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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November 2018
Research-Article
A Linear Poroelastic Analysis of Time-Dependent Crack-Tip Fields in Polymer Gels
Yalin Yu,
Yalin Yu
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Engineering Mechanics,
University of Texas,
Austin, TX 78712
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Nikolaos Bouklas,
Nikolaos Bouklas
Sibley School of Mechanical and
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
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Chad M. Landis,
Chad M. Landis
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Search for other works by this author on:
Rui Huang
Rui Huang
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu
Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu
Search for other works by this author on:
Yalin Yu
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Nikolaos Bouklas
Sibley School of Mechanical and
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
Chad M. Landis
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Engineering Mechanics,
University of Texas,
Austin, TX 78712
Rui Huang
Department of Aerospace Engineering &
Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: ruihuang@mail.utexas.edu
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. Nov 2018, 85(11): 111011 (15 pages)
Published Online: August 31, 2018
Article history
Received:
June 11, 2018
Revised:
July 26, 2018
Citation
Yu, Y., Bouklas, N., Landis, C. M., and Huang, R. (August 31, 2018). "A Linear Poroelastic Analysis of Time-Dependent Crack-Tip Fields in Polymer Gels." ASME. J. Appl. Mech. November 2018; 85(11): 111011. https://doi.org/10.1115/1.4041040
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