Dynamics of Fragmentation: Developing a non-Equilibrium Mechanism for Impact-loading tests on Rock Materials

Abstract:

Formation of fragments as the result of dynamic processes associated with impulsive loads has been the subject of numerous studies ranging from shaped-charge jet break up and rock blasting to bolide impacts, and, more recently, earthquake rupture. The dynamic strength of solids is varies as a strong function of loading rate, and, in completely failed solids, the characteristic size of fragments is related to the loading dynamics. In this study, we present some novel results using fragmentation of an “order” parameter in an isotropic body, while we use a non-equilibrium thermodynamic formulation to infer characteristics of the fragments. The order parameter is related to general rigidity of the system and is investigated in 3D space including amplitude and phase modes. To this end, we use the idea of the formation of topological defects in the course of rapid pressure changes and show that a power-law scaling describes transient strength versus inverse of the stress-ramp time. Furthermore, we illustrate that the coefficient of this power-law is deeply connected to relaxation (healing) time of the body. In addition, we show that dynamic polarization patterns of the dynamic cracks are analogous to the transition from ferrimagnets to paramagnets, providing insight to the dynamics of microscopic-scale catastrophic failure. This connection helps us to use the Kibble-Zurek mechanism (KZM) to infer the size of fragments from loading rate when considering a linear loading ramp. The idea behind the KZM is to compare the relaxation time (or healing time of the system in equilibrium) with the timescale of change of the control parameter (ε). In addition, we discuss a case where inherent defects are present prior to the impulse load and discuss the effect of impurities on the scaling coefficients. To support our approach, we use the results of fast-loading experiments on Westerly Granite supported by recording multiple acoustic emissions.