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Dynamic stresses around an interface crack between a nonhomogeneous bonding layer and two dissimilar orthotropic half‐spaces subject to an impact load
Author(s) -
Itou Shouetsu
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600114
Subject(s) - orthotropic material , laplace transform , half space , materials science , stress intensity factor , boundary value problem , mathematical analysis , composite material , mathematics , geometry , structural engineering , fracture mechanics , finite element method , engineering
Two dissimilar orthotropic half‐spaces are bonded by a nonhomogeneous orthotropic layer. An internal pressure is applied suddenly to the surfaces of an interface crack that is situated at the lower interface between the lower half‐space and the layer. The material properties of the bonding layer are assumed to vary continuously from the lower half‐space to the upper half‐space. The boundary conditions are reduced to dual integral equations using the Fourier transform technique in the Laplace domain. In order to satisfy the boundary conditions outside the crack, the differences in displacements at the crack surfaces in the Laplace domain are expanded in a series of functions that vanish outside the crack. The unknown coefficients in each series are evaluated using the Schmidt method in the Laplace domain. The stress intensity factors are determined, and these are inverted using a numerical method. The stress intensity factors are calculated numerically for the case in which the lower and upper half‐spaces are made of unidirectional glass‐fiber‐reinforced epoxy composites.