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 新的成形极限曲线（FLC）检测国家标准GB/T 24171-2009分为两个部分,第一部分GB/T 24171.1-2009 和第二部分GB/T 24171.2-2009。第一部分的内容与传统的测试方法基本相同,适合大多数实验室及现场条件下的成形极限曲线检测,第二部分提出了一种更准确的实验室成形极限曲线测定方法,现阶段只有部分实验室能够满足试验条件要求。本文针对标准第二部分,对其中关于试样、试验装置、试验条件、应变分析等一些关键内容做了试验研究,就新标准的应用提出了一些建议。     

An overview of stabilizing deformation mechanisms in incremental sheet forming

In incremental sheet forming (ISF) strains can be obtained well above the forming limit curve (FLC) that is applicable to common sheet forming operations like deep drawing and stretching. This paper presents an overview of mechanisms that have been suggested to explain the enhanced formability. The difference between fracture limit and necking limit in sheet metal forming is discussed. The necking limit represents a localized geometrical instability. Localized deformation is an essential characteristic of ISF and proposed mechanisms should stabilize the localization before it leads to fracture. In literature six mechanisms are mentioned in relation to ISF: contact stress; bending-under-tension; shear; cyclic straining; geometrical inability to grow and hydrostatic stress. The first three are able to localize deformation and all but the last, are found to be able to postpone unstable growth of a neck. Hydrostatic pressure may influence the final failure, but cannot explain stability above the FLC.     

Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming

Formability of sheet metal is usually assessed by the useful concept of forming limit diagrams (FLD) and forming limit curves (FLC) represent a first safety criterion for deep drawing operations. The level of FLC is strongly strain path dependent as observed by experimental and numerical results and therefore non-proportional strain paths need to be incorporated when analyzing formability of sheet metal components. Simulations using finite element method allow accurate predictions of stress and strain distributions in complex stamped parts. However, the prediction of localized necking is a difficult task and the combination of forming limit diagram analysis with finite element simulations often fail to give the right answer, if complex strain paths are not included in these predictions.     

Forming limit diagram of auto-body steel sheets for high-speed sheet metal forming

This paper is concerned with the uniaxial tensile properties and formability of steel sheets in relation to the strain rate effect. The elongation at fracture for CQ increases at a high strain rate while the elongation at fracture for DP590 decreases slightly in relation to the corresponding value for a quasi-static strain rate. The uniform elongation and the strain hardening coefficient decrease gradually when the strain rate increases. The r-value of CQ and DP590 was measured with a high-speed camera in relation to the strain rate. The r-value is slightly sensitive to the strain rate. Static forming limit curves (FLCs) and high-speed FLCs were constructed with the aid of punch-stretch tests with arc-shaped and square-shaped specimens. In addition, a high-speed crash testing machine with a specially designed high-speed forming jig was used for the high-speed punch-stretch tests. Compared with the static FLC, the high-speed FLC of CQ is higher in a simple tension region and lower in a biaxial stretch forming region. The high-speed FLC for DP590 decreases in relation to the static FLC throughout the entire region. The elongation at fracture appears to be closely related to the simple tension region of the FLC. The shear fracture is observed from SEM images of specimens tested in the biaxial stretch forming region under the high-speed forming condition. The dimples indicating the shear fracture have elongated horseshoe shape. The high-speed FLC is lower than the static FLC in the biaxial stretch forming region because the shear fracture induces the decrease of ductility. The results confirm that the strain rate has a noticeably influence on the formability of steel sheets. Thus, the forming limit diagram of high-speed tests should be considered in the design of high-speed sheet metal forming processes.     

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 采用动态应变测量方法对成形极限曲线（FLC）检测中网格的大小,测量的时机(破裂前或破裂后测量),测量的位置等因素进行了试验研究。研究结果表明,试样破裂前和破裂后测量的应变,以及使用不同大小的网格测量的结果都存在较大的差异,测量位置的不同会导致应变路径存在差异,影响FLC的准确度。最后将这些测量结果绘制的FLC同采用最佳反抛物线拟合计算得到的FLC进行了比较,分析了彼此的差别,并对FLC的检测提出了一些建议。     

Experimental evaluation of strains in the tension–compression using a new tool geometry, X-Die

Sheet-metal forming involves a complex distribution of strains throughout the part. The strains occur due to tension, compression and a mix of both. A geometry has been developed, the X-Die, in order to gain insight into the strain behavior of different materials. The X-Die enables strain paths far into the tension–compression region, thus creating the possibility to extend the experimental base both for definition and for further extrapolation of the forming limit curve (FLC) in the tension–compression region, as well as to evaluate FE-simulation results for the same region.

The experimental results show that the strain signature is impacted by material quality. In qualities such as extra high strength steel (EHSS) and aluminum the strains do not reach as far into the tension–compression region as the strains do in e.g. mild steel. This is due to failure in plane strain tension. Strain paths in materials such as mild steel and high strength steel (HSS) reach far into the tension–compression region before failure. Use of the X-Die provides possibilities to reach farther into the tension–compression region compared with traditional test methods for creating a forming limit diagram (FLD).

Use of the X-Die yields well-defined strain signatures. These clearly defined strain signatures are favorable for comparison with numerical simulations, especially for strain signatures in the tension–compression region.

Furthermore, the experiments using the X-Die indicate that a possible additional forming limit curve, which intersects the original forming limit curve (shear failure), exists so far into the tension–compression region that it is not applicable.

Even though the experiments indicate compression strains >100% (material DX56D), the experiments show potential for an experimentally determined extrapolation of the FLC up to 75% compression strain. The results of the experiments indicate that the X-Die geometry is suitable as a supplementary tool in identifying the strain behavior of different materials far into the tension–compression region and is also a good tool for verification of numerical results in the tension–compression region.     

A new method for predicting Forming Limit Curves from mechanical properties

Forming Limit Curves (FLCs) are an important tool in steel sheet metal forming. Experimental measurements of FLCs are costly, and therefore, empirical prediction methods are of practical use. Difficulties in accurately defining FLCs for new steel grades, such as AHSS, have necessitated a review of the existing prediction methods. Four points were defined to characterise an FLC, and correlations between the coordinates of these points and the mechanical properties from tensile testing were found. The results show that the total elongation, Lankford coefficient and thickness are strongly related to the FLC values. Predictive equations were derived from the statistical relations between the measured FLC points and the mechanical properties. To verify the predictive equations, predicted FLCs for approximately fifty steel grades in various thickness ranges were compared with measured FLCs. It was found that the newly developed method accurately predicts the FLCs.     

Failure of high strength steel sheets: Experiments and modelling

Failure in sheet metal structures of ductile material is usually caused by one of, or a combination of, ductile fracture, shear fracture or localised instability. In this paper the failure of the high strength steel Docol 600DP and the ultra high strength steel Docol 1200M is explored. The constitutive model used in this study includes plastic anisotropy and mixed isotropic-kinematic hardening. For modelling of the ductile and shear fracture the models presented by Cockroft–Latham and Bressan–Williams have been used. The instability phenomenon is described by the constitutive law and the finite element (FE) models. For calibration of the failure models and validation of the results, an extensive experimental series has been conducted including shear tests, plane strain tests and Nakajima tests. The geometries of the Nakajima tests have been chosen so that the first quadrant of the forming limit diagram (FLD) were covered. The results are presented both in an FLD and using prediction of force–displacement response of the Nakajima test employing element erosion during the FE simulations. The classical approach for failure prediction is to compare the principal plastic strains obtained from FE simulations with experimental determined forming limit curves (FLCs). It is well known that the experimental FLC requires proportional strains to be useful. In this work failure criteria, both of the instability and fracture, are proposed which can be used also for non-proportional strain paths.     

Failure During Sheared Edge Stretching

Failure during sheared edge stretching of sheet steels is a serious concern, especially in advanced high-strength steel (AHSS) grades. The shearing process produces a shear face and a zone of deformation behind the shear face, which is the shear-affected zone (SAZ). A failure during sheared edge stretching depends on prior deformation in the sheet, the shearing process, and the subsequent strain path in the SAZ during stretching. Data from laboratory hole expansion tests and hole extrusion tests for multiple lots of fourteen grades of steel were analyzed. The forming limit curve (FLC), regression equations, measurement uncertainty calculations, and difference calculations were used in the analyses. From these analyses, an assessment of the primary factors that contribute to the fracture during sheared edge stretching was made. It was found that the forming limit strain with consideration of strain path in the SAZ is a major factor that contributes to the failure of a sheared edge during stretching. Although metallurgical factors are important, they appear to play a somewhat lesser role.     

A new approach for user-independent determination of formability of a steel sheet sheared edge

It is common to use a forming limit curve (FLC) for a feasibility study of a deep-drawn steel part based on a finite element analysis (FEA). However, in such an approach a neglected fact is that a blank edge in industrial production is often produced by shear cutting. Especially, for many high strength steel grades, this cutting process notably reduces edge formability. An overestimation of formability of the blank edge, with an FLC, is the consequence that may lead to cracks at the sheared edge of a part. The following paper describes a new approach to determine formability of a sheet-steel sheared edge by hole expansion test that uses an FLC tool set. This approach delivers a hole expansion ratio with considerably lower scattering compared to the hole expansion according to ISO 16630. Additionally, information on the planar isotropy, flow and necking behavior of the material, is supplied. Finally, a pragmatical way of transferring test results into an FEA of the forming process for a sheet blank with a sheared edge is presented.     

Forming limit diagrams of tubular materials by bulge tests

This study uses bulge tests to establish the forming limit diagram (FLD) of tubular material AA6011. A self-designed bulge forming apparatus of fixed bulge length and a hydraulic test machine with axial feeding are used to carry out the bulge tests. Loading paths corresponding to the strain paths with a constant strain ratio at the pole of the bulging tube are determined by FE simulations linked with a self-compiled subroutine and are used to control the internal pressure and axial feeding punch of the test machine. After bulge tests, the major and minor strains of the grids beside the bursting line on the tube surface are measured to construct the forming limit diagram of the tubes. Furthermore, Swift's diffused necking criterion and Hill's localized necking criterion associated with Hill's non-quadratic yield function are adopted to derive the critical principal strains at the onset of plastic instability. The critical major and minor strains are plotted to construct the forming limit curve (FLC). The effects of the exponent in the Hill's non-quadratic yield function and the normal anisotropy of the material on the yield locus and FLC are discussed. Tensile tests are used to determine the anisotropic values in different directions with respect to the tube axis and the K and n values of the flow stress of the tubular material. The analytical FLCs using the n values obtained by tensile tests and bulge tests are compared with the forming limits from the forming limit experiments.     

Study on formability of tube hydroforming through elliptical die inserts

This paper proposes a novel experimental approach to evaluate the formability for tube hydroforming under biaxial stretching through elliptical bulging. The idea comes from the hydraulic stretch-drawing tests with elliptical dies for the right hand side of forming limit curve (FLC). Based on the deformation theory and the classical Hosford yield criterion, an analytical model is constructed for the elliptical bulging of tube hydroforming. Then the novel experimental device is designed with five upper elliptical die inserts and one lower die insert used to produce ellipsoidal bulged domes and some experiments are performed. The linear strain paths in different strain states are verified and the right hand side of FLC for roll-formed QSTE340 seamed tube is determined through the proposed experimental approaches. Finally, a comparison between the theoretical results and experimental data is performed. The theoretical predictions show good agreement with the experimental results.     

Prediction of forming limit curve for pure titanium sheet

Commercially pure titanium (CP Ti) has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformation characteristics and press formability of the CP Ti sheet are not much in comparison with automotive steels and aluminum alloys. The mechanical properties and hardening behavior evaluated in stress–strain relation of the CP Ti sheet are clarified in relation with press formability. The flow curve denoting true stress–true strain relation for CP Ti sheet is fitted well by the Kim–Tuan hardening equation rather than Voce and Swift models. The forming limit curve (FLC) of CP Ti sheet as a criterion for press formability was experimentally evaluated by punch stretching test and analytically predicted via Hora's modified maximum force criterion. The predicted FLC by adopting Kim–Tuan hardening model and appropriate yield function shows good correlation with the experimental results of punch stretching test.     

Influence of non-proportional load paths and change in loading direction on the failure mode of sheet metals

Many studies have shown that failure following non-proportional load paths cannot be predicted by a linear Forming Limit Curve (FLC), as the deformation history and a change in loading direction influence the formability and failure mode. In this paper, the different failure modes due to different load paths are investigated, for the first time, by conducting Nakajima tests with pre-formed specimens. The main objective of the investigation is to better understand the influence of pre-forming and change in loading direction on the formability. To predict this behaviour, regardless of the failure mode, the Generalized Forming Limit Concept (GFLC) is extended.     

成形极限曲线测定GB/T24171-2009国家标准简介及应用建议

新的成形极限曲线(FLC)检测国家标准GB/T 24171-2009分为两个部分,第1部分GB/T 24171.1-2009和第2部分GB/T 24171.2-2009。第1部分的内容与传统的测试方法基本相同,适合大多数实验室及现场条件下的成形极限曲线检测,第2部分提出了一种更准确的实验室成形极限曲线测定方法,现阶段只有部分实验室能够满足试验条件要求。针对标准第2部分,对其中关于试样、试验装置、试验条件和应变分析等一些关键内容做了试验研究,就新标准的应用提出了一些建议。     

Fundamental studies on the incremental sheet metal forming technique

The idea of incremental forming technique has been investigated for production of sheet metal components. With this technique, the forming limit curve (FLC) appears in a different pattern, revealing an enhanced formability, compared to conventional forming techniques. In the present study, the formability of an aluminum sheet under various forming conditions was assessed and difficult-to-form shapes were produced with the technique. By utilizing knowledge and experience obtained during the present study, it became possible to produce some free surfaces.     

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.     

Determination of forming limit diagrams - a new analysis method for characterization of materials' formability

This paper introduces a new analysis method for characterization of materials' formability independent of individual expertise. Therefore forming limit diagrams (FLDs) are determined using the Nakazima method. Investigations on the influence of the analysis method and the failure criterion in detail will be presented. The new analysis method avoids misinterpretation of the forming limits of any material and the FLD. The forming behavior of materials has to be recorded with a frequency up to 20 Hz, in order to detect the forming limits within a sequence of pictures from onset of necking to failure by cracking.     

The effect of yield criteria on the forming limit curve prediction and the deep drawing process simulation

The increasing application of numerical simulation in the field of metal forming has helped engineers to solve problems one after another to manufacture a qualified formed product in a reduced time. Accurate simulation results are vital for die and product designs. Many factors can influence the final simulation result, the most important of which is a suitable yield criterion. The proposed Forming Limit Curve (FLC), which is used to evaluate the necking risk, differs a lot while different yield criteria used. In this study, the theoretical FLC is calculated using Swift model, which considers three-yield criteria Hill 48, Hill 90 and Hill 93. Also, the simulation processes with two yield criteria, Hill 48 and Hill 90, are carried out with two types of material, SPCC (JIS G3141) and Al6xxx. The strain evolutions of elements located in two trajectories of two materials are investigated and compared. The simulation results are compared with the experimental ones to evaluate the effectiveness of the yield criterion.