Surface Energy for Creation of Multiple Curved Cracks in Rubbery Materials

[+] Author and Article Information
J. H. Chang, J. S. Lin

Department of Civil Engineering,  National Central University, Chungli 32001, Taiwan

J. Appl. Mech 74(3), 488-496 (Mar 24, 2006) (9 pages) doi:10.1115/1.2338058 History: Received July 29, 2005; Revised March 24, 2006

A fracture parameter Mc is proposed for evaluation of the surface energy associated with the creation of multiple curved cracks in 2D rubbery solids under the action of large deformation. Based on the concept of the M-integral, the parameter is developed by performing the integration along a closed contour enclosing all the cracks and with respect to a reference coordinate system originated at the geometric center of all the crack tips. The integration is shown to be path-independent so that the complicated singular stress field in the near-tip areas need not be involved in the calculation. It is thus suggested that Mc be possibly used as a fracture parameter for describing the degradation of material and∕or structural integrity caused by irreversible evolution of multiple curved cracks in a rubbery media.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A rubbery body containing a two-tip curved crack at its original state

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Figure 2

A homogeneous rubbery body containing N distributed curved cracks at its original state (N=5 in this figure)

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Figure 3

The integration contours for an infinite medium subjected to uniform remote loads

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Figure 4

A plane stress rubbery specimen containing multiple curved cracks (Problem 1)

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Figure 5

Three contours, each encloses different portion of the specimen, are used for the integration

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Figure 6

The values of M(=Mc) versus the number of cracks (Problem 1). (a) (σ∞,β)=(400Pa,60°), (b) (σ∞,β)=(100Pa,90°). (Note: w=150m, B=150m.)

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Figure 7

A plane stress rubbery specimen containing N cracks under nonhomogeneously stressed state (Problem 2)

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Figure 8

Three geometric instances containing cracks of different relative sizes (Problem 2)

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Figure 12

(a) An intermediate state during evolution of the multi-cracked system shown in Fig. 2. (b) The enlarged portion of the extended configuration in the local near-tip area.

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Figure 11

The curved crack in Fig. 1 is approximated by a winding kinked crack with m segments (m=4 in this figure)

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Figure 10

The values of Mc versus the number of cracks for Figs.  888, respectively (Problem 2)

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Figure 9

The deformed mesh for the specimen in Fig. 8




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