Chapter 15 Using Crack Geometry to Determine Fracture Properties Kimberley A. Mac Donald and Guruswami Ravichandran Abstract Linear elastic fracture mechanics theory predicts a parabolic crack opening profile. However, direct observation of crack tip shape in situ for brittle materials is challenging due to the small size of the active crack tip region. By leveraging advances in optical microscopy techniques and using a soft brittle hydrogel material, we can measure crack geometry on the micron scale. For glasses and ceramics, expected crack opening displacements are on the order of nanometers. However, for hydrogels, we can achieve crack opening displacements on the order of hundreds of microns or larger while maintaining brittle fracture behavior. Knowing the elastic properties, we can use crack geometry to calculate the stress intensity factor, K, and energy release rate, G, during propagation. Assuming the gel is hyperelastic, we can also approximate the size of the nonlinear region ahead of the crack tip. Geometric measurement of fracture properties eliminates the need to measure complex boundary and loading conditions, allowing us to explore new methods of inducing crack propagation. Further, this allows us to define measures of fracture resistance in materials that do not fit the traditionally defined theories of fracture mechanics. Keywords Brittle fracture · Confocal microscopy · Crack geometry · Polymers · Soft gels 15.1 Introduction With advances in fields such as wearable devices and implants, soft robotics, and additive manufacturing, the structural performance of soft materials has become of great interest [1–3]. Materials that are mechanically compatible with biological tissues can help improve comfort of wearable devices and reduce inflammation, scarring, and rejection of implants [4]. Soft actuation and reducing joint friction are critical topics in robotics development [5]. Additionally, customized scaffolds, with the porosity to provide critical nutrients, are being used to grow cells into simple organs, where it has been shown that the scaffold’s stiffness has a strong impact on cell growth [6–8]. In all these fields, the mechanical properties of soft polymers are of great interest. However, conventional gels exhibit very low toughness and brittle fracture properties, making them too delicate for most of these high demand applications [9–11]. While brittle fracture is well understood within the linear elastic regime for crystalline materials such as metals and ceramics, the microstructure of polymers is significantly different [12, 13]. Polymers consist of chains of monomers, typically hundreds to hundreds of thousands of monomer units in a chain, where strong covalent bonds form the backbone and weaker hydrogen bonds between chains combine with physical entanglement to form the polymer [14]. Crosslinking, such as in many polymer hydrogels, can provide further strong covalent bonds to form a networked polymer system. This means that mechanisms of polymer failure are significantly different from metals and ceramics. Where there are identifiable slip and cleavage planes in the crystalline structure of metals and ceramics, even networked polymers show complex chain interactions such as chain stretching and pull-out before the strong bonds between monomer units are affected and fracture occurs [15, 16]. Many polymers exhibit features of brittle fracture: no observable permanent deformation and smooth fracture surfaces perpendicular to the loading direction [17]. However, traditional measures of fracture properties were developed based on K. A. Mac Donald ( ) Mechanics of Materials, Sandia National Laboratories, Livermore, CA, USA e-mail: kamacdo@sandia.gov G. Ravichandran Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA e-mail: ravi@caltech.edu © The Society for Experimental Mechanics, Inc. 2021 S. Xia et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-60959-7_15 93
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