Prediction and Verifcation of Forming Limit Diagrams Based on a Modifed Shear Failure Criterion

The forming limit diagram plays an important role in predicting the forming limit of sheet metals.Previous studies have shown that,the method to construct the forming limit diagram based on instability theory of the original shear failure criterion is efective and simple.The original shear instability criterion can accurately predict the left area of the forming limit diagram but not the right area.In this study,in order to improve the accuracy of the original shear failure criterion,a modifed shear failure criterion was proposed based on in-depth analysis of the original shear failure criterion.The detailed improvement strategies of the shear failure criterion and the complete calculation process are given.Based on the modifed shear failure criterion and diferent constitutive equations,the theoretical forming limit of TRIP780 steel and 5754O aluminum alloy sheet metals are calculated.By comparing the theoretical and experimental results,it is shown that proposed modifed shear failure criterion can predict the right area of forming limit more reasonably than the original shear failure criterion.The efect of the pre-strain and constitutive equation on the forming limits are also analyzed in depth.The modifed shear failure criterion proposed in this study provides an alternative and reliable method to predict forming limit of sheet metals.

Theoretical prediction of forming limit diagram of AZ31 magnesium alloy sheet at warm temperatures

A theoretical prediction on forming limit diagram（FLD） of AZ31 magnesium alloy sheet was developed at warm temperatures based on the M-K theory. Two different yield criteria of von Mises and Hill＇48 were applied in this model. Mechanical properties of AZ31 magnesium alloy used in the prediction were obtained by uniaxial tensile tests and the Fields-Backofen equation was incorporated in the analysis. In addition, experimental FLDs of AZ31 were acquired by conducting rigid die swell test at different temperatures to verify the prediction. It is demonstrated from a comparison between the predicted and the experimental FLDs at 473 K and 523 K that the predicted results are influenced by the type of yield criterion used in the calculation, especially at lower temperatures. Furthermore, a better agreement between the predicted results and experimental data for AZ31 magnesium alloy sheet at warm temperatures was obtained when Hill＇48 yield criterion was applied.

Influence of material models on theoretical forming limit diagram prediction for Ti-6Al-4V alloy under warm condition

Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti?6Al?4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson?Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M?K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.

Stress based forming limit diagram for formability characterization of 6061 aluminum

Two numerical criteria of forming limit diagram（FLD） criterion and ductile fracture criterion（DFC） are presented for FLD prediction of 6061 aluminum. The numerical results are compared with the experimental FLD and also punch＇s load-displacement curve of experimental samples. Experimental FLD of this study is calculated using hemispherical punch test of Hecker. Experimental FLD is converted to FLSD and imported to the Abaqus software to predict necking of samples. Numerical results for FLSD prediction were compared with experimental FLSD. Results show that ductile fracture criterion has higher accuracy for FLD and FLSD prediction of 6061 aluminum. Comparison of numerical and experimental results for force-displacement curve of punch shows that numerical results have a good agreement with experiment.

Prediction of Forming Limit Diagrams for Materials with HCP Structure

The forming limit diagram（FLD） is an important tool to be used when characterizing the formability of metallic sheets used in metal forming processes. Experimental measurement and determination of the FLD is timeconsuming and therefore the analytical prediction based on theory of plasticity and instability criteria allows a direct and efficient methodology to obtain critical values at different loading paths, thus carrying significant practical importance.However, the accuracy of the plastic instability prediction is strongly dependent on the choice of the material constitutive model [1–3]. Particularly for materials with hexagonal close packed（HCP） crystallographic structure, they have a very limited number of active slip systems at room temperature and demonstrate a strong asymmetry between yielding in tension and compression [4, 5]. Not only the magnitude of the yield locus changes, but also the shape of the yield surface is evolving during the plastic deformation [4]. Conventional phenomenological constitutive models of plasticity fail to capture this unconventional mechanical behavior [4, 6]. Cazacu and Plunkett [6] have proposed generic yield criteria, by using the transformed principal stress, to account for the initial plastic anisotropy and strength differential（SD） effect simultaneously. In this contribution, a generic FLD MATLAB script was developed based on Marciniak–Kuczynski analytical theory and applied to predict the localized necking. The influence of asymmetrical effect on the FLD was evaluated. Several yield functions such as von Mises, Hill, Barlat89, and Cazacu06 were incorporated into analysis. The paper also presents and discusses the influence of different hardening laws on the formability of materials with HCP crystal structures. The findings indicate that the plastic instability theory coupled with Cazacu model can adequately predict the onset of localized necking for HCP materials under different strain paths.

Forming limit of textured AZ31B magnesium alloy sheet at different temperatures

Repeated unidirectional bending （RUB） was carried out to improve the texture of commercial AZ31B magnesium alloy sheets. All specimens were prepared in the rolling direction. The forming limit diagrams （FLDs） of AZ31B magnesium alloy sheet were determined experimentally by conducting stretch-forming tests at room temperature, 100, 200 and 300 ℃ Compared with the as-received sheet, the lowest limited strain of AZ31B magnesium alloy sheet with tilted texture in the FLD increased by 79% at room temperature and 104% at 100 ℃. The texture also affected the extension of the forming limit curves （FLC） in the FLD. However, the FLCs of two kinds of sheets almost overlapped at temperature above 200 ℃. It can be concluded that the reduction of （0002） texture intensity is effective to the improvement of formability not only at room temperature but also at low-and-medium temperature. The effect of texture on FLDs becomes weak with increasing temperature.

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.

Prediction of fracture limits of Ni-Cr based alloy under warm forming condition using ductile damage models and numerical method

The stretch forming and the deep-drawing processes were carried out at 300 and 673 K to determine the safe forming and fracture limits of IN625 alloy.The experimentally obtained strain-based fracture forming limit diagram(FFLD)was transformed into a stress-based(σ-FFLD)and effective plastic strain(EPS)vs triaxiality(η)plot to remove the excess dependency of fracture limits over the strains.For the prediction of fracture limits,seven different damage models were calibrated.The Oh model displayed the best ability to predict the fracture locus with the least absolute error.Though the experimentally obtained fracture limits have only been used for the numerical analysis,none of the considered damage models predicted the fracture strains over the entire considered range of stress triaxiality(0.33<η<0.66).The deep drawing process window helped to determine wrinkling,safe and fracture zones while drawing the cylindrical cups under different temperature and lubricating conditions.Further,the highest drawing ratio of 2 was achieved at 673 K under the lubricating condition.All the numerically predicted results of both stretch forming and deep drawing processes using the Hill 1948 anisotropic yielding function were found to be good within the acceptable range of error.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Hot Granules Medium Pressure Forming Process of AA7075 Conical Parts

High strength aluminum alloy plate has a low elongation at room temperature, which leads to the forming of its components need a high temperature. Liquid or gas is used as the pressure-transfer medium in the existing flexible mould forming process, the heat resistance of the medium and pressurizing device makes the application of aluminum alloy plate thermoforming restricted. To solve this problem, the existing medium is replaced by the heat-resisting solid granules and the general pressure equipments are applied. Based on the pressure-transfer performance test of the solid granules medium, the feasibility that the assumption of the extended Drucker-Prager linear model can be used in the finite element analysis is proved. The constitutive equation, the yield function and the theoretical forming limit diagram（FLD） of AA7075 sheet are established. Through the finite element numerical simulation of hot granules medium pressure forming（HGMF） process, not only the influence laws of the process parameters, such as forming temperature, the blank-holder gap and the diameter of the slab, on sheet metal forming performance are discussed, but also the broken area of the forming process is analyzed and predicted, which are coincided with the technological test. The conical part whose half cone angle is 15° and relative height H/d0 is 0.57, is formed in one process at 250℃. The HGMF process solves the problems of loading and seal in the existing flexible mould forming process and provides a novel technology for thermoforming of light alloy plate, such as magnesium alloy, aluminium alloy and titanium alloy.

Research on technological parameters of pressure forming with hot granule medium on AA7075 sheet

Hot granule medium pressure forming （HGMF） process is a new process in which granule medium replaces the medium in existing flexible-die hot forming process, such as liquids, gases or viscous medium. Hot forming of light alloy sheet parts can be realized based on the properties of granule medium, such as withstanding high temperature and pressure, filling well, sealing and loading easily. In this work, the forming of AA7075 cylindrical parts by HGMF process is taken as an example to establish the constitutive relation and forming limit diagram （FLD） of AA7075 sheet which is related to temperature by hot uniaxial tensile test of sheet metal. Based on the assumption that granule medium is applied to extended Drucker-Prager linear material model, the finite element model of HGMF process is established and the effect of technological parameters, such as forming temperature, blank-holder gap and drawing ratio, on the sheet metal formability, is studied. The limit drawing ratio curve of AA7075 cylindrical parts at forming temperature of 175-300 ℃ is obtained by HGMF process test, and the limit drawing ratio reaches the maximum value of 1.71 at 250 ℃. The results of numerical simulation are consistent with the results of process test, and the forming force, distribution of wall thichness and form of instability are predicted correctly, which provides reference for the application of HGMF process.

Forming Limit Stress Diagram Prediction of Aluminum Alloy 5052 Based on GTN Model Parameters Determined by In Situ Tensile Test

The conventional forming limit diagram （FLD） is described as a plot of major strain versus minor strain. However, FLD is dependent on forming history and strain path. In the present study, a forming limit stress-based diagram （FLSD） has been adopted to predict the fracture limit of aluminum alloy （AA） 5052-O1 sheet. Nakazima test is simulated by plastic constitutive formula derived from the modified Gurson-Tvergaard-Needleman （GTN） model. An in situ tensile test with scanning electron microscope （SEM） is proposed to determine the parameters in GTN model. The damage evolution is observed and recorded, and the parameters of GTN model are identified through counting void fraction at three damage stages of AA5052-O 1. According to the experimental results, the original void volume fraction, the volume fraction of potential nucleated voids, the critical void volume fraction, the void volume fraction at the final failure of material are assigned as 0.002 918, 0.024 9, 0.030 103, 0.048 54, respectively. The stress and strain are obtained at the last loading step before crack. FLSD and FLD of AA5052-O 1 are plotted. Compared with the experimental Nakazima test and uniaxial tensile test, the predicted results show a good agreement. The parameters determined by in situ tensile test can be applied to the research of the forming limit for ductile metals.

Theoretical prediction and experimental investigation on formability of tailor-welded blanks

Based on the elastoplastic mechanical properties of the weld and heat affected zone metals obtained by a nanoindentation test, a theoretical calculation model was established for the forming limit diagram（FLD） of tailor-welded blanks（TWBs） on the basis of plastic constitutive relations and Hosford yield criteria. Hemispherical punch bulging tests were performed to verify the FLD theoretical calculation results. The results demonstrated that not only the FLD theoretical calculation of base materials but also that of TWBs had a good agreement with their experiments. Besides, poorer formability of TWBs caused its FLD significantly lower than that of base materials. The theoretical calculation model offers a reliable approach to obtain the specific FLD of TWBs.

Viscous warm pressure bulging process of AZ31B magnesium alloy with different ellipticity dies

Based on the bulging principle of different ellipticity dies, the methyl vinyl silicone rubber with excellent thermal stability and heat transfer performance was chosen as the viscous medium. The finite element analysis and experiments of viscous warm pressure bulging （VWPB） of AZ31B magnesium alloy were conducted to analyze the influence of different ellipticity dies on the formability of AZ31B magnesium alloy. At the same time, based on the grid strain rule, the forming limit diagram （FLD） of VWPB of AZ31B magnesium alloy was obtained through measuring the strain of bulging specimens. The results showed that at the temperature range of viscous medium thermal stability, the viscous medium can fit the geometry variation of sheet and generate non-uniform pressure field, and as the die ellipticity increases, the difference value of non-uniform pressure reduces. Meanwhile, according to the FLD, the relationship between part complexity and ultimate deformation was investigated.

Formability of AA5052/polyethylene/AA5052 sandwich sheets

The formability of AA5052/polyethylene/AA5052 sandwich sheets was experimentally studied. Three kinds of AA5052/polyethylene/AA5052 sandwich specimens with different thicknesses of core materials were prepared by the hot pressing adhesive method. Then, the uniaxial tensile tests were conducted to investigate the mechanical properties of AA5052/polyethylene/ AA5052 sandwich sheets, and the stretching tests were carried out to investigate the influences of polymer core thickness on the limit dome height of the sandwich sheet. The forming limit curves for three kinds of sandwich sheets were obtained. The experimental results show that the forming limit of the AA5052/polyethylene/AA5052 sandwich sheet is higher than that of the monolithic AA5052 sheet, and it increases with increasing the thickness of polyethylene core.

Formability improvement and blank shape definition for deep drawing of cylindrical cup with complex curve profile from SPCC sheets using FEM

In the current work, to predict and improve the formability of deep drawing process for steel plate cold rolled commercial grade （SPCC） sheets, three parameters including the blanking force, the die and punch comer radius were considered. The experimental plan according to Taguchi＇s orthogonal array was coupled with the finite element method （FEM） simulations. Firstly, the data from the test of stress-strain and forming limit curves were used as input into ABAQUS/Explicit finite element code to predict the failure occurrence of deep drawing process. The three parameters were then validated to establish their effects on the press formability. The optimum case found via simulation was finally confirmed through an experiment. In order to obtain the complex curve profile of cup shape after deep drawing, the anisotropic behavior of earring phenomenon was modeled and implemented into FEM. After such phenomenon was correctly predicted, an error metric compared with design curve was then measured.

The Formablity of AZ31B Magnesium Alloy Sheet

The forming limit diagrams （ FLD ） of AZ31B magnesium alloy sheet were tested by means of the electro etching grid method based on the forming experiment of magnesium alloy sheet carried out with a BCS- 30D sheet forming testing machine and the strain testing analysis made with an advanced ASAME automatic strain measuring system. Experiments show that, at room temperature, the mechanical properties and deep drawing peorformance of AZ31B cold-rolled magnesium alloy sheet were so poor that it failed to test the forming limit diagrams without an ideal forming and processing capacity, while the hot-rolled magnesium alloy sheet was of a little better plasticity and forming peorformance after testing its forming limit diagrams. It can be concluded that the testing of the forming limit curves （ FLC ） offers the theoretical foundation for the drawing of the deep drawing and forming process of magnesium alloy sheet.

Development and evaluation of a hot-rolled 780 MPa steel sheet with an ultra-high expansion ratio

This paper explores the development of a 780 MPa hot-rolled high-strength steel with an ultra-high hole expansion ratio(HER) by using a nanoprecipitation-controlled technology.Systematic analysis and evaluation of an industrially produced steel sheet have been performed to investigate the microstructure, nanoprecipitates, tensile properties, HER,bendability, and forming limit diagram.The newly developed 780 MPa hot-rolled high-strength steel sheet is composed of a fully ferritic microstructure of approximately 5 μm with precipitates of approximately 4-5 nm in ferrite grain interiors.The yield strength and tensile strength can reach above 700 and 780 MPa, respectively.Moreover, the fractured elongation is higher than 19% in the transversal direction, and the average HER exceeds 70%.Furthermore, the newly developed 780 MPa high-strength steel has good bendability reaching R/t=0.2 at 90°.Compared with the conventional 780 MPa high-strength steel, the newly developed 780 MPa high-strength steel exhibits superior forming ability, which is suitable for the production of complex components.High-cycle fatigue indicates that the fatigue limit of the newly developed high-strength steel is 430 MPa under a stress ratio of r=-1,indicating good fatigue properties.The excellent combined mechanical properties of the newly developed 780 MPa high-strength steel are attributed to the grain-refined ferritic microstructure with nanoprecipitates in ferrite grain interiors.

Strain Limit of Extra Galvannealed Interstitial-Free and Bake Hardened Steel Sheets Under Different Stress Conditions

The formability of bake hardened steel （thickness 0.82 mm）, and the extra galvannealed IF steel （thickness 0.82 mm） have been studied. The suitability of the above steels for forming applications has been critically examined. The microstructure, tensile properties, and formability parameters of the above sheet metals were determined. The manufacturing process of the steels and the significance with reference to its formability were studied.

Fracture Loci in Sheet Metal Forming: A Review

Fracture in sheet metal forming usually occurs as ductile fracture, rarely as brittle fracture, at the operating temperatures and rates of loading that are typical of real processes in two different modes：（1） tensile and（2） in-plane shear（respectively, the same as modes I and II of fracture mechanics）. The circumstances under which each mode will occur are identified in terms of plastic flow and ductile damage by means of an analytical approach to characterize fracture loci under plane stress conditions that takes anisotropy into consideration. Fracture loci was characterized by means of the fracture forming limit line and by the shear fracture forming limit line in the fracture forming limit diagram. Experiments were performed with single point incremental forming and double-notched test specimens loaded in tension, torsion and in-plane shear give support to the presentation and allow determining the fracture loci of AA1050-H111 aluminium sheets with1 mm thickness. The relation between fracture toughness and the fracture forming limits was also investigated by comparing experimental values of the strains at fracture obtained from a truncated conical part produced by single point incremental forming and from double-notched test specimens loaded in tension.