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Research Papers

A Linear Poroelastic Analysis of Time-Dependent Crack-Tip Fields in Polymer Gels

[+] Author and Article Information
Yalin Yu, Chad M. Landis

Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712

Nikolaos Bouklas

Sibley School of Mechanical and
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853

Rui Huang

Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 11, 2018; final manuscript received July 26, 2018; published online August 31, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(11), 111011 (Aug 31, 2018) (15 pages) Paper No: JAM-18-1340; doi: 10.1115/1.4041040 History: Received June 11, 2018; Revised July 26, 2018

Based on a linear poroelastic formulation, we present an asymptotic analysis of the transient crack-tip fields for stationary cracks in polymer gels under plane-strain conditions. A center crack model is studied in detail, comparing numerical results by a finite element method to the asymptotic analysis. The time evolution of the crack-tip parameters is determined as a result of solvent diffusion coupled with elastic deformation of the gel. The short-time and long-time limits are obtained for the stress intensity factor and the crack-tip energy release rate under different chemo-mechanical boundary conditions (immersed versus not-immersed, displacement versus load controlled). It is found that, under displacement-controlled loading, the crack-tip energy release rate increases monotonically over time for the not-immersed case, but for the immersed case, it increases first and then decreases, with a long-time limit lower than the short-time limit. Under load control, the energy release rate increases over time for both immersed and not-immersed cases, with different short-time limits but the same long-time limit. These results suggest that onset of crack growth may be delayed until the crack-tip energy release rate reaches a critical value if the applied displacement or traction is subcritical but greater than a threshold.

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Figures

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Fig. 1

Schematic of a center-cracked specimen under tension. A polar coordinate at the crack tip is used for the asymptotic crack-tip fields. A finite element mesh is shown for one quarter of the specimen.

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Fig. 2

Superposition of two linear elasticity problems (A and B) for the long-time limit of the not-immersed case under displacement control

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Fig. 6

Time evolution of chemical potential (upper row) and solvent concentration (lower row) in an immersed center-cracked specimen (showing one quarter only) with εh=0.001, h/a=10 and ν=0.24

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Fig. 5

The normalized crack-tip parameters versus the normalized time for center-cracked specimens (immersed and not-immersed) with h/a=10 and ν=0.24: (a) stress intensity factor, (b) T-stress, (c) chemical potential at the crack tip, and (d) additional parameters for chemical potential (normalized as μ3a/(ΩGεh) and μ4a/(ΩGεh))

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Fig. 3

Numerical results for the angular distributions of the stress components (a)–(c) and solvent concentration (d) around the crack tip at t/τ=10−4, in comparison with the asymptotic predictions, for the immersed case with h/a=10 and ν=0.24

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Fig. 4

Angular distributions of the chemical potential for the immersed (a) and not-immersed (b) cases (t/τ=10−4, h/a=10 and ν=0.24)

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Fig. 10

Delay time for onset of crack growth under load control for the immersed and not-immersed specimens

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Fig. 7

Chemical potential straight ahead of the crack tip at different times for an immersed center-cracked specimen with εh=0.001, h/a=10 and ν=0.24

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Fig. 8

Chemical potential straight ahead of the crack tip at different times for a not-immersed center-cracked specimen with εh=0.001, h/a=10 and ν=0.24

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Fig. 9

Energy release rate (J*), normalized by J0, as a function of the normalized time (t/τ) for immersed and not-immersed center-cracked specimens with h/a=10 and ν=0.24: (a) Underdisplacement control and (b) under load control. The horizontal dashed and dotted lines are the short-time and long-time limits.

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Fig. 11

(a) Finite element mesh for the crack tip model and (b) effect of Poisson's ratio on the crack-tip stress intensity factor, comparing the numerical results with analytical predictions

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