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Toughness of soft materials such as elastomers and gels depends on their ability to dissipate energy and to reduce stress concentration at the crack tip. The primary energy dissipation mechanism is viscoelasticity. Most analyses and models of fracture are based on linear viscoelastic theory (LVT) where strains are assumed to be small and the relaxation mechanisms are independent of stress or strain history. A well-known paradox is that the size of the dissipative zone predicted by LVT is unrealistically small. Here we use a physically based nonlinear viscoelastic model to illustrate why the linear theory breaks down. Using this nonlinear model and analogs of crack problems, we give a plausible resolution to this paradox. In our model, viscoelasticity arises from the breaking and healing of physical cross-links in the polymer network. When the deformation is small, the kinetics of bond breaking and healing are independent of the strain/stress history and the model reduces to the standard linear theory. For large deformations, localized bond breaking damages the material near the crack tip, reducing stress concentration and dissipating energy at the same time. The damage zone size is a new length scale which depends on the strain required to accelerate bond breaking kinetics. These effects are illustrated by considering two cases with stress concentrations: the evolution of spherical damage in a viscoelastic body subjected to internal pressure, and a zero degree peel test.
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Mapping deformation and dissipation during fracture of soft viscoelastic solid
Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel.
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- PAR ID:
- 10499371
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 186
- Issue:
- C
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 105595
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jmps.2024.105595
