Two Possible Defect Growth Modes in Soft Solids

Abstract

Guided by the experimental observations in the literature, this paper discusses two possible modes of defect growth in soft solids for which the size-dependent fracture mechanics is not always applicable. One is omni-directional growth, in which the cavity expands irreversibly in all directions; and the other is localized cracking along a plane. A characteristic material length is introduced, which may shed light on the dominant growth mode for defects of different sizes. To help determine the associated material properties from experimental measurement, the driving force of defect growth as a function of the remote load is calculated for both modes accordingly. Consequently, one may relate the measured critical load to the critical driving force and eventually to the associated material parameters. For comprehensiveness, the calculations here cover a class of hyperelastic materials. As an application of the proposed hypothesis, the experimental results (Cristiano et al., 2010, “An Experimental Investigation of Fracture by Cavitation of Model Elastomeric Networks,” J. Polym. Sci. Part B: Polym. Phys., 48(13), pp. 1409–1422) from two polymers with long and short chain elastomeric network are examined. The two polymers seem to be susceptible to either of the two dominating modes, respectively. The results are interpreted, and the material characteristic length and other growth parameters are determined.

Energy-Based Strength Theory for Soft Elastic Membranes

“…We proposed two defect growth modes in Ref. [48], one is omnidirectional dissipation mode and the other is cracking. There is a characteristic material length that separate the two modes.…”

“…When the defect is very small, we proved in Ref. [48] that the omnidirectional growth mode is predominant. As the defect grows to a characteristic size of A*, scaled with the ratio Γ s /Γ p , the growth mode transits from the first mode to the cracking mode.…”

“…To compare with the previous results, we define and normalize the driving force in the same way as in Eq. (1) using the size of an imaginary circular hole, A = 2A c /π, that gives the same surface area as the crack [47,48]. The material is neo-Hookean.…”

“…In a recent study by the authors [47,48], we proposed two defect growth modes, omnidirectional growth, and cracking. In the first mode, energy is dissipated all around the defect, and in the second mode, energy is only dissipated in a layer next to the cracking plane.…”

“…In Refs. [47,48], we considered the simple case of a solid under hydrostatic tension p at the remote. Due to the large compliance of the elastomer materials, the defect was modeled as a spherical cavity of radius A.…”