction were obtained by uniaxial tensile tests and the Fields-Backofen equation was incorporated in the analysis. In addition, experimental FLDs of AZ31 were acquired by conducting rigid die swell test at different temperatures to verify the prediction. It is demonstrated from a comparison between the predicted and the experimental FLDs at 473 K and 523 K that the predicted results are influenced by the type of yield criterion used in the calculation, especially at lower temperatures. Furthermore, a better agreement between the predicted results and experimental data for AZ31 magnesium alloy sheet at warm temperatures was obtained when Hill＇48 yield criterion was applied.

Stress based forming limit diagram for formability characterization of 6061 aluminum

Two numerical criteria of forming limit diagram（FLD） criterion and ductile fracture criterion（DFC） are presented for FLD prediction of 6061 aluminum. The numerical results are compared with the experimental FLD and also punch＇s load-displacement curve of experimental samples. Experimental FLD of this study is calculated using hemispherical punch test of Hecker. Experimental FLD is converted to FLSD and imported to the Abaqus software to predict necking of samples. Numerical results for FLSD prediction were compared with experimental FLSD. Results show that ductile fracture criterion has higher accuracy for FLD and FLSD prediction of 6061 aluminum. Comparison of numerical and experimental results for force-displacement curve of punch shows that numerical results have a good agreement with experiment.

Influence of material models on theoretical forming limit diagram prediction for Ti-6Al-4V alloy under warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti?6Al?4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson?Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M?K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.

Experimental and Numerical Analysis of Forming Limit Diagram (FLD) and Forming Limit Stress Diagram (FLSD)

In this work, forming limit diagram for aluminum alloy 3105 is performed experimentally and forming limit based on stress (FLSD) calculated from strains that resulted from experimental procedure. In addition, numerical prediction by ductile fracture criteria using simulation is considered and it is shown that they are well suited with the experimental results. The strain paths from finite element simulations are found fairly acceptable to represent both sides of the FLD.

Determination and application of stress-based forming limit diagram in aluminum tube hydroforming

The stress-based forming limit diagram(FLSD) established with limit stress is independent of the strain paths. Compared with traditional strain-based forming limit diagram(FLD),it is more convenient and practical to use as the criterion of forming limit under complex strain paths. The forming limit of 3A21 aluminum alloy sheet was tested and its forming limit diagram(FLD) was determined. Then the FLSD of 3A21 was constituted by transformation formulas between limit strain and limit stress. This FLSD was used in conjunction with LS-DYNA finite element simulations to predict the onset of fracture and limit forming pressure in tube hydroforming. The results indicate that the fracture often occurs in the transition region between corner and straight side of the tube,and the limit forming pressure is 46.4 MPa. The simulation result agrees with the experimental result,and the FLSD is able to predict the forming limit of tube hydroforming with remarkable accuracy.

Forming limit of textured AZ31B magnesium alloy sheet at different temperatures

Repeated unidirectional bending （RUB） was carried out to improve the texture of commercial AZ31B magnesium alloy sheets. All specimens were prepared in the rolling direction. The forming limit diagrams （FLDs） of AZ31B magnesium alloy sheet were determined experimentally by conducting stretch-forming tests at room temperature, 100, 200 and 300 ℃ Compared with the as-received sheet, the lowest limited strain of AZ31B magnesium alloy sheet with tilted texture in the FLD increased by 79% at room temperature and 104% at 100 ℃. The texture also affected the extension of the forming limit curves （FLC） in the FLD. However, the FLCs of two kinds of sheets almost overlapped at temperature above 200 ℃. It can be concluded that the reduction of （0002） texture intensity is effective to the improvement of formability not only at room temperature but also at low-and-medium temperature. The effect of texture on FLDs becomes weak with increasing temperature.

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.

Prediction of fracture limits of Ni-Cr based alloy under warm forming condition using ductile damage models and numerical method

The stretch forming and the deep-drawing processes were carried out at 300 and 673 K to determine the safe forming and fracture limits of IN625 alloy.The experimentally obtained strain-based fracture forming limit diagram(FFLD)was transformed into a stress-based(σ-FFLD)and effective plastic strain(EPS)vs triaxiality(η)plot to remove the excess dependency of fracture limits over the strains.For the prediction of fracture limits,seven different damage models were calibrated.The Oh model displayed the best ability to predict the fracture locus with the least absolute error.Though the experimentally obtained fracture limits have only been used for the numerical analysis,none of the considered damage models predicted the fracture strains over the entire considered range of stress triaxiality(0.33<η<0.66).The deep drawing process window helped to determine wrinkling,safe and fracture zones while drawing the cylindrical cups under different temperature and lubricating conditions.Further,the highest drawing ratio of 2 was achieved at 673 K under the lubricating condition.All the numerically predicted results of both stretch forming and deep drawing processes using the Hill 1948 anisotropic yielding function were found to be good within the acceptable range of error.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Forming limits of nickel coating on right region

The forming limits of nickel coating on the right region were studied, so as to direct the preparation of the material and help the production of workpieces. The electrodeposited nickel coating was prepared on steel substrate to form advanced structures, and its plastic instability was investigated by the Swift Plastic Instability Theory. By using the compound law for laminated sheet metals, explicit equations for the calculation of the instable eigen values were deduced. The forming limit diagrams of the nickel coating on the right region were plotted. It is exhibited that the forming limit of the coating sheet is between the forming limits of the individual nickel coating and steel substrate. The forming limit of the nickel coating is not so good as that of the steel substrate, and the forming limit strain of the coating sheet tends to diminish with the increase of thickness of the coating. The greater the normal anisotropic coefficient of the materials is, the better the forming limit is.

Hot Granules Medium Pressure Forming Process of AA7075 Conical Parts

High strength aluminum alloy plate has a low elongation at room temperature, which leads to the forming of its components need a high temperature. Liquid or gas is used as the pressure-transfer medium in the existing flexible mould forming process, the heat resistance of the medium and pressurizing device makes the application of aluminum alloy plate thermoforming restricted. To solve this problem, the existing medium is replaced by the heat-resisting solid granules and the general pressure equipments are applied. Based on the pressure-transfer performance test of the solid granules medium, the feasibility that the assumption of the extended Drucker-Prager linear model can be used in the finite element analysis is proved. The constitutive equation, the yield function and the theoretical forming limit diagram（FLD） of AA7075 sheet are established. Through the finite element numerical simulation of hot granules medium pressure forming（HGMF） process, not only the influence laws of the process parameters, such as forming temperature, the blank-holder gap and the diameter of the slab, on sheet metal forming performance are discussed, but also the broken area of the forming process is analyzed and predicted, which are coincided with the technological test. The conical part whose half cone angle is 15° and relative height H/d0 is 0.57, is formed in one process at 250℃. The HGMF process solves the problems of loading and seal in the existing flexible mould forming process and provides a novel technology for thermoforming of light alloy plate, such as magnesium alloy, aluminium alloy and titanium alloy.

Research on technological parameters of pressure forming with hot granule medium on AA7075 sheet

Hot granule medium pressure forming （HGMF） process is a new process in which granule medium replaces the medium in existing flexible-die hot forming process, such as liquids, gases or viscous medium. Hot forming of light alloy sheet parts can be realized based on the properties of granule medium, such as withstanding high temperature and pressure, filling well, sealing and loading easily. In this work, the forming of AA7075 cylindrical parts by HGMF process is taken as an example to establish the constitutive relation and forming limit diagram （FLD） of AA7075 sheet which is related to temperature by hot uniaxial tensile test of sheet metal. Based on the assumption that granule medium is applied to extended Drucker-Prager linear material model, the finite element model of HGMF process is established and the effect of technological parameters, such as forming temperature, blank-holder gap and drawing ratio, on the sheet metal formability, is studied. The limit drawing ratio curve of AA7075 cylindrical parts at forming temperature of 175-300 ℃ is obtained by HGMF process test, and the limit drawing ratio reaches the maximum value of 1.71 at 250 ℃. The results of numerical simulation are consistent with the results of process test, and the forming force, distribution of wall thichness and form of instability are predicted correctly, which provides reference for the application of HGMF process.

新型汽车覆盖件钢板性能研究

UF340作为一种新型超细晶高强钢,在汽车外覆盖件的应用上具有替代HC180BD的潜力,研究了UF340力学性能和成形性能。结果表明,在塑性、加工硬化指数和各向异性方面,UF340与HC180BD具有相似的力学性能,与HC180BD相比UF340没有明显的烘烤硬化性,2种材料的成形性能基本一致。通过Keeler模型计算获得UF340的成形极限曲线与成形试验结果存在一定差异,采用线性分段拟合方式获得的成形极限图与试验结果吻合度更高,采用该方法获得的成形极限曲线可为新材料的成形应用提供参考。

Theoretical prediction and experimental investigation on formability of tailor-welded blanks

Based on the elastoplastic mechanical properties of the weld and heat affected zone metals obtained by a nanoindentation test, a theoretical calculation model was established for the forming limit diagram（FLD） of tailor-welded blanks（TWBs） on the basis of plastic constitutive relations and Hosford yield criteria. Hemispherical punch bulging tests were performed to verify the FLD theoretical calculation results. The results demonstrated that not only the FLD theoretical calculation of base materials but also that of TWBs had a good agreement with their experiments. Besides, poorer formability of TWBs caused its FLD significantly lower than that of base materials. The theoretical calculation model offers a reliable approach to obtain the specific FLD of TWBs.

Formability of AA5052/polyethylene/AA5052 sandwich sheets

The formability of AA5052/polyethylene/AA5052 sandwich sheets was experimentally studied. Three kinds of AA5052/polyethylene/AA5052 sandwich specimens with different thicknesses of core materials were prepared by the hot pressing adhesive method. Then, the uniaxial tensile tests were conducted to investigate the mechanical properties of AA5052/polyethylene/ AA5052 sandwich sheets, and the stretching tests were carried out to investigate the influences of polymer core thickness on the limit dome height of the sandwich sheet. The forming limit curves for three kinds of sandwich sheets were obtained. The experimental results show that the forming limit of the AA5052/polyethylene/AA5052 sandwich sheet is higher than that of the monolithic AA5052 sheet, and it increases with increasing the thickness of polyethylene core.

AZ31镁合金板材准静态-动态冲击流体介质温热复合成形极限研究

基于Nakazima半球凸模胀形试验,对AZ31镁合金板材进行了成形极限试验,探究了AZ31镁合金板材在准静态-动态冲击流体温热复合成形下成形极限分布规律。结果表明,温度升高会提升AZ31镁合金板材的极限应变,对比准静态与复合成形两种方式下的极限应变发现, AZ31镁合金板材在准静态-动态复合成形下极限应变值更高,塑性成形性能得到改善。对两种成形方式下的断口形貌扫描进行分析,结果表明,准静态-动态复合成形的韧窝比准静态成形的韧窝多且深。对不同成形方式试样在室温、 100及200℃下进行了EBSD分析,发现在室温时,复合成形出现了少量{10-12}拉伸孪晶协调变形。在100℃时,复合成形引入细而薄的拉伸孪晶片层,切割细化晶粒,塑性较准静态成形得到提升。200℃下比准静态成形产生更多的再结晶晶粒是复合成形塑性提高的主要原因。

5052铝合金成形极限预测及数值模拟

基于Nakazima半球凸模胀形实验,利用有限元软件建立其简化模型。分析了润滑条件、冲压速度和凹模圆角半径对5052铝合金成形极限的影响。结果显示:随着摩擦因数的增大,成形极限曲线(FLC)向下偏移,表明理想的润滑条件有利于板材在复杂工艺下的成形;增大冲压速度也使FLC呈现下降的趋势,即在不考虑实际生产效率的情况下,降低冲压速度可以改善材料的延展性;而增大凹模圆角半径使FLC向上偏移,提高了板料的成形极限。将模拟结果与实验结果对比,两者较高的吻合度验证了有限元预测的可靠性。

贯通式Nakajima模型在预测不同厚度钢板成形性中的应用

在AutoForm中创建贯通式Nakajima模型,将钢板属性加载到模型中并仿真,分析了最大失效值随板厚增大时的变化趋势。结果显示,多数材料最大失效值均随厚度增大而降低,但存在以下3种不同情况:①常规深冲钢,如DC06在进行双向等拉、一般胀形及平面应变时,0.8 mm和1.6 mm厚时最大失效值偏低,而1.2 mm厚时最高;②特种深冲钢,如DC57D+Z钢,0.8 mm厚时最大失效值偏高,而其进行等向双拉和双拉胀形时,0.8、1.2mm厚时该值不变;③高碳合金钢,当屈服强度为280~400 MPa,最大失效值变化趋势呈现多样性,如HC340LA,对平面应变、类似单向拉伸或拉压变形,该值随厚度增大而降低,而对其他变形类型,随厚度增大先降低后升高,其中0.8 mm厚时该值最高,1.2 mm厚时最低,镀锌板HC340-590DPD-Z在发生双拉变形时,随厚度增大该值逐渐降低,而对于平面应变和接近单向拉伸的变形,1.2 mm厚时该值最高,HC340-590DP钢板在所有类型的变形中,该值均随厚度增大先降低后升高,其中1.2 mm厚时该值最低;④超高强度钢,如HC420-780DPD-Z,在发生双拉变形时,1.2 mm厚的最大失效值最高,对于副应变较大的变形,0.8、1.2 mm厚的该值接近且偏低,而对于非镀锌板HC420-780DP,该值随厚度增大均降低。

侧围外板腰线后三角窗位置起皱分析及对策

从冲压成型理论出发,结合成型极限图(FLD)阐述冲压起皱机理,为分析起皱问题提供了思路,以某车型SUV侧围外板为例,对腰线后三角窗位置的起皱问题进行解析,并于同步工程阶段,借助AutoForm分析软件找到了一种解决该起皱问题的对策,产品实物证实了该方法的有效性,对于同类结构的产品或工艺提供了参考,具有一定的推广和借鉴意义。