Experimental identification of fracture toughness of a carbon black-filled styrene butadiene rubber undergoing energy dissipation by Mullins softening

Highlights

• Experimental characterization of the toughness of a carbon-black filled SBR.

• Energy dissipation by Mullins softening upon crack propagation in a rubber.

• Local strain field measures during pure shear crack propagation.

• Estimate of a crack propagation criterion in a filled rubber.

Abstract

The impact of the loading history on the resistance to break of a carbon-black filled styrene butadiene rubber is explored experimentally. Carbon-black filled rubberlike materials soften significantly upon the first loading due to the well known Mullins effect. The impact of this effect on the critical energy release rate at break, $G_c$, of the considered material is quantitatively estimated. For this purpose, the classical notched pure shear geometry is considered and the seminal global analysis from Rivlin and Thomas (1953) is adopted. Moreover, the same analysis is extended to non-elastic materials in order to account for the Mullins softening and define the critical energy release rate, $G_c^{\ast }$, characterizing the creation of new crack surfaces without including the energy dissipated by Mullins softening. Both global quantities, $G_c$ and $G_c^{\ast }$, appear decreasing with the increase of softening already undergone by the material, stressing the difficulty of proposing a predictive criterion for the material resistance to failure. Finally, thanks to the local measures of the strain fields on the free surface of the pure shear specimen just before the crack propagation, it has been possible to evaluate the amount of Mullins dissipation upon the crack propagation and to explore the possible existence of an intrinsic value, $G_0$, characterizing the crack propagation independently of any other source of dissipation.

Introduction

The strength of elastomers can be affected by the presence of cracks initiated during use by fatigue or accidentally by sharp objects. The growth of pre-existing cracks has been studied for several decades, following the seminal work of Rivlin and Thomas (1953). These authors proposed an energy fracture criterion defined as an extension of the linear elastic fracture mechanics Griffith criterion (Griffith, 1921). The latter applies to non-dissipative elastic materials only and was extended to rubbers under the assumption that any source of energy dissipation is confined in the crack tip vicinity, and can therefore be neglected in the global energy balance. This assumption was experimentally verified by Rivlin and Thomas (1953) on non-filled natural rubbers. It allows calculating the energy release rate, commonly noted $G$, which designates the decrease in total potential energy per increase of crack surface area. In a structure, when $G$ reaches a material critical energy release rate $G_c$, the crack propagates creating new surfaces. Therefore, when G can be determined, the growth of a crack can be predicted independently of the specimen shape or size.

The energy criterion such as defined by Rivlin and Thomas (1953) has been commonly used for filled rubbers (Glucklich and Landel, 1976, Medalia, 1987, De and Gent, 1996, Hamed and Park, 1999, Gherib et al., 2010 among others), and $G_c$ is often asserted on a pure shear geometry, which provides a simple analysis and reliable values (Roucou et al., 2019). However, carbon-black filled elastomers undergo significant softening when first submitted to a level of strain never applied before, due to the well known Mullins effect (Mullins, 1969, Diani et al., 2009). The phenomenon is rate independent and induces energy dissipation due to the degradation of the bonded layer around the carbon-black particles (Diaz et al., 2014). Therefore, when considering a notched pure shear sample of such a material, submitted to a monotonic loading, the energy dissipation cannot be considered localized to the vicinity of the crack tip only. Recently, Qi et al. (2018) have proposed a theoretical framework to account for bulk energy dissipation for mode-I plane stress cracks under steady state propagation in a model rubber undergoing Mullins softening. The strain energy release rate $G$ is defined as the sum of an intrinsic material parameter $G_0$, and a dissipative part $G_D$ depending on the amount of energy consumed by Mullins softening upon loading and crack propagation. Such a decomposition is inspired by the same decomposition adopted in order to account for the viscoelasticity of soft materials (see the topical review from Persson et al., 2005). Their theory is developed for an incompressible Neo-Hookean material modified by the Ogden and Roxburgh (1999) model to account for the Mullins softening. Their computational approach aims to estimate the value of $G_0$. Capitalizing on this remarkable theoretical work, the present study intends to investigate experimentally the resistance to failure of an actual elastomer undergoing Mullins softening, in order to estimate the dissipative part of the energy release rate $G_D$ and address the possible existence of an intrinsic parameter $G_0$.

For this purpose, thin plates of carbon black filled SBR were manufactured by the French tire manufacturer and cut into pure shear test geometries. Fracture tests were run on virgin and preloaded notched samples in order to estimate the contribution of the Mullins energy dissipation on the critical energy release rate. On one side, a simple global energy balance analysis using the experimental macroscopic stress–strain curves provides access to two quantities, the classical global critical strain energy release rate $G_c$ as defined by Rivlin and Thomas (1953), which characterizes the global material resistance to fracture, and the original critical energy release rate $G_c^{\ast }$ characterizing the change of stored energy during the crack growth. On the other side, monitoring the local strain using digital image analysis on the free surfaces of the pure shear specimens, allows estimating the data required to calculate $G_0$ and $G_D$ by following the theoretical analysis of Qi et al. (2018). Moreover, the calculations carried out give access to quantitative separation of the Mullins energy dissipation during the loading driving to the crack propagation, and of the Mullins energy dissipation during crack propagation. This work provides a direct comparison between the theory proposed by Qi et al. (2018) and actual experiments.