An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials

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 situa...

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Autores principales:	Kotaro MIURA, Makoto SAKAMOTO, Koichi KOBAYASHI, Jonas A. PRAMUDITA, Yuji TANABE
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2018
Materias:	elasticity fracture mechanics penny-shaped crack stress intensity factor mixed boundary value problem axisymmetric stress sandwiched material internal pressure dual integral equations Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/6f0bc9c4e4d448f4ba444f14cbd2275e
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spelling	oai:doaj.org-article:6f0bc9c4e4d448f4ba444f14cbd2275e2021-11-26T07:20:09ZAn analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials2187-974510.1299/mej.18-00125https://doaj.org/article/6f0bc9c4e4d448f4ba444f14cbd2275e2018-06-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/5/3/5_18-00125/_pdf/-char/enhttps://doaj.org/toc/2187-9745Herein, 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.Kotaro MIURAMakoto SAKAMOTOKoichi KOBAYASHIJonas A. PRAMUDITAYuji TANABEThe Japan Society of Mechanical Engineersarticleelasticityfracture mechanicspenny-shaped crackstress intensity factormixed boundary value problemaxisymmetric stresssandwiched materialinternal pressuredual integral equationsMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 5, Iss 3, Pp 18-00125-18-00125 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	elasticity fracture mechanics penny-shaped crack stress intensity factor mixed boundary value problem axisymmetric stress sandwiched material internal pressure dual integral equations Mechanical engineering and machinery TJ1-1570
spellingShingle	elasticity fracture mechanics penny-shaped crack stress intensity factor mixed boundary value problem axisymmetric stress sandwiched material internal pressure dual integral equations Mechanical engineering and machinery TJ1-1570 Kotaro MIURA Makoto SAKAMOTO Koichi KOBAYASHI Jonas A. PRAMUDITA Yuji TANABE An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
description	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.
format	article
author	Kotaro MIURA Makoto SAKAMOTO Koichi KOBAYASHI Jonas A. PRAMUDITA Yuji TANABE
author_facet	Kotaro MIURA Makoto SAKAMOTO Koichi KOBAYASHI Jonas A. PRAMUDITA Yuji TANABE
author_sort	Kotaro MIURA
title	An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
title_short	An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
title_full	An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
title_fullStr	An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
title_full_unstemmed	An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
title_sort	analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials
publisher	The Japan Society of Mechanical Engineers
publishDate	2018
url	https://doaj.org/article/6f0bc9c4e4d448f4ba444f14cbd2275e
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An analytical solution for the axisymmetric problem of a penny-shaped crack in an elastic layer sandwiched between dissimilar materials

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