Microstructural effects in aqueous foam fracture

Abstract

We examine the fracture of a quasi two-dimensional aqueous foam under an applied driving pressure, using a network modelling approach developed for metallic foams by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543). In agreement with experiments, we observe two distinct mechanisms of failure analogous to those observed in a crystalline solid: a slow ductile mode when the driving pressure is applied slowly, where the void propagates as bubbles interchange neighbours through the T1 process, and a rapid brittle mode for faster application of pressures, where the void advances by successive rupture of liquid films driven by Rayleigh-Taylor instability. The simulations allow detailed insight into the mechanics of the fracturing medium and the role of its microstructure. In particular, we examine the stress distribution around the crack tip and investigate how brittle fracture localizes into a single line of breakages. We also confirm that pre-existing microstructural defects can alter the course of fracture.

Cracks and fingers: Dynamics of ductile fracture in an aqueous foam

“…We previously constructed a network model for foam fracture encompassing brittle and ductile effects [19] in a long Hele-Shaw cell of thickness (gap between the plates) b * and lateral width W * . In this study we use the same equations and notation with only small modifications which are detailed below.…”

“…In network modeling of ductile fracture we neglect all out-of-plane motion and represent the foam by evolving the fluid structures on the plates, which we now consider in turn. A more complete description of each structure is given by [19].…”

“…Each Plateau border node (PBN) is modeled as a single point in space, denoted x p , moving in the plane of the plates with velocity u p , which are both functions of time, t. The PBN liquid structure on the plates is assumed to have uniformly curved gas-liquid interfaces with equal radii of curvature a p in both directions (a sketch of the PBN geometry is given in figure 3 of [19]); a p is assumed fixed for all time. The equation of motion takes the form…”

“…For a given bubble, each constituent PBN experiences a surface tension force from the attached film that does not form part of the bubble outline; the components of the microscopic stress tensor can be found by summing the moments of these forces about the centre of the bubble. Further details are given in [19]. The principal stresses and their directions are then computed as the eigenvalues and eigenvectors of the deviatoric stress tensor S j .…”

“…We have previously developed a large-scale network model to understand and quantify both modes of foam fracture under an applied driving pressure [19], based on a methodology developed for studying coalescence in molten metallic foams [20,21]. This approach uses a simplified description of each of the fluid structures and incorporates an explicit film rupture criterion in the brittle case [22].…”