When elastomers are loaded under a nearly hydrostatic tensile stress, failure generally occurs by the formation of cavities. This phenomenon often called cavitation in the literature is of great practical interest since rubbers are often loaded in confined geometries, for example, in coatings or in the vicinity of particles in highly filled rubbers. Also, a dilatant stress of considerable magnitude is set up at the tip of a sharp crack.1
Yet, the details of the cavity nucleation and growth are still poorly understood and a reliable cavitation criterion based on material properties is still lacking. A variety of models have been proposed to describe the expansion of a pre-existing cavity as a function of the elastic properties of the material, its surface tension, or its fracture toughness.2–12 However, experimental studies in well-controlled conditions have been much less available to the theoretical community. It is the goal of this study to investigate experimentally and for materials with a well-defined molecular structure, the fracture of simple elastomer networks in nearly hydrostatic tension.
The earliest documented evidence of the cavitation process is rather old13, 14 and experiments were carried out with commercial rubbers (neoprene and natural rubber) using a relatively confined geometry called “poker-chip.” The rubber disks were glued to a cylindrical sample holder and stretched in the thickness direction. Both studies observed that the stress–strain curve obtained in that geometry showed a marked and irreversible softening above a well-defined value of stress and noted that the fracture surfaces after failure contained the evidence of what they called “internal cracks” or macroscopic cavities.
Some years later Gent and Lindley15 used the same “poker-chip” geometry on natural rubber formulations to carry out their widely known systematic investigation. They prepared vulcanized rubber disks of identical diameter and different thicknesses varying therefore the aspect ratio (i.e., level of confinement). They found that the critical stress (defined as the inflection point in the stress–strain curve) decreased as the test-piece thickness was increased from very small values, becoming substantially constant for moderately thick samples. Postmortem observations showed that a series of small internal cracks were formed in the thin disks (uniformly distributed across the section), and only one or two large cracks were formed in the center in moderately thick disks. The most important observation of that study was that the fracture strength of the poker-chip samples appeared to be a reproducible material constant proportional to the elastic modulus. This certainly brought Gent and Lindley to name this internal cracking process a cavitation process and to model it as a simple deformation process (i.e., independent of initial cavity size) rather than as a fracture process.
They used the elastic theory of cavity inflation developed by Green and Zerna16 for neoHookean behavior to justify that the apparent yield point in the stress–strain curve appeared when the local hydrostatic pressure reached a critical value of 5E/6 (where E is the small strain Young's modulus of the rubber).
This criterion of critical pressure was also confirmed by the studies of Cho and Gent17 using layers of transparent silicone rubber bonded to two steel balls or to two parallel steel cylinders. Upon loading, an inflection point appeared in the stress–strain curve when the applied stress reached a value of the order of the Young's modulus E, and optical observations showed concomitantly the presence of large cavities in the rubber layers. For thinner layers (layer thickness less than 5% of sphere diameter), two interesting effects were observed: in a continuous tensile test, the critical stress increased markedly above the elastic modulus, and if the load was instead kept constant just below the critical value, cavities appeared over time. These two results seem to indicate that the material is in a metastable state when the applied stress exceeds the small strain elastic modulus.
Experiments with rigid spherical inclusions have also been performed and reported in the literature, to characterize cavitation phenomena. Some earlier studies used samples of transparent polyurethane with rigid spherical inclusions18, 19 and observed that cavities appeared at the edge of the inclusion due to the local high-triaxial stress there. They performed experiments with different types of polyurethanes and found a strong correlation between the critical stress and the modulus.
In conclusion, existing evidence shows a strong correlation between the critical stress (i.e., described from a change in stiffness) and the elastic modulus of the rubber, whereas postmortem observations and common sense point to a fracture process which should introduce the idea of defect size and should not be necessarily proportional to the modulus. This apparent discrepancy has been pointed out theoretically20, 21 but never really verified experimentally.
The difficulty of studying cavitation experimentally lies mainly in the control of the stress field in nearly hydrostatic conditions, since this requires a reproducible and well-controlled confined geometry. The flat-to-flat geometry (“poker-chip”) for producing cavitation samples has been the most commonly used geometry reported in the literature. The main reason to use the poker-chip geometry is to introduce a large hydrostatic tension component in the sample. Furthermore, the incompressibility of the rubbery materials, which usually undergo large deformations during testing, is limited to relatively small strains before failure. This provides the benefit that the infinitesimal elasticity theory can be used in the analytical work without introducing large errors. In this study, the choice of the experimental geometry was guided by the dual goal to minimize multiple cavitation (possibly to focus on a single cavitation event near the center of the sample) and to avoid aligment problems. A sphere-to-flat geometry was used to obtain a moderate confinement of the elastomer. The designed geometry for the study was chosen and fixed at the following degree of confinement: a ratio h/R = 0.055 and a/h = 10 where h is the minimum separation between the sphere and the flat, R is the radius of curvature of the sphere, and a is the diameter of the elastomer sample.
The elastomers chosen were unfilled and fully transparent model polyurethanes22 synthesized directly in the sample holder by end-linking monodisperse polypropylene glycol chains of different molecular weights with a triisocyanate. Perfect adhesion to the glass surfaces was obtained by covalent bonds. Special care was taken to obtain fully transparent bubble-free samples with a very well-controlled chemical structure and to investigate the effect of variations in chemical structure on the cavitation process, three specific model networks were selected: two monodisperse networks made, respectively, with short (unentangled) and long (entangled) precursor chains and a bimodal network made with a blend of long and very short chains. The rationale behind using a bimodal network composed of short and long chains was to obtain a network which would display a more pronounced strain hardening at lower levels of strain than a homogeneous network with an identical Young's modulus. In turn, we expected this feature to influence the resistance to cavitation based on Gent and Wang's theoretical predictions.20