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.     

Logistic regression analysis for experimental determination of forming limit diagrams

The forming limit diagram (FLD) is probably the most common representation of sheet metal formability and can be defined as the locus of the principal planar strains where failure is most likely to occur. Experimental determination of the FLD consists in performing a set of formability tests on a sheet metal blank, where a regular grid has been previously etched. After each test, the deformation of the grid is measured and the relative strains computed. Strains observed closely at the fracture location are related to as ‘failed’ points, while strains observed on the sound areas of the specimens are labelled as ‘safe’ points. Starting from a set of experimental tests, the FLD should be empirically determined through a statistical analysis of collected data. In fact, statistical approaches (such as linear regression) are required to properly account for the internal randomness of failure occurrence. Linear regression, as well as most of the other empirical approaches in the scientific literature, takes into account only information related to the safe points.This paper proposes a different approach, the logistic regression, for the empirical determination of FLDs. Logistic regression allows to directly derive the probability of an event (e.g. the failure) as a function of different predictor variables (both the principal planar strains). Therefore, by using logistic regression, the process designer can directly associate the failure probability to the scrapping costs, in order to economically evaluate a new sheet metal forming operation.Logistic regression allows the determination of the FLD by including information concerning both safe and failed points.     

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.     

Development of a new procedure for the experimental determination of the Forming Limit Curves

The objective of the paper is to define a new method for the experimental determination of the Forming Limit Curves (FLCs). The procedure is based on the hydraulic bulging of two specimens. The most important advantages of the method are the capability of investigating the whole strain range specific to the sheet metal forming processes, simplicity of the equipment, and reduction of the parasitic effects induced by the friction, as well as the occurrence of the necking in the polar region. The comparison between the FLCs determined using the new procedure and the Nakazima test shows minor differences.     

A new method of determining forming limit diagram for sheet materials by gas blow forming

A new methodology is proposed to obtain forming limit diagrams (FLDs) of sheet materials using gas blow forming process at elevated temperatures. Tension–tension side of the forming FLD is achieved by using circular as well as elliptical dies of different aspect ratios. To achieve tension–compression side of FLD un-bonded bi-layer specimen with slots are utilized. The widths between the slots are varied to achieve different strain paths. A correlation is established between the hemispherical punch-based tests and GBF tests of samples with slots to achieve different strain paths. FLDs for automotive AZ31 magnesium sheet at 300 °C and 400 °C in two different orientations are determined. Increase in forming limits of AZ31 with increase in temperature is observed.     

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.     

History of plasticity and metal forming analysis

The research history of mechanics, physics and metallurgy of plastic deformation, and the development of metal forming analysis are reviewed. The experimental observations of plastic deformation and metal forming started in France by Coulomb and Tresca. In the early 20th century, fundamental investigation into plasticity flourished in Germany under the leadership of Prandtl, but many researchers moved out to the USA and UK when Hitler came in power. In the second half of the 20th century, some analyzing methods of metal forming processes were developed and installed onto computers as software, and they are effectively used all over the world.     

Sheet metal forming of piezoceramic-metal-laminar structures—Simulation and experimental analysis

Adaptive systems with piezoelectric components offer significant opportunities for the active control of dynamic behaviour. Vibration and acoustics control as well as structural health monitoring are also possible. However ineffective production technologies prevent industrial applications. The authors are therefore proposing the integration of piezo-modules inside a double-layer sheet. The use of semi-cured adhesive avoids shear-forces being transferred to the piezo-modules during forming. After forming the adhesive will cure and the transfer of piezoelectric strain to the sheet is made possible. A detailed finite-element-model incorporating the electro-mechanical characteristics of the piezo-modules has been developed. The simulation results were validated experimentally.     

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.     

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.     

Effect of Ti addition on forming limit diagrams of Nb-bearing ferritic stainless steel

In order to better understand the grain size, texture evolution and forming limit major strain of ferritic stainless steel, two kinds of ultrapure ferritic stainless steels (Nb single stabilization and Nb + Ti dual stabilization) with 15 wt%Cr content of the same thickness processed by the same annealing treatment have been studied in this work. Ti addition does not improve the r-value as much, but it appears to refine the grain size of the ferrite and increase the {1 1 1}〈1 1 2〉 texture component in the γ-fiber, especially reduce the planer anisotropy value. The enhancement of the formabilities especially the drawability in forming limit diagram of Nb + Ti dual stabilization 15%Cr ferritic stainless steel mainly due to the refinement of the grain size, higher average r-value and lower planer anisotropy value.     

The strain path and forming limit analysis of the lubricated sheet metal forming process

Few previous attempts have been made to analyze numerically the strain path and the forming limit in complex lubricated sheet metal forming. Since usual approaches of solving the lubrication model are limited to axisymmetric and plane strain cases only, this paper developed a unified procedure for combining the finite element code of sheet metal forming, the current lubrication/friction model and forming limit theory, to predict the strain path and fracture strains for either a steady or an unsteady three-dimensional process including both axisymmetric and plane strain cases. The availability of the method must be proved by a published problem, and an axisymmetric stretch forming process was therefore adopted as a benchmark. Numerical results showed that the present analysis provides good agreement with the experimental data of the strain path and the fracture strain for various tribological parameters such as lubricant viscosity and composite roughness of tooling and workpiece, and the advantage of the developed model is that it can be applied to solve the complicated 3D geometric problems.     

Determination of forming limit of a structural aluminum tube in rubber pad bending

Rubber pad bending is a novel technique for producing space frame to reduce the weight of automobiles because it can produce bent profiles with various curvatures in a single production set-up. As in other bending processes, cross-section of the aluminum tube deforms during the process. Such a deformed geometry diminishes bending rigidity, making it inappropriate for a structural use in some cases. Thus, it is important to determine a minimum radius of curvature with sufficient bending resistance. In this study, experimental set-up was developed to investigate deformation characteristics of an extruded rectangular aluminum tube in rubber pad bending. For better understanding of the effect of process parameters such as the material property of rubber and roller diameter, finite element (FE) analyses were also conducted. The ratio of the second moment of inertia of the initial and deformed cross-sections of the tube was introduced as a measure of cross-sectional deformation to represent the variation of bending rigidity of the bent tube. In result, a critical value of sectional deformation and minimum formable radius of curvature with maintaining suitable sectional bending rigidity were, respectively, determined under the present process conditions investigated.     

A new forming method of solid bosses on a cup made by deep drawing

A new process for forming bosses on the bottom of a cup made by deep drawing is proposed: solid bosses are formed by compression of the cup bottom during deep drawing. By the combined effect of compression and deep drawing, bosses are formed with a lower load than simple compression or backward extrusion. It is found that high bosses can be formed with moderate punch pressure when only one side of the blank is lubricated.     

A new contact judgement method for sheet metal forming simulation

A new contact judgement method for sheet metal forming simulation is proposed. The method can overcome miss-judgement and error-judgement, and improve numerical stability and computational accuracy effectively. Based on the proposed contact judgement method, a static–implicit FE code is developed. Some typical sheet metal forming processes and the benchmark of NUMISHEET’93 are simulated, and satisfactory results being obtained.     

数字图像相关法在薄板成形极限测定中的应用

成形极限曲线可展现板料在塑性失稳前所能达到的最大变形程度,是板料成形分析中的重要判据。为获得准确的试验成形极限曲线,该文通过刚性半球凸模胀形试验、采用数字散斑图像相关方法对AA6061铝板的成形极限曲线进行测定,得出了成形极限试验测定和极限应变提取的方法;通过对AA6061铝板进行盒形件拉深试验,建立拉深过程的有限元模型,比较了数值模拟和试验测定的极限拉深深度。比较结果表明,数字图像相关方法能够有效获取变形过程中的全场应变信息、搜索临界破裂状态,且能采用曲线拟合方式计算极限应变,避免了人为误差,提高了测量精度。拉深试验表明,所测成形极限曲线对拉深极限具有较高的预测精度。     

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。     

A theoretical and experimental study on forming limit diagram for a seamed tube hydroforming

The purpose of this work is to establish the forming limit diagram (FLD) for a seamed tube hydroforming. A new theoretical model is developed to predict the FLD for a seamed tube hydroforming. Based on this theoretical model, the FLD for a seamed tube made of QSTE340 sheet metal is calculated by using the Hosford yield criterion. Some forming limit experiments are performed. A classical free hydroforming tool set is used for obtaining the left hand side forming limit strains, and a novel hydroforming tool set is designed for the right hand side of FLD. The novel device required the simultaneous application of lateral compression force and internal pressure to control the material flow under tension–tension strain states. Furthermore, the suitable loading paths for the left hand side of FLD by theoretical formulas and for the right hand side of FLD by finite element (FE) simulations are calculated. Finally, a comparison between the theoretical results and experimental data is performed. The theoretical predicting results show good agreement with the experimental results.     

A new rotary forming process for rim thickening of a disc-like sheet metal part

A new rotary forming process used to thicken the rim of a disc-like part was proposed. The paper details the results, design and manufacture of the corresponding apparatus. The center point of a ring roller moves around the axis of a stationary work-piece in a plane spiral locus, like a rounding hula hoop. Thereby, the rim of stationary work-piece is rolled and thickened. A design rule for the rotary thickening process of the disc-like part was proposed, and a formula for calculating the feeding force of the roller was deduced. Both the design rule and the formula were verified by the results of experiment and finite element simulation. The forming and flow law during the thickening process were also illustrated.