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TECHNICAL PAPERS

# An Effective Numerical Approach for Multiple Void-Crack Interaction

[+] Author and Article Information
Xiangqiao Yan

Research Laboratory on Composite Materials, Harbin Institute of Technology, Harbin 150001, Chinayanxiangqiao@hotmail.com

J. Appl. Mech 73(4), 525-535 (Sep 20, 2005) (11 pages) doi:10.1115/1.2127955 History: Received July 20, 2005; Revised September 20, 2005

## Abstract

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

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## Figures

Figure 1

A generalization of Bueckner’s principle

Figure 2

Schematic of two different segments over which two different sets of displacement discontinuities are imposed

Figure 3

One circular hole and one crack subjected to remote tension

Figure 4

One crack in horizontal position and another in inclined position subjected to remote uniform stress σ

Figure 5

An inclined center crack in rectangular plate under tension

Figure 6

Schematic of a fair of cracks emanating from a square hole in rectangular plate under biaxial loads

Figure 7

An oblique edge crack in a half-infinite plane under uniform tension

Figure 8

Schematic of modeling a half-infinite plane

Figure 9

A collinear elliptical microdefect (hole) in the vicinity of a finite main crack

Figure 10

A pair of symmetric collinear elliptical microdefects (holes) in the vicinity of a finite main crack

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