Energy release rate of a single edge cracked specimen subjected to large deformation
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ORIGINAL PAPER
Energy release rate of a single edge cracked specimen subjected to large deformation Zezhou Liu · Michael Zakoworotny Jingyi Guo · Alan T. Zehnder · Chung-Yuen Hui
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Received: 8 June 2020 / Accepted: 20 August 2020 © Springer Nature B.V. 2020
Abstract The single edge notch specimen (SEN) is commonly used to measure the fracture toughness, or critical energy release rate of soft elastic materials. To measure toughness, an expression for the energy release rate, J , the mechanical energy available for growing the crack per unit area, is needed. Since strains in these fracture experiments can easily exceed several hundred percent, large deformation analysis is needed to calculate J . An approximate formula for J in SEN samples subjected to moderately large deformation was given by Rivlin and Thomas in J Polym Sci 10:291–318. https://doi.org/10.1002/ pol.1953.120100303 (1953) and Greensmith in J Appl Polymer Sci 7:993–1002. https://doi.org/10.1002/app. 1963.070070316 (1963). However, this formula works only for small crack lengths, for stretch ratio up to two Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10704-020-00479-7) contains supplementary material, which is available to authorized users. Z. Liu · J. Guo · A. T. Zehnder · C.-Y. Hui (B) Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA e-mail: [email protected] M. Zakoworotny Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA C.-Y. Hui Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan
and does not match the linear elastic result in the limit of small strains. In this paper we carry out a series of finite element (FE) simulations to obtain accurate approximations that are valid for all practical crack lengths and strain levels. Our FE result shows that the small crack approximation of by Rivlin and Thomas in J Polym Sci 10:291–318. https://doi.org/10.1002/pol. 1953.120100303 (1953) does not work well in the small strain regime, and in particular, result of Greensmith in J Appl Polymer Sci 7:993–1002. https://doi.org/10. 1002/app.1963.070070316 (1963) underestimates the energy release rate for stretch ratios less than 1.5. Keywords Single edge notch specimen · Energy release rate · Large deformation · Finite element method
1 Introduction and previous works Recent advances in soft materials, especially the ability to make highly compliant and tough hydrogels (Gong et al. 2003; Sun et al. 2012) have renewed interest in the study of fracture behavior of elastic, stretchable materials (Tanaka et al. 2005; Kundu and Crosby 2009; Sun et al. 2012; Kim et al. 2020). In elastic solids, the driving force for crack growth is the energy release rate J , defined as the change in the sum of the elastic strain energy stored in the crack specimen and the potential energy of the loading system per unit area of crack growth. The resistance to fracture is
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