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 antiplane 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.
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References
Abramowitz, M. and Stegun, I. A., 1972,Handbook of Mathematical Functions, Dover Pub., New York.
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.
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.
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.
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.
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.
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.
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.
Choi, H. J., 2002, “Driving Forces and Kinking of an Oblique Crack in Bonded Nonhomogeneous Materials,”Arch. Appl. Mech., Vol. 72, pp. 342–362.
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.
Churchill, R. V., 1981,Operational Mathematics, 3rd ed., McGraw-Hill, New York.
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.
Davis, P. J. and Rabinowitz, P., 1984,Methods of Numerical Integration, 2nd ed., Academic Press, New York.
Eischen, J. W., 1987, “Fracture of Nonhomogeneous Materials,”Int. J. Fract., Vol. 34, pp. 3–22.
Erdogan, F., 1998, “Crack Problems in Non-homogeneous Materials,” Cherepanov, G.P. (Ed.),Fracture, A Topical Encyclopedia of Current Knowledge, Krieger Pub. Company, FL, pp. 72–98.
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.
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.
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.
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.
Jin, Z.-H. and Noda, N., 1994, “Crack-Tip Singular Fields in Nonhomogeneous Materials,”ASME J. Appl. Mech., Vol. 61, pp. 738–740.
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.
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.
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.
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.
Muskhelishvili, N. I., 1953,Singular Integral Equations, Noordhoff, Groningen, the Netherlands.
Noda, N., 1999, “Thermal Stresses in Functionally Graded Materials,”J. Thermal Stresses, Vol. 22, pp. 477–512.
Parameswaran, V. and Shukla, A., 1999, “Crack-Tip Stress Fields for Dynamic Fracture in Functionally Gradient Materials,”Mech. Mater., Vol. 31, pp. 579–596.
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.
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.
Sih, G. C. and Chen, E. P., 1981,Mechanics of Fracture 6: Cracks in Composite Materials, Martinus Nijhoff Publishers, The Hague.
Stehfest, H., 1970, “Numerical Inversion of Laplace Transforms,”Commun. ACM., Vol. 13, pp. 47–49, 624.
Suresh, S. and Mortensen, A., 1998,Fundamentals of Functionally Graded Materials, The Institute of Materials, London.
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.
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.
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Kim, S., Choi, H.J. Elastodynamic response of a crack perpendicular to the graded interfacial zone in bonded dissimilar materials under antiplane shear impact. KSME International Journal 18, 1375–1387 (2004). https://doi.org/10.1007/BF02984252
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DOI: https://doi.org/10.1007/BF02984252