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TECHNICAL PAPERS

T-Stresses Across Static Crack Kinking

[+] Author and Article Information
Xian-Fang Li

 Institute of Mechanics and Sensor Technology, School of Civil Engineering and Architecture, Central South University, Changsha, Hunan 410083, China

L. Roy Xu1

Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235l.roy.xu@vanderbilt.edu

1

Author to whom correspondence should be addressed.

J. Appl. Mech 74(2), 181-190 (Jan 20, 2006) (10 pages) doi:10.1115/1.2188016 History: Received May 09, 2005; Revised January 20, 2006

This paper is concerned with the T-stress change before and after crack kinking in two-dimensional elastic solids. By using asymptotic analysis and the Westergaard stress function method, approximate analytical formulas for calculating the T-stress as well as stress intensify factors of an infinitesimal kink are given. Contributions from the T-stress before crack kinking, to the T-stress and the stress intensity factors of the kinked crack, are clearly described. It is noted that since the sign of the T-stress of a kinked open crack might be different from that of a main crack, simply using the sign of the T-stress before crack kinking is not sufficient to determine crack growth stability as observed in recent experiments.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Conceptions of “load-induced kinking” and “material-induced kinking” as observed in a brittle polymer plate with a weak interface after projectile impact (4). (b) schematic of a kinked crack from a main crack along with two coordinate systems.

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Figure 2

Possible formats of main cracks and their kinks (a,b), main cracks are open and their kinks are open in (a) and closed in (b); and (c,d) main cracks are closed and their kinks are open in (c) and closed in (d)

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Figure 3

Schematic of superposition of elastic field for a crack with a small kink (only σθθ is depicted)

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Figure 4

Variation of three angle functions with respect to kink angles

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Figure 5

Hoop stresses ασϕϕk at the kink tip with α=0.01 and θ=10deg in the absence of mode-II stress intensity factors KII=0: (a) neglecting Tk and (b) taking Tk into account

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Figure 6

Hoop stresses ασϕϕk at the kink tip with α=0.01 and θ=10deg in the presence of mode-II stress intensity factors: (a)KIIm∕KIm=0.5 and (b)KIIm∕KIm=−0.5

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Figure 7

(a) Variation of Tk∕Tm with crack length ratio and kink angle for B=−1 and (b) variation of Tk∕Tm with crack length ratio and biaxiality ratio for kink angle θ=10deg

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Figure 8

(a) Variation of F with biaxiality ratio B and kink angle for α=0.01 and (b) variation of F with crack length ratio and kink angle for B=−1

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Figure 9

Variation of Tk∕Tm with biaxiality ratio B and kink angle for α=0.01

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