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.     

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.     

Prediction of ductile fracture for advanced high strength steel with a new criterion: Experiments and simulation

This paper is concerned with prediction of the onset of ductile fracture by a newly proposed micro-mechanism-motivated macroscopic ductile fracture criterion in various stress states from shear to plane strain tension where most ductile fracture takes place in sheet metal forming processes. The new ductile fracture criterion (Lou et al., 2012) is calibrated by the equivalent plastic strain to fracture measured by the hybrid experimental–numerical method from four types of specimens manufactured from DP980 sheet whose fracture locus is eventually constructed. The calibrated criterion is utilized to construct the fracture locus of DP980. The constructed fracture locus is then implemented into the ABAQUS/Explicit code to predict the onset of ductile fracture for these three types of specimens. Three types of notched specimens are further designed for the validation of the ductile fracture criterion from uniaxial tension to plane strain tension by comparison of experimental results to those numerically predicted by the ductile fracture criterion. Three types of shear specimens are then utilized to validate predictability of the ductile fracture criterion between shear and uniaxial tension. The validation demonstrates that the ductile fracture criterion can accurately predict the onset of ductile fracture for these specimens. The comparison result with high accuracy reveals that the criterion can correctly describe ductile fracture behaviors of metals in various stress states from shear to the plane strain tension.     

Yield locus evolution and constitutive parameter identification using plane strain tension and tensile tests

An inverse calibration strategy to determine the constitutive parameters of phenomenological advanced yield criteria in a convenient and economical manner is presented. The studies on the shape of the yield loci for various steel types revealed that their work contours exhibit almost no evolution in the vicinity of the equibiaxial tension after roughly 4% equivalent strain. In other words, the ratio between balanced biaxial and uniaxial stresses of the yield locus reaches a saturation value after undergoing some deformation. Accordingly, the balanced biaxial stresses can be associated with the tensile flow stresses in the rolling direction by means of a constant factor, which can be generalized for different steel families. Based on this, an alternative inverse-analysis strategy using the tensile and plane strain tension tests will be proposed and validated within this work. Cup drawing tests have been applied to assess the accuracy of the optimized yield loci for different strain paths.     

泡沫金属在单、双向载荷作用下的拉伸破坏行为初探

采用低载拉伸试验机对多孔体的单、双向拉伸进行了系列实验，通过分析该材料的单向拉伸破坏机制，发现开孔泡沫金属材料的宏观断裂特点既不同于最大拉应力准则的横向断裂，也不同于最大剪应力准则的塑性流动破坏，而是表现为介于它们之间的一种复杂断裂形式；拉伸断裂过程中多孔体的延伸率主要由三维网络中的金属丝体发生的塑性偏转所造成。通过其双向承载时断裂形态的观测分析，发现泡沫体十字型样品在双向等速拉伸载荷作用下的应力场分布与双向异速拉伸载荷作用下的类似，且其应力场的最大应力线为靠近样品中央载荷区边缘的四次对称曲边四边形。     

Sheet metal forming limit prediction based on plastic deformation energy

For sheet metals, the endurance to fracture under different strain paths may be different. Based on plastic deformation energy, the sheet metal forming limit is calculated, and the relationship model between maximum allowable integral value of the general plastic work criterion and the strain path is built. In addition, the strain-hardening exponent, anisotropy coefficient and the initial thickness of the material are also taken into account to consider their effects on forming limit. In order to simplify the process of parameter determination, only uniaxial tension test is used to calculate the material property parameters and necessary limit strain, and the expression of the criterion is determined finally. Then the limit strains under other strain paths between uniaxial tension to equi-biaxial tension are predicted by the criterion combined with numerical simulation of the forming process. The criterion is also applied to limit strain prediction under bilinear strain path.     

铝合金板材胀形极限的数值模拟研究

应用韧性断裂准则与有限元数值模拟相结合的方法预测了铝合金板料的胀形极限.将有限元模拟获得板材的应力、应变值代入考虑应力三轴度的Oyane韧性断裂准则进行断裂判断,预测出初始断裂点.准则中的材料常数通过单向拉伸和平面拉伸试验确定.计算了三种铝合金板的半球形凸模胀形极限,计算结果表明,应用Oyane韧性断裂准则能有效地预测铝合金板材的胀形极限.     

Anisotropy and formability of AA5182-0 aluminium alloy sheets

This paper presents a new yield criterion for orthotropic sheet metals and its implementation in a theoretical model of the forming limit diagrams. The equivalent stress equation shows that the shape of the yield surface is defined by eight material parameters. The minimisation of an error-function has been used for the numerical identification of these coefficients. The parameters are established in such a way that the constitutive equation associated to the yield surface reproduces the plastic behaviour of the actual material. The uniaxial yield stresses (σ₀, σ₄₅, σ₉₀), biaxial yield stress (σ_b), uniaxial anisotropy coefficients (r₀, r₄₅, r₉₀) have been used in identification. The new yield criterion has been implemented in the Marciniak-Kuczynski theory in order to predict the limit strains. The theoretical forming limit curves have been compared with the experimental ones. The friction free tests, the hydraulic bulge test (for the positive minor strains) and the tensile test for plane strain and for uniaxial tensile test (for the negative minor strains) are used. The predicted yield surface and forming limit diagrams for AA5182-0 aluminium alloy sheets are in good agreement with the experimental ones.     

一种建立板料成形极限应力图的新方法

基于塑性理论建立了比例加载条件下双向拉伸应力应变关系,结合Swift分散性失稳准则,提出了一种建立板料成形极限应力图的方法。分别应用Hill 48和Hosford屈服准则以及单向拉伸性能参数,建立了铝合金板(r<1)和薄钢板(r>1)两种材料的成形极限应力图(FLSD),分析表明,不同的屈服准则的选取对于成形极限应力曲线有不同的影响,对于不同类型的材料屈服准则的影响程度也不同。与由通常的成形极限图(FLD)转换所得到的成形极限应力图(FLSD)进行了对比分析,结果表明,所提出的方法计算过程更为简便,并能较为准确地建立成形极限应力图,可以作为复杂加载路径下的成形极限破裂判据。     

Validity assessment of ductile fracture criteria in cold forming

This paper describes the assessment of various empirical and semiempirical ductile fracture criteria to determine their ability to predict the occurrence of fracture in metalforming processes. The criteria assessed are reformulated such that each is expressed in terms of mostly nondimensional material-dependent quantities and constants. The constants in each criterion are determined using data from published experimental results on cold upsetting of aluminum and steel specimens. The limit strain or the forming limit corresponding to each criterion is then determined and compared with the experimental data. There is clearly good agreement between theory and experiment for several criteria, but the predictions of other criteria fall far from experimental results.     

基于韧性断裂准则的铝合金板材成形极限预测

为了准确地预测铝合金板材成形极限，将韧性断裂准则引入到数值模拟中。在数值模拟获得的应力应变值基础上，采用简单拉伸试验和数值模拟相结合的方法确定了韧性断裂准则中的材料常数，并应用该韧性断裂准则预测了铝合金LYl2(M)的圆筒件拉深和半球形凸模胀形的成形极限。预测结果与实验值吻合较好，该韧性断裂准则能够预测铝合金板材成形极限。     

不同加载路径下的AZ31B镁合金的成形极限

为了分析实际成形过程中AZ31B镁合金产生破裂的原因,并为改善工艺条件提供实用可靠的判据,采用实验和有限元模拟相结合的方法研究AZ31B镁合金的成形极限.分别对沿轧制方向、垂直于轧制方向、与轧制方向成45°的3种方向的试件进行单向拉伸实验,获得AZ31B镁合金的工程应力-工程应变曲线,获得材料的真实应力-真实应变曲线和...     

A DUCTILE FRACTURE CRITERION BASED ON THREE-DIMENSIONAL VOID MODEL

A fracture criterion derived from a microscopic point of view is proposed and has proved to be effective in the analysis of uniaxial tension. On the one hand, a method of predicting a ductile fracture is proposed using a three-dimensional void model and the assumption of velocity discontinuity. The relationship between the void volume fraction and the critical strain to fracture, calculated with the help of the new model, shows the same tendency as that obtained from the modified Thomason model. On the other hand, the mechanical and metallographic analyses of the uniaxial tension experiment are performed using four kinds of carbon steel. The relationship between the void volume fraction and the critical strain to fracture, calculated from the new model, agrees better with the result obtained from the experiment, rather than that calculated by the modified Thomason model, which confirms the validity of the ductile fracture criterion based on the three-dimensional void model.     

Formability prediction of advanced high strength steels using constitutive models characterized by uniaxial and biaxial experiments

Sheet formability, as determined by the limiting dome height (LDH) test, was evaluated for DP and TRIP steel sheet samples. The LDH test was also predicted with finite element (FE) simulations using various constitutive models. Three yield functions, von Mises, Hill's 1948, and Yld2000-2d, were considered to examine the effect of the yield criterion on formability. The anisotropy parameters were determined from different experimental tests and their influences on LDH predictions were analyzed. For Hill's 1948 model, the coefficients were calculated either using the yield stresses or r-values measured in different tension directions. The anisotropy coefficients of the Yld2000-2d were determined using in-plane biaxial test data in addition to the conventional uniaxial test-based data. The stress-strain curves for hardening characterization were measured using uniaxial and bulge tests. The latter provides the flow stress over an extended strain range, compare with uniaxial tension, without showing instability. The constitutive models were implemented in a FE code with a user material subroutine. They were evaluated by comparing the experimental and predicted punch load–displacement and sheet thickness variations after forming in the LDH test. The results for this particular example demonstrated that the non-quadratic yield function and the hardening curve of the bulge test improve the prediction accuracy for sheet forming and formability analyzes significantly.     

中心区减薄的十字形试件拉伸性能研究

中心区减薄的十字形试件拉伸,是实现板料双向拉伸变路径条件下,达到大变形以至破裂的可行试验方法,对于复杂加载路径板料屈服行为及成形极限研究,有重要的试验意义。通过标准单向拉伸试验,对比研究了板材减薄前后单向拉伸性能的变化。对于中心区方形减薄的十字形试件,进行了单臂试件和十字形试件的单向拉伸试验,验证了中心区减薄后应力计算的正确性。     

Prediction of forming limit in hydro-mechanical deep drawing of steel sheets using ductile fracture criterion

It has been observed that the forming limit curve at fracture (FLCF) of steel sheets, with a relatively higher ductility limit have linear shapes, similar to those of a bulk forming process. In contrast, the FLCF of sheets with a relatively lower ductility limit have rather complex shapes approaching the forming limit curve at neck (FLCN) towards the equi-biaxial strain paths. In this study, the FLCFs of steel sheets were measured and compared with the fracture strains predicted from specific ductile fracture criteria, including a criterion suggested by the authors, which can accurately describe FLCFs with both linear and complex shapes. To predict the forming limit for hydro-mechanical deep drawing of steel sheets, the ductile fracture criteria were integrated into a finite element simulation. The simulation, results based on the criterion suggested by authors accurately predicted the experimetal, fracture limits of steel sheets for the hydro-mechanical deep drawing process.     

Evaluation of forming limit in viscous pressure forming of automotive aluminum alloy 6k21-T4 sheet

A ductile fracture criterion is introduced into numerical simulation to predict viscous pressure forming limit of the automotive body aluminum alloy 6k2 l-T4. The material constant in the ductile fracture criterion is determined by the combination of the viscous pressure bulging （VPB） test with numerical simulation. VPB tests of the aluminum alloy sheet are carried out by using various elliptical dies with different ratios of major axis to minor axis（β）, and the bugling processes are simulated by the aid of the finite element method software LS-DYNA3D. On the basis of the stress and strain calculated from numerical simulations, the forming limits of bulging specimens obtained are predicted by the ductile fracture criterion, and compared with experimental results. The fracture initiation site and the minimal thickness predicted by the ductile fracture criterion are in good agreement with the experimental results.     

Effects of plastic strain and strain path on youngs modulus of sheet metals

The effects of plastic strain and strain path on Young’s modulus of sheet metals are experimentally investigated using low carbon steel, stainless steel, aluminium, copper and brass sheets of 1 mm thickness. These sheets are firstly deformed to different plastic strains under a few strain paths from balanced biaxial stretching to uniaxial tension. Then, a small uniaxial tension test specimen is cut from each deformed sheet and Young’s modulus is measured using electrical-resistance strain gauges glued to both surfaces of the specimen. The experimental results show that Young’s moduli of the low carbon steel and stainless steel sheets decrease with increasing plastic strain, while those of aluminium, copper and brass sheets hardly change with the plastic strain. In all materials, however, the effect of the strain path on Young’s modulus is not necessarily evident. It is confirmed that Young’s modulus of the low carbon steel sheet can be recovered to the initial value of undeformed sheet by a subsequent annealing. In addition to Young’s modulus, the effects of the plastic strain and the strain paths on Poisson’s ratio of these materials are also shown.     

The application of a ductile fracture criterion to the prediction of the forming limit of sheet metals

To predict accurately the forming limit in sheet metal forming, the combination of FE simulation with tension tests is adopted in this paper to determine the material constants p and C in a ductile fracture criterion (DFC), which is advanced by the author. Forming limits of bore-expanding, hemispherical punch bulging and deep drawing (cylindrical, square-cup parts) are predicted by means of the DFC. Comparison of the results predicted by the DFC with experimental values shows that the precision of forming limit predicted by material constants obtained by the combination method is more accurate than that predicted by material constants obtained by the tension method, and that the critical punch stoke and the fracture initiation position in forming processes above mentioned are predicted accurately by the DFC.     

The effect of stress state on high-temperature deformation of fine-grained aluminum–magnesium alloy AA5083 sheet

The effect of stress state on high-temperature deformation of fine-grained aluminum–magnesium alloy AA5083 sheet is investigated over a range of temperatures and strain rates for which the grain-boundary-sliding and solute-drag creep mechanisms govern plastic flow. Experimental data from uniaxial tension and biaxial tension are used in conjunction with finite-element-method simulations to examine the role of stress state. Three different material constitutive models derived from uniaxial tensile data are used to simulate bulge-forming experiments. Comparison of simulation results with bulge-forming data indicates that stress state affects grain-boundary-sliding creep by increasing creep rate as hydrostatic stress increases. Thus, creep deformation is faster under biaxial tension than under uniaxial tension for a constant effective stress. No effect of stress state is observed for solute-drag creep. A new material model that accounts for the effect of stress state on grain-boundary-sliding creep is proposed.