Dynamic stress intensity factors around a cylindrical crack in an infinite elastic medium subject to impact load

Abstract

This paper investigates transient stresses around a cylindrical crack in an infinite elastic medium subject to impact loads. Incoming stress waves resulting from the impact load impinge on the crack in a direction perpendicular to the crack axis. In the Laplace transform domain, by means of the Fourier transform technique, the mixed boundary value equations with respect to stresses and displacements were reduced to two sets of dual integral equations. To solve the equations, the differences in the crack surface displacements were expanded in a series of functions that are zero outside the crack. The boundary conditions for the crack were satisfied by means of the Schmidt method. Stress intensity factors were defined in the Laplace transform domain and were numerically inverted to physical space. Numerical calculations were carried out for the dynamic stress intensity factors corresponding to some typical shapes assumed for the cylindrical crack.

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

“…The solving process and method in the present paper are quite different from those adopted in the literatures . The crack‐shaped was assumed to be penny‐shaped , rectangular‐shaped , or cylindrical‐shaped . At the same time, the method (the Schmidt method) of the present paper is different from 3D finite element analyses method , singular integral equations , hypersingular integral equation method , extended displacement discontinuity integral equation method , the potential theory method , and the extended finite element method .…”

“…The surfaces of the composite structure are subjected to both mechanical and electrical loads, and the crack surfaces are assumed to be electrically impermeable. In order to obtain the exact solutions, the crack‐shaped was often assumed to be penny‐shaped , rectangular‐shaped , or cylindrical‐shaped . For instances, Chen et al derived an impermeable penny‐shaped crack subjected to a concentrated thermal load (prescribed point temperature) applied arbitrarily at the crack surfaces by using the generalized potential theory method.…”

Dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half-planes subject to an impact load

“…When the Schmidt method is used to solve crack problems, the stress field, the displacement field, the temperature field, and the stress intensity factors can be obtained in a straightforward manner, even for three-dimensional rectangular cracks (Itou, 2007a), a single cylindrical crack (Itou, 2003(Itou, , 2005b(Itou, , 2007b, and two cylindrical cracks (Itou, 2007c(Itou, , 2008. Takakuda solved the dynamic stress intensity factors around two parallel cracks during the passage of a time-harmonic stress wave (1982).…”

A boundary integral equation method in the frequency domain for cracks under transient loading

“…A cylindrical crack in an infinite elastic medium under impact loading was considered by Itou in [5]. The 3D impact response of the crack subjected to a longitudinal stress wave was investigated.…”

“…A numerical solution was obtained for a circular crack of a finite radius. Using the method employed for a solution of longitudinal stress wave incidence [5], the problem can be solved for an incident shear stress wave.…”