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Viscous control of shallow elastic fracture: peeling without precursors

  • John R. Lister (a1), Dominic J. Skinner (a1) (a2) and Timothy M. J. Large (a1) (a2)

Abstract

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.

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Corresponding author

Email address for correspondence: lister@damtp.cam.ac.uk

References

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Viscous control of shallow elastic fracture: peeling without precursors

  • John R. Lister (a1), Dominic J. Skinner (a1) (a2) and Timothy M. J. Large (a1) (a2)

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