Mechanical Engineering Journal
Online ISSN : 2187-9745
ISSN-L : 2187-9745
Solid Mechanics and Materials Engineering
An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
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2018 Volume 5 Issue 3 Pages 18-00125


Herein, we consider the axisymmetric problem of a penny-shaped crack in an elastic material sandwiched between other materials. It is assumed that the central substance is composed of an elastic layer held between two semi-infinite bodies with different elastic constants, and that the crack is situated in the central plane of the elastic layer and subjected to uniform pressures on its internal surfaces. We consider two contact conditions; perfectly bonded and frictionless contact at the interfaces with the dissimilar materials. Dual integral equations are reduced to an infinite system of simultaneous equations by expressing normal displacements on the crack surfaces as an appropriate series function. Numerical results were obtained to examine the effects of the elastic constants of the layer and semi-infinite bodies and contact conditions on the stress intensity factor at the tip of the penny-shaped crack, the distribution of normal displacement, and stress on the crack plane. Based on the results of these numerical calculations, several conclusions can be made, as follows. 1) The distributions of normal displacement and stress at the crack plane and the stress intensity factor at the tip of the crack become larger than the results for an infinite solid when the ratio of the shear modulus of the layer to that of the semi-infinite bodies is larger than 1. 2) The numerical results for normal displacement and stress, and for stress intensity factors, in the frictionless case are higher than for the perfectly bonded case regardless of the shear modulus ratio and layer thickness ratio. The difference between the perfectly bonded and frictionless cases becomes greater as the layer thickness ratio becomes smaller. 3) There is a slight difference in the stress intensity factor values obtained from the present work and the corresponding results previously reported in the literature.

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© 2018 The Japan Society of Mechanical Engineers
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