The poker-chip experiments of synthetic elastomers explained

Abstract

In a recent study, Kumar and Lopez-Pamies (J. Mech. Phys. Solids 150: 104359, 2021) have provided a complete quantitative explanation of the famed poker-chip experiments of Gent and Lindley (Proc. R. Soc. Lond. Ser. A 249: 195–205, 1959) on natural rubber. In a nutshell, making use of the fracture theory of Kumar, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 112: 523–551, 2018), they have shown that the nucleation of cracks in poker-chip experiments in natural rubber is governed by the strength — in particular, the hydrostatic strength — of the rubber, while the propagation of the nucleated cracks is governed by the Griffith competition between the bulk elastic energy of the rubber and its intrinsic fracture energy. The main objective of this paper is to extend the theoretical study of the poker-chip experiment by Kumar and Lopez-Pamies to synthetic elastomers that, as opposed to natural rubber: (i) may feature a hydrostatic strength that is larger than their uniaxial and biaxial tensile strengths and (ii) do not typically exhibit strain-induced crystallization. A parametric study, together with direct comparisons with recent poker-chip experiments on a silicone elastomer, show that these two different material characteristics have a profound impact on where and when cracks nucleate, as well as on where and when they propagate. In conjunction with the results put forth earlier for natural rubber, the results presented in this paper provide a complete description and explanation of the poker-chip experiments of elastomers at large. As a second objective, this paper also introduces a new fully explicit constitutive prescription for the driving force that describes the material strength in the fracture theory of Kumar, Francfort, and Lopez-Pamies.