Design and analysis of new test method for evaluation of sheet metal formability

A new test method including the tool shape and test procedure was developed to evaluate sheet metal formability using the finite element method (FEM). This method is intended to generate the various modes of deformation and to control the onset of failure independently under each mode so that the forming limit diagram (FLD) achieves a good representation of a wide range of strains.A blank holder force-punch stroke diagram with three failure loci is introduced to define the optimum process condition and the formability index by which each material is quantitatively evaluated. The test procedure of this method consists of three steps: drawing a blank holder force (BHF)-punch stroke diagram, measuring strains from the part stamped at the optimum process condition, and grading the test materials using the formability index. In numerical simulations under optimum process conditions, sheet metals can fail due to multi-mode rupture; this failure leads to a widely balanced strain distribution in the FLD such that strains are developed near the forming limit over a wide range of forming modes.Experiments were conducted on three grades of steel sheets to validate the proposed method. Stamping results yield well-defined strain signatures having a wide range of strain distribution in the FLD in all materials tested. The outcomes of the shape and strain behaviors agree well with the numerical 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.     

Prediction of Forming Limit Diagrams for 22MnB5 in Hot Stamping Process

Hot stamping of ultra-high strength steels possesses many superior characteristics over conventional room temperature forming process and is fairly attractive in improving strength and reducing weight of vehicle body product. However, the mechanical and failure behavior of hot stamping boron steel 22MnB5 are both strongly affected by strain hardening, temperature, strain rate, and microstructure. In this paper, the material yield and flow behavior of 22MnB5 within the temperature and strain rate range of hot stamping are described by an advanced anisotropic yield criterion combined with two different hardening laws. The elevated temperature forming limit diagram (ET-FLD) is constructed using the M-K theoretical analysis. The developed model was validated by comparing our predicted result with experimental data in the literature under isothermal conditions. Based on the verified model, the influence of temperature and strain rate on the forming limit curve for 22MnB5 steel under equilibrium isothermal condition are discussed. Furthermore, the transient forming limit diagram is developed by performing a transient forming process simulation under non-isothermal transient condition.     

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。     

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.     

Time dependent determination of forming limit diagrams

The forming limit diagram (FLD) is a convenient tool for classification of sheet metals’ formability in the finite element analysis as well as in the press shop. The FLD indicates the maximum strain values which can be applied on a material without failure as a function of the strain condition. In contrast to the standardized evaluation method described in the standard ISO 12004-2 a new time dependent analysis method is presented. Using a regression analysis the onset of necking can be detected automatically independent of the strain state. Results will be presented and discussed in contrast to the existing standard procedure.     

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.     

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.     

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.     

流动应力-应变关系对5754O铝合金板成形极限的影响(英文)

为了合理描述单向拉伸试验曲线,给出了一种修正的Swift型流动应力—应变关系。基于两种流动应力—应变关系,采用Yld2000-2d屈服准则计算5754O铝合金板的成形极限应变图(FLD-strain)。通过对比理论和实验结果,发现基于修正的Swift型的应力—应变关系所计算的FLD-strain能够合理地描述实验结果。虽然常用的Voce型应力—应变关系能够精确地描述均匀变形阶段的变形行为,但基于该应力—应变关系计算的FLD-strain明显低于实验结果。结果表明,板料的强化率越高则相应的成形极限也越高。为了描述板料在非均匀变形阶段的变形行为和成形极限,建议了一种用于确定合理的流动应力—应变关系的方法。     

Tensile Behavior and Formability Evaluation of Titanium-40 Material Based on the Forming Limit Diagram Approach

The formability of Titanium alloy sheet material Ti-40 has been experimentally assessed in the present investigation. The investigation is divided into two parts: In the first part, the effect of the strain rate applied during testing, as well as the effect of material axes’ orientation, on the tensile behavior is evaluated via standard tensile tests. In addition, the hardening characteristics as well as the anisotropy parameters (plastic strain ratio) have also been extracted. In the second part, the formability limits of Ti-40 material are experimentally derived using Nakajima tests and the corresponding forming limit diagrams are compared against other commercially available titanium sheet alloys.     

超声振动效应对TA2钛合金板材力学及胀形性能影响

针对钛合金板材塑性变形能力差的问题,进行了超声振动辅助成形工艺的研究,分析超声振动对钛合金TA2板材力学性能及与接触面之间摩擦系数的影响。在此基础上进行了不同宽长比坯料的超声振动辅助胀形实验,分析超声振动对TA2板材胀形力、极限胀形高度的影响。同时,基于网格应变原理,通过不同宽长比坯料极限应变的测量,建立TA2板材的成形极限图。研究结果表明,选择合适的超声振动辅助成形工艺参数, 不仅可以提高TA2板材变形能力,还可以减小摩擦对板材成形性能的影响,从而有效提高了TA2板材的成形极限。     

板料成形中材料模型的研究进展

介绍了板料成形数值模拟中材料模型的研究进展。将材料模型的理论研究分为屈服准则、强化模型、流动法则、加卸载历史4个方面,并进行简要综述;对材料在循环加载条件下应力应变曲线的实验获取方法进行了探讨,重点介绍了板料压缩、三点弯曲实验确定材料反向加载应力应变曲线的原理和方法;对当前屈服准则、强化模型的研究热点和发展方向进行了分析。     

Formability of a more randomly textured magnesium alloy sheet: Application of an improved warm sheet formability test

The warm formability of three sheet magnesium alloys was measured using the OSU formability test adapted for testing at elevated temperatures under isothermal conditions. The adapted test is shown to reliably enforce plane strain tension over a significant fraction of the sample, thus providing an assessment of FLD(0), typically the minimum major strain value on a forming limit diagram. By mathematically modeling the strain as a function of punch displacement, a case is made that the punch displacement itself provides an expedient approach to ranking the relative formability of sheet metals. Combined with knowledge of the constitutive behavior of the material, the punch displacement–strain relationship provides an explanation for the observed shape of the punch load versus displacement curves. OSU formability test results show that a new magnesium sheet alloy, yttrium-containing ZW41, is significantly more formable than traditional magnesium alloys AZ31 and ZK10. The improvement is linked to a more random texture in the new alloy, which diminishes the tendency for gross, catastrophic shear instability typical of the strongly textured traditional alloys.     

Rate and Orientation Dependence of Formability in Fine-Grained AZ31B-O Mg Alloy Thin Sheet

Uniaxial tension and press forming tests were carried out at two different strain rates and temperatures to investigate the formability of fine-grained AZ31B-O Mg alloy thin sheet. Formability parameters were determined by tensile test results. The tensile properties and formability parameters were correlated with the forming limit diagrams. The present work focused on the effects of loading orientation and deformation rate on formability. Anisotropic behaviors were observed in the mechanical properties. Maximum strengths were obtained in the direction perpendicular to the rolling direction (RD). It can be concluded that the formability of the rolled fine-grained AZ31B-O Mg alloy sheet can be influenced by loading orientation and deformation rate. Stretch formability can be enhanced at a higher deformation rate, resulting from a lower anisotropy and a higher work hardening effect. In contrast, the drawing processes can be performed at a lower deformation rate to take advantage of a higher anisotropic behavior. Specimens with the RD parallel to the major strain in the press forming tests can enhance stretch formability, whereas specimens with the RD perpendicular to the major strain can improve deep-drawability.     

Formability limits by fracture in sheet metal forming

The aim of this paper is twofold: first, to revisit the forming limit diagram (FLD) in the light of fundamental concepts of plasticity, damage and ductile fracture mechanics and, second, to propose a new experimental methodology to determine the formability limits by fracture in sheet metal forming. The first objective makes use of the theory of plasticity applied to proportional strain loading paths, under plane stress conditions, to analyze the fracture forming limit line (FFL) and to introduce the shear fracture forming limit line (SFFL). The second objective makes use of single point incremental forming (SPIF), torsion and plane shear tests to determine the experimental values of the in-plane strains at the onset of fracture. Results show that the proposed methodology provides an easy and efficient procedure to characterize the formability limits by fracture in sheet metal forming. In particular, the paper shows that the FFL determined by means of tensile and conventional sheet formability tests is identical to that determined from SPIF tests on conical and pyramidal truncated specimens. The new proposed approach is expected to have impact in the established methodologies to outline the formability limits on the basis of the forming limit curves (FLC's) at the onset of necking.     

板料成形极限理论与实验研究进展

成形极限是板材成形领域中重要的性能指标和工艺参数。文章在阐述成形极限在板料成形中的意义的基础上,综述并分析了成形极限在理论和实验方面的研究进展。成形极限图受应变路径的影响,给工业生产应用带来极大不便。以极限应力构成的成形极限应力图不受应变路径的影响,作为复杂加载路径的成形极限判据更加方便和实用。FLSD研究与FLD相结合,成为精确地确定破裂判别准则的主要途径之一,是近来研究的热点。十字形双向拉伸是实现复杂加载路径有效实用的试验方法。最后对成形极限应力图和十字形双向拉伸试验需要解决的关键问题作了阐述。     

Damage and Failure Analysis of AZ31 Alloy Sheet in Warm Stamping Processes

In this study, a combined experimental-numerical investigation on the failure of AZ31 Mg alloy sheet in the warm stamping process was carried out based on modified GTN damage model which integrated Yld2000 anisotropic yield criterion. The constitutive equations of material were implemented into a VUMAT subroutine for solver ABAQUS/Explicit and applied to the formability analysis of mobile phone shell. The morphology near the crack area was observed using SEM, and the anisotropic damage evolution at various temperatures was simulated. The distributions of plastic strain, damage evolution, thickness, and fracture initiation obtained from FE simulation were analyzed. The corresponding forming limit diagrams were worked out, and the comparison with the experimental data showed a good agreement.     

Evaluation and prediction of the forming limit of AZ31B magnesium alloy sheets in a cross-shaped cup deep drawing process

In this study, the formability of AZ31B magnesium alloy sheets was investigated through experimental and numerical approaches. Tensile tests and limit dome height tests were carried out at several temperatures between 25 °C and 300 °C to obtain the mechanical properties and forming limit diagram (FLD). The interfacial heat transfer coefficient between two adjacent tools, and the convection coefficient were estimated by comparing the tool temperatures obtained from trial heat transfer analyses with actual measured data. The FLD-based criterion considering the strain path and the blank temperature was used to predict by finite element analysis (FEA) the forming limit in a cross-shaped cup deep drawing process. A comparison of the FEA and experimental data showed that this criterion was very useful and reasonable. In particular, the temperature of each forming tool that provided the best formability of AZ31 sheets was determined by coupled temperature-deformation analyses. A practical method that can greatly reduce the forming time by increasing the punch speed during the forming process was suggested.     

Assessment of the Cold Formability of Ferritic Steels Using Parameters Determined in Uniaxial Tensile Testing

Possibilities and limits of the uniaxial tensile testing in the assessment of cold formability of ferritic low alloy steels are evaluated in the paper. Cold formability covering both sheet and massive forming, including entire formability maps, strain hardening etc., can be estimated from six material parameters determined in a uniaxial tensile test. A master stress strain curve to explain multiple n behavior is proposed. Effects of alloying, especially chromium, and other metallurgical parameters on cold formability are discussed.