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.     

Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets

Recent work on sheet metal formability had shown that the position of forming limit diagrams (FLDs) in punch stretching is higher than that in in-plane stretching because of a strain gradient effect resulting from bending a flat sheet into a curved sheet by punch stretching. To our knowledge, none of the developed theoretical models in the study of localized necking can be used to predict this phenomenon accurately so far. In this study, a new model, using Barlat and Lian’s new nonquadratic anisotropic yield criterion, is proposed by introducing a strain gradient term in the constitutive equation to consider the effect of the first order strain gradient (curvature), in the thickness direction resulting from bending, on the localized necking in anisotropic sheets. The developed model is used to study the effects of curvature on FLDs and to predict FLDs in punch stretching and inplane stretching for various materials. It is found that the theoretical predicted results are in good agreement with experimental data.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Formability evaluation for hot-rolled HB780 steel sheet based on 3-D non-quadratic yield function

A common practice to evaluate formability in the typical sheet metal forming process is to measure hardening behavior and a forming limit diagram as separate material properties, and perform numerical forming simulations utilizing various yield functions. The measured forming limit diagram is applied as the failure criterion. However, the performance of material properties such as hardening behavior and yield functions in predicting strain localization in the simple tension and forming limit diagram tests is seldom validated before their application to forming simulation. In this study, a new numerical formability evaluation procedure was proposed, in which not only hardening behavior but also measured forming limit data were employed in characterizing the input data for the hardening behavior and the yield function. Besides, strain localization was directly monitored to determine failure without employing any forming limit criterion. The new procedure was applied for rather thick advanced high strength hot-rolled steel sheet so that 3-D continuum elements were utilized along with 3-D non-quadratic Hosford and quadratic Hill yield functions.     

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.     

Finite element analysis of sheet Hydromechanical forming of circular cup

Sheet hydroforming is a process of converting flat sheet into desired component geometry by using water pressure in a controlled manner. This paper dealt with sheet Hydromechanical forming (SHMF) of circular cup. In this process, blank is first placed on the lower die (a fluid chamber combined with draw ring) and then after sealing the blank between blank holder and draw ring, punch progresses to deform the blank. Pressure of the fluid chamber is also increased simultaneously with the punch progression. The present work endeavours to understand the effect of strain hardening exponent, anisotropy ratio and interfacial friction between blank and tools surfaces for different modes of deformation––stretching to drawing mode on sheet Hydromechanical forming of circular cups.A finite element (FE) model was developed for simulating the SHMF process using dynamic explicit, commercial code, LsDyna. The model after experimental validation used for studying the effect of above parameters on the process. The analysis reveals that higher cup depth with minimum thinning for forming dominated by stretching mode can be achieved with material of higher anisotropy ratio, strain hardening exponent by using a rough punch and effective lubrication at blank-die–blank holder interfaces. On the other hand in case of drawing as mode of deformation, thinning is influenced mainly by interfacial friction condition between blank and tool surfaces as compared to material properties.     

板材拉伸成形中损伤、失稳与成形极限曲线的建立

失稳理论是建立成形极限曲线（ＦＬＣ）的理论基础。本文论述了ＦＬＣ理论研究中存在的问题。指出：一般出厂板的表面状况不会影响板材的集中失稳；板内损伤平面应变时最严重。双拉时，板内损伤的积累、发展，导致应力状态向平面应变漂移；拉压时，载荷失稳后引起的双拉，也会导致平面应变。因此平面应变状态的出现是双拉与拉压状态板材集中失稳的共同原因。在此基础上提出了建立ＦＬＣ的统一的模型。试验结果表明，新模型优于Ｍ－Ｋ理论。     

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。     

Improvement of formability of Mg–Al–Zn alloy sheet at low temperatures using differential speed rolling

The differential speed rolling (DSR) with a roll speed ratio of 1.167 was carried out on an AZ31B magnesium alloy in order to investigate its effects on the formability. Compared with the normal rolled sheet exhibiting approximately the same average grain size, the Erichsen values of the DSR processed sheet with an inclination of basal pole in the rolling direction significantly increased by about 1.5 and 1.9 times at room temperature and at 423 K, respectively. The deep-drawing temperature limit for a drawing ratio of 1.5 was also lowered from 443 K to 423 K. The improvement of the press formability at low temperatures can be attributed to the texture modifications, which led to a lower 0.2% proof stress, a larger uniform elongation, a smaller Lankford value and a larger strain hardening exponent.     

Numerical simulation of two-stage deep drawing of complex-shaped parts

1　INTRODUCTIONInrecentyears ,withtherapiddevelopmentofcomputersoftwareandhardware ,andtheintersectionandcombinationofcomputertechnology ,graphics ,mechanicsandprocessengineering ,thecomputeraid edengineering(CAE)technologybasedonnumericalsimulationhasbeenwidelyappliedinthesheetmetalformingfield[1,2 ] .Nevertheless ,untilnow ,thenu mericalsimulationisconfinedtosimulatesomebasicmodesofdeformationsuchasbending ,deepdraw ing ,bulgingandflanging .Forthedeformationofcomplexwork pieces ,forexa…     

Electromagnetically assisted sheet metal stamping

A new approach, electromagnetically assisted sheet metal stamping, has been developed to alter strain distribution and improve formability in sheet metal stamping. In this study, this new approach was applied to form a non-symmetric panel from Al 6111-T4. The results show that this new approach greatly increased the draw depth of the formed panel, compared with conventional stamping. A detailed analysis of strain distribution, stretching and draw-in shows that both a more homogeneous strain distribution and enhanced draw-in contribute to producing deeper pans in a single press operation. This work demonstrates the feasibility of electromagnetically assisted sheet metal stamping, which offers a much improved ability to make complex components in a single press stroke as compared to conventional stamping.     

Improvement in formability by control of temperature in hot stamping of ultra-high strength steel parts

The formability in hot stamping of an ultra-high strength steel part was improved by preventing a temperature drop of the flange increasing resistance to drawing. The temperature drop was reduced by high speed forming using a servo press and by less contact with a die and blankholder using spacers thicker than the sheet. In addition, hardening of the flange was prevented by slow cooling for the less contact using the spacers to facilitate trimming of the hot-stamped part. From a hot deep drawing experiment with a hemispherical punch, the effectiveness of the present approaches of temperature control was demonstrated.