Path independent limiting criteria in sheet metal forming

Paul, Surajit Kumar

doi:10.1016/j.jmapro.2015.06.025

Cited by 33 publications

(15 citation statements)

References 43 publications

(58 reference statements)

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“…It is desirable to note that the hardening curves described in Equations (5) and (6) are consistent with experimental ones only at a certain strain stage, and with large strains, the flow curve reaches saturation [38]. Thus, necking and fracture were judged by a forming limit curve [39]. Concerning the yield locus, both anisotropic criteria came from directionally measured plastic strain ratios, while Hill 48 is well adapted for strongly anisotropic materials (r > 1) and Hill 90 is used for materials with planar anisotropy (r < 1) [40].…”

Section: Discussionmentioning

confidence: 56%

“…However, constant strain paths are required during deep drawing, and their linearity was confirmed using software. This is also supported by the fact that the strain pathways in the first drawing of axisymmetric and uniform sectioned parts are satisfactorily linear, and the FLD for the as-received condition can be used comfortably when making formability assessments [39].…”

Section: Discussionmentioning

confidence: 83%

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Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination

Tomáš

Evin

Kepič

et al. 2019

Metals

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Similitude theory helps engineers and scientists to accurately predict the behaviors of real systems through the application of scaling laws to the experimental results of a scale model related to the real system by similarity conditions. The theory was applied when studying the deep drawing process of a bathtub made from cold rolled low carbon aluminum-killed steel from the point of view of material limits. The bathtub model was created on the basis of geometric, physical, and mechanical similarity on a scale of 1:5. Thus, simulations and physical models were created. The simulation model was used to verify the combination yield locus/hardening law on the basis of comparing the thickness change. As a result, Hill 48/Krupkowski showed the minimal deviation by comparing data evaluated from numerical simulations and that measured on the physical model. Additionally, material anisotropy was modelled when virtual materials were defined from experimentally measured values of the plastic strain ratio. As an outcome, extra deep drawing quality steel with an average plastic strain ratio of rm ≥ 1.47 and an average strain hardening exponent of nm ≥ 0.23 must be used for the deep drawing of the bathtub.

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Section: Discussionmentioning

confidence: 56%

Section: Discussionmentioning

confidence: 83%

Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination

Tomáš

Evin

Kepič

et al. 2019

Metals

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“…If α and β are defined as the stress ratio and strain ratio, respectively, the relationship between α and β can be expressed as Equation (7) [ 15 ]:

…”

Section: Tfd With Anisotropymentioning

confidence: 99%

“…Therefore, when the path-independent strain/stress-based forming limit criterion is calculated to avoid the strain path dependence of the FLD, inherent calculation errors can arise owing to the selection of the yield criterion and hardening law. Paul [ 15 ] showed that these calculation errors in the strain-based forming limit criterion are caused by the yield criterion, whereas in the stress-based criterion, they are caused by the hardening law as well as the yield criterion. When various forming limit criteria are converted based on the experimental FLD, the effect of material anisotropy is almost excluded.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy

Kim

Hong

2020

Materials

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In this study, the experimental two-dimensional forming limit diagram (FLD) data for a ZIRLO™ sheet, which is used in nuclear fuel rod support grids, were converted and presented as a triaxiality failure diagram (TFD). Most previous studies assumed ZIRLO™ to be isotropic when calculating the effective stress and strain. However, for highly anisotropic materials, the anisotropy should be considered for calculations of effective stress and strain; hence, in this study, they were calculated by introducing the normal anisotropy coefficient. To obtain this parameter of the ZIRLO™ specimens, tensile tests were performed on specimens with 0°, 45°, and 90° angles with respect to the rolling direction. It was observed that the average normal anisotropy coefficient measured during the tests was 4.94, which is very high. The von Mises isotropic and Hill 48 anisotropic yield criterion were applied to the FLD data that were experimentally determined using a limit dome height test and were converted into effective stress and effective strain. When the FLD is converted to TFD, the curve will increase in the top-right direction if the r-value is greater than 1, and this become more severe as the r-value increases. The TFD, which was converted considering the anisotropy, is almost the same to the TFD obtained using the digital image correlation method in the tensile tests of four specimens with different stress states. If anisotropy is not considered, then the formability is normally underestimated. However, a highly accurate TFD can be obtained with the method proposed in this study.

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“…FLSD is a failure criterion plotted with principal stress. It is always a unique curve under complex loading paths, which makes up for the limitation of strain paths in FLD and is more practical than FLD [10,11,12,13]. However, it is very difficult to measure the stress on the deformed sheet by experiment.…”

Section: Introductionmentioning

confidence: 99%

Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model

et al. 2019

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In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.

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Path independent limiting criteria in sheet metal forming

Cited by 33 publications

References 43 publications

Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination

Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy

Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model

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