• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.7
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• pp.1107-1118
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• 2001

The forming limit diagram introduced by Keeler and Goodwin has been used generally to analyze the formability of sheet metal. However, path dependent forming limit curves based on the state of strain can be explained only by a single criterion which is based on the state. In this study, experimental forming limits in strain space of some metal sheets are transformed into forming limit curves in stress space. Effects of yield criterion are investigated in transforming the forming limit curves. Some important design aspects which are based on the close prediction of movements in forming limit curves during sheet forming are concluded.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.10a
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• pp.156-159
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• 2004

Most formulations for a forming limit diagram (FLD) have been based on yield stress potentials defined in the stress field. Nevertheless, there are formulations where potentials defined in the stain-rate field are especially convenient to formulate the rigid plastic material. Based on a strain-rate potential proposed for materials exhibiting planar anisotropic, the formulations for the forming limit diagram has been developed applying M-K theory. As verification example, the formulation is applied for anisotropic AA5182-O sheet. The good verification results show that the formulation for the forming limit diagram has been successfully developed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.8
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• pp.833-838
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• 2007

In tube hydroforming process, several defective products could be obtained such as bursting, wrinkling, folding, buckling. Because, especially, bursting is most frequently occurred failure among the well known failures, it is mostly important to predict the onset of bursting failure on tube hydroforming process. For most sheet metal forming processes, strain based forming limit diagram(FLD) is used often as a criteria to estimate the possibility of onset of the failures proposed above. However, FLD has a shortcoming that it is dependent on strain path while stress based diagram is independent on strain history. Generally, tube hydroforming consists of three main processes such as pre-bending, pre-forming, and hydroforming and it means that the strain histories of final products are nonlinear. Therefore, forming limit stress diagram(FLSD) is more suitable to predict forming limit for hydroforming parts. In this study, FLSD is applied to estimate bursting failure for an engine cradle of an automobile part. Consequently, it is proved that application of FLSD to predict forming limit is available for tube hydroforming parts.

• Transactions of Materials Processing
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• v.14 no.6 s.78
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• pp.527-532
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• 2005

Among the failure modes which can occur in tube hydroforming such as wrinkling, bursting or buckling, the bursting by local instability under excessive tensile stresses is irrecoverable phenomenon. Thus, the accurate prediction of bursting condition plays an important role in producing the successfully hydroformed part without any defects. As the classical forming limit criteria, strain-based forming limit diagram (FLD) has widely used to predict the failure in sheet metal forming. However, it is known that the FLD is extremely dependant on strain path throughout the forming process. Furthermore, The application of FLD to hydroforming process, where strain path is no longer linear throughout forming process, may lead to misunderstanding for fracture initiation. In this work, stress-based forming limit diagram (FLSD), which is strain path-independent and more general, was applied to prediction of forming limit in tube hydroforming. Combined with the analytical FLSD determined from plastic instability theory, finite element analyses were carried out to find out the state of stresses during hydroforming operation, and then FLSD is utilized as forming limit criterion. In addition, the approach is verified by a series of bulge tests in view of bursting pressure and shows a good agreement. Consequently, it is shown that the approach proposed in this paper will provide a feasible method to satisfy the increasing practical demands for judging the forming severity in hydroforming processes.

• Transactions of Materials Processing
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• v.23 no.4
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• pp.199-205
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• 2014

The current study examines the effect of the analytical parameter values on the theoretical forming limit diagram (FLD) based on the Marciniak-Kuczynski model (M-K model). Tensile tests were performed to obtain stress-strain curves and determine the anisotropic properties in the rolling, transverse and diagonal direction of SPCC sheet materials. The experimental forming limit curve for SPCC sheet material was obtained by limiting dome stretching tests. To predict the theoretical FLD based on the M-K model, the Hosford 79 yield function was employed. The effects of three analytical parameters - the exponent of the yield function, the initial imperfection parameter and the fracture criterion parameter - on the M-K model, were examined and the results of the theoretical FLD were compared to the experimentally measured FLD. It was found that the various analytical parameters should be carefully considered to reasonably predict the theoretical FLD. The comparison of the acceptable forming limit area between the theoretical and experimental FLD is used to compare the two diagrams.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.05a
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• pp.92-96
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• 2005

Among the failure modes which can be occurred in tube hydroforming such as wrinkling, bursting or buckling, the bursting by local instability under excessive tensile stresses is irrecoverable phenomenon. Thus, the accurate prediction of bursting condition plays an important role in producing the successfully hydroformed part without any defects. As the classical forming limit criteria, strain-based forming limit diagram has widely used to predict the failure in sheet metal forming. However, it is known that the FLD is extremely dependant on strain path throughout the forming process. Furthermore, the path-dependent limitation of FLD makes the application to hydroforming process, where strain path is no longer linear throughout forming process, more careful. In this work, stress-based forming limit diagram (FLSD), which is strain path-independent and more general, was applied to prediction of forming limit in tube hydroforming. Combined with the analytical FLSD determined from plastic instability theory, finite element analyses were carried out to find out Ihe state of stresses during hydroforming operation, and then FLSD is utilized as forming limit criterion. In addition, the approach is verified with a series of bulge tests in view of bursting pressure and shows a good agreement. Consequently, it is shown that the approach proposed in this paper will provide a feasible method to satisfy the increasing practical demands for judging the farming severity in hydroforming processes.

• Transactions of Materials Processing
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• v.27 no.2
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• pp.115-122
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• 2018

Most domestic and international standards on the forming limit diagram (FLD) including ISO 12004-2, use a 'position-dependent method,' which determines the forming limit from a strain distribution measured on the specimen after necking or fracture. However, the position-dependent method has inherent problems such as the incidence of asymmetry of a strain distribution, the estimation of missing data near fracture, the termination time of test, and the deformation due to the new stress equilibrium after a fracture, which is blamed for causing sometimes a significant lab-to-lab variation. The 'time-dependent method,' which is anticipated to be a new international standard for evaluating the forming limit, is expected to greatly improve these intrinsic disadvantages of the position-dependent method. It is because the time-dependent method makes it possible to identify and accurately determine the forming limit, just before the necking point from the strain data as continuously measured in a short time interval. In this study, we propose a new time-dependent method based on a Gaussian fitting of strain acceleration with the introduction of 'normalized correlation coefficient.' It has been shown in this study that this method can determine the forming limit very stably and gives a higher value, which is in comparison with the results of the previously studied position-dependent and time-dependent methods.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.10a
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• pp.285-288
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• 2009

The purpose of this study is to predict the forming limit diagram (FLD) of strain-rate sensitive materials on the basis of the Marciniak and Kuczynski (M-K) theory. The strain-rate effect is taken into consideration in such a way that the stress-strain curves for various strain-rates are inputted into the formulation as point data, not as curve-fitted models such as power function. Tensile tests and R-value tests were carried out at several levels of temperature and strain-rate from $25^{\circ}C$ to $300^{\circ}C$ and 0.16 to 0.00016/s, respectively to obtain the mechanical properties of AZ31B magnesium alloy sheet. The FLD of this material was experimentally obtained by limit dome height tests with the punch velocity of 0.1 and 1.0 mm/s at $250^{\circ}C$. The M-K theory-based FLD predicted using Yld2000-2d yield criterion was compared with the experimental results.

• Transactions of Materials Processing
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• v.24 no.5
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• pp.348-353
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• 2015

The PEPS(Polar-coordinated Effective Plastic Strain) FLD(Forming Limit Diagram), a new type of FLD based on a polar representation of the EPS(Effective Plastic Strain), appears to be an effective solution to the problem of non-linear strain path effects. This method has the advantages of the familiar strain-based diagram for linear loading, but without the strain-hardening limitations of the stress-based diagram, or non-intuitive aspects of alternate Cartesian diagrams based on effective plastic strain. In the current study, the PEPS FLD was applied to the development process of an aluminum automobile-body panel, including the necking or crack prediction, die design, and die modification. As a result, the PEPS FLD provided improved formability of aluminum sheet as compared to deriving the potential formability with non-linearity.

• Transactions of Materials Processing
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• v.20 no.2
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• pp.146-153
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• 2011

This study aimed at providing an experimental database for the mechanical properties of AZ31B magnesium alloy sheet such as stress-strain curve, yield stress, R-value and forming limit diagram(FLD) at various strain-rates and temperatures. Tensile tests were carried out on specimens having the orientations of $0^{\circ}$, $45^{\circ}$ and $90^{\circ}$ to the rolling direction with different crosshead speeds in the range between 0.008 and 8 mm/s at temperature from 25(room temperature) to $300^{\circ}C$. The influence of the specimen gage length on the tensile properties was investigated. FLD tests were performed at punch speed of 0.1 and 1.0 mm/s in the same temperature range as that of the tensile tests. Swift cup tests were conducted to verify the usefulness of the material database and the reliability of the finite element analysis(FEA). The effects of strain-rate as well as temperature were taken into account in these simulations. It was shown that the FLD-based failure was reasonably well predicted by the thermal-deformation coupled analysis for this rate-sensitive material.