[Paper Review] The single edge notch fracture test for viscoelastic elastomers

Farhad Kamarei, Fabio Sozio+1 more|arXiv (Cornell University)|Oct 20, 2024

Orthopaedic implants and arthroplastyMedicine3 citations

TL;DR

This paper proposes a refined application of the Griffith criticality condition (−∂W^Eq/∂Γ₀ = G_c) to single edge notch fracture tests in viscoelastic elastomers, accounting for non-Gaussian elasticity and nonlinear viscosity. It demonstrates that fracture initiation depends critically on loading rate due to viscous effects, with shear-thinning materials showing the strongest rate sensitivity, and reveals that classical models overestimate critical tearing energy when cracks are large relative to specimen size.

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.

Motivation & Objective

• To analyze the single edge notch fracture test in viscoelastic elastomers using a recently derived Griffith criticality condition that separates equilibrium and non-equilibrium energy contributions.
• To investigate how non-Gaussian elasticity and nonlinear viscosity influence fracture initiation under quasi-static loading.
• To quantify the limitations of classical fracture models that neglect viscous dissipation and geometric effects in real specimens.
• To validate the proposed framework against experimental data and demonstrate its predictive power for fracture onset in large pre-existing cracks.
• To explore the potential of single edge notch tests as indirect tools for measuring nonlinear viscoelastic properties at large deformations.

Proposed method

• Applies the refined Griffith criticality condition (−∂W^Eq/∂Γ₀ = G_c) to model crack growth in viscoelastic elastomers under quasi-static loading.
• Uses finite viscoelastic constitutive models to compute stored equilibrium energy (W^Eq), non-equilibrium energy (W^NEq), and dissipated viscous energy (W^v) during deformation.
• Performs a parametric study varying material properties such as non-Gaussian elasticity, viscosity nonlinearity, and loading rate to assess their influence on critical global stretch (Λ_c) and stress (S_c).
• Compares model predictions with experimental data from single edge notch tests, using normalized global stretch (Λ = l(t)/L) and global stress (S = P(t)/(HB)).
• Evaluates the accuracy of classical Rivlin-Thomas and Greensmith-Lindley approximations (formula 4 and 5) under realistic conditions with finite cracks.
• Derives the critical tearing energy as T_c = G_c(1 + f_c) = G_c − ∂W^NEq/∂Γ₀ − ∂W^v/∂Γ₀, linking it directly to intrinsic fracture energy and viscous dissipation.

Experimental results

Research questions

• RQ1 How do non-Gaussian elasticity and nonlinear viscosity affect the critical global stretch and stress at fracture in single edge notch tests?
• RQ2 To what extent do classical models (e.g., Rivlin-Thomas) fail when applied to elastomers with significant viscous dissipation and finite pre-existing cracks?
• RQ3 Can the refined Griffith criterion (−∂W^Eq/∂Γ₀ = G_c) accurately predict fracture onset across varying loading rates and material behaviors?
• RQ4 How does the loading rate influence the sensitivity of fracture initiation to material nonlinearity, particularly in shear-thinning elastomers?
• RQ5 Can single edge notch tests be repurposed to infer nonlinear viscoelastic properties at large strains and strain rates?

Key findings

• Fracture initiation in single edge notch tests is strongly dependent on loading rate due to nonlinear viscous effects, with critical global stretch (Λ_c) increasing non-monotonically and critical global stress (S_c) increasing monotonically with rate.
• Shear-thinning elastomers exhibit the highest sensitivity to loading rate, highlighting the importance of nonlinear viscosity in fracture prediction.
• The classical Rivlin-Thomas formula (4) and Greensmith approximation (5) significantly overestimate the critical tearing energy T_c when the pre-existing crack is not much smaller than the specimen dimensions.
• The refined Griffith criterion (−∂W^Eq/∂Γ₀ = G_c) accurately predicts fracture onset and explains rate-dependent behavior through the balance of equilibrium elastic energy and intrinsic fracture energy.
• The critical tearing energy T_c is decomposed into contributions from fracture (G_c) and viscous dissipation (−∂W^NEq/∂Γ₀ − ∂W^v/∂Γ₀), clarifying its physical origin.
• Experimental results show good agreement with model predictions, confirming the framework’s validity and suggesting that single edge notch tests can serve as indirect probes for large-strain viscoelastic properties.