대한기계학회논문집A (Transactions of the Korean Society of Mechanical Engineers A)

  • 제35권9호
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  • Pages.1041-1050
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  • 2011
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  • 1226-4873(pISSN)
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  • 2288-5226(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
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변형률 구배 소성 저차 유한요소에 의한 크기 의존 구조 문제의 모델링 및 해석

Modeling and Analysis of Size-Dependent Structural Problems by Using Low-Order Finite Elements with Strain Gradient Plasticity

  • 박문식 (한남대학교 기계공학과) ;
  • 서영성 (한남대학교 기계공학과) ;
  • 송승 (한남대학교 기계공학과)
  • 투고 : 2011.05.03
  • 심사 : 2011.07.18
  • 발행 : 2011.09.01
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초록

미크론 단위의 크기를 갖는 구조물의 소성변형에서 나타나는 길이 효과를 고려하여 유한요소 해석을 하기 위하여 변형률 구배 소성이론을 이용하는 탄소성 유한요소 모델링 및 해석법을 제안하였다. 기존의 연구에서 주로 고차, 고자유도 및 혼합요소, 초 요소 등을 필요로 하였던 것에 비하여 본 논문에서는 이들을 배제하는 변위법 저차 평면 요소 및 삼차원 요소를 도입하였다. 이는 비선형 증분 해석의 프레임워크에서 계산된 소성 변형률의 절점 평균값으로 보간하여 적분점에서의 변형률 구배를 구하고 테일러 전위 모델에 의한 변형률 경화 구성방정식을 적용하므로서 가능하였다. 제안된 방법론은 선형 삼각 및 사각요소, 선형 사면체, 육면체 요소에 대해 적용되었으며 마이크로 굽힘, 마이크로 비틀림, 마이크로 기공과 같은 대표적인 길이 스케일 문제를 통하여 수치적으로 검증하였다. 본 논문에서 제안한 방법은 계산이 매우 쉬우면서도 실험값들과 비교해 볼 때, 변형률 구배 소성이론 즉, 길이 효과를 잘 나타내어 주었다.

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

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피인용 문헌

  1. Hardness estimation for pile-up materials by strain gradient plasticity incorporating the geometrically necessary dislocation density vol.27, pp.2, 2013, https://doi.org/10.1007/s12206-012-1243-4