Determination Of Forming Limit Diagrams Research Articles

Experimental Investigation on Forming Limit Diagram of Mild Carbon Steel Sheet

The sheet metal forming process is the process of deforming the sheet metal into a desired shape without fracture or excessive localized necking. Variables in sheet metal forming process can be discussed together with formability and test methods. There are many defects occurring during sheet metal forming processes, such as cracking, wrinkling, local necking, buckling etc. The strain measurement in a deformed sheet metal is necessary for measurement comparison. As the thickness of sheet metal is very small as compare to other dimensions of the sheet metal, the sheet metal operation is usually considered as a plane stress problem. The Forming Limit Diagram (FLD) was also determined from surface strain measurement. The FLD is the graph between major strain (℮1) and minor strain (℮2). The Forming Limit Curve (FLC) or the Forming Limit Diagram (FLD) is useful concept for characterizing the formability of sheet metal, which reflects the maximum principal strains that can be sustained by sheet materials prior to the onset of localized necking. Generally there are three methods to establish FLD i.e. theoretical, numerical and experimental. In this paper experimental method is used to develop FLD. For experimental determination of FLD of Mild Carbon steel sheet Limit Dome Height testing is used according to the American Society of Testing Material (ASTM) as published in ASTM E 2218-02. In this paper the procedure of grid marking, punch stretching and strain measurement is used. For punch stretching operation the set up of spherical die and punch has developed on the hydraulic Universal Testing Machine (UTM). The material used for the die and punch is High Carbon High Chromium Steel (HCHCr). For printing the grids on sheet material chemical etching method is used. In this grid making process grids of 5 mm diameter circles printed. For trial experiment the sheet metal sample is stretched at the force of 23 KN. The deformed circles were converted into ellipse and from that deformed ellipse major and minor strains are to be calculated. After that the FLD will give the two different regions of safe and failure zone.

Predicting FLDs Using a Multiscale Modeling Scheme

The measurement of a single forming limit diagram (FLD) requires significant resources and is time consuming. We have developed a multiscale modeling scheme to predict FLDs using a combination of limited laboratory testing, crystal plasticity (VPSC) modeling, and dual sequential-stage finite element (ABAQUS/Explicit) modeling with the Marciniak-Kuczynski (M-K) criterion to determine the limit strain. We have established a means to work around existing limitations in ABAQUS/Explicit by using an anisotropic yield locus (e.g., BBC2008) in combination with the M-K criterion. We further apply a VPSC model to reduce the number of laboratory tests required to characterize the anisotropic yield locus. In the present work, we show that the predicted FLD is in excellent agreement with the measured FLD for AA5182 in the O temper. Instead of 13 different tests as for a traditional FLD determination within Novelis, our technique uses just four measurements: tensile properties in three orientations; plane strain tension; biaxial bulge; and the sheet crystallographic texture. The turnaround time is consequently far less than for the traditional laboratory measurement of the FLD.

An evolving non-associated Hill48 plasticity model accounting for anisotropic hardening and r-value evolution and its application to forming limit prediction

Experimental and numerical investigations on the characterisation and prediction of cold formability of a ferritic steel sheet were performed in this study. Tensile tests and Nakajima tests were conducted for the plasticity characterisation and the forming limit diagram determination, respectively. For the plasticity behaviour description, an evolving non-associated Hill48 anisotropic plasticity model was formulated to accurately characterise the anisotropy evolution under monotonic loading, including anisotropic hardening as well as the r-value evolution. The detailed model parameter calibration procedure was also demonstrated. Eventually the model was applied to the forming limits prediction in conjunction with the modified maximum force criterion. A systematic and detailed study was performed addressing the impacts of the evolving and non-associated characteristics of the model formulation on the forming limits prediction by comparing the proposed model with the classical ones. Both the plasticity model and its application to the formability prediction were validated by the experimental results.

Cold formability prediction by the modified maximum force criterion with a non-associated Hill48 model accounting for anisotropic hardening

Experimental and numerical investigations on the characterisation and prediction of cold formability of a ferritic steel sheet are performed in this study. Tensile tests and Nakajima tests were performed for the plasticity characterisation and the forming limit diagram determination. In the numerical prediction, the modified maximum force criterion is selected as the localisation criterion. For the plasticity model, a non-associated formulation of the Hill48 model is employed. With the non-associated flow rule, the model can result in a similar predictive capability of stress and r-value directionality to the advanced non-quadratic associated models. To accurately characterise the anisotropy evolution during hardening, the anisotropic hardening is also calibrated and implemented into the model for the prediction of the formability.

Digital speckle based strain measurement system for forming limit diagram prediction

A digital speckle based strain measurement system is developed to investigate the forming limit diagram (FLD) of sheet metal. A stochastic speckle pattern is sprayed on the surface of flat sheet metal before forming. A series of images are recorded by two cameras during the forming process. The strain field is then calculated for FLD determination, which involves the following key issues. First, to solve the problem of large deformation and strain measurement in sheet metal forming, a fractionized matching algorithm using deformation continuity of adjacent images is proposed. Second, an algorithm for three-dimensional (3-D) strain calculation is discussed, and a spline model is specially used to calculate the strain of the sheet metal in deep drawing. Third, a limit strain determination algorithm is proposed for forming limit curve (FLC) calculation by creating sections in the measured strain fields. Finally, a forming limit strain measurement system (also called Xi'an Jiaotong University Forming Limit Curve measurement system, XJTUFLC) is developed on the Visual Studio 2010 platform. With our self-developed image acquisition instrument and sheet metal bulging setup, FLD determination tests are conducted to validate the performance of the system. And the measured FLD is compared with the traditional experimental FLD as well as with that predicted by the empirical model. From the analysis of the experimental results, it can be concluded that the proposed system is feasible to measure the full-field strain during sheet metal forming processes and provides a better solution for forming limit diagram prediction.

A new method for determining limit strains of materials that show post-uniform elongation behavior

In this study, a new method is proposed to determine limit strains at the onset of localized necking for ductile materials that show post-uniform elongations. The new method is first applied for AA 5754-O using the ISO 12004-2 forming limit diagram determination standard. The method is also applied for ductile materials of 7114 steel, 304 stainless steel, and CuZn37 brass and finally for AA 2024-T4 having brittle fracture behavior. The results indicate that the new proposed method is quite successful, easy, and accurate for ductile materials that show post-uniform elongations.

The Effect of the Imposed Boundary Rate on the Formability of Strain Rate Sensitive Sheets Using the M-K Method

In spite of the fact that the experimental results indicate the significant effect of strain rate on forming limits of sheets, this effect is neglected in all theoretical methods of prediction of Forming Limit Diagrams (FLDs). The purpose of this paper is to modify the most renowned theoretical method of determination of FLDs (e.g., M-K model) so as to enable it to take into account the effect of strain rate. To achieve this aim, the traditional assumption of preexistence of an initial geometrical inhomogeneity in the sheet has been replaced with the assumption of a preexisting “material” inhomogeneity. It has been shown that using this assumption, the strain rate would not be omitted from equations; thus, it is possible to demonstrate its effect on FLDs. To validate the results, they are compared with some published experimental data. The good agreement between the theoretical and experimental results shows capabilities of the proposed method in predicting the effect of the imposed rate at the boundary (which is physically the effect of the punch speed difference in sheet forming) on FLDs.

Determination of forming limit diagrams of sheet materials with a hybrid experimental–numerical approach

A new methodology is proposed to obtain the forming limit diagram (FLD) of sheet materials by utilizing routinely obtained experimental punch load versus displacement traces from hemispherical punch stretching experiments and by analyzing strain history of the test samples from finite element simulations of the experiments. The simulations based characteristic points of diffuse and localized necking are utilized to obtain the limit strains. The proposed method for FLD determination considers out-of-plane displacement, punch–sheet contact and friction, and avoids using experimental strain measurement in the vicinity of the neck on the dome specimens and the rather arbitrary inhomogeneity factor to trigger localization such as in the commonly used Marciniak–Kuczynski method. A criterion of maximum in the ‘pseudo’ major strain acceleration for the onset of localized necking, proposed earlier by the present authors, is utilized to determine the limit strain in FE simulations as well as in FLD verification experiments. The proposed overall approach for obtaining FLD is rapid and accurate and could be implemented for routine FLD generation in a laboratory setting with significant reduction in cost, effort and subjectivity.

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.