Cracking of an orthotropic substrate reinforced by an orthotropic plate

R. Mahajan, F. Erdogan, B. Kilic, Erdogan Madenci

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A solution method is derived to determine the stress intensity factors for both an internal crack and an edge crack in an orthotropic substrate that is reinforced on its boundary by a finite-length orthotropic plate. The method utilizes the Green's functions for a pair of dislocations and a concentrated force on the boundary while invoking the concept of superposition. Enforcing the traction-free boundary condition along the crack surfaces and the continuity of displacement gradients along the plate/substrate interface results in a coupled system of singular integral equations. An asymptotic analysis of the kernels in these equations for the region of the junction point between the plate corner and the substrate boundary reveals the strength of the singularity in the case of an edge crack. The numerical solution of the integral equations provides results for the stress intensity factors for both an internal crack and an edge crack perpendicular to the substrate boundary and aligned with one of the corners of the plate. The present results have been validated against previously published stress intensity factors for an internal crack and an edge crack in an isotropic substrate.

Original languageEnglish (US)
Pages (from-to)6389-6415
Number of pages27
JournalInternational Journal of Solids and Structures
Volume40
Issue number23
DOIs
StatePublished - Nov 2003

Fingerprint

orthotropic plates
Orthotropic plates
edge cracks
Cracking
Crack
Substrate
stress intensity factors
Cracks
Substrates
cracks
Stress Intensity Factor
Stress intensity factors
Internal
singular integral equations
surface cracks
free boundaries
Integral equations
traction
continuity
integral equations

Keywords

  • Crack
  • Plate
  • Stress intensity factors
  • Substrate
  • Thin film

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Cracking of an orthotropic substrate reinforced by an orthotropic plate. / Mahajan, R.; Erdogan, F.; Kilic, B.; Madenci, Erdogan.

In: International Journal of Solids and Structures, Vol. 40, No. 23, 11.2003, p. 6389-6415.

Research output: Contribution to journalArticle

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N2 - A solution method is derived to determine the stress intensity factors for both an internal crack and an edge crack in an orthotropic substrate that is reinforced on its boundary by a finite-length orthotropic plate. The method utilizes the Green's functions for a pair of dislocations and a concentrated force on the boundary while invoking the concept of superposition. Enforcing the traction-free boundary condition along the crack surfaces and the continuity of displacement gradients along the plate/substrate interface results in a coupled system of singular integral equations. An asymptotic analysis of the kernels in these equations for the region of the junction point between the plate corner and the substrate boundary reveals the strength of the singularity in the case of an edge crack. The numerical solution of the integral equations provides results for the stress intensity factors for both an internal crack and an edge crack perpendicular to the substrate boundary and aligned with one of the corners of the plate. The present results have been validated against previously published stress intensity factors for an internal crack and an edge crack in an isotropic substrate.

AB - A solution method is derived to determine the stress intensity factors for both an internal crack and an edge crack in an orthotropic substrate that is reinforced on its boundary by a finite-length orthotropic plate. The method utilizes the Green's functions for a pair of dislocations and a concentrated force on the boundary while invoking the concept of superposition. Enforcing the traction-free boundary condition along the crack surfaces and the continuity of displacement gradients along the plate/substrate interface results in a coupled system of singular integral equations. An asymptotic analysis of the kernels in these equations for the region of the junction point between the plate corner and the substrate boundary reveals the strength of the singularity in the case of an edge crack. The numerical solution of the integral equations provides results for the stress intensity factors for both an internal crack and an edge crack perpendicular to the substrate boundary and aligned with one of the corners of the plate. The present results have been validated against previously published stress intensity factors for an internal crack and an edge crack in an isotropic substrate.

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