Creep of a Fracture Line in Paper Peeling

Abstract

The slow motion of a crack line is studied via an experiment in which sheets of paper are split into two halves in a "peel-in-nip" (PIN) geometry under a constant load, in creep. The velocity-force relation is exponential. The dynamics of the fracture line exhibits intermittency, or avalanches, which are studied using acoustic emission. The energy statistics is a power-law, with the exponent β ∼ 1.8 ± 0.1. Both the waiting times between subsequent events and the displacement of the fracture line imply complicated stick-slip dynamics. We discuss the correspondence to tensile PIN tests and other similar experiments on in-plane fracture and the theory of creep for elastic manifolds.

Line creep in paper peeling

“…The main finding, interpreted via Eq. (2) then indicates that the effective roughness exponent ζ ∼ 1/3, which is the expected equilibrium value for a long-range elastic problem with α = 1 [7].…”

“…[6] and an early account of the creep results published as Ref. [7]. The mathematical description of the line is a crack position h(x, t), where h is the position coordinate along the direction of line propagation and x is the coordinate perpendicular to h. On the average, the crack moves with the creep velocity v (h = vt).…”

Line Creep in Paper Peeling

“…At T = 0, there is a depinning transition at a critical force (or stress intensity factor) separating a moving line from a frozen one, and the transition is described by a set of exponents appropriate for a second-order non-equilibrium one. The thermal fluctuations become important in the low-velocity regime since then the line velocity attains its value due to thermally-excited local avalanches [4,8].…”

“…It has been recently realized to be related to the way the interface averages the disorder (fracture toughness here) during its motion: due to the jerky, intermittent dynamics one has "cusps" or discontinuities in the auto-correlation function of the position and in the disorder as well [2,9]. The experimental device is the same used in [4,10]. A 30 mm wide paper sheet is peeled in half along its major plane between two rotating cylinders.…”

“…The setup can be studied in several separate cases starting from constant strain rate conditions to creep (constant load, discussed here [4]). It is analogous to fracture mechanics for a crack that is confined to a plane, for example using a solid-solid interface between two bulks [5].…”