0
Research Papers

Fracture Analyses of Soft Materials With Hard Inclusion

[+] Author and Article Information
Pengyu Pei, Guang Yang

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics & Astronautics,
Nanjing 210016, China

Yan Shi

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics & Astronautics,
Nanjing 210016, China
e-mail: yshi@nuaa.edu.cn

Cunfa Gao

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics & Astronautics,
Nanjing 210016, China
e-mail: cfgao@nuaa.edu.cn

1P. Pei and Y. Shi contributed equally to this work.

2Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 27, 2018; final manuscript received June 24, 2018; published online July 17, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(11), 111003 (Jul 17, 2018) (9 pages) Paper No: JAM-18-1313; doi: 10.1115/1.4040694 History: Received May 27, 2018; Revised June 24, 2018

This paper presents a detailed study on the fracture behaviors of soft materials with hard inclusion. Stress concentrations on the interfaces of hard and soft materials are considered as the key factor for structure fracture. Based on linear fracture theory, the fracture behaviors of soft materials with elliptical hard inclusion are investigated. Stress concentrations, consisting of tensile, hoop, and compressive stress, are observed with changes of inclusion geometries and the modulus ratio of hard and soft materials. And their influences on the categories of principal stress concentration are shown in a phase diagram in the current paper. Finite element analysis is carried out with consideration of the large deformation of soft material, which demonstrates the effectiveness of the theoretical predictions in a great scope of applied loading. Finally, the predictions based on theoretical and simulation results are validated by experiments. This work points out that the hard line inclusion is the source of danger in soft materials just like the crack in brittle materials.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Vacanti, J. P. , Langer, R. , Upton, J. , and Marler, J. J. , 1998, “ Transplantation of Cells in Matrices for Tissue Regeneration,” Adv. Drug Deliv. Rev., 33(1–2), pp. 165–182. [PubMed]
Lee, K. Y. , and Mooney, D. J. , 2001, “ Hydrogels for Tissue Engineering,” Chem. Rev., 101(7), pp. 1869–1879. [CrossRef] [PubMed]
Pelrine, R. , Kornbluh, R. , Pei, Q. , and Joseph, J. , 2000, “ High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287(5454), pp. 836–839. [CrossRef] [PubMed]
Anderson, I. A. , Gisby, T. A. , Mckay, T. G. , O'brien, B. M. , and Calius, E. P. , 2012, “ Multi-Functional Dielectric Elastomer Artificial Muscles for Soft and Smart Machines,” J. Appl. Phys., 112(4), p. 041101. [CrossRef]
Lee, S. , Reuveny, A. , Reeder, J. , Lee, S. , Jin, H. , Liu, Q. , Yokota, T. , Sekitani, T. , Isoyama, T. , and Abe, Y. , 2016, “ A Transparent Bending-Insensitive Pressure Sensor,” Nat. Nanotechnol., 11(5), pp. 472–478. [CrossRef] [PubMed]
Lipomi, D. J. , Tee, B. C. , Vosgueritchian, M. , and Bao, Z. , 2011, “ Stretchable Organic Solar Cells,” Adv. Mater., 23(15), pp. 1771–1775. [CrossRef] [PubMed]
Shepherd, R. F. , Ilievski, F. , Choi, W. , Morin, S. A. , Stokes, A. A. , Mazzeo, A. D. , Chen, X. , Wang, M. , and Whitesides, G. M. , 2011, “ Multigait Soft Robot,” Proc. Natl. Acad. Sci. U. S. A., 108(51), p. 20400. [CrossRef] [PubMed]
Zhao, H. , Li, Y. , Elsamadisi, A. , and Shepherd, R. , 2015, “ Scalable Manufacturing of High Force Wearable Soft Actuators,” Extreme Mech. Lett., 3, pp. 89–104. [CrossRef]
Rivlin, R. S. , and Thomas, A. G. , 1953, “ Rupture of Rubber. I. Characteristic Energy for Tearing,” J. Polym. Sci. Part A Polym. Chem., 10(3), pp. 291–318.
Thomas, A. G. , 1955, “ Rupture of Rubber. II. The Strain Concentration at an Incision,” J. Polym. Sci. Part A Polym. Chem., 18(88), pp. 177–188.
Greensmith, H. W. , Mullins, L. , and Thomas, A. G. , 1960, “ Rupture of Rubber,” Trans. Soc. Rheol., 4(1), pp. 179–189. [CrossRef]
Lake, G. J. , and Thomas, A. G. , 1967, “ The Strength of Highly Elastic Materials,” Proc. R. Soc. London, 300(1460), pp. 108–119. [CrossRef]
Thomas, A. G. , 1962, “ Rupture of Rubber,” Rheol. Acta, 2(1), pp. 63–66. [CrossRef]
Ma, Z. , Feng, X. C. , and Hong, W. , 2016, “ Fracture of Soft Elastic Foam,” ASME J. Appl. Mech., 83(3), p. 031007. [CrossRef]
Pourmodheji, R. , Qu, S. , and Yu, H. , 2018, “ Two Possible Defect Growth Modes in Soft Solids,” ASME J. Appl. Mech., 85(3), p. 031001. [CrossRef]
Mao, Y. M. , and Anand, L. , 2018, “ Fracture of Elastomeric Materials by Crosslink Failure,” ASME J. Appl. Mech., 85(8), p. 081008.
Ko, H. C. , Stoykovich, M. P. , Song, J. , Malyarchuk, V. , Choi, W. M. , Yu, C. J. , Rd, G. J. , Xiao, J. , Wang, S. , and Huang, Y. , 2008, “ A Hemispherical Electronic Eye Camera Based on Compressible Silicon Optoelectronics,” Nature, 454(7205), pp. 748–753. [CrossRef] [PubMed]
Dagdeviren, C. , Shi, Y. , Joe, P. , Ghaffari, R. , Balooch, G. , Usgaonkar, K. , Gur, O. , Tran, P. L. , Crosby, J. R. , and Meyer, M. , 2015, “ Conformal Piezoelectric Systems for Clinical and Experimental Characterization of Soft Tissue Biomechanics,” Nat. Mater., 14(7), pp. 728–736. [CrossRef] [PubMed]
Wang, A. , Avila, R. , and Ma, Y. J. , 2017, “ Mechanics Design for Buckling of Thin Ribbons on an Elastomeric Substrate Without Material Failure,” ASME J. Appl. Mech., 84(9), p. 094501. [CrossRef]
Huang, Y. , Yuan, J. H. , Zhang, Y. C. , and Feng, X. , 2016, “ Interfacial Delamination of Inorganic Films on Viscoelastic Substrates,” ASME J. Appl. Mech., 83(10), p. 101005. [CrossRef]
Sun, J. Y. , Zhao, X. , Illeperuma, W. R. K. , Chaudhuri, O. , Oh, K. H. , Mooney, D. J. , Vlassak, J. J. , and Suo, Z. , 2012, “ Highly Stretchable and Tough Hydrogels,” Nature, 489(7414), pp. 133–136. [CrossRef] [PubMed]
Long, R. , and Hui, C. Y. , 2015, “ Crack Tip Fields in Soft Elastic Solids Subjected to Large Quasi-Static Deformation—A Review,” Extreme Mech. Lett., 4, pp. 131–155. [CrossRef]
Chen, C. , Wang, Z. , and Suo, Z. , 2017, “ Flaw Sensitivity of Highly Stretchable Materials,” Extreme Mech. Lett., 10, pp. 50–57. [CrossRef]
Creton, C. , and Ciccotti, M. , 2016, “ Fracture and Adhesion of Soft Materials: A Review,” Rep. Prog. Phys. Phys. Soc., 79(4), p. 046601. [CrossRef]
Wang, L. , Qiao, S. , Ameri, S. K. , Jeong, H. , and Lu, N. , 2017, “ A Thin Elastic Membrane Conformed to a Soft and Rough Substrate Subjected to Stretching/Compression,” ASME J. Appl. Mech., 84(11), p. 111003. [CrossRef]
Meng, X. M. , Wang, Z. W. , Vinnikova, S. , and Wang, S. , 2018, “ Mechanics of Periodic Film Cracking in Bilayer Structures Under Stretching,” ASME J. Appl. Mech., 85(7), p. 071006. [CrossRef]
Mukherjee, B. , Batra, R. C. , and Dillard, D. A. , 2017, “ Edge Debonding in Peeling of a Thin Flexible Plate From an Elastomer Layer: A Cohesive Zone Model Analysis,” ASME J. Appl. Mech., 84(2), p. 021003. [CrossRef]
Ding, J. Q. , Remmers, J. J. C. , Leszczynski, S. , and Huyghe, J. M. , 2018, “ Swelling Driven Crack Propagation in Large Deformation in Ionized Hydrogel,” ASME J. Appl. Mech., 85(2), p. 021007. [CrossRef]
Lü, C. , 2013, “ Mechanics of Tunable Hemispherical Electronic Eye Camera Systems That Combine Rigid Device Elements With Soft Elastomers,” ASME J. Appl. Mech., 80(6), p. 061022. [CrossRef]
Wang, S. , Li, M. , Wu, J. , Kim, D. H. , Lu, N. , Su, Y. , Kang, Z. , Huang, Y. , and Rogers, J. A. , 2012, “ Mechanics of Epidermal Electronics,” ASME J. Appl. Mech., 79(3), p. 031022. [CrossRef]
Luo, J. C. , and Gao, C. F. , 2009, “ Faber Series Method for Plane Problems of an Arbitrarily Shaped Inclusion,” Acta Mech., 208(3–4), pp. 133–145. [CrossRef]
Gao, C. F. , and Noda, N. , 2004, “ Faber Series Method for Two-Dimensional Problems of an Arbitrarily Shaped Inclusion in Piezoelectric Materials,” Acta Mech., 171(1–2), pp. 1–13.
Muskhelishvili, N. I. , 1975, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, The Netherlands.
Jiang, C. P. , 1991, “ The Plane Problem of Collinear Rigid Lines Under Arbitrary Loads,” Eng. Fract. Mech., 39(2), pp. 299–308. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

The leading roles of the tension, compressive, and hoop stresses on the interfaces. The phase diagram of the tension and compressive stresses with respect to (a) semi-axis ratio (k = a/b) and elastic modular ratio (E2/E1), and (b) semi-axis ratio (k = a/b) and Poisson's ratio (ν1), respectively. (c) The phase diagram of the hoop and compressive stresses with respect to semi-axis ratio (k = a/b) and Poisson's ratio (ν1). (d) The influence of axis ratio (k) on the normal stress concentration factor predicted by the theoretical analysis, and Poisson's ratio of soft material is 0.3. (e) The influence of Poisson's ratio (ν1) on the normal stress concentration factor predicted by the theoretical analysis, and the semi-axis ratio (k) is 19. (f) The influence of Poisson's ratio (ν1) on the stress intensity factor at the tip of rigid line predicted by the theoretical analysis.

Grahic Jump Location
Fig. 2

The influence of modulus ratio on (a) normal stress concentration factor, (b) hoop stress concentration factor, and (c) shear stress concentration factor on the interfaces, respectively

Grahic Jump Location
Fig. 1

(a) Diagrammatic sketch of the theoretical model for soft matrix with an elliptical hard inclusion subjected to uniform single tension. (b) A rigid line inclusion inserted in soft matrix, a local polar coordinate system was built at the tip of the inclusion. (c) Schematic diagram of FEA model for an elliptical inclusion in a square matrix (100 mm × 100 mm).

Grahic Jump Location
Fig. 4

Stress diagram based on FEA. The stress components σxx and σyy are shown in the left ((a), (c), and (e)) and right ((b), (d), and (f)) columns, respectively.

Grahic Jump Location
Fig. 5

Stress diagram at the inclusion tips based on the FEA. The stress components σxx and σyy are shown in the left ((a), (c), and (e)) and right ((b), (d), and (f)) columns, respectively.

Grahic Jump Location
Fig. 6

The influence of semi-axis ratio (k = a/b) on the normal stress concentration factor predicted by theoretical analysis and FEA. (a) compressive stress at the point of θ = 0 and (b) tensile stress at the point of θ = 2.

Grahic Jump Location
Fig. 7

(a) Tensile test samples, consisting of rubber matrix (tangogray plx980) and a rigid elliptical inclusion (rigid plastics), painted with grid lines. (b) Reflective strips bonded on the soft matrix close to both tips of hard inclusion. (c) Two air-actuated clamps bonded on the edges of soft matrix. (d) Shape of a grid line without tensile load. (e) Hard inclusion punctured weakly in soft matrix for a tensile load of 20 mm. (f) Hard inclusion punctured distinctly in soft matrix for a tensile load of 40 mm. (g) Deformation of test samples from FEA for a tensile load of 20 mm. (h) The influence of displacement load on the distance between two tips of hard inclusion predicted by theoretical model, simulation and experiment, respectively, where Lh and Li denote the current and initial distance between two reflective strips, respectively; Ls and Lsp are displacement load and specimen length, respectively.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In