An Analysis of Eigenvalues and Eigenvectors for V-notched Cracks in Pseudo-isotropic Dissimilar Materials

유사등방성 이종재료 내의 V-노치 균열에 대한 고유치와 고유벡터 해석

  • Kim, Jin-Gwang (Dept.of Mechanical Design and Production Engineering, Graduate School of Kyungnam University) ;
  • Jo, Sang-Bong (Kyungnam University)
  • 김진광 (경남대학교 대학원 기계설계학과) ;
  • 조상봉 (경남대학교 공과대학 기계자동화공학부)
  • Published : 2000.11.01

Abstract

The problem of eigenvalue and eigenvector is obtained from a V-notched crack in pseudo-isotropic dissimilar materials by the traction free boundary and the perfect bonded interface conditions. The complex stress function is assumed as the two-term William's type. The eigenvalue is solved by a commercial numerical program, MATHEMATICA to discuss stress singularities for V-notched cracks in pseudo-isotropic dissimilar materials. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination to eigenvector coefficients associated with eigenvalues. The RWCIM algorithm is also coded by the MATHEMATICA.

Keywords

References

  1. Bogy. D. B, 'On the Problem of Edge-bonded Elastic Quarter-planes Loaded at the Boundary,' Int. J. Solids Structures, Vol. 6, pp. 1287-1313, 1970 https://doi.org/10.1016/0020-7683(70)90104-6
  2. Bogy. D. B, 'Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles under Surface Tractions,' J.Applied Mechanics, Vol. 38, pp. 377-386, 1971
  3. Hein. V. L. and Erdogan. F, 'Stress Singularities in a Two-material Wedge,' Int. J. Fract. Mech., Vol. 7, pp. 317-330, 1971 https://doi.org/10.1007/BF00184307
  4. Carpenter. W. C. and Byers. C, 'A Path Independent Integral for Computing Stress Intensities for V-notched Cracks in a Bi-material,' Int. J. Fract., Vol. 35, pp. 245-268, 1987 https://doi.org/10.1007/BF00276356
  5. Ting. T. C. T. and Chou. S. C,'Edge Singularities in Anisotropic Composites,' Int. J. Solids Structures, Vol. 17, No. 11, pp. 1057-1068, 1981 https://doi.org/10.1016/0020-7683(81)90013-5
  6. Zwiers. R. I. ,Ting. T. C. T and Spiker. R. L, 'On the Logarithmic Singularity of Free-edge Stress in Laminated Composites under Uniform Extension,' J.Applied Mechanics, Vol. 49, pp. 561-569, 1982
  7. Ting. T. C. T, 'Explicit Solution and Invariance of the Singularities at an Interface Crack in Anisotropic Composites,' Int. J. Solids Structures, Vol. 22, No. 9, pp. 965-983, 1986 https://doi.org/10.1016/0020-7683(86)90031-4
  8. Lekhnitskii. S. G, 'Theory of Elasticity of an Anisotropic Elastic Body,' Holden-Day, Inc., 1963
  9. Dunn, M. L., Suwito, W., and Cunningham, S., 1997, 'Stress intensities at Notch Singularities,' Engng Fracture Mech., Vol. 57, No. 4, pp. 417-430, 1997 https://doi.org/10.1016/S0013-7944(97)00019-2
  10. 조상봉, 윤성관, '이종재료간 V-노치균열의 응력특이성과 응력강도계수의 특성 및 결정에 관한 연구', 대한기계학회논문집, 제16권 제10호, pp. 1890-1899, 1992
  11. 조상봉, 양장흥, '이종재료 내의 V-노치 균열에 대한 응력특이성에 관한 연구', 대한기계학회논문집, A권, 제22권 제7호, pp. 1307-1315, 1998
  12. ANSYS User's Manual, Revision 5.3
  13. R. Yuuki, and S. B. Cho, 'Efficient boundary element analysis of stress intensity factors for interface crack in dissimilar materials,' Engng. Frac. Mech, Vol. 34, pp. 179-188, 1989 https://doi.org/10.1016/0013-7944(89)90251-8