Research Papers

Flaw Tolerance in a Viscoelastic Strip

[+] Author and Article Information
Shaohua Chen

e-mail: chenshaohua72@hotmail.com
Institute of Mechanics,
Chinese Academy of Sciences,
Beijing 100190,China

Huajian Gao

School of Engineering,
Brown University,
Providence, RI 02912
e-mail: Huajian_Gao@brown.edu

1Corresponding authors.

Manuscript received June 21, 2012; final manuscript received September 25, 2012; accepted manuscript posted October 22, 2012; published online May 16, 2013. Assoc. Editor: Anand Jagota.

J. Appl. Mech 80(4), 041014 (May 16, 2013) (10 pages) Paper No: JAM-12-1252; doi: 10.1115/1.4007864 History: Received June 21, 2012; Revised September 25, 2012; Accepted October 22, 2012

Load-bearing biological materials such as bone, teeth, and nacre have acquired some interesting mechanical properties through evolution, one of which is the tolerance of cracklike flaws incurred during tissue function, growth, repair, and remodeling. While numerous studies in the literature have addressed flaw tolerance in elastic structures, so far there has been little investigation of this issue in time-dependent, viscoelastic systems, in spite of its importance to biological materials. In this paper, we investigate flaw tolerance in a viscoelastic strip under tension and derive the conditions under which a pre-existing center crack, irrespective of its size, will not grow before the material fails under uniform rupture. The analysis is based on the Griffith and cohesive zone models of crack growth in a viscoelastic material, taking into account the effects of the loading rate along with the fracture energy, Young’s modulus, and theoretical strength of material.

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Fig. 1

A center-cracked viscoelastic strip of width 2W and crack size 2a under tension

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Fig. 2

The standard viscoelastic model used in the present study

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Fig. 3

Analysis of the viscoelastic strip problem with Griffith’s model of crack growth via the correspondence principle. (a) The auxiliary problem of an elastic strip of width 2W and crack size 2a, and (b) the corresponding viscoelastic problem.

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Fig. 4

A bi-linear loading profile in the viscoelastic problem

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Fig. 5

The stress-strain relationship of a viscoelastic butyl rubber under different loading rates τ0/t0

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Fig. 6

The normalized critical strip width Wcr/lft for crack growth as a function of the normalized crack length β=a/W in the viscoelastic Griffith problem under different loading rates

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Fig. 7

A center-cracked elastic strip of width 2W subject to remote tension σ∞. The length of the cohesive zone is l and the effective crack length is c=a+l.

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Fig. 8

Superposition scheme used to determine the crack opening displacement in the elastic Dugdale problem. (a) A perfect strip without crack under applied stress σ∞; a strip with crack length 2c subjected to (b) a uniformly normal compressive stress σ∞ on the crack face, and (c) a uniformly normal tensile stress σs in the cohesive zone.

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Fig. 9

The normalized critical strip width Wcr/lft for crack growth as a function of the normalized crack length β=a/W in the elastic Dugdale problem

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Fig. 10

The normalized effective crack length as a function of the loading time for the viscoelastic problem with β=0.2

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Fig. 11

The normalized crack opening displacement as a function of the loading time in the viscoelastic Dugdale problem with β=0.33 and W/lft=1.83

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Fig. 12

The nondimensional critical strip width Wcr/lft for crack growth as a function of the normalized crack length β=a/W in the viscoelastic Dugdale problem under different loading rates

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Fig. 13

The nondimensional flaw tolerance width Wft/lft as a function of the total loading time (different loading rates) with β=0.33

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Fig. 14

Dugdale model of a finite crack in an infinite space

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Fig. 15

Dugdale model of a periodic array of cracks in an infinite space. Each crack has a length a and a cohesive zone length c-a. The length of the period is 2W.




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