Abstract
We investigate diffraction of reduced traction shear waves applied at the faces of a stationary crack in an elastic solid with microstructure, under antiplane deformation. The material behaviour is described by the indeterminate theory of couple stress elasticity and the crack is rectilinear and semi-infinite. The full-field solution of the crack problem is obtained through integral transforms and the Wiener–Hopf technique. A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack, localized waves irradiating from the crack-tip with, possibly, super-Rayleigh speed and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission. Dynamic stress intensity factors are presented, which generalize to Elastodynamics the corresponding results already obtained in the static framework. The correction brings out the important role of wave diffraction on stress concentration.
Highlights
The study of wave diffraction has attracted major interest since its discovery, in the XVII century, by Francesco MariaGrimaldi in the context of light wave propagation
Elastic wave diffraction and stress concentration are almost always investigated within the classical theory of Elastodynamics, which fails to account for the discontinuous nature of many engineering materials, the so-called microstructure
Diffraction of reduced traction shear waves applied at the faces of a semi-infinite rectilinear crack in an elastic halfspace with microstructure is considered
Summary
The study of wave diffraction has attracted major interest since its discovery, in the XVII century, by Francesco Maria. Elastic wave diffraction and stress concentration are almost always investigated within the classical theory of Elastodynamics, which fails to account for the discontinuous nature of many engineering materials, the so-called microstructure. As an example, this theory cannot predict dispersion of Rayleigh waves at high frequency, when the wavelength becomes comparable to the material characteristic length (Georgiadis and Velgaki, 2003). Elastodynamic stress intensity factors are given, which generalize the corresponding results presented in Radi (2008) for the static regime They incorporate the effect of the applied loading frequency and thereby account for the interplay of the diffracted waves
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