Summary
Transient dynamic stresses around two rectangular cracks in a nonhomogeneous interfacial layer sandwiched between two dissimilar elastic half-spaces are examined. The material properties vary continuously in the layer within a range from those of the upper half-space to those of the lower half-space. An incoming shock stress wave impinges perpendicular on the crack surfaces. In order to solve the problem, the interfacial layer is divided into several homogeneous layers that have different material properties. Application of Laplace and Fourier transforms reduces the problem to the solution of a pair of dual integral equations. To solve the equations, the differences in the crack surface displacements are expanded into a series of functions that vanish outside the crack. The unknown coefficients in the series are solved using the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted numerically in physical space. Numerical calculations are carried out for composite materials made of a ceramic half-space and a steel half-space.
Similar content being viewed by others
References
Delale F. and Erdogan F. (1988). On the mechanical modeling of the interfacial region in bonded half-planes. ASME J. Appl. Mech. 55: 317–324
Ozturk M. and Erdogan F. (1995). An axisymmetric crack in bonded materials with a nonhomogeneous interfacial zone. ASME J. Appl. Mech. 62: 116–125
Ozturk M. and Erdogan F. (1996). Axisymmetric crack problem in bonded materials with a graded interfacial region. Int. J. Solids Struct. 33: 193–219
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. Engng. Fract. Mech. 60: 479–487
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. 38: 3631–3645
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. 69: 303–308
Li C. and Weng G. J. (2002). Dynamic fracture analysis for a penny-shaped crack in an FGM interlayer between dissimilar half spaces. Math. Mech. Solids. 7: 149–163
Li C. and Weng G. J. (2001). Dynamic stress intensity factor of a cylindrical interface crack with a functionally graded interlayer. Mech. Mater. 33: 325–333
Li C., Weng G. J. and Duan Z. P. (2001). Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading. Int. J. Solids Struct. 38: 7473–7485
Feng W. J., Su R. K. L. and Jiang Z. Q. (2005). Torsional impact response of a cylindrical interface crack between a functionally graded interlayer and a homogeneous cylinder. Composite Structures 68: 203–209
Itou, S.: Transient dynamic stresses around a rectangular crack in a nonhomogeneous layer between two dissimilar elastic half-spaces, In: IUTAM Symposium on dynamics of advanced materials and smart structures (Watanabe, K., Ziegler, F., eds.), pp. 147–156. IUTAM Symposium, Yonezawa, Japan 2002. Dordrecht: Kluwer Academic Publishers 2003.
Morse P. M. and Feshbach H. (1958). Methods of theoretical physics, vol. 1. McGraw-Hill, New York, 926–931
Itou S. (1972). Indentations of an elastic Cosserat layer by moving punches. ZAMM 52: 93–99
Miller M. and Guy T. (1966). Numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM J. Numer. Anal. 3: 624–635
Itou S. (1983). Dynamic stress concentration around a circular hole in an infinite elastic strip. ASME J. Appl. Mech. 50: 57–62
Itou S. (1981). Transient analysis of stress waves around two rectangular cracks under impact load. Engng. Frac. Mech. 14: 685–695
Itou S. (1980). Transient analysis of stress waves around a rectangular crack under impact load. ASME J. Appl. Mech. 47: 958–959
Itou S. (2005). Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials. Arch. Appl. Mech. 75: 18–30
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Itou, S. Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load. Acta Mechanica 192, 89–110 (2007). https://doi.org/10.1007/s00707-006-0415-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-006-0415-7