# 혼합 체적-경계 적분방정식법을 이용한 응력확대계수 계산

• 이정기 (홍익대학교 기계정보학과) ;
• 이형민 (홍익대학교 대학원 기계정보학과)
• Published : 2003.07.01
• 78 58

#### Abstract

A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

#### Keywords

Mixed Volume and Boundary Integral Equation Method;Cracks;Stress Intensity Factors;Anisotropic Inclusions;Volume Integral Equation Method;Boundary Integral Equation Method

#### References

1. ANSYS User's Manual, 1997, Version 5.4, SAS IP, Inc.
2. Yang, H. C. and Chou, Y. T., 1976, 'Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids',' Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, pp. 424-430 https://doi.org/10.1115/1.3423884
3. PATRAN User's Manual, 1998, Version 7.0, MSCIPATRAN
4. Liu, Y. J. and Xu, N., 2000, 'Modeling of Interface Cracks in Fiber-Reinforced Composites with the Presence of Interphases Using the Boundary Element Method,' Mechanics of Materials, Vol. 32(12), pp. 769-783 https://doi.org/10.1016/S0167-6636(00)00045-4
5. Choi, S. J., Ra, W. S. and Lee, J. K., 1999, 'Elastic Analysis of Unbounded Solids with Anisotropic Inclusions,' Transactions of the KSME, A, Vol. 23, No. 11, pp. 1993-200
6. Lee, J. K., Choi, S. J., and Mal, A., 2001, '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), pp. 2789-2802 https://doi.org/10.1016/S0020-7683(00)00182-7
7. Lee, J. K., 1997, 'Elastic Wave Field Calculations,' Journal of the Computational Structural Engineering Institute of Korea, Vol. 10, No.2, pp. 213-223
8. Lee, K. J. and Mal, A. K., 1990, 'A Boundary Element Method for Plane Anisotropic Elastic Media,' Journal of Applied Mechanics, Vol. 57, pp. 600-606 https://doi.org/10.1115/1.2897065
9. Banerjee, P. K., 1993, The Boundary Element Methods in Engineering, McGraw-Hill, England
10. Hwu, C. and Yen, W. J., 1993, 'On the Anisotropic Elastic Inclusions in Plane Elastostatics,' Transactions of ASME, Journal of Applied Mechanics, Vol. 60, pp. 626-632 https://doi.org/10.1115/1.2900850
11. Xiao Z. M. and Chen B. J., 2001, 'Stress Intensity Factor for a Griffith Crack Interacting with a Coated Inclusion,' International Journal of Fracture, Vol. 108, pp. 193-205 https://doi.org/10.1023/A:1011066521439
12. Knight M. G., Wrobel L. C., Henshall J. L. and De Lacerda L. A., 2002, 'A Study of the Interaction between a Propagating Crack and an Uncoated/Coated Elastic Inclusion Using the BE Technique,' International Journal of Fracture, Vol. 114, pp. 47-61 https://doi.org/10.1023/A:1014837509347
13. Lim, W. K. and Choi, S. Y., 2002, 'Analysis of Inclined Crack Extension -in Orthotropic Solids Under Biaxial Loading,' Transactions of the KSME, A, Vol. 26, No.6, pp. 993-1000 https://doi.org/10.3795/KSME-A.2002.26.6.993
14. Lee, J. K. and Mal, A. K., 1995, 'A Volume Integral Equation Technique for Multiple Scattering Problems in Elastodynamics,' Applied Mathematics and Computation, Vol. 67, pp. 135-159 https://doi.org/10.1016/0096-3003(94)00057-B
15. Lee, J. K. and Mal, A. K., 1997, 'A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 64, pp. 23-31 https://doi.org/10.1115/1.2787282
16. Hwu, C., Liang, Y. K. and Yen, W. J., 1995, 'Interactions between Inclusions and Various Types of Cracks,' International Journal of Fracture, Vol. 73, pp. 229-245 https://doi.org/10.1007/BF00027272
17. Chang, J. H., 1995, 'Evaluation of Energy Release Rate for a Planar Crack in Heterogeneous Media,' International Journal of Fracture, Vol. 74, pp. 163 -179 https://doi.org/10.1007/BF00036263
18. Kassam, Z. H. A., Zhang, R. J. and Wang, Z., 1995, 'Finite Element Simulation to Investigate Interaction between Crack and Particulate Reinforcements in Metal-Matrix Composites,' Materials Science and Engineering, Vol. A203, pp. 286-299 https://doi.org/10.1016/0921-5093(95)09828-3
19. Cheeseman B. A. and Santare M. H., 2001, 'The Effect of the Interphase on Crack-Inclusion Interactions,' International Journal of Fracture, Vol. 109, pp. 303-323 https://doi.org/10.1023/A:1011092801013
20. Theotokoglou E. N. and Theotokoglou E. E., 2002, 'The Interface Crack along a Circular Inclusion Interacting with a Crack in the Infinite Matrix,' International Journal of Fracture, Vol. 116, pp. 1-23 https://doi.org/10.1023/A:1020186628869
21. Pahn L. O. and Earmme Y. Y., 2000, 'Analysis of a Short Interfacial Crack from the Corner of a Rectangular Inclusion,' International Journal of Fracture, Vol. 106, pp. 341-356 https://doi.org/10.1023/A:1026599122610
22. Wang Y. B. and Chau K. T., 2001, 'A New Boundary Element Method for Mixed Boundary Value Problems Involving Cracks and Holes: Interactions between Rigid Inclusions and Cracks,' International Journal of Fracture, Vol. 110, pp. 387-406 https://doi.org/10.1023/A:1010853804657
23. Helsing J., 1999, 'Stress Intensity Factors for a Crack in front of an Inclusion,' Engineering Fracture Mechanics, Vol. 64, pp. 245-253 https://doi.org/10.1016/S0013-7944(99)00061-2
24. Cheeseman B. A. and Santare M. H., 2000, 'The Interaction of a Curved Crack with a Circular Elastic Inclusion,' International Journal of Fracture, Vol. 103, pp. 259-277 https://doi.org/10.1023/A:1007663913279
25. Chen D.-H., 1997, 'The Effect of an Elliptical Inclusion on a Crack,' International Journal of Fracture, Vol. 85, pp. 351-364 https://doi.org/10.1023/A:1007420011592
26. Chen, D.-H. and Nakamichi, S., 1996, 'Stress Intensity Factors for an Interface Crack along an Elliptical Inclusion,' International Journal of Fracture, Vol. 82, pp. 131-152 https://doi.org/10.1007/BF00034660
27. Li, R. and Chudnovsky, A., 1994, 'The Stress Intensity Factor Green's Function for a Crack Interacting with a Circular Inclusion,' International Journal of Fracture, Vol. 67, pp. 169-177 https://doi.org/10.1007/BF00019602
28. Sung J. C. and Wong D. C., 1995, 'Effect of an Inclusion on the Interaction of Elastic Waves with a Crack,' Engineering Fracture Mechanics, Vol. 51, pp. 679-695 https://doi.org/10.1016/0013-7944(94)00286-Q
29. Li, R. and Chudnovsky, A., 1993, 'Variation of the Energy Release Rate as a Crack Approaches and Passes through an Elastic Inclusion,' International Journal of Fracture, Vol. 59, pp. R69-R74
30. Erdogan, F. and Gupta, G. D., 1975, 'The Inclusion Problem with a Crack Crossing the Boundary,' International Journal of Fracture, Vol. 11, pp. 13-27 https://doi.org/10.1007/BF00034709
31. Erdogan, F., Gupta, G. D. and Ratwani, M., 1974, 'Interaction between a Circular Inclusion and an Arbitrarily Oriented Crack,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 41, pp. 1007-1013 https://doi.org/10.1115/1.3423424
32. Atkinson, C., 1972, 'The Interaction between a Crack and an Inclusion,' International Journal of Engineering Science, Vol. 10, pp. 127-136 https://doi.org/10.1016/0020-7225(72)90011-0
33. Bush, M. B., 1997, 'The Interaction between a Crack and a Particle Cluster,' International Journal of Fracture, Vol. 88, pp. 215-232 https://doi.org/10.1023/A:1007469631883
34. Lee, J. K. and Ra, W. S., 1999, 'Numerical Analysis of a Crack in the Vicinity of an Inclusion,' Journal of the Computational Strutural Engineering Institute of Korea, Vol. 12, No.3, pp. 465-474
35. Lee, J. K. and Mal, A., 1998, 'Characterization of Matrix Damage in Metal Matrix Composites under Transverse Loads,' Computational Mechanics, Vol. 21, pp. 339-346 https://doi.org/10.1007/s004660050310