(265c) Cavitation Or Fracture? Measuring Material Properties With a Mechanical Instability

The quantitative characterization of mechanical properties for soft materials, such as gels and biological tissues, remains a significant challenge for the field of materials science.  The difficulties lie in the following: large strain and low force responses; nonlinear constitutive behavior; and the impact of surface energy on deformation responses. This talk describes a simple, though not yet broadly adopted, procedure referred to as Cavitation Rheology, which has been shown to provide data that quantitatively corresponds to Young’s modulus and strain energy release rate in gels.^1,2 Most importantly, this technique provides direct measurement of mechanical properties on local length scales, ranging from sub-micron to millimeter, allowing for characterization of material property gradients^1,3. Although quantitative correlation has been demonstrated previously, many open questions remain with regard to the underlying deformation mechanisms related to Cavitation Rheology. The principal concern of this talk is the observed deformation response, which is comprised of a triggered instability whose partially understood physical mechanisms and limitations are explained in detail and verified by experiment.

Cavitation rheology consists of the insertion, pressurization, and monitoring of a fluid filled needle. Pressurization is accomplished through displacement of the plunger of an attached syringe. At the tip of the embedded needle, optical microscopy reveals that a cavity first grows in direct response to plunger displacement (corresponding to increased pressure). At a critical point, the cavity expands rapidly, independently of plunger movement, often resulting in a marked pressure drop within the needle/syringe system, which is monitored using a pressure sensor. It is this pressure peak value, or critical pressure, that has been shown to correspond to both fracture toughness and elastic moduli in several hydrogel materials depending on the size of needle used.

The rapidity of the bubble expansion at the critical pressure indicates that the deformation is associated with the onset of instability. The nature of this instability, either elastic (reversible) or corresponding to the onset of fracture, has been predicted through estimates of the deformation using a spherically symmetric cavity ⁴ and a membrane approximation for the embedded needle geometry². Both approximations lack key elements, preventing their utilization in fully explaining experimental observations. This talk eliminates these shortcomings. It describes the limited parameter space for which the instability may correlate to an elastic instability while comparing the needle geometry with analytical spherical results. It also leverages existing mechanisms for fracture via a spherical void to describe a new formulation for fracture in the embedded needle geometry using a combination of analytical theory and finite element analysis. These deformation mechanisms are then translated into predicted critical pressures dependent on needle size, void surface energy, and ability of the pressurizing fluid to store energy.  Using this new understanding of the relation between critical pressure and material properties, a transition between cavitation and fracture is illustrated for a triblock co-polymer gel system. These results not only provide a basis of understanding for a promising new experimental technique, but also hold implications for void formation governed failure mechanisms, such as crazing, in soft materials.

1.        Zimberlin, J. A., Sanabria-DeLong, N., Tew, G. N. & Crosby, A. J. Cavitation rheology for soft materials. Soft Matter 3, 763 (2007).

2.        Kundu, S. & Crosby, A. J. Cavitation and fracture behavior of polyacrylamide hydrogels. Soft Matter 5, 3963 (2009).

3.        Cui, J., Lee, C. H., Delbos, A., McManus, J. J. & Crosby, A. J. Cavitation rheology of the eye lens. Soft Matter 7, 7827 (2011).

4.        Zhu, J., Li, T., Cai, S. & Suo, Z. Snap-through Expansion of a Gas Bubble in an Elastomer. The Journal of Adhesion 87, 466–481 (2011).