TY - JOUR

T1 - Three-dimensional stress intensity factors of a central square crack in a transversely isotropic cuboid with arbitrary material orientations

AU - Chen, Chao Shi

AU - Chen, Chia Hau

AU - Pan, Ernian

N1 - Funding Information:
The work of E.P. was partially supported by ARL and AFRL. We thank Prof. Xu Wang for his constructive discussion and the reviewers and editor for their beneficial comments and suggestions.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2009/2

Y1 - 2009/2

N2 - In this paper, we present the dual boundary element method (dual-BEM) or single-domain BEM to analyze the mixed three-dimensional (3D) stress intensity factors (SIFs) in a finite and transversely isotropic solid containing an internal square crack. The planes of both the transverse isotropy and square crack can be oriented arbitrarily with respect to a fixed global coordinate system. A set of four special nine-node quadrilateral elements are utilized to approximate the crack front as well as the outer boundary, and the mixed 3D SIFs are evaluated using the asymptotic relation between the SIFs and the relative crack opening displacements (COD) via the Barnett-Lothe tensor. Numerical examples are presented for a cracked cuboid which is transversely isotropic with any given orientation and is under a uniform vertical traction on its top and bottom surfaces. The square crack is located in the center of the cuboid but is oriented arbitrarily. Our results show that among the selected material and crack orientations, the mode-I SIF reaches the largest possible value when the material inclined angle ψ1=45° and dig angle β1=45°, and the crack inclined angle ψ2=0° and dig angle β2=0°. It is further observed that when the crack is oriented vertically or nearly vertically, the mode-I SIF becomes negative, indicating that the crack closes due to an overall compressive loading normal to the crack surface. Variation of the SIFs for modes II and III along the crack fronts also shows some interesting features for different combinations of the material and crack orientations.

AB - In this paper, we present the dual boundary element method (dual-BEM) or single-domain BEM to analyze the mixed three-dimensional (3D) stress intensity factors (SIFs) in a finite and transversely isotropic solid containing an internal square crack. The planes of both the transverse isotropy and square crack can be oriented arbitrarily with respect to a fixed global coordinate system. A set of four special nine-node quadrilateral elements are utilized to approximate the crack front as well as the outer boundary, and the mixed 3D SIFs are evaluated using the asymptotic relation between the SIFs and the relative crack opening displacements (COD) via the Barnett-Lothe tensor. Numerical examples are presented for a cracked cuboid which is transversely isotropic with any given orientation and is under a uniform vertical traction on its top and bottom surfaces. The square crack is located in the center of the cuboid but is oriented arbitrarily. Our results show that among the selected material and crack orientations, the mode-I SIF reaches the largest possible value when the material inclined angle ψ1=45° and dig angle β1=45°, and the crack inclined angle ψ2=0° and dig angle β2=0°. It is further observed that when the crack is oriented vertically or nearly vertically, the mode-I SIF becomes negative, indicating that the crack closes due to an overall compressive loading normal to the crack surface. Variation of the SIFs for modes II and III along the crack fronts also shows some interesting features for different combinations of the material and crack orientations.

UR - http://www.scopus.com/inward/record.url?scp=56949083081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56949083081&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2008.06.001

DO - 10.1016/j.enganabound.2008.06.001

M3 - Article

AN - SCOPUS:56949083081

VL - 33

SP - 128

EP - 136

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

IS - 2

ER -