Invariant fractocohesive length in thermally aged elastomers

TL;DR

The paper shows that the fractocohesive length $\xi = G_c/W_c$ remains invariant during homogeneous thermo-oxidative aging of elastomers, even as both $W_c$ and $G_c$ decline substantially. Through experiments on SBR and SR across multiple aging temperatures and times, complemented by a phase-field AT1 framework that links $\ell$ to $\xi$ via $\ell = \frac{3}{16}\xi$, the authors demonstrate consistent flaw-transition behavior governed by $\xi$ and provide a practical pathway to predict $G_c$ from tensile data. The invariant $\xi$ connects bulk and fracture responses, enabling fracture-toughness predictions for aged elastomers without extensive fracture testing, and it integrates with phase-field or cohesive-zone models using a network-morphology state variable. Limitations arise under non-homogeneous aging or mesoscale reorganization, but the work establishes a robust, physics-based bridge between aging kinetics and fracture resistance with broad implications for predictive durability of elastomeric components.

Abstract

The fractocohesive length - the ratio between fracture toughness and work-to-fracture - provides a material-specific length scale that characterizes the size-dependent fracture behavior of pristine elastomers. However, its relevance to thermally aged materials, where both toughness and work of fracture degrade dramatically, remains unexplored. Here, we demonstrate that despite severe thermal embrittlement, the fractocohesive length remains invariant throughout thermal aging, independent of temperature or duration. We verify this invariance experimentally for two elastomer systems (Styrene Butadiene Rubber and Silicone Rubber) at multiple aging temperatures for aging times up to eight weeks. This finding bridges a critical gap in fracture mechanics of aged polymers: while the evolution of work-to-fracture can be predicted from well-established constitutive models that track network changes (crosslink density and chain scission), the evolution of fracture toughness has lacked predictive frameworks. The invariance of fractocohesive length enables direct calculation of fracture toughness at any aging state from the predicted work of fracture, eliminating the need for extensive fracture testing on aged elastomers and providing a crucial missing link for computational fracture predictions in aged elastomeric components.

Figures (4)

• Figure 1: (a) Schematic representation of the thermal aging process in elastomers. Exposure to elevated temperatures for extended durations can induce significant changes in the polymer network, including chain scission and crosslinking. (b) After thermal aging, the mechanical response of elastomers can change, resulting in increased stiffness and reduced stretchability.
• Figure 2: (a) and (b) show the evolution of the stress–strain response during tensile tests and the force–displacement response during trouser tear tests, respectively, for SR after aging at $120\celsius$. (c) and (d) present the variation of the work of fracture, $W_c$, and the fracture toughness, $G_c$, respectively, with aging for SBR and SR.
• Figure 3: Evolution of the fractocohesive length, $\xi = G_c / W_c$, for SBR and SR during aging at various exposure times and temperatures. The constant value of $\xi$ indicates that the fracture energy evolves in the same proportion as the work of fracture during thermal aging.
• Figure 4: (a) Relationship between phase-field length scale $\ell$ and fractocohesive length $\xi$ demonstrating the constant factor of 3/16 from AT1 formulation across all aging times. (b) Flaw sensitivity analysis showing stretch-to-rupture versus cut depth for unaged (blue) and aged (red) SBR, with the transition occurring at the same critical depth corresponding to the fractocohesive length (vertical gray dashed line)