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.

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.

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.

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 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.

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.

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。

镁合金板材成形极限图(FLD)的实验研究

首次利用电蚀网格法,在 BCS-30D 板材成形性试验机上进行镁合金板材成形实验,利用先进的 ASAME 自动应变测量系统进行应变测量分析,测试镁合金板材的成形极限图(FLD)。实验表明,室温下 AZ31B 镁合金冷轧态板材的力学性能和冲压性能不佳,难以完成成形极限图的测试,不具备成形加工能力;热轧态镁合金板材具有一定的塑性和成形性能,并测试了其成形极限图。成形极限曲线 FLC 的测试对制订镁合金板材的冲压成形工艺提供了理论依据。

轿车零件应变分析与FLD选材预测

对ＣＡ７２２０红旗轿车主要零件使用的钢板进行了冲压级别分类，采用网格法测定了零件冲压后的应变值并绘制了零件应变图和成形极限图（ＦＬＤ）。用有限元模拟分析（ＦＥＡ）确定出油底壳零件变形的危险部位，计算了危险部位的成形安全裕度，并对零件优化选材进行了性能预测。

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.

基于多元线性回归的6016汽车铝板FLD_0预测模型

成形极限图中FLD0(平面应变处的主应变)的准确性关系到汽车零件CAE仿真分析和安全裕度判定的精度。文章针对15种不同性能的6016汽车铝板,采用相关性分析方法研究了材料厚度、屈强比、延伸率、n值和r值等对6016汽车铝板FLD0的影响规律,并基于多元线性回归方法建立了6016汽车铝板FLD0的预测模型。

薄板成形极限图(FLD)的多项式拟合分析

基于多项式拟合的基本原理以及相关性与方差的综合分析,探讨了成形极限散点与高次多项式之间的相关特性以及表面工程主应变极值点FLD0与拟合曲线的关系。在所得的拟合曲线基础上配合数理统计与概率理论分析,拟合曲线的上下置信函数可以成为描绘成形极限曲线(FLC)的重要依据,也可以为FLD0值的区间估计提供可靠科学的置信分析。