• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.248-258
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• 1992

Three-dimensional rigid-plastic finite element formulation based on the membrane theory was described and a computer program for large deformation analysis was developed. In the formulation, normal and planar anisotropy of sheet material and rotation of the principal axes of anisotropy was taken into consideration. Sheet metal was assumed to be rigid-plastic material obeying Hill's quadratic yield criterion and its associated flow rule. Deep drawing process, as a preliminary test, for normal anisotropic material was analyzed in order to examine the validity of developed finite element program. The results were consistent with the existing finite element solutions or experimental data. The present study was mainly concerned with the influence of planar anisotropy on deformation behaviour. Finite element analysis and experiment were carried out for the whole process of deep drawing of planar anisotropic material. The computational and experimental results on the shape of ear, strain distribution and punch load were in good agreement.

• 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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.05a
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• pp.199-202
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• 2006

The hardening and anisotropy based on the crystal plasticity is considered in the numerical simulation of hemispherical sheet forming process to find more realistic simulation results For calculating the yield shear stresses of each crystal, Taylor's model of the crystalline aggregate is employed. The yield stress of crystalline aggregate is computed by averaging the yield stresses of the crystal. The hardening is evaluated by using the Taylor factor and the critical resolved shear stress of the crystal. In addition, by observing the crystallographic texture and slip system, the anisotropy of the sheet is traced during the forming process. The anisotropy and hardening behaviors of the sheet found by the crystal plasticity are described better than those of obtained from the Hill's quadratic criterion based on the continuum plasticity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.8
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• pp.889-897
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• 2011

In this work, we investigated the theoretical forming limit models for Zircaloy-4 and Zirlo used for spacer grid of nuclear fuel rods. Tensile and anisotropy tests were performed to obtain stress-strain curves and anisotropic coefficients. The experimental forming limit diagrams (FLD) for two materials were obtained by dome stretching tests following NUMISHEET 96. Theoretical FLD depends on FL models and yield criteria. To obtain the right hand side (RHS) of FLD, we applied the FL models (Swift's diffuse necking, M-K theory, S-R vertex theory) to Zircaloy-4 and Zirlo sheets. Hill's local necking theory was adopted for the left hand side (LHS) of FLD. To consider the anisotropy of sheets, the yield criteria of Hill and Hosford were applied. Comparing the predicted curves with the experimental data, we found that the RHS of FLD for Zircaloy-4 can be described by the Swift model (with the Hill's criterion), while the LHS of the FLD can be explained by Hill model. The FLD for Zirlo can be explained by the S-R model and the Hosford's criterion (a = 8).

• Transactions of Materials Processing
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• v.6 no.4
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• pp.279-290
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• 1997

The sectional forming analysis of stamping pocesses for aluminum alloy sheet metals was investigated. For the modeling of the anomalous behavior of aluminum alloy sheet. the Barlat's strain rate potential and Hill's 1990 non-quadratic yield theory with an isotropic hardening rule were employed. The rigid-viscoplastic FEM formulation which solves equilibrium equation for plane-strain stage with mesh-normal geometric constraints was derived. A new method to determine the Barlat's anisotropic coefficients was also suggested. To verify the validity of the formulation, the stretch and draw forming processes of a square cup were simulated.

• Journal of the Korean Society of Safety
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• v.12 no.3
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• pp.52-59
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• 1997

Hill's anisotropy theory and isotropy theory under the deformed profile assumed two separate cases(that is circular and ellipitical) are applied to predict the plastic deformation characteristics of bulge, the strain and polar height under instability condition, using thin square diaphragms of stainless steel, mild steel, brass, copper and aluminum. In this study it was found that the pressure-polar height curves, and the polar height-the polar radius of curvature curve, under anisotropy theory and isotropy theory, assuming a circle profile, agree well with the experimental results, and the equivalent strains of the instability condition under anisotropy theory are better good agreement with the experimental results than those of the instability condition under isotropy theory. Beside, FLCo(plane Strain Intercept) obtained by Bethlehem FLC method and standard FLC method (modified) agree well with the experimental result.

• Transactions of Materials Processing
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• v.9 no.6
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• pp.590-597
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• 2000

A finite element formulation lot the simulation of axisymmetric sheet hydroforming is proposed, and an implicit program is coded. In order to describe normal anisotropy of steel sheet, Hill's non-quadratic yield function (Hill, 1979) is employed. Frictional contacts among sheet surface, rigid tool surface, and flexible hydrostatic pressure are considered using mesh normal vectors based on finite element of the sheet. Applied hydraulic pressure is also considered as a function of forming rate and time and treated as an external loading. The complete set of the governing relations comprising equilibrium and interfacial equations is approximately linearized for Newton-Raphson algorithm. In order to verify the validity of the developed finite element formulation, the axisymmetric bulge test is simulated. Simulation results are compared with other FEM results and experimental measurements and showed good agreements. In axisymmetric hydroforming processes of a disk cover, formability changes are observed according to the hydraulic pressure curve changes.

• 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.

• Transactions of Materials Processing
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• v.20 no.8
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• pp.595-600
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• 2011

This paper investigates the effect of strain rate on the anisotropic deformation behavior of advanced high strength steel sheets. Uniaxial tensile tests were carried out on TRIP590 and DP780 steel sheets at strain rates ranging from 0.001/sec to 100/sec to determine yield stresses and r-values at various loading angles from the reference rolling direction. R-values were determined by the digital image correlation technique. Hill48 and Yld2000-2d yield functions were tested for their capability to describe the plastic deformation anisotropy of the materials. Initial yield loci were constructed using the Yld2000-2d yield function, which adequately described the anisotropic behavior of the materials. The shape of the initial yield loci was found to change with different strain rate, and the anisotropic behavior decreased with increasing strain rate.

• 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.