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.

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.

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.

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.

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.

Formability of TRIP/TWIP Steel Containing Manganese of 18.8%

The mechanical property and forming limit experiments were carried out on a higli manganese TRIP/TWIP steels with manganese of 18.8%. And the forming /imit diagram was obtained. This hig：h manganese steel shows outstanding mechanical properties comhining high strength with good formability. Its limit plane strain corresponding to the lowest point in the plain strain condition is about 38%. The effects of conventional mechanical property on the limit plane strain were analyzed. With increasing the content of Mn, the limit plane strain increases, indicating that TWlP effect is advantageous to the increase of formability. Combining with three classical models and volume invaria ble principle, a FLD model was buih, which is suitable for high manganese steels very well.

Formability of Fe-Mn-C Twinning Induced Plasticity Steel

A comparative analysis of formability was investigated between F^Mn-C twinning induced plasticity steel with different Mn contents and interstitial free steel. Tensile test combing with the morphology of fracture reveals that element Mn is helpful for the forming of inclusion or particles with film or rod shapes inducing the crack initia- tion and propagation. During stamping process, twinning induced plasticity steel without earing shows better anisot- ropy than interstitial-free steel because a typical 〈111〉 fiber texture forms accompanied by a weaker 〈100〉 fiber texture. The difference between the two steels is not evident during Erichsen cone cupping test, but the result of cone cupping test indicates that the twinning induced plasticity steel has superior drawing ability compared with intersti tial-free steel. The different performances can be attributed to the different deformation mechanism during cupping test. FED （forming limit diagram） of tested steels further suggests twinning induced plasticity steel has slightly su- perior deep drawability but low stretchability than that of IF steel, whose FLD0 value can reach 30%.