Composites Research

  • 제23권4호
  • /
  • Pages.7-13
  • /
  • 2010
  • /
  • 2288-2103(pISSN)
  • /
  • 2288-2111(eISSN)
한국복합재료학회 (The Korean Society for Composite Materials)
권호 표지
DOI QR코드

DOI QR Code

인장 하중을 받는 무한 고체에 포함된 다수의 이방성 함유체 문제 해석을 위한 체적 적분방정식법

Volume Integral Equation Method for Multiple Anisotropic Inclusion Problems in an Infinite Solid under Uniaxial Tension

  • 이정기 (홍익대학교 기계정보공학과)
  • 발행 : 2010.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

체적 적분방정식법(Volume Integral Equation Method)이라는 새로운 수치해석 방법을 이용하여, 서로 상호작용을 하는 이방성 함유체를 포함하는 등방성 무한고체가 정적 인장하중을 받을 때 무한고체 내부에 발생하는 응력분포 해석을 매우 효과적으로 수행하였다. 즉, 등방성 기지에 다수의 이방성 함유체가 1) 정사각형 배열 형태 또는 2) 정육각형 배열 형태로 포함되어 있는 경우에 대하여, 다양한 함유체의 체적비에 대하여, 중앙에 위치한 이방성 함유체와 등방성 기지의 경계면에서의 인장응력 분포의 변화를 구체적으로 조사하였다. 또한, 단일의 이방성 함유체에 대한 체적 적분방정식법을 이용한 해와 해석해를 비교해 봄으로서, 체적 적분방정식법을 이용하여 구한 해의 정확도를 검증하였다.

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solids containing interacting multiple anisotropic inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. Effects of the number of anisotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy of the method is validated by solving the single inclusion problem for which solutions are available in the literature.

키워드

참고문헌

  1. Eshelby, J.D., "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proceedings of the Royal Society of London, Series A, A241, 1957, pp. 376-396.
  2. Hashin, Z., Theory of Fiber Reinforced Materials, NASA CR-1974, 1972.
  3. Yang, H.C. and Chou, Y.T., "Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids1," Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, 1976 (Sep.), pp. 424-430. https://doi.org/10.1115/1.3423884
  4. Achenbach, J.D. and Zhu, H., "Effect of Interphases on Micro and Macromechanical Behavior of Hexagonal-Array Fiber Composites," Transactions of ASME, Journal of Applied Mechanics, Vol. 57, 1990, pp. 956-963. https://doi.org/10.1115/1.2897667
  5. Christensen, R.M., Mechanics of Composite Materials, Krieger Pub. Co., Florida, 1991.
  6. Nimmer, R.P., Bankert, R.J., Russel, E.S., Smith, G.A. and Wright, P.K., "Micromechanical Modeling of Fiber/Matrix Interface Effects in Transversely Loaded SiC/Ti-6-4 Metal Matrix Composites," Journal of Composites Technology & Research, Vol. 13, 1991, pp. 3-13. https://doi.org/10.1520/CTR10068J
  7. Zahl, D.B. and Schmauder, S., "Transverse Strength of Continuous Fiber Metal Matrix Composites," Computational Materials Science, Vol. 3, 1994, pp. 293-299. https://doi.org/10.1016/0927-0256(94)90144-9
  8. Lee, J.K. and Mal, A.K., "A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems," Transactions of the ASME, Journal of Applied Mechanics, Vol. 64, 1997 (Mar.), pp. 23-31. https://doi.org/10.1115/1.2787282
  9. Lee, J. and Mal, A., "Characterization of Matrix Damage in Metal Matrix Composites under Transverse Loads," Computational Mechanics, Vol. 21, 1998, pp. 339-346. https://doi.org/10.1007/s004660050310
  10. Naboulsi, S., "Modeling Transversely Loaded Metal-Matrix Composites," Journal of Composite Materials, Vol. 37, 2003, pp. 55-72. https://doi.org/10.1177/0021998303037001468
  11. Aghdam, M.M. and Falahatgar, S.R., "Micromechanical Modeling of Interface Damage of Metal Matrix Composites Subjected to Transverse Loading," Composite Structures, Vol. 66, 2004, pp. 415-420. https://doi.org/10.1016/j.compstruct.2004.04.063
  12. Lee, J.K., Han, H.D. and Mal, A., "Effects of Anisotropic Fiber Packing on Stresses in Composites," Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33-36, 2006, pp. 4544-4556. https://doi.org/10.1016/j.cma.2005.10.012
  13. Ju, J.W. and Ko, Y.F., "Micromechanical Elastoplastic Damage Modeling for Progressive Interfacial Arc Debonding for Fiber Reinforced Composites," International Journal of Damage Mechanics, Vol. 17, 2008, pp. 307-356. https://doi.org/10.1177/1056789508089233
  14. Mal, A.K. and Knopoff, L., "Elastic Wave Velocities in Two Component Systems," Journal of the Institute of Mathematics and its Applications, Vol. 3, 1967, pp. 376-387. https://doi.org/10.1093/imamat/3.4.376
  15. Lee, J.K. and Mal, A.K., "A Volume Integral Equation Technique for Multiple Scattering Problems in Elastodynamics," Applied Mathematics and Computation, Vol. 67, 1995, pp. 135-159. https://doi.org/10.1016/0096-3003(94)00057-B
  16. Lee, K.J. and Mal, A.K., "A Boundary Element Method for Plane Anisotropic Elastic Media," Journal of Applied Mechanics, Vol. 57, 1990, pp. 600-606. https://doi.org/10.1115/1.2897065
  17. Buryachenko, V.A., Micromechanics of Heterogeneous Materials, Springer, New York, 2007.
  18. Banerjee, P.K., The Boundary Element Methods in Engineering, McGraw-Hill, England, 1993.
  19. PATRAN User's Manual, Version 7.0, MSC/PATRAN, 1998.
  20. Hwu, C. and Yen, W.J., "On the Anisotropic Elastic Inclusions in Plane Elastostatics," Transactions of ASME, Journal of Applied Mechanics, Vol. 60, 1993 (Sep.), pp. 626-632. https://doi.org/10.1115/1.2900850
  21. Lee, J.K., Choi, S.J. and Mal, A., "Stress Analysis of an Unbounded Elastic Solid with Orthotropic Inclusions and Voids Using a New Integral Equation Technique," International Journal of Solids and Structures, Vol. 38 (16), 2001, pp. 2789-2802. https://doi.org/10.1016/S0020-7683(00)00182-7
  22. Mal, A.K. and Singh, S.J., Deformation of Elastic Solids, Prentice Hall, New Jersey, 1991.

피인용 문헌

  1. Elastic Analysis in Composite Including Multiple Elliptical Fibers vol.24, pp.6, 2011, https://doi.org/10.7234/kscm.2011.24.6.037