Papers by Keyword: Forming Limit Curve

Abstract: The forming limit curve (FLC) is commonly used to predict the formability behavior of sheet metal after the forming process. In this research, the forming limit curve generated from the Materials Model was applied to analyze and predict the fracture behavior of the fuel tank workpiece, a motorcycle part made of AA5754-O material, using the deep drawing process simulated by the finite element method. The research involved a comparison with actual cracks that occur in the automotive industry after molding. To determine the mechanical properties of the AA5754-O material for use in the forming limit curve, a specimen with a thickness of 1.5 mm was subjected to a tensile strength test, providing the necessary input for the mechanical properties in the forming limit curve based on the Keeler-Beizer equation. The forming limit curve is a correlation graph between major strain and minor strain. When the FLC is created from the Materials Model, it is utilized in conjunction with deep drawing drag simulation in the PAM-STAMP program to predict the fracture point. The accuracy of the mathematically generated FLC in predicting fracture behavior was verified after the deep drawing process. The study found that the FLC based on the Keeler-Beizer equation can accurately predict the cracking behavior of AA5754-O sheet metal, enabling identification of the fracture location during the deep drawing process. One advantage of creating the FLC from the material models is its compatibility with the same material but with different workpiece shapes, allowing its use in conjunction with molding simulations using various programs. This approach saves costs associated with testing to obtain the FLC.

Abstract: With the goal to define a cost-effective and efficient process to identify adequate materials for sheet metal forming processes, it is crucial to evaluate the formability of materials. Forming limit curves (FLC) are used to analyze the forming and failure limits of sheet metals and dependence of the major (φ₁) and minor strain (φ₂) from the uniaxial stress-strain area through the plane-strain point to the biaxial strain area. According to ISO 12004-2, the FLC is performed by Nakajima or Marciniak tests. Due to the experimental setup and the preconditions, pre-stretching occurs in the specimens and bending and friction effect are the result. The determination of the onset of necking (FLC) results mathematically from a “best-fit inverse parabola” on section lines. In addition, the failure point, i.e. the maximum strain value one frame before failure, is also analyzed. In contrast, tensile, notched tensile and hydraulic bulge tests, which together have a potential to map an alternative FLC, exhibits a linear strain path evolution. The behavior of the various strain paths of Nakajima and the alternative methods are examined for necking and cracking. Furthermore, the fracture surfaces are investigated by confocal laser scanning microscopy to identify influences of the different FLC methods on the fracture mechanics. FLCs were conducted with the Nakajima and the alternative FLC characterization method for a ductile steel (DX54D). To ensure transferability, the tensile tests are also performed with a high-strength steel (DP800). The FLC of the ductile steel, generated through the alternative method, exhibits a similar shape to the Nakajima generated FLC with the advantage of a constant strain rate leading to linear strain paths and a lower number of tests. The same results are achieved for the uniaxial strain tests with DP800.

Abstract: To assess the suitability of different packaging steels for complex deep drawing applications, nowadays, the total elongation and the Lankford coefficients in simple tensile tests are used. However, the simple use of uniaxial tensile tests is not supposed to predict the limiting drawing ratio precisely and thus the suitability for deep drawing applications. At the same time, the conduction of limiting drawing ratio experiments is extensive and requires a high testing effort. Therefore, in this work, the correlation between the forming limit curve results were compared to the results of limiting drawing ratio experiments to predict the formability of packaging steel by a much simpler criterion. At the same time, different approaches to calculate the plane strain forming limit by tensile test data were used to assess the drawing capability of packaging steel. Results revealed a strong correlation between the measured plane strain forming limit and the limiting drawing ratio at a fixed blank holder force. However, calculation methods based on tensile test data were not able to predict the drawing capability sufficiently.

Abstract: Since its foundation, the concept of forming limit diagram has been widely accepted in sheet metal forming community as a powerful tool for studying formability. There are pyramid models that were developed to estimate the forming limit curve theoretically, for example, Swift's diffuse necking criterion, Hill's localized necking criterion, Marciniak and Kuczynski model, Modified Maximum Force Criterion, etc.. Implement of these models, however, is a laborious task. To simply the task, this study presents a graphical method to estimate forming limit curve of sheet metal. Some new insights into the Modified Maximum Force Criterion, the Hora method, are discussed. The insights pertain to the use of a graphic tool to estimate limit strains at three critical forming modes in sheet metal forming that are the uniaxial tension, plane strain, and equi-biaxial tension. Connecting three points by linear lines yields to a simple graph of forming limit curve. Method validation is supported by comparing the estimated forming limit curve with experimentally measured data for several automotive sheet metals.

Abstract: Lightweight design for vehicle industry is not anymore an optional condition but a mandatory need to reduce the fuel consumption and adhere to environmental regulations. To achieve this goal many single parts have been removed and complex design have been implied. This includes implementation of tailored-welded blanks and multi-layer materials. Due to the increase use of dissimilar materials in a component it is also called as hybrid components. It was observed that due to use of hybrid component the part weight decrease and thus increase fuel efficiency. To continue this aspect, in this bilayer tube flaring is investigated. The metal tubular material from inside and polymer from outside is considered for flaring. The flaring behavior of the tube is analyzed and compared with the single metal layer. The strength difference and effect of that on the formability is discussed and resulted. It was observed that due to contact of lower strength material from outside the formability of the metal tube increased and failure is delayed.

Abstract: In this work, the experimental and numerical analyses of Forming Limit Curve (FLC) and Forming Limit Stress Curve (FLSC) for Advanced High Strength Steel (AHSS) sheet, grade JAC780Y, are performed. Initially, the FLC is experimentally determined by means of the Nakazima Stretch forming test. Subsequently, the FLSC of investigated steel was plastically calculated using the experimental FLC data. Different yield criteria including Hill48, and Yld89, are applied to describe plastic flow behavior of the AHS steel and Swift hardening law is taken into account. Hereby, influences of the constitutive yield models on the numerically determined FLSCs are evaluated regarding to those results from the experimental data. The obtained stress based forming limits are affected significantly by the yield criteria. Finally, the experimental and numerical formability analyses of Fukui stretch-drawing and square cup drawing tests are studied through FLC and FLSCs. It is observed that all stress based curves can be used very well to describe material formability of the examined steel compared to the strain based FLC. The strain based FLC depend on forming history and strain paths change. In the other hand, the stress based FLC do not depend on these issue. In this study, it can be concluded that the FLSCs could predict failure more realistically and better than the strain based FLC.

Abstract: Present work analyses mathematical modelling to predict the onset of localized necking and rupture by shear in industrial processes of sheet metal forming of aluminium alloy 5083 such as biaxial stretching and deep drawing. Whereas the AA5083 sheet formability at room temperature is moderate, it increases significantly at high temperature. The Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulations by FEM, of AA 5083 sheet was assessed experimentally by tensile and Nakajima testing performed at room and 400°C temperatures. Tensile test specimens at 0o, 45o and 90o to the direction of rolling (RD) and Nakazima type specimens at 0o RD of aluminium AA5083 were fabricated. Simple tensile tests at room and 400°C temperatures were performed to obtain the coefficients of plastic anisotropy and material strain and strain rate hardening behavior at different temperatures. Nakazima biaxial tests at room and high temperature, employing spherical punch were carried out to plot the limit strains in the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of aluminium AA5083 sheet. The “Forming Map of Principal Surface Limit Strains”, MPLS, shows the experimental FLC which is the plot of principal true strains in the sheet metal surface (ε₁,ε₂), occurring at critical points obtained in laboratory formability tests or in the fabrication process of parts. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and rupture by induced shear stress. Therefore, two kinds of limit strain curves can be plotted in the forming map: the local necking limit curve FLC-N and the shear stress rupture limit curve FLC-S. Localized necking is theoretically anticipated to occur by two mathematical models: Marciniak-Kuczynski modelling, hereafter M-K approach, and D-Bressan modeling. Prediction of limit strains are presented and compared with the experimental FLC. The shear stress rupture criterion modeling by Bressan and Williams and M-K models are employed to predict the forming limit strain curves of AA5083 aluminium sheet at room and 400°C temperatures. As a result of analysis, a new concept of ductile rupture by shear stress and local necking are proposed. M-K model has good agreement with both D-Bressan models.

Abstract: There is a continuing interest in using laminated materials for the production of lightweight parts, the resulting parts having the same functionality and even an increased stiffness and length of operation compared to conventional materials. The present paper aims to study the forming behavior of the laminated materials that requires the unfolding of tests to determine the tensile mechanical properties and the intrinsic properties, determining the forming limit curves by means of the Nakajima test and the analysis of the behavior at unconventional incremental forming.

Abstract: In this work, the formability behavior of Interstitial-Free (IF) steel sheet, grade DC07 with 0.65 mm of nominal thickness, was evaluated by means of both linear and bi-linear strain-paths to define the Forming Limit Curve (FLC) at the onset of necking according to ASTM E22182 standard. In the first strain-path, flat-bottomed punch with 200 mm diameter and 10 mm corner die radius was adopted together with counter-blanks of an IF steel sheet grade DC07 with 0.80 mm nominal thickness in order to yield two equal amounts of plastic work under uniaxial tension and under equibiaxial stretching strain-paths. Afterwards, Nakajima’s 100 mm hemispherical punch stretching procedure and bulge tests were adopted to determine the FLC of both as-received and strained DC07 blanks with the help of an automated digital image correlation system to define the linear and bi-linear limit strains. Increasing the straining level (5 and 10%) of the first strain-path in uniaxial tension improved the limit strains of the DC07 steel sheet between the plane-strain intercept (FLC₀) and the biaxial stretching region of the FLC. On the other hand, blanks which were firstly pre-strained in equibiaxial stretching mode (4.8 and 9%) provided better formability in the FLC drawing region and reduced limit strains in plane-strain and biaxial stretching regions.

Abstract: This paper is focused on the performance evaluation of two theoretical models that can be used to predict the Forming Limit Curve (FLC) for an AA6016-T4 aluminium alloy sheet. The FLC is calculated based on the Marciniak-Kuczynski (M-K) model and the Modified Maximum Force Criterion (MMFC) using the Hill '48, Barlat '89 and BBC 2005 yield criteria, the latter identified in three variants, namely with 6, 7, and 8 material parameters. The performance assessment of the M-K and MMFC models combined with different yield functions is based on the comparison between the theoretical predictions and the experimental data provided by the Nakazima test (ISO 12004: 2008) as well as by an experimental procedure recently developed by the authors for the FLC determination.