Viscous control of shallow elastic fracture: peeling without precursors
| Autor: | John R. Lister, Dominic J. Skinner, Timothy M. J. Large |
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| Přispěvatelé: | Apollo - University of Cambridge Repository |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Fluid Mechanics. 868:119-140 |
| ISSN: | 1469-7645 0022-1120 |
| DOI: | 10.1017/jfm.2019.185 |
| Popis: | We consider peeling of an elastic sheet away from an elastic substrate through propagation of a fluid-filled crack along the interface between the two. The peeling is driven by a bending moment applied to the sheet and is resisted by viscous flow towards the crack tip and by the toughness of any bonding between the sheet and the substrate. Travelling-wave solutions are determined using lubrication theory coupled to the full equations of elasticity and fracture. The propagation speed $v$ scales like $M^{3}/\unicode[STIX]{x1D707}\bar{E}^{2}d^{5}=Bd\unicode[STIX]{x1D705}^{3}/144\unicode[STIX]{x1D707}$, where $d$ is the sheet’s thickness, $B=\bar{E}d^{3}/12$ its stiffness, $\bar{E}=E/(1-\unicode[STIX]{x1D708}^{2})$ its plane-strain modulus, $\unicode[STIX]{x1D707}$ the fluid viscosity, $M$ the applied bending moment and $\unicode[STIX]{x1D705}=M/B$ the sheet’s curvature due to bending; and the prefactor depends on the dimensionless toughness. If the toughness is small then there is a region of dry shear failure ahead of the fluid-filled region. The expressions for the propagation speed have been used to derive new similarity solutions for the spread of an axisymmetric fluid-filled blister in a variety of regimes: constant-flux injection resisted by elastohydrodynamics in the tip leads to spread proportional to $t^{4/13}$, $t^{4/17}$ and $t^{7/19}$ for peeling-by-bending, gravitational spreading and peeling-by-pulling, respectively. |
| Databáze: | OpenAIRE |
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