• 대한기계학회논문집
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• 제16권2호
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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.

• 소성∙가공
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• 제25권2호
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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.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2006년도 춘계학술대회 논문집
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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.

• 대한기계학회논문집A
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• 제35권8호
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• pp.889-897
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• 2011

본 연구에서는 핵연료 지지격자체의 재료인 Zircaloy-4 와 Zirlo 판재의 이론적 성형한계 예측모델을 제시했다. 먼저 인장시험 및 이방성시험으로 응력-변형률곡선과 이방성계수를 획득했으며, NUMISHEET 96을 따르는 돔장출시험으로 두 재료의 실험적 성형한계도들을 얻었다. 이론적 성형한계도는 성형한계모델과 항복조건의 영향을 받는다. Swift 확산네킹이론, Marciniak-Kuczynski 의 재료결함 모델, Storen-Rice 의 정점이론을 이용해 부변형률이 양인 구간에서의 성형한계 곡선을 구했으며, 부변형률이 음인 구간에는 Hill 의 국부네킹 이론을 적용했다. 또한 재료이방성을 고려하기 위해 Hill 48, Hosford 79 항복조건을 사용 했다. Swift 확산네킹모델 (Hill 48 항복조건 적용)과 Hill 모델은 각각 변형률비가 양과 음인 영역에 대해 Zircaloy-4의 성형한계도를 비교적 정확히 예측하며, Zirlo의 성형한계도는 Hosford 79 항복조건 (a = 8)을 적용한 Storen-Rice 모델로 나타낼 수 있다.

• 소성∙가공
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• 제6권4호
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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.

• 한국안전학회지
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• 제12권3호
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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.

• 소성∙가공
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• 제9권6호
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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.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1997년도 춘계학술대회논문집
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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.

• 소성∙가공
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• 제20권8호
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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.

• 대한기계학회논문집
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• 제8권5호
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• pp.435-441
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• 1984

본 연구에서는 반경 방항으로 균일하게 잡아당기는 문제에 대하여 등방성, 직 교 이방경, 평면 이방성의 해를 비교하고, 성형성에 중요한 의미를 갖는 두께방항 변 형도와 원주방항 응력의 분포에 대하여 해석한다. 또 냉간 압연된 철판을 사용하여 평저 펀치(flat punch)에 의한 스트레칭(stretching) 실험을 하고, 실험과 같은 경계 조건으로 시뮬레이션(simulation)하여 결과를 비교한다.