Viscous control of shallow elastic fracture: peeling without precursors

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/mu(E) over bar (2)d(5)=Bd kappa(3)/144 mu, where d is the sheet's thickness, B = (E) over bar d(3)/12 its stiffness, (E) over bar = E/(1 -nu(2)) its plane-strain modulus, mu the fluid viscosity, M the applied bending moment and kappa = 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.