• 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.

• 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.

• 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.

• Transactions of Materials Processing
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• v.14 no.6 s.78
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• pp.514-519
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• 2005

A tube hydroformability testing system was designed and fabricated enabling to apply the forming condition along arbitrarily pre-programmed internal pressure-axial feed path. The free-bulging and T-forming tests were carried out on the extruded aluminum (A6063) tube specimens with 40.6 mm outer diameter and 2.25 mm thickness. Nine different combinations of internal pressure and axial feed, yielding different strain paths from one another, were taken into consideration in order to induce bursting at various deformation modes. Major and minor strains were automatically measured from deformed grids around the fracture using a stereo-vision-based surface strain measurement system, named ASIAS. The forming limit diagram of the A6063 tube material was successfully obtained. Most of the data points acquired from free bulging and T-forming tests appeared in the range of negative minor strain on the FLD and are mostly located near the strain paths calculated from explicit finite element simulations. The forming limit obtained from tests after pre-tension was considerably lower than that from tests without pre-tension, which showed the strain path-dependency of the forming limit as well known in the sheet forming fold.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.210-216
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• 2001

This paper presents an analytical study that can predict the path-dependent forming limit of anisotropic sheet materials that experience various combinations of strain paths. To predict the forming limit diagrams(FLD), the proposed analytical procedure is performed within the framework of the Marciniak and Kuczynski(M-K) approach by using the Barlat and Lians non-quadratic anisotropic yield criterion and introducing the effect of the existence of a strain gradient over a stretching punch. The predicted path-dependent forming limit of an anisotropic sheet has been compared with the published experimental results. It has been found that the predicted path-dependent forming limits are in good agreement with the experimental data.

• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.1
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• pp.127-130
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• 2010

This paper deals with the formability of DP590 steel considering the strain rate. The strain hardening coefficient, elongation and r-value were obtained from the static and dynamic tensile test. As strain rate increases from static to 100/s, the strain hardening coefficient and the uniform elongation decrease and the elongation at fracture and r-value decrease to 0.1/s and increase again to 100/s. The high speed forming limit tests with hemi-spherical punch were carried out using the high speed crash testing machine and high speed forming jig. The high speed forming limit of DP590(order of $10^2$/s) decreases compared to the static forming limit(order of $10^{-3}$/s) and the forming limit band in high speed forming test is narrower than that in the static forming test. This tendency may be due to the development of brittleness with increase of stain rate.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.386-389
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• 2008

Forming limit diagram is created by graphical illustration indicating major and minor strain. In order to provide the criterion for forming safety, FLC(forming limit curve) need to be fitted to the diagram. However, the standard method for the strain measurement and FLC plotting are not fixed yet, which results in inconvenience in digitalized analysis. In this study, new construction method for FLC was suggested in order to minimize operator dependency. For this purpose, major and minor strain were measured automatically and analyzed. Then, a second order equation is adopted to fit the FLC. Optimized by response surface method was performed to ensure particular characteristics of the FLC.

• Transactions of Materials Processing
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• v.24 no.5
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• pp.361-367
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• 2015

The forming limit diagram (FLD) is the most commonly used tool for evaluating of sheet metal formability in the manufacturing field as well as the finite element analysis (FEA)-based design process. Determination of the forming limits is considerably influenced by testing/measuring machines, techniques and conditions. These influences may cause a large scatter in FLD from laboratory to laboratory. Scatter is especially true when the ‘position-dependent method’, as is specified in most national and international standards, is used. In the current study a new ‘time-dependent method’ is proposed, which is to determine the forming limit strains more accurately and reasonably when producing a FLD from experimental data. This method is based on continual strain measurement during the test. The results are compared to those from the existing standardized methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.935-943
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• 1988

The forming limit diagram is assessed as a means of estimating the forming characteristics of sheet metal and is usually determined experimentally. The strain rates used in the determination are likely to be low. However, often in practice, the strain rates are much higher, so if forming limit diagram is determined at low rates, it may not be appropriate. This paper reconsiders the forming limit diagram for mild steel and aluminum sheet up to variation in strain rate from 10$^{-2}$ sec to 20/sec where its forming has been carried out under oil pressure using a hydraulic bulge test with circular and elliptical dies. To obtain higher strain rate, an impact bulge test had been employed with the same die sets as those used for a hydraulic bulge test. The results obtained are as follows: (1) As the strain rate increases, the fracture pressure increases and the polar height at fracture decreases. (2) Experiment has shown that, in the positive quadrant of the forming limit diagram, the diagram is lowered with increasing strain rate and the effect of strain rate changes according to strain paths and materials..