Speed of crack propagation in dry aqueous foam

Abstract

Applying pressure driving to a single layer of aqueous foam bubbles induces a void propagation that is a surprisingly close analog of dynamic crack propagation. Depending on the rate of applied stress, both a ductile and a brittle mode of propagation are observed, the latter at much higher propagation speeds. A pronounced velocity gap is found, with a well-defined upper limit to the ductile crack speed and a well-defined lower limit to the brittle propagation speed. Both limits can be quantitatively explained by analyzing processes on the scale of single bubbles and single films, respectively, confirming the importance of the microscopic (single-bubble) scale for the overall description of these fracture phenomena. We find that the brittle crack velocity is limited by the speed of wave propagation in the foam, so that the brittle mode can be understood as a supersonic crack.

Response of a two-dimensional liquid foam to air injection: Influence of surfactants, critical velocities and branched fracture

“…Consistently with [1], we have also found that the fragile cracks do not propagate slower than a certain velocity. To measure such a minimal velocity, we have considered experiments where a spontaneous fragile-ductile transition occurs, as considered also in [15]; we then take the displacement of the crack tip between the two images in the fragile regime closest to the transition as an estimate of the minimal velocity of fragile propagation v min .…”

“…The injection rate is quantitatively captured by a simple model balancing the air overpressure with known foam/wall friction laws for incompressible interfaces. We also revisit the critical velocity criteria for the injected air proposed by Arif et al [1]. The upper bound of velocity in the ductile regime, based on the resistance of soap films against wall friction, is shown to hold much better for mobile than for incompressible interfaces.…”

“…We now consider the critical velocities introduced by Hilgenfeldt and colleagues [1]. They have proposed that the speed of propagation of the ductile fracture, i. e. the fastest speed of the injected bubble in our case, cannot exceed a certain threshold, for which friction forces destabilise the Plateau borders in contact with the wall.…”

“…Initially motivated by pattern formation [13,14], this configuration was shown by Hilgenfeldt and coworkers to be ideal to study the limit of stability of a flowing foam [1,15]. They showed that the injected air can propagate either in a ductile regime, pushing bubbles apart by plastic rearrangements without bursting; or in a fragile regime, breaking series of soap films to form narrow cracks, like fracture in brittle materials [16].…”

“…To study the opposite interfacial behaviour, we will show results with a surfactant mixture giving incompressible interfaces. Second, we will test the critical velocities proposed by Hilgenfeldt and colleagues [1,15], namely the maximal velocity of ductile fracture and the minimal velocity of brittle fracture. Third, we will describe branching effects in the regime of fragile fracture.…”