# 직교이방성 압전재료에서 전파 하는 모드 III 균열의 응력장과 변위장

• Lee, Kwang-Ho (Dept. of Mechanical and Automotive Engineering, Kyungpook Nat'l Univ.)
• 이광호 (경북대학교 기계자동차공학부)
• Accepted : 2010.04.05
• Published : 2010.06.01
• 87 7

#### Abstract

The stress and displacement fields of a permeable propagating crack in orthotropic piezoelectric materials under anti-plane shear mechanical load and in-plane electric load are analyzed. The equations of motion for the propagating crack in piezoelectric materials are developed and the solution on the stress and the displacement fields through an asymptotic analysis was obtained. The influences of the piezoelectric constant and of the dielectric permittivity on the stress and displacement fields at the crack tip are explicitly clarified. Using the stress and displacement fields obtained in this study, the characteristics of stress and displacement at a propagating crack tip in piezoelectric materials are discussed.

#### Keywords

Orthotropic Piezoelectric Materials;Propagating Crack;Stress and Displacement Fields;Permeable Crack

#### Acknowledgement

Supported by : KNU

#### References

1. Pak, Y. E., 1990, “Crack Extension Force in a Piezoelectric Materials,” Journal of Applied Mechanics, Vol. 57, pp. 647-653. https://doi.org/10.1115/1.2897071
2. Pak, Y. E., 1992, “Linear Electroelastic Fracture Mechanics of Piezoelectric Materials,” International Journal of Fracture , Vol. 54, pp. 79-100. https://doi.org/10.1007/BF00040857
3. Shindo, Y., Narita, F. and Tanaka, K., 1996, “Electroelastic Intensification Near Anti-Plane Shear Crack in Orthotropic Piezoelectric Ceramic Strip,” Theoretical and Applied Fracture Mechanics, Vol. 25, pp. 65-71. https://doi.org/10.1016/0167-8442(96)00008-0
4. Shindo, Y., Tanaka, K. and Narita, F., 1997, “Singular Stress and Electric Fields of a Piezoelectric Ceramic Strip with a Finite Crack Under Longitudinal Shear,” Acta Mechanica ,Vol. 120, pp. 31-45. https://doi.org/10.1007/BF01174314
5. Li, X. F. and Duan X. Y., 2001,”Closed-Form Solution for a Mode-III Crack at the Mid-Plane of a Piezoelectric Layer,” Mechanics Research Communication, Vol. 28, pp.703-710. https://doi.org/10.1016/S0093-6413(02)00222-7
6. Sosa, H. A., 1991, ”Plane Problem in Piezoelectric Media with Defects,” International Journal of Solids and Structures , Vol. 28, pp.491-505. https://doi.org/10.1016/0020-7683(91)90061-J
7. Ou, Y. L., Chue, C. H., 2006,”Mode III Eccentric Crack in Functionally Graded Piezoelectric Strip,” International Journal of Solids and Structures, Vol. 43, pp.6148-6164. https://doi.org/10.1016/j.ijsolstr.2005.05.033
8. Chen, Z.T., Yu, S. W., 1997,” Antiplane Yoffe Crack Problem in Piezoelectric Materials,” Int. J. Fract., Vol. 84, pp. L41-L45.
9. Hou, M. A., Quan, X. Q., Bian, W. F., 2001,” Energy Release Rate and Bifurcation Angles of Piezoelectric Materials with Antiplane Moving Crack,” Int. J. Fract. , Vol. 107, pp.297-306. https://doi.org/10.1023/A:1007678728046
10. Kwon, S. M. and Lee, K. Y, 2001,”Constant Moving Crack in a Piezoelectric Block:Anti-Plane Problem,” Mechanics of Materials, Vol. 33, pp.649-657. https://doi.org/10.1016/S0167-6636(01)00082-5
11. Piva, A., Tornabene, F. and Viola E., 2006,” Crack Propagation in a Four-Parameter Piezoelectric Medium,” European Journal of Mechanics A/Solids , Vol. 25, pp. 230-249 https://doi.org/10.1016/j.euromechsol.2005.09.002
12. Lee, K. H., Hawong, J. S. and Choi, S. H., 1996,” Dynamic Stress Intensity Factors $K_1, K_{11}$ and Crack Propagation Characteristics of Orthotropic Materials,” Engng. Fract. Mech, Vol. 53(1), pp. 19-140.
13. Lee, K. H. 2000, “Stress and Displacement Fields for Propagating the Crack Along the Interface of Dissimilar Orthotropic Materials Under Dynamic Mode I and II Load,” J. Appl. Mech., Vol. 67, pp. 223-228. https://doi.org/10.1115/1.321171
14. Lee, K. H., 2004 “Characteristics of a Crack Propagating Along the Gradient in Functionally Gradient Materials,” Int. J. of Solids Struct., Vol. 41, pp. 2879-2898. https://doi.org/10.1016/j.ijsolstr.2004.01.004
15. Lee, K. H., Lee, Y. J. and Cho, S. B., 2009, “Characteristics of a Transiently Propagating crack in Functionally Graded Materials,” JMST, Vol. 23, pp.1306-1322.
16. Lee, K. H., Cho, S. B., 2006, “ Stress and Displacement Fields of a Propagating Mode III Crack in Orthotropic Functionally Gradient Materials with Property Graduation Along X Direction,” Trans of KSME (A), Vol. 30(3), pp. 249-259.

#### Cited by

1. Influence of Density Variation on Stress and Displacement Fields at a Propagating Mode-III Crack Tip in Orthotropic Functionally Graded Materials vol.35, pp.9, 2011, https://doi.org/10.3795/KSME-A.2011.35.9.1051