# V-노치균열의 응력장과 경계배치법에 의한 파괴변수

• 배정배 (영남대학교 대학원 기계공학과) ;
• 최성렬 (영남대학교 기계공학부)
• Published : 2003.01.01
• 61 6

#### Abstract

The arbitrary V-notched crack problem is considered. The general expressions for the stress components on this problem are obtained as explicit series forms composed of independent unknown coefficients which are denoted by coefficients of eigenvector. For this results eigenvalue equation is performed first through introducing complex stress functions and applying the traction free boundary conditions. Next solving this equation, eigenvalues and corresponding eigenvectors are obtained respectively, and finally inserting these results into stress components, the general equations are obtained. These results are also shown to be applicable to the symmetric V-notched crack or straight crack. It can be shown that this solutions are composed of the linear combination of Mode I and Mode II solutions which are obtained from different characteristic equations, respectively. Through performing asymptotic analysis for stresses, the stress intensity factor is given as a closed form equipped with the unknown coefficients of eigenvector. In order to calculate the unknown coefficients. based on these general explicit equations, numerical programming using the overdetermined boundary collocation method which is algorithmed originally by Carpenter is also worked out. As this programming requires the input data, the commercial FE analysis for stresses is performed. From this study, for some V-notched problems, unknown coefficients can be calculated numerically and also fracture parameters are determined.

#### Keywords

V-notched Crack;Boundary Collocation Method;Stress Intensity Factor;T-Stress

#### References

1. Sang Bong Cho, Hwi Won Jeong and Jin Kwang Kim, 2000, 'Determination of Strf:SS Intensity Factors for Interface Cracks in Dissimilar Materials Using the RWCIM,' Journal of the Korean Society of Precision Engineering. Vol. 17, pp. 180-185
2. Hong-Rae Roh, Jin-Kwang Kim and Sang-Bong Cho, 2000, ' A Study On the Eigenvector Analyses for V-notched Cracks in Anisotropic Dissimilar Materials by the Reciprocal Work Contour Integral Method,' Proceedings of the KSME 2000 Spring Meeting A, pp. 115-120
3. Muskhelishvili, N.l., Some Basic Problems of the mathematical Theory of Elasticity, Noordoff, 1963
4. Suresh, S., Fatigue of Materials, Cambridge Univ., 1991
5. Gross, B. and Mendelson, A., 1972, 'Plane Elastostatic Analysis of V-Notched Plates,' International Journal of Fracture, Vol. 8(3), pp. 267-276 https://doi.org/10.1007/BF00186126
6. Lin, K.Y. and Tong, P., 1980,'Singular Finite Elements for the Fracture Analysis of V-Notched Plate,' International Journal for Numerical Methods in Engineering, Vol. 15, pp. 1343-1354 https://doi.org/10.1002/nme.1620150907
7. Carpenter, W.C., 1984, 'A Collocation Procedure for determining Fracture Mechanics Parameters at a Comer,' International Journal of Fracture, Vol. 24, pp. 255-266 https://doi.org/10.1007/BF00020740
8. Carpenter, W.C., 1985, 'The Eigenvector Solution for a General Comer or Finite Opening Crack with Further Studies on the Collocation Procedure,' International Journal of Fracture, Vol. 27, pp. 63-74 https://doi.org/10.1007/BF00017213
9. Carpenter, W.C., 1984, 'Calculation of Fracture Mechanics Parameters for a General Comer,' International Journal of Fracture, Vol. 24, pp. 45-58 https://doi.org/10.1007/BF00020267
10. Carpenter, W.C., 1984, 'Mode I and Mode II stress Intensities for Plates with Cracks of Finite Opening,' International Journal of Fracture, Vol. 26, pp. 201-214 https://doi.org/10.1007/BF01140628
11. Carpenter, W.C. and Byers, C., 1987, 'A Path Independent Integral for Computing Stress Intensities for V-notched Cracks in a Bi-Material,' International Journal of Fracture, Vol. 35, pp. 245-268 https://doi.org/10.1007/BF00276356
12. Williams, M.L.,1957, 'On the Stress Distribution at the Base of a Stationary Crack,' Journal of Applied Mechanics, Vol. 19, pp. 526-528
13. England, A.H., 1971, 'On Stress Singularities in Linear Elacticity,' International Journal of Engineering Science, Vol. 9, pp. 571-585 https://doi.org/10.1016/0020-7225(71)90039-5