• Transactions of Materials Processing
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• v.25 no.2
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• pp.91-95
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• 2016

This paper is concerned with modeling of a ductile fracture criterion for sheet metal considering anisotropy to predict the sudden fracture of advanced high strength steel (AHSS) sheets during complicated forming processes. The Lou−Huh ductile fracture criterion is modified using the Hill’s 48 anisotropic plastic potential instead of the von Mises isotropic plastic potential to take account of the influence of anisotropy on the equivalent plastic strain at the onset of fracture. To determine the coefficients of the model proposed, a two dimensional digital image correlation (2D-DIC) method is utilized to measure the strain histories on the surface of three different types of specimens during deformation. For the derivation of an anisotropic ductile fracture model, principal stresses (𝜎₁,𝜎₂, 𝜎₃) are expressed in terms of the stress triaxiality, the Lode parameter, and the equivalent stress (𝜂_𝐻, 𝐿,) based on the Hill’s 48 anisotropic plastic potential. The proposed anisotropic ductile fracture criterion was quantitatively evaluated according to various directions of the maximum principal stress. Fracture forming limit diagrams were also constructed to evaluate the forming limit in sheet metal forming of AHSS sheets over a wide range of loading conditions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.5
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• pp.435-441
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• 1984

The matrix method, as an effective FEM formulation for the analysis of rigid-plastic deformation, was applied to the bore expanding of anisotropic sheet metal. The effect of planar anisotropy on sheet metal deformation was studied for bore expanding process under the uniform radial stretching condition, and the results were compared with isotropic and normal anisotropic solutions. Experiments were carried out using a flat punch for cold-rolled sheet metal. The experimental results were compared with computations from the matrix method with the boundary conditions corresponding to actual experiment. Both in theory and experiment, it is found that the maximum thinning which results in necking occurs in the direction of the minimum R-value. The results also suggest that the matrix method is efficient for analyzing planar anisotropic sheet metal. The comparison between theory and experiment suggests that Hill's theory of planar anisotropy is somewhat exaggerated. However, the theoretical predictions are in qualitative agreement with the experimental results.

• Transactions of Materials Processing
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• v.10 no.2
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• pp.160-166
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• 2001

Uniaxial necking is studied for steel sheets with initial anisotropy. The state of anisotropy is continuously altered by subsequent tensile deformation at angles to the rolling direction. The orientations of orthotropy axes are changed before the onset of necking. A simple hardening rule which incorporates the rotations of orthtropy axes is proposed and the necking strains are predicted at angles to the rolling direction. Predicted results show good agreement with the experiments.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.24-27
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• 1997

In the present work, rigid-plastic continuum elements employing the shape change and anisotropic effects are derived for the purpose of applying more realistic blankholding force condition in three-dimensional finite element analysis of sheet metal forming process. In order to incorporate the effect of shape change effectively in the derivation of finite element equation using continuum element for sheet metal forming, the convected coordinate system is introduced, rendering the analysis more rigorous and accurate. The formulation is extended to cover the orthotropic material using Hill's quadratic yield function. For the purpose of applying more realistic blankholding force condition, distributed normal and associated frictional tangent forces are employed in the blankholder, which is pressed normal and associated frictional tangent forces are employed in the blankholder, which is pressed against the flange until the resultant contact force with the blank reaches the prescribed value. As an example of sheet metal forming process coupling the effect of planar anisotropy and that of blankholding boundary condition, circular cup deep drawing has been analyzed considering both effects together.

• Transactions of Materials Processing
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• v.8 no.3
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• pp.252-261
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• 1999

The 3-dimensional finite element program is developed to analyze the non-isothermal forming processes of aluminum-alloy sheet metals. Bishop's method is introduced to solve the heat balance and force equilibrium equations. Also, Barlat's non-quadratic anisotropic yield function depicts the planar anisotropy of the aluminum-alloy sheet. To find an appropriate constitutive equation, four different forms are reviewed. For the verification of the reliability of the developed program, the computational try-outs of the non-isothermal cylindrical cupping processes of AL5052-H32 and Al1050-H16 are carried out. As results, the constitutive equation relating to strain and strain-rate, in which the constants are represented by the 5th-degree polynomials of temperature, is in good agreement with measurement. The computational try-outs can predict optimal forming conditions in non-isothermal forming processes.

• Transactions of Materials Processing
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• v.22 no.3
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• pp.133-142
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• 2013

Recently, electric vehicles and hybrid cars are being promoted as alternatives to reduce automobile emissions. Generally, thin sheet materials such as aluminum alloy AA300X and cold-rolled steel sheet such as JIS-G-3141 are used for the container for the lithium-ion secondary batteries. In this study, a multi-stage deep drawing process is used to produce a rectangular cup from thin stainless steel sheet material, SUS409L, with an initial blank thickness of 0.4mm for the battery container application. Numerical simulations of the first through the fifth stages for the multi-stage deep drawing with thin SUS409L sheet were conducted using LS-Dyna3D Implicit/Explicit. Special consideration was given to the deformation characteristics due to the normal anisotropy of the sheet material. The numerical simulations were conducted with both isotropic properties and the anisotropic properties of the initial blank material. An unexpected forming failure, barreling in the bottom region of the deep drawn rectangular cup, was observed. This failure mode can be avoided by additional ironing thickness control during the process.

• Journal of Astronomy and Space Sciences
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• v.28 no.2
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• pp.117-122
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• 2011

In this paper, the anisotropic nature of the magnetic turbulence associated with magnetic dipolarizations in the Earth's plasma sheet is examined. Specifically, we determine the power spectral indices for the perpendicular and parallel components of the fluctuating magnetic field with respect to the background magnetic field, and compare them in order to identify possible anisotropic features. For this study, we identify a total of 47 dipolarization events in February 2008 using the magnetic field data observed by the THEMIS A, D and E satellites when they are situated near the neutral sheet in the near-Earth tail. For the identified events, we estimate the spectral indices for the frequency range from 1.3 mHz to 42 mHz. The results show that the degree of anisotropy, as defined by the ratio of the spectral index of the perpendicular components to that of the parallel component, can range from ~0.2 to ~2.6, and there are more events associated with the ratio greater than unity (i.e., the perpendicular index being greater than the parallel index) than those which are anisotropic in the opposite sense. This implies that the dipolarization-associated turbulence of the magnetic field is often anisotropic, to some non-negligible degree. We then discuss how this result differs from what the theory of homogeneous, anisotropic, magnetohydrodynamic turbulence would predict.

• Journal of Ocean Engineering and Technology
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• v.13 no.3 s.33
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• pp.21-28
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• 1999

In this paper, a finite element method for the determination of initial blank shape in sheet metal forming process will be introduced. The initial blank shape is determined by the only one step from the final to the initial blank. The used finite element inverse method adopted Henky's deformation theory, Hill's anisotropic yield criterion and simplified boundary conditions. Based on this theory. a three-dimensional membrane finite element code was developed. The developed code will be applied to several sheet metal forming examples for the demonstration of its validity.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.03a
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• pp.183-187
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• 1997

A membrane element is regarded as more preferable rather than other elements in the sense of its computing efficiency and the merit with respect to contact treatment. However, it cannot consider the bending effect during the deformation. Moreover, due to the characteristics of rolling process, sheet metal has anisotropy with respect to the direction in the plane. To take the bending effect into account, a modified membrane element was introduced and improved to consider planar anisotropic characteristics with the aid of Hill's quadratic criterion.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.21-27
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• 1998

An analysis for the prediction of wrinkling formation in curved sheets during metal froming is presented. We construct "Wrinkling Limit diagram"(WLD) which represent the combinations of the critical principal stresses for wrinkling formation in curved sheet elements subjected to biaxial plane stress. Here the scheme of plastic bifurcation theory for thin shells based on the Donnell-Mushtari-Vlasov shell theory is used. In this study, the effects of the material variables (yield stress, plastic hardening coefficient, plastic anisotropic parameter, and so on) and sheet geometry on the critical conditions for wrinkling is carried out numerically.merically.