The Effect of the Imposed Boundary Rate on the Formability of Strain Rate Sensitive Sheets Using the M-K Method

In spite of the fact that the experimental results indicate the significant effect of strain rate on forming limits of sheets, this effect is neglected in all theoretical methods of prediction of Forming Limit Diagrams (FLDs). The purpose of this paper is to modify the most renowned theoretical method of determination of FLDs (e.g., M-K model) so as to enable it to take into account the effect of strain rate. To achieve this aim, the traditional assumption of preexistence of an initial geometrical inhomogeneity in the sheet has been replaced with the assumption of a preexisting “material” inhomogeneity. It has been shown that using this assumption, the strain rate would not be omitted from equations; thus, it is possible to demonstrate its effect on FLDs. To validate the results, they are compared with some published experimental data. The good agreement between the theoretical and experimental results shows capabilities of the proposed method in predicting the effect of the imposed rate at the boundary (which is physically the effect of the punch speed difference in sheet forming) on FLDs.     

Curvature prediction in air bending of metal sheet

The paper describes the use of bending models for air bending and focuses in particular on the importance of adequate determination of sheet curvatures, especially the curvature under the punch nose. After an introduction to air bending, the principles of models which are based on the assumption that the sheet wraps around the punch are described. This ‘wrap-around’ assumption is a limitation and often not in accordance with industrial practice. A method to predict the sheet curvature under the punch, thus eliminating the need for the wrap-around assumption, is discussed and its results are compared with experimental results. The paper then describes how models based on this method can be used to improve adaptive control methods in air bending.     

Prediction of the forming limit curves of sheet materials using the rigid-plastic finite element method

An incremental rigid-plastic finite element method is used to predict the forming limit curves (FLCs) of sheet materials. In this analysis, the deforming sheet materials is assumed to obey Hill's anisotropic yield criterion and its associated flow rule. To obtain the critical strain paths in both the positive and negative minor strain regions, simulations are performed using hemispherical punch stretching of a circular blank with various circular cutoffs and various friction conditions at the tool-sheet interface. A critical slope condition derived from the computed load-displacement curve is employed as a criterion to determine the limiting major and minor strains. FLCs of several sheet materials are predicted and the results are compared with the existing experimental data.     

A Novel Approach to the Determination of Forming Limit Diagrams for Tailor-Welded Blanks

This paper presents the results of simulated hemispherical die stretching of laser-welded, low carbon steel (ST12 and ST14) blanks of various thicknesses. The simulations were designed to produce forming limit diagrams (FLDs) for the tailor-welded blanks. Multiple criteria, including the second time derivatives of major strain, thickness strain, and equivalent plastic strain extracted from the strain history of simulations, were used to accurately detect the start of necking in FLDs. This is to say that necking starts when the second derivative of the thickness strain, major strain or plastic strain reaches its maximum value. Knowing the onset of necking, one can measure the major and minor strains at the critical area and produce the corresponding FLD. Results from the proposed method and those from experimental tests are compared to demonstrate the efficiency of the proposed method.     

Forming limit of electrodeposited nickel coating in the left region

A uniform nickel (Ni) coating was bilaterally electrodeposited on the low-carbon steel substrate for the application of advanced battery shells. Its forming limit was investigated by Hill localized necking theory coupled with finite element simulation and scanning electron microscopy. The effective stress and effective strain in the Ni coating and steel substrate are deduced using Hill’s anisotropic yield function. The localized necking condition is derived by sandwich sheet analysis, and the forming limit strains are obtained by solving the nonlinear equation of the localized necking condition. Extensive calculations are carried out using the proposed model. This study exhibits the nickel coating thickness and the normal anisotropic coefficients of the coating and substrate have little influence on the forming limit curve (FLC) in the left region of the coated sheet, but the strain hardening exponents of the coating and substrate have much effect on it. The calculated result matches well with the measured data in uniaxial tension. This investigation is useful for the preparation of the electrodeposited Ni coating and helpful for the forming operation of the battery shells.     

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

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 针对冷轧薄钢板St14在单向拉伸试验中出现的试样“双缩颈”现象,结合观察试样缩颈断裂处的形态,引用薄板单向拉伸分散性失稳和集中性失稳理论对其做出合理解释。通过拉伸过程应变网格分析,验证了薄板拉伸分散性失稳和集中性失稳的存在。明确薄板拉伸失稳的特性,更加有利于正确判定和合理利用深冲压用冷轧薄钢板的塑性指标。     

Theoretical and numerical study of strain rate influence on AA5083 formability

With the application of new forming techniques (hydroforming, incremental forming), it is necessary to improve the characterization of the formability of materials and in particular the influence of strain rate. This paper begins with the characterization of material behavior of an aluminum alloy 5083 at high temperatures. To describe its visco-plastic behavior, Swift’s hardening law is used and the corresponding parameter values are identified. Then, two different approaches are introduced to construct FLDs (forming limit diagrams) of this alloy sheet and evaluate the effect of the rate sensitivity index on its formability. The first one is theoretical (the M-K model), and an algorithm is developed to calculate the limit strains by this model. In the second approach, the Marciniak test is simulated with the commercially available finite-element program ABAQUS. Based on FEM results, different failure criteria are discussed and an appropriate one is chosen to determine the onset of localized necking. With the material behavior data corresponding to AA5083 at 150 °C, parametric studies are carried out to evaluate the effect of the strain rate sensitivity index. The comparison of results by these two approaches shows the same tendency that an improvement of the formability with increasing strain rate sensitivity is observed. Finally, by consideration of the compensating effects of the strain hardening and rate sensitivity indices, the FLDs of this sheet at 150, 240 and 300 °C are determined and compared. Results show that the formability of AA5083 seems not to be improved up to a certain temperature (between 240 and 300 °C), above this temperature, the formability is greatly enhanced.     

Microstructures,Forming Limit and Failure Analyses of Inconel 718 Sheets for Fabrication of Aerospace Components

Recently, aerospace industries have shown increasing interest in forming limits of Inconel 718 sheet metals, which can be utilised in designing tools and selection of process parameters for successful fabrication of components. In the present work, stress-strain response with failure strains was evaluated by uniaxial tensile tests in different orientations, and two-stage work-hardening behavior was observed. In spite of highly preferred texture, tensile properties showed minor variations in different orientations due to the random distribution of nanoprecipitates. The forming limit strains were evaluated by deforming specimens in seven different strain paths using limiting dome height (LDH) test facility. Mostly, the specimens failed without prior indication of localized necking. Thus, fracture forming limit diagram (FFLD) was evaluated, and bending correction was imposed due to the use of sub-size hemispherical punch. The failure strains of FFLD were converted into major-minor stress space (σ-FFLD) and effective plastic strain-stress triaxiality space (ηEPS-FFLD) as failure criteria to avoid the strain path dependence. Moreover, FE model was developed, and the LDH, strain distribution and failure location were predicted successfully using above-mentioned failure criteria with two stages of work hardening. Fractographs were correlated with the fracture behavior and formability of sheet metal.     

宽板V型自由弯曲智能化控制过程的解析定量描述

板料在弯曲卸载过程中,由于弹性变形回复,从而产生回弹。回弹的结果使弯曲件的精度降低。影响回弹的因素很多,也很复杂。根据弹塑性弯曲理论,在平面变形假设的前提下,考虑了材料的硬化、各向异性及弹性变形,对宽板V型自由弯曲应力应变进行了分析,得到了弹塑性交界处曲率半径,推导出了弯曲力及目标弯曲角随弯曲行程变化的关系式。理论计算与实验及数值模拟结果进行了比较,为宽板V型自由弯曲智能化控制中参数识别及预测模型输入层和输出层变量的确定提供了理论依据。     

Effects of temperature and blank holding force on biaxial forming behavior of aluminum sheet alloys

Biaxial forming behavior is investigated for three aluminum sheet alloys (Al 5182 containing 1% Mn (5182+Mn), Al 5754, and 6111-T4) using a heated die and punch in the warm forming temperature range of 200–350 °C. It is found that, while all three alloys exhibit significant improvement in their formability compared with that at room temperature, the non-heat-treatable alloys 5182 + Mn and 5754 give higher part depths than that of heat-treatable 6111-T4. The formability generally increases with decreasing BHP (BHP), but increasing the forming temperature and/or BHP minimizes the wrinkling tendency and improves the forming performance. The stretchability of the sheet alloys increase with increasing temperature and increasing BHP. For the alloys and forming conditions involved in the current study, the formability, measured in terms of part depth, comes mainly from the drawing of metal into the die cavity, although stretching effects do influence the overall forming behavior. The optimum formability is achieved by setting the die temperature 50 °C higher than the punch temperature to enhance the drawing component. Setting the die temperature higher than the punch temperature also improves the strain distribution in a part in such a manner that postpones necking and fracture by altering the location of greatest thinning.     

Development of a new model for plane strain bending and springback analysis

A new mathematical model is presented for plane strain bending and springback analysis in sheet metal forming. This model combines effects associated with bending and stretching, considers stress and strain distributions and different thickness variations in the thickness direction, and takes force equilibrium into account. An elastic-plastic material model and Hill’s nonquadratic yield function are incorporated in the model. The model is used to obtain force, bending moment, and springback curvature. A typical two-dimensional draw bending part is divided into five regions along the strip, and the forces and moments acting on each region and the deformation history of each region are examined. Three different methods are applied to the two-dimensional draw bending problems: the first using the new model, the second using the new model but also including a kinematic directional hardening material model to consider the bending and unbending deformation in the wall, and the third using membrane theory plus bending strain. Results from these methods, including those from the recent benchmark program, are compared. University of Michigan, Dept. of Mechanical Engineering and Applied Mechanics, Ann Arbor, Mi 48109, USA.     

Investigation on deformation behavior of sheet metals in viscous pressure bulging based on ESPI

In order to analyze the effect of viscous medium on the deformation behavior of sheet metals in viscous pressure bulging (VPB), the entire deformation process including instability and fracture was investigated real-timely by the aid of electronic speckle pattern interferometry (ESPI). Images of speckle patterns were captured continuously to obtain fringe patterns representing the full field strain rate. Values of strain rates were calculated based on the fringe patterns. The evolution of the weak region from the initial defect to the groove until crack was also observed through the fringe patterns. The onset of diffuse and localized necking were determined qualitatively and quantitatively. Experimental results show that the deformation of sheet metals in VPB passed through five states, namely, uniform deformation, strain localization, diffuse necking, localized necking and fracture. A defect emerged in strain localization. The growth of the defect caused the diffuse necking and generated a groove. The groove expanded mainly in length direction until the localized necking occurred. Finally the specimen fractured as a result of groove deepening. The tangential adhesive stress provided by viscous medium in VPB restricted the locally larger strain of the specimen. The diffuse necking was postponed greatly. Theoretical prediction of the limit strains of sheet metals in VPB would be made based on the experimental results in further work.     

Prediction of shear-induced fracture in sheet metal forming

Necking has been the dominant failure mode in sheet metal forming industry and several analytical and numerical tools were developed to predict the onset of necking. However, the introduction of Advanced High Strength Steels (AHSS) with reduced ductility brought up an issue of a shear fracture which could not be predicted using the concept of Forming Limit Curve (FLC). The Modified Mohr-Coulomb fracture criterion (MMC) was recently shown to be applicable to problems involving ductile fracture of materials and sheets. In the limiting case of plane stress, the fracture locus consists of four branches when represented on the plane of the equivalent strain to fracture and the stress triaxiality. A transformation of above 2D fracture locus to the space of principal strains was performed which revealed the existence of two new branches not extensively studied before. The existence of those branches explains the formation of shear-induced fracture. As an illustration of this new approach, initiation and propagation of cracks is predicted and compared with series of deep-drawing punch tests of ThyssenKrupp AHSS (grade RA-K 40/70, standard HCT690T) performed at ThyssenKrupp. It was shown that the location of fracture as well as the magnitude of punch travel corresponding to first fracture was correctly predicted by MMC fracture criterion for both circular and square punch.     

Numerical simulation for the multi-point stretch forming process of sheet metal

Multi-point stretch forming (MPSF) is a flexible manufacturing technique to form large sheet panels of mild curvature. The traditional fixed shape-stretching die is replaced by a matrix of punch elements, and the sheet metal are stretch-formed over the multi-point stretching die (MPSD) generated by the punch element matrix. In this paper, extensive numerical simulations of the processes for stretching parabolic cylinder, toroidal saddle and sphere parts were carried out by dynamic explicit finite element analysis. The forming results using multi-point die were compared with those of using traditional die. The use of an elastic cushion to suppress dimpling of the part caused by the discrete punch elements was investigated along with a discussion of its influence on part shape accuracy. The effect of the size of punch element and the shape of MPSD on the shape accuracy of formed parts were analyzed. The results may provide useful guidance on determining MPSF parameters and optimizing MPSF manufacture processes.     

工业AA1200铝合金薄板拉伸成形模拟和实验研究(英文)

对工业AA1200铝合金薄板拉伸成形的模拟和实验结果进行比较和评估。采用单向拉伸试验得到模拟所需输入参数。根据von Mises和Hill-1948屈服准则,采用Abaqus/Explicit有限元软件分析成形过程。将冲压力和应变分布的模拟结果与实验结果进行比较和验证。结果表明:在这两种情况下,使用各向异性屈服准则模拟的结果与实验结果更吻合。     

Coupled thermomechanical finite element analysis to improve press formability for camera shape using AZ31B magnesium alloy sheet

In this study, a finite element analysis aimed at predicting and improving the press formability for a camera casing made of AZ31B magnesium alloy sheet was conducted. First, stress-strain curves and forming limit curves (FLDs) for warm temperatures were obtained. The data from these curves and the ductile fracture criterion of FLDs were then input into ABAQUS/Explicit finite element code to predict the failure occurrence of the camera casing. In the finite element method (FEM) simulation, for investigating the effect of reduced temperature during the punch cooling process on the formability of the camera casing, coupled thermomechanical computational modeling was considered and verified by comparison with experimental results. Based on the good agreement between the simulation and the experimental results, three parameters-blank holding force, elevated temperature, and friction coefficient-were selected to improve the press formability of the camera casing in the coupling of the FEM simulations and Taguchi??s orthogonal array experiment. The optimum simulation case was confirmed through an experiment.     

Identification of Post-necking Tensile Stress–Strain Behavior of Steel Sheet: An Experimental Investigation Using Digital Image Correlation Technique

The stress–strain behavior of sheet metal is commonly evaluated by tensile test. However, the true stress–strain curve is restricted up to uniform elongation of the material. Usually, after the uniform elongation of the material the true stress–strain is obtained by extrapolation. The present work demonstrates a procedure to find out the true tensile stress–strain curve of the steel sheet after necking using digital image correlation (DIC) technique. Hill’s normal anisotropic yield criteria and local strains measured by DIC technique are used to correct the local stress and strain states at the diffuse necked area. The proposed procedure is shown to successfully determine the true tensile stress–strain curve of ferritic and dual-phase steel sheets after necking/uniform elongation.     

板料自由弯曲成形及回弹理论解析

对宽板自由弯曲成形及弹复过程进行理论分析,将弯曲过程分为板料未包覆凸模和已包覆凸模两个成形阶段,在每个成形阶段将弯曲板料分为弹性和弹塑性变形区。基于单向应力和小变形假设,分别建立了两个成形阶段的回弹计算模型,导出了任一成形阶段中性层上任一质点卸载前后的转角和弯曲半径数学表达式。基于VC++软件平台,对回弹计算模型进行编程计算,并进行了实验验证,计算结果与实验结果吻合较好,最大误差为0.58°。     

Characterizing steel tube for hydroforming applications

With the increased use of tubular steel products, especially for hydroforming applications, it is important to be able to predict the performance of tube from sheet tensile tests. In the present study, two aluminum killed draw quality (AKDQ) steels and one high strength low alloy (HSLA) steel were evaluated. Tensile properties and plastic strain ratios were measured on sheet material in the longitudinal and transverse directions. Axial tensile tests were performed on material extracted from production tubes. Material from quasi tubes, which are strip material bent to the same curvature as the tubes but not welded or sized, was also tested. Residual stresses in the production and quasi tube were determined by displacement methods. A hydraulic burst test was performed on the production tubes to simulate a hydroforming operation. Effective strains resulting from tubemaking are calculated for two discrete operations: bending and sizing. For the production tubes, a linear relationship was found between a load factor (strength times thickness) and effective sizing strain. The relationship between load factor and residual stress was also linear. Predictions of the maximum pressure and the strain at instability during a hydraulic burst test are shown to compare favorably with experimental values, based on flat sheet properties and tubemaking strains. The prediction of the yield strength in the tube based on flat sheet properties is shown to be fairly accurate when the effective sizing strain is small compared to the effective bending strain.