Interfacial Cavitation with Surface Tension: New Insights into Failure of Particle Reinforced Polymers

TL;DR

This work reframes failure in particle-reinforced elastomers as an interfacial cavitation problem controlled by surface tension, rather than solely bulk cavitation. By combining a semi-analytical energy-based model with Finite Element simulations, it demonstrates that interfacial defects can cavitate at lower pressures than bulk defects and that surface tension introduces a finite, length-scale-dependent threshold. A phase diagram distinguishes cavitation-dominated and delamination-dominated regimes, offering explanations for Gent and Park’s bead-size trends and bonding effects, and enabling rough estimates of interfacial toughness from experimental data. The findings shift design emphasis toward interfacial properties to optimize multi-material systems and provide a framework for tuning reinforced polymers through surface-tension and adhesion control.

Abstract

Understanding and mitigating the failure of reinforced elastomers has been a long-standing challenge in many industrial applications. In an early attempt to shed light on the fundamental mechanisms of failure, Gent and Park presented a systematic experimental study examining the field that develops near rigid beads that are embedded in the material and describe two distinct failure phenomena: cavitation that occurs near the bead in the bulk of the material, and debonding at the bead--rubber interface [Gent, A.N. and Park, B., 1984. Journal of Materials Science, 19, pp.1947-1956]. Although the interpretation of their results has not been challenged, several questions stemming from their work remain unresolved. Specifically, the reported dependence of the cavitation stress on the diameter of the bead and the counterintuitive relationship between the delamination threshold and the material stiffness. In this work, we revisit the work of Gent and Park and consider an alternative explanation of their observations, interfacial cavitation. A numerically validated semi-analytical model shows that in {the} presence of surface tension, defects at the bead-rubber interface may be prone to cavitate at lower pressures compared to bulk cavitation, and that surface tension can explain the reported length-scale effects. A phase-map portrays the distinct regions of `cavitation dominated' and `delamination dominated' failure and confirms that for the expected range of material properties of the rubbers used by Gent and Park, interfacial cavitation is a likely explanation. Crucially, this result offers a new avenue to tune and optimize the performance of reinforced polymers and other multi-material systems.

Figures (7)

• Figure 1: Experimental results recreated from gent1984failure. (a) Illustration of loaded sample with embedded glass bead alongside typical observations of cavitation and debonding shown for $1.2$ mm beads. (b) Illustration of loaded sample with two embedded glass beads alongside a typical sequence of cavitation progress shown for $1.25$ mm beads in matrix of stiffness $E=2.2$ MPa. (c) Critical pressure at cavitation shown for different elastomers with stiffness modulated by varying degrees of cross-linking and with $600\mu$m diameter beads. (d) Influence of bead diameter on critical pressure at cavitation shown for poybutidiene (Cis-4) samples. (c,d) Dashed line denotes theoretical cavitation limit $(p_{bc}=5/6E)$. (e) Influence of bonding strength on critical pressure shown for Natsyn 2200 with three different surface treatments (blue -- bonded, black -- untreated, grey -- treated). Results in (c-e) are shown for experiments with single beads as in (a) and inserted images are provided to indicate the corresponding mode of failure.
• Figure 2: Surface tension induces cavitation instability in strain-stiffening materials. Pressure-stretch response using neo-Hookean material model and a two-parameter Lopez-Pamies material model poulain2017damage for PDMS with base to cross-linker ratio of 20:1 with and without surface tension for (a) Bulk cavitation and (b) Interfacial cavitation. The pressure is normalized by the shear modulus $\mu$. Here for the case with surface tension we use the representative value of the normalized surface tension $\alpha = \gamma/(\mu d_0) = 2.5$.
• Figure 3: Problem setting and results in absence of surface tension. The black curve shows the relationship between normalized cavity volume and applied pressure for case without surface pressure, reproduced from henzel2022interfacial. Grey dashed lines represent the bulk and interfacial cavitation pressures $(p_{bc}, p_{ic})$ without surface tension $(\gamma=0)$, respectively. Illustration shows shapes of the interfacial cavity is at grows (in absence of surface tension) where curve shades correspond to the diamond markers along the pressure-volume curve. The pressure can be applied remotely (as illustrated), or internally at the cavity wall.
• Figure 4: The role of surface tension on interfacial cavitation, without delamination. (a) Pressure volume response for varying levels of normalized surface tension $(\alpha)$ shown using three different models. Grey dashed curves correspond to analytical model using surface area approximation based on expansion without surface tension (i.e. with $S_n$); black curves correspond to the spherical cap approximation (i.e. with $S_0$); and blue dots correspond to the simulation results, in agreement with the legend on the right panel. (b) Critical pressures for interfacial cavitation correspond to the curves in (a). Black dash-dotted curve corresponds to bulk cavitation.
• Figure 5: Theoretical model explains experimental trends without delamination and for constant bead size. Experimental results here are rescaled from Fig. \ref{['gent_rep']}(c) -- see caption therein for details. Theoretical curves are obtained via the analytical model detailed in Section \ref{['analitical']} with the spherical cap approximation and shown for different values of $d/\gamma$.