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

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Numerical Assessment of Dislocation-Punching Theories for Continuum Structural Analysis of Particle-Reinforced Metal Matrix Composites

입자 강화 금속기지 복합재의 연속체 강도해석을 위한 전위 펀칭 이론의 전산적 평가

  • 서영성 (한남대학교 기계공학과) ;
  • 김용배 (한남대학교 기계공학과)
  • Received : 2010.10.06
  • Accepted : 2011.01.04
  • Published : 2011.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

The yield strength of particle-reinforced composites increases as the size of the particle decreases. This kind of length scale has been mainly attributed to the geometrically necessary dislocation punched around the particle as a result of the mismatch of the thermal expansion coefficients of the particle and the matrix when the composites are cooled down after consolidation. In this study, two dislocation-punching theories that can be used in continuum structural modeling are assessed numerically. The two theories, presented by Shibata et al. and Dunand and Mortensen, calculate the size of the dislocationpunched zone. The composite yield strengths predicted by finite element analysis were qualitatively compared with experimental results. When the size of the particle is less than $2{\mu}m$, the patterns of the composite strength are quite different. The results obtained by Shibata et al. are in qualitatively better agreement with the experimental results.

입자 강화 복합재료는 입자의 크기가 감소할수록 그 항복강도가 증가하므로, 입자의 크기에 대한 길이 스케일을 보인다. 항복강도에 대한 이러한 길이 스케일은 복합재가 압밀된 후 냉각될 때 기지재와 입자간 열팽창계수의 상이함에 의하여 입자 주위 기지재에 펀칭되는 기하적 필수 전위가 주된 영향을 미치는 것으로 알려져 있다. 본 연구에서는 입자 강화 복합재의 연속체 강도해석 모델링에 사용할 수 있는 두 가지 전위 펀칭이론들에 대하여 전산적으로 검토하였다. 즉, 입자 주위에 펀치되는 전위 영역의 크기를 계산하는 대표적인 두 가지 이론들인 Shibata 등 및 Dunand and Mortensen 이론으로부터 전위 펀치 영역의 크기를 계산하고, 이를 유한요소해석에 적용하여 복합재의 항복 강도를 예측하였으며 실험값과 정성적으로 비교하였다. 본 연구에서 입자가 매우 작은 경우, 즉, 입자의 크기가 2.m이하인 경우에 두 이론 간에 극명한 차이를 보여주었으며, Shibata 등의 정식이 정성적으로 실험값에 더 근사한 것을 확인하였다.

Keywords

References

  1. Arsenault, R. J. and Shi, N., 1986, “Dislocation Generation due to Differences Between the Coefficients of Thermal Expansion,” Materials Science and Engineering, Vol. 81, pp. 175-187. https://doi.org/10.1016/0025-5416(86)90261-2
  2. Lloyd, D. J., 1994, “Particle Reinforced Aluminium and Magnesium Matrix Composites,” International Materials Reviews, Vol. 39, No. 1, pp. 1-23. https://doi.org/10.1179/imr.1994.39.1.1
  3. Suh, Y. S., Joshi, S. P. and Ramesh, K., 2009, “An Enhanced Continuum Model for Size-Dependent Strengthening and Failure of Particle-Reinforced Composites,” Acta Materialia, Vol. 57, No. 19, pp. 5848-5861. https://doi.org/10.1016/j.actamat.2009.08.010
  4. Shibata, S., Taya, M., Mori, T. and Mura, T., 1992, “Dislocation Punching from Spherical Inclusions in a Metal Matrix Composite,” Acta Metallurgica et Materialia, Vol. 40, No. 11, pp. 3141-3148. https://doi.org/10.1016/0956-7151(92)90477-V
  5. Dunand, D. C. and Mortensen, A., 1991, “On Plastic Relaxation of Thermal Stresses in Reinforced Metals,” Acta Metallurgica et Materialia, Vol. 39, No. 2, pp. 127-139. https://doi.org/10.1016/0956-7151(91)90261-X
  6. Hill, R., 1998, The Mathematical Theory of Plasticity, Oxford University Press, U.S.A.
  7. Eshelby, J., 1959, “The Elastic Field Outside an Ellipsoidal Inclusion,” Proceedings of the Royal Society of London, Series A 27, Vol. 252, No. 1271, pp. 561-569. https://doi.org/10.1098/rspa.1959.0173
  8. Peach, M. and Koehler, J., 1950, “The Forces Exerted on Dislocations and the Stress Fields Produced by Them,” Physical Review, Vol. 80, No. 3, pp. 436-439. https://doi.org/10.1103/PhysRev.80.436
  9. Hansen, N., 1977, “The Effect of Grain Size and Strain on the Tensile Flow Stress of Aluminium at Room Temperature,” Acta Metallurgica, Vol. 25, No. 8, pp. 863-869. https://doi.org/10.1016/0001-6160(77)90171-7
  10. Dassault Systemes Simulia, Inc., 2010, ABAQUS v. 6.9, Providence, U.S.A.
  11. Suh, Y. S., Kim, Y. and Rhee, Z., 2009, “Strength Analysis of Particle-Reinforced Aluminum Composites with Length-Scale Effect based on Geometrically Necessary Dislocations,” Transactions of Materials Processing, Vol. 18, No. 6, pp. 482-487. https://doi.org/10.5228/KSPP.2009.18.6.482
  12. Qu, S., Siegmund, T., Huang, Y., Wu, P. D., Zhang F.and Hwang, K. C., 2005, “A Study of Particle Size Effect and Interface Fracture in Aluminum Alloy Composite via an Extended Conventional Theory of Mechanism-Based Strain-Gradient Plasticity,” Composites Science and Technology, Vol. 65, No. 7-8, pp. 1244-1253. https://doi.org/10.1016/j.compscitech.2004.12.029
  13. Arsenault, R.J., Wang, L. and Feng, C. R., 1991, “Strengthening of Composites due to Microstructural Changes in the Matrix,” Acta Metallurgica et Materialia, Vol. 39, No. 1, pp. 47-57. https://doi.org/10.1016/0956-7151(91)90327-W