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박판 인장 시험에서 가공열의 영향에 관한 유한요소 해석
김용환,Wagoner, R.H. 대한기계학회 1989 대한기계학회논문집 Vol.13 No.4
본 연구의 목적은 2차원 유한요소법을 이용하여 변형과 열전달의 복합된 열소성 문제를 해석하여 재료의 성형성에 대한 가공열의 영향을 연구하는 것이다. 2차원 해석은 종래 단순 인장시험의 해석에 사용되던 1차원 해석에 비해 보다 정확한 해를 가지며 특히 넥킹의 발생 이후의 해석에 유용하다. A numerical method for analyzing non-isothermal plastic deformation of sheet metals has been developed and sheet tensile tests have been analyzed using a two-dimensional finite element formulation. A modified Bishop`s method is used to solve the thermoplasticity problem in decoupled form at each time step. The accuracy of the analysis is confirmed by comparison with experimental data. The uniform elongation is found is drop by 0.1 to 2.7% at moderate strain rates, while total elongation decreases upto 6.0% during tensile testing in air compared to the isothermal case. The effect of deformation heating, becomes more pronounced as necking develops and at higher testing speed.
김용환,Wagoner, R. H. 대한기계학회 1990 대한기계학회논문집 Vol.14 No.5
본 연구에서는 박판의 프레스 성형에 관련된 열소성 문제를 해석할 수 있는 효과적이고, 신뢰도가 높은 수치적 방법을 개발하는 것이다. 박판 성형에서 변형과 열전달이 결합된 문제의 해석을 위하여 3차원 유한 요소 해석을 행하고 그를 이용하여 박판의 스트레치 성형 공정을 해석하였다. 해석 결과를 기존의 실험 결과와 비교하 여 본 해석의 타당성을 보이고, 재료 거동에 영향을 미치는 여러가지 공정 변수의 영 향을 검토하였다. A numerical method for analyzing non-isothermal, rigid-viscoplastic deformation problems has been presented. As an application, a stretch forming of sheet metals, including temperature effect, has been analyzed by a three-dimensional finite element method. Bishop`s step-wise decoupled method is adopted to solve thermomechanical coupling between deformation and heat transfer. Using the method, the effect of temperature on strain distribution during stretch forming is investigated. By comparison of the non-isothermal results with isothermal analysis, the importance of including temperature effects in the analysis of metal forming problems is emphasized. The predicted results were in good agreement with the existing experimental measurements at the different punch temperatures and dome heights investigated. It is also found that any increase of the punch temperature appeared to postpone the strain localization process by lowering the peak strain in the critical punch-sheet contact region and by normalizing strain distribution within the specimen.
Invariance of Plastic Strains with Respect to Imposed Rate at Boundary
Chung, Kwansoo,Wagoner, Robert H 대한금속재료학회(대한금속학회) 1998 METALS AND MATERIALS International Vol.4 No.1
The concept of material $quot;formability$quot; is often related to imposed boundary velocity in the literature and in discussions of practical forming operations. While material strain-rate sensitivity is frequently cited, without proof, as the source of this dependence, other factors may contribute, including contact and friction conditions, temperature changes, and inertial forces in the workpiece and tooling, all of which may depend on boundary velocity. The authors showed in 1986 that strain localization in a tensile test (and other operations not involving friction and contact) was theoretically independent of boundary velocity (and material strength) for certain rate-sensitive constitutive equations, contrary to the common perception [1]. In the present paper, we generalize the principle of invariance to operations involving contact and friction and state the conditions under which the invariance is valid. These conditions are closely met for many forming operations. This expands the usefulness of the idea, which can therefore help interpretation of the role of imposed boundary velocity (and material strength) in altering material formability. The generalized principle is presented and proven using a variational formulation for rigid plasticity and the principle is discussed with respect to several analyses of common forming operations.