The single edge notch fracture test for viscoelastic elastomers

TL;DR

This paper advances the fracture analysis of viscoelastic elastomers by applying the Griffith criticality condition in its Eq- and NEq-plus-dissipation form to the single edge notch test in full 3D. It couples a two-potential viscoelastic constitutive model with a nonlinear, deformation-sensitive viscosity to compute equilibrium energy, non-equilibrium energy, and dissipated energy, then uses the derivative of the equilibrium energy with respect to crack area to predict crack nucleation and the associated tearing energy. A large parametric study across elasticity, viscosity, and 3D crack geometries shows nonmonotonic rate dependence of the critical stretch, monotonic rate dependence of the critical stress, and substantial deviations from the classical Rivlin–Thomas estimate when dissipation and 3D effects are non-negligible. Comparisons with acrylate-elastomer experiments demonstrate overall agreement in trends and validate the approach, while highlighting the need to characterize large-strain viscoelastic properties to accurately predict rate-sensitive fracture in elastomers.

Abstract

Making use of the Griffith criticality condition recently introduced by Shrimali and Lopez-Pamies (Extreme Mechanics Letters 58: 101944, 2023), this work presents a comprehensive analysis of the single edge notch fracture test for viscoelastic elastomers. The results -- comprised of a combination of a parametric study and direct comparisons with experiments -- reveal how the non-Gaussian elasticity, the nonlinear viscosity, and the intrinsic fracture energy of elastomers interact and govern when fracture nucleates from the pre-existing crack in these tests. The results also serve to quantify the limitations of existing analyses, wherein viscous effects and the actual geometries of the pre-existing cracks and the specimens are neglected.

Figures (16)

• Figure 1: Schematic of the single edge notch fracture test for a viscoelastic elastomer illustrating the geometry of the specimen, the applied time-dependent separation $l(t)$ between the grips, and the corresponding force $P(t)$ at the grips. It is standard practice to use the normalized quantities $\mathrm{\Lambda}=l(t)/L$ and $S=P(t)/(H B)$. We refer to them, respectively, as the global stretch and the global nominal stress. The focus of this work is on initial sizes $A$ of the crack (the "notch") that are larger than the initial thickness $B$ of the specimen.
• Figure 2: Rheological representation of the two-potential viscoelastic model (\ref{['S-I1-J']})-(\ref{['Evolution-I1-J']}).
• Figure 3: Representative FE solution for the equilibrium stored-energy function $\psi^{{\rm Eq}}(I_1)$ (shown in MPa) over the initial $\mathrm{\Omega}_0$ and current $\mathrm{\Omega}(t)$ configurations of a specimen, with pre-existing crack of length $A=2$ mm, at a global stretch $\mathrm{\Lambda}=1.5$, that has been stretched at the global stretch rate $\dot{\mathrm{\Lambda}}_0=10^0$ s$^{-1}$.
• Figure 4: Representative examples of the equilibrium energy (\ref{['Int-WEq']}) and its derivative (\ref{['Eq Release Rate']}) plotted as functions of the global stretch rate $\dot{\mathrm{\Lambda}}_0$ and the initial crack size $A$ at a fixed global stretch $\mathrm{\Lambda}$.
• Figure 5: Representative example of the derivative (\ref{['Eq Release Rate']}) of the equilibrium elastic energy plotted as a function of the global stretch $\mathrm{\Lambda}$ and the global stretch rate $\dot{\mathrm{\Lambda}}_0$ for a fixed initial crack size $A$.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4