Abstract
The anti-plane impact fracture analysis was performed for a weak-discontinuous interface in a symmetrical functionally gradient composite strip. A new bi-parameter exponential function was introduced to simulate the continuous variation of material properties. Using Laplace and Fourier integral transforms, we reduced the problem to a dual integral equation and obtained asymptotic analytical solution of crack-tip stress field. Based on the numerical solution of the second kind of Fredholm integral equation transformed from the dual integral equation, the effects of the two non-homogeneity parameters on DSIF were discussed. It was indicated that the relative stiffness of the interface and the general stiffness of the whole structure are two important factors affecting the impact fracture behavior of the weak-discontinuous interface. The greater the relative stiffness of the interface is, the higher the value of the dynamic stress intensity factor will be. The greater the general stiffness of the whole structure is, the shorter the time for DSIF to arrive at the peak value and then to stabilize to the steady one. If the general stiffness of the whole structure is great enough, there will be an oscillation between the peak and steady values of DSIF.
Similar content being viewed by others
References
Williams M.L. (1959). The stress around a fault or crack in dissimilar media. Bull. Seismol. Soc. Am. 49(2): 199–204
Comninou M. (1977). The interface crack. J. Appl. Mech. 44(4): 631–636
Knowles J.K. and Sternberg E. (1983). Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. J. Elast. 13(2): 257–293
Delale F. and Erdogan F. (1988). On the mechanical modeling of the interfacial region in bonded half-planes. J. Appl. Mech. 55: 317–324
Chen Y.F. and Erdogan F. (1996). The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. J. Mech. Phys. Solids 44: 771–787
Choi H.J., Lee K.Y. and ** T.E. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone—part A: mechanical response. Int. J. Fract. 94(2): 103–122
Choi H.J., ** T.E. and Lee K.Y. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone—part B: thermal shock response. Int. J. Fract. 94(2): 123–135
Guo L.C., Wu L.Z. and Zeng T. (2004). Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface—Part I: static problem. Int. J. Fract. 127(1): 21–38
Guo L.C., Wu L.Z. and Zeng T. (2004). Fracture analysis of a functionally graded coating-substrate structure with acrack perpendicular to the interface—Part II: transient problem. Int. J. Fract. 127(1): 39–59
Erdogan F. (1985). The crack problem for bonded nonhomogeneous materials under antiplane shear loading. J. Appl. Mech. 52: 823–828
Hu K.Q., Zhong Z. and ** B. (2002). Anti-plane shear crack in a functionally gradient piezoelectric material. Acta Mech. Solida Sin. 15(2): 140–148
Zhou Z.G., Wang B. and Yang L.J. (2004). Investigation of the Behavior of an Interface Crack between Two Half-Planes of Orthotropic Functionally Graded Materials by Using a New Method. JSME Int. J. Ser. C, Mech. Syst. Mach. Elem. Manuf. 47(3): 467–478
Zhou Z.G., Wang B. and Wu L.Z. (2005). Investigation of the behavior of a crack between two half-planes of functionally graded materials by using the Schmidt method. Struct. Eng. Mech. 19(4): 425–440
Ou Y.L. and Chue C.H. (2005). Mode III crack problems for two bonded functionally graded piezoelectric materials. Int. J. Solids Struct. 42: 3321–3337
Ou Y.L. and Chue C.H. (2006). Two mode internal cracks located within two bonded functionally graded piezoelectric half planes respectively. Arch. Appl. Mech. 75(6/7): 364–378
Yong H.D. and Zhou Y.H. (2006). Analysis of a mode III crack problem in a functionally graded coating-substrate system with finite thickness. Int. J. Fract. 141: 459–467
Li Y.D., Jia B., Zhang N., Tang L.Q. and Dai Y. (2006). Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating. Int. J. Solids Struct. 43: 4795–4809
Li Y.D., Zhang H.C. and Tan W. (2006). Fracture Analysis of functionally gradient weak/micro-discontinuous interface with finite element method. Comput. Mater. Sci. 38: 454–458
Li Y.D., Tan W. and Zhang H.C. (2006). Anti-plane transient fracture analysis of the functionally gradient elastic bi-material weak/infinitesimal-discontinuous interface. Int. J. Fract. 142: 163–171
Li Y.D., Jia B., Zhang N., Dai Y. and Tang L.Q. (2006). Anti-plane fracture analysis of functionally gradient material infinite strip with finite width (Engl. Ed.). Appl. Math. Mech. 27(6): 773–780
Zhang, H.C., Tan, W., Li, Y.D.: Effect of the transitional gradient of material property on the mechanical behavior of a non-homogeneous interlayer. Comput. Mater. Sci. doi: 10.1016/j.commatsci.2007.06.016 (2007)
Wang Y.S., Huang G.Y. and Gross D. (2003). On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. J. Appl. Mech. 70: 676–680
Huang G.Y. and Wang Y.S. (2004). A new model for fracture analysis of a functionally graded interfacial zone under anti-plane harmonic loading. Eng. Fract. Mech. 71: 1841–1851
Gao X.X., Wang Y.S. and Huang G.Y. (2006). The anti-plane dynamic fracture analysis of functionally graded materials with arbitrary spatial variations of material properties. Arch. Appl. Mech. 76: 159–170
Zhong, Z., Cheng, Z.Q.: Fracture Analysis of a Functionally Graded Strip with Arbitrary Distributed Material Properties. Int. J. Solids Struct. doi: 10.1016/j.ijsolstr.2007.09.023 (2007)
Guo, L.C., Noda, N.: Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model. Int. J. Solids Struct. doi: 10.1016/j.ijsolstr.2007.03.012 (2007)
Li Y.D., Zhang H.C., Zhang N. and Dai Y. (2005). Stress analysis of functionally gradient beam using effective principal axes. Int. J. Mech. Mater. Des. 2: 157–164
Miller M.K. and Guy W.T. (1966). Numerical inversion of the Laplace transform by use of Jacobi polynomials. J. Numer. Anal. 3: 624–635
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, YD., Lee, K.Y. Fracture analysis of a weak-discontinuous interface in a symmetrical functionally gradient composite strip loaded by anti-plane impact. Arch Appl Mech 78, 855–866 (2008). https://doi.org/10.1007/s00419-007-0194-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-007-0194-1