Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Elastodynamic Response of a Crack Perpendicular to the Graded Interfacial Zone in Bonded Dissimilar Materials Under Antiplane Shear Impact

  • Kim, Sung-Ho (School of Mechanical and Automotive Engineering, Kookmin University) ;
  • Choi, Hyung-Jip (School of Mechanical and Automotive Engineering, Kookmin University)
  • Published : 2004.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of anti plane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

Keywords

References

  1. Abramowitz, M. and Stegun, I. A., 1972, Handbook of Mathematical Functions, Dover Pub., New York
  2. Babaei, R. and Lukasiewicz, S. A., 1998, 'Dynamic Response of a Crack in a Functionally Graded Material Between Two Dissimilar Half-Planes Under Anti-Plane Shear Impact Load,' Eng. Fract. Mech., Vol. 60, pp.479-487 https://doi.org/10.1016/S0013-7944(98)00013-7
  3. Bahr, H.-A., Balke, H., Fett, T., Hofinger, I., Kirchhoff, G., Munz, D., Neubrand, A., Semenov, A. S., Weiss, H.-J. and Yang, Y. Y., 2003, 'Cracks in Functionally Graded Materials,' Mater. Sci. Eng. A, Vol. 362, pp. 2-16 https://doi.org/10.1016/S0921-5093(03)00582-3
  4. Becker Jr., T. L., Cannon, R. M. and Ritchie, R. O., 2001, 'Finite Crack Kinking and T-Stresses in Functionally Graded Materials,' Int. J. Solids Struct., Vol. 38, pp. 5545-5563 https://doi.org/10.1016/S0020-7683(00)00379-6
  5. Chiu, T.-C. and Erdogan, F., 1999, 'One-Dimensional Wave Propagation in a Functionally Graded Elastic Medium,' J. Sound Vib., Vol. 222, pp. 453-487 https://doi.org/10.1006/jsvi.1998.2065
  6. Choi, H. J., 2001a, 'Mode I and Mode II Analyses of a Crack Normal to the Graded Interlayer in Bonded Materials,' KSME Int. J., Vol. 15, pp. 1386-1397
  7. Choi, H. J., 2001b, 'The Problem for Bonded Half-Planes Containing a Crack at an Arbitrary Angle to the Graded Interfacial Zone,' Int. J. Solids Struct., Vol. 38, pp. 6559-6588 https://doi.org/10.1016/S0020-7683(01)00090-7
  8. Choi, H. J., 2001c, 'Effects of Graded Layering on the Tip Behavior of a Vertical Crack in a Substrate Under Frictional Hertzian Contact,' Eng. Fract. Mech., Vol. 68, pp. 1033-1059 https://doi.org/10.1016/S0013-7944(01)00003-0
  9. Choi, H. J., 2002, 'Driving Forces and Kinking of an Oblique Crack in Bonded Nonhomogeneous Materials,' Arch. Appl. Mech., Vol. 72, pp. 342-362 https://doi.org/10.1007/s00419-002-0219-8
  10. Chung, Y. M., Kim, C. and Choi, H. J., 2003, 'Anti-Plane Shear Behavior of an Arbitrarily Oriented Crack in Bonded Materials With a Nonhomogeneous Interfacial Zone,' KSME Int. J., Vol. 17, pp. 269-279
  11. Churchill, R. V., 1981, Operational Mathematics, 3rd ed., McGraw-Hill, New York
  12. Dag, S. and Erdogan, F., 2002, 'A Surface Crack in a Graded Medium Under General Loading Conditions,' ASME J. Appl. Mech., Vol. 69, pp. 580-588 https://doi.org/10.1115/1.1488661
  13. Davis, P. J. and Rabinowitz, P., 1984, Methods of Numerical Integration, 2nd ed., Academic Press, New York
  14. Eischen, J. W., 1987, 'Fracture of Nonhomogeneous Materials,' Int. J. Fract., Vol. 34, pp. 3-22 https://doi.org/10.1007/BF00042121
  15. Erdogan, F., 1998, 'Crack Problems in Nonhomogeneous Materials,' Cherepanov, G.P. (Ed.), Fracture, A Topical Encyclopedia of Current Knowledge, Krieger Pub. Company, FL, pp. 72-98
  16. Guo, L.-C., Wu, L. Z. and Ma, L., 2004, 'The Interface Crack Problem Under a Concentrated Load for a Functionally Graded Coat-Substrate Composite System,' Comp. Struct., Vol. 63, pp. 397-406 https://doi.org/10.1016/S0263-8223(03)00188-0
  17. Huang, G.-Y. and Wang, Y.-S., 2004, 'A New Model for Fracture Analysis of a Functionally Graded Interfacial Zone Under Harmonic Anti-Plane Loading,' Eng. Fract. Mech., Vol. 71, pp. 1841-1851 https://doi.org/10.1016/j.engfracmech.2003.12.001
  18. Itou, S., 2001, 'Transient Dynamic Stress Intensity Factors Around a Crack in a Nonhomogeneous Interfacial Layer Between Two Dissimilar Elastic Half-Planes,' Int. J. Solids Struct., Vol. 38, pp. 3631-3645 https://doi.org/10.1016/S0020-7683(00)00231-6
  19. Jiang, L. Y. and Wang, X. D., 2002, 'On the Dynamic Crack Propagation in an Interphase With Spatially Varying Elastic Properties Under Inplane Loading,' Int. J. Fract., Vol. 114, pp. 225-244 https://doi.org/10.1023/A:1015529931715
  20. Jin, Z.-H. and Noda, N., 1994, 'Crack-Tip Singular Fields in Nonhomogeneous Materials,' ASME J. Appl. Mech., Vol. 61, pp. 738-740 https://doi.org/10.1115/1.2901529
  21. Li, C., Duan, Z. and Zou, Z., 2002, 'Torsional Impact Response of a Penny-Shaped Interface Crack in Bonded Materials With a Graded Material Interlayer,' ASME J. Appl. Mech., Vol. 69, pp. 303-308 https://doi.org/10.1115/1.1459066
  22. Marur, P. R. and Tippur, H. V., 2000, 'Dynamic Response of Bimaterial and Graded Interface Cracks Under Impact Loading,' Int. J. Fract., Vol. 103, pp. 95-109 https://doi.org/10.1023/A:1007621303220
  23. Miyamoto, Y., Kaysser, W. A., Rabin, B. H., Kawasaki, A. and Ford, R. G. (Eds.), 1999, Functionally Graded Materials: Design, Processing, and Applications, Kluwer Academic Pub., MA
  24. Morrissey, J. W. and Geubelle, P. H., 1997, 'A Numerical Scheme for Mode III Dynamic Fracture Problems,' Int. J. Num. Meth. Eng., Vol. 40, pp. 1181-1196 https://doi.org/10.1002/(SICI)1097-0207(19970415)40:7<1181::AID-NME108>3.0.CO;2-X
  25. Muskhelishvili, N. I., 1953, Singular Integral Equations, Noordhoff, Groningen, the Netherlands
  26. Noda, N., 1999, 'Thermal Stresses in Functionally Graded Materials,' J. Thermal Stresses, Vol. 22, pp. 477-512 https://doi.org/10.1080/014957399280841
  27. Parameswaran, V. and Shukla, A., 1999, 'Crack-Tip Stress Fields for Dynamic Fracture in Functionally Gradient Materials,' Mech. Mater., Vol. 31, pp. 579-596 https://doi.org/10.1016/S0167-6636(99)00025-3
  28. Selvadurai, A. P. S., 2000, 'The Penny-Shaped Crack at a Bonded Plane With Localized Elastic Non-Homogeneity,' Eur. J. Mech. A/Solids, Vol. 19, pp. 525-534 https://doi.org/10.1016/S0997-7538(00)00167-4
  29. Shul, C. W. and Lee, K. Y., 2002, 'A Subsurface Eccentric Crack in a Functionally Graded Coating Layer on the Layered Half-Space Under an Anti-Plane Shear Impact Load,' Int. J. Solids Struct., Vol. 39, pp. 2019-2029 https://doi.org/10.1016/S0020-7683(02)00016-1
  30. Sih, G. C. and Chen, E. P., 1981, Mechanics of Fracture 6: Cracks in Composite Materials, Martinus Nijhoff Publishers, The Hague
  31. Stehfest, H., 1970, 'Numerical Inversion of Laplace Transforms,' Commun. ACM., Vol. 13, pp. 47-49, 624 https://doi.org/10.1145/361953.361969
  32. Suresh, S. and Mortensen, A., 1998, Fundamentals of Functionally Graded Materials, The Institute of Materials, London
  33. Wang, B. L., Han, J. C. and Du, S. Y., 2000, 'Cracks Problem for Non-Homogeneous Composite Material Subjected to Dynamic Loading,' Int. J. Solids Struct., Vol. 37, pp. 1251-1274 https://doi.org/10.1016/S0020-7683(98)00292-3
  34. Zhang, Ch., Savaidis, A., Savaidis, G. and Zhu, H., 2003, 'Transient Dynamic Analysis of a Cracked Functionally Graded Material by a BIEM,' Comput. Mater. Sci., Vol. 26, pp. 167-174 https://doi.org/10.1016/S0927-0256(02)00395-6