Only recently has a theory been developed for the plastic deformation of amorphous materials (e.g. polymer solids, metallic alloys, or polydisperse granular mixtures). While crystalline materials are understood to deform through the creation and propagation of dislocations, such a theoretical construct does not apply when there is no long-range order between particles. It has now been proposed that plastic deformation in samples lacking long-range order is brought about through localized shear transformational zones (STZs), and predictions of STZ theory have been observed in molecular dynamics simulations.
This EAGER proposal conducts an exploratory investigation of shear deformation in granular mixtures in an 'annular planar Couette' geometry that allows arbitrarily large values of approximately pure shear. Particles are constrained to move in an annular ring whose diameter is much larger than the size of an individual particle. As a result, the particle motion is to good approximation planar, hence the awkward name. A distinguishing feature of this proposal, separating it from previous work in this geometry, is the use of birefringence to accurately calculate forces on individual particles. Such analysis has been carried out in Couette shear, which has a rotational component, and simple 'pure' shear to low strains, but these experiments will be the first to have the benefits of both irrotational deformation as well as extremely large strains. In addition to measuring the forces, the individual particle motion will be tracked, and regions of plastic deformation defined. This exploratory work will establish the efficacy of video and birefringent analysis in this geometry, while determining appropriate stress and strain-rate limits for subsequent investigations. The theory of shear transformational zones makes several testable predictions. Most importantly, it predicts a relation between a particle's elastic potential energy, caused by interactions with surrounding particles, and that particle's plastic (irreversible) motion. The proposed experiments will test our ability to measure simultaneously the elastic forces, and hence energies, and particle motion, enabling the first direct test this prediction. STZ theory also predicts a relation between the global strain-rate, the creation of STZs, and the applied global stress field. The annular planar geometry allows for control of the externally imposed stress field, so these predictions can also be tested. Because many of the predictions center on the behavior of the shear band, which has not been observed in previous experiments, our preliminary investigation will focus on the suitability of this geometry for such a study. The intellectual merit of this proposal lies in the development of the first experiments to allow for arbitrary, irrotational flow while simultaneously tracking particles and the forces on them. Particle mobility will be measured and correlated with the local potential energy field, and regions of irreversible motion (shear transformational zones) identified. How the size, frequency, and speed of these zones depend on particle size, packing fraction, and externally imposed stress and strain-rate will be measured. All proposed research will involve undergraduates. There is a broad consensus of the value of undergraduate research in general, and benefits include increased retention and participation of women and minorities. The broader impact of this project lies in the training of 1-2 undergraduate researchers for future graduate work in soft condensed matter.
The PI has a long track record of working with undergraduates in general, and women and under-represented groups in particular.