Fragment velocity distribution in the impact disruption of thin glass plates

Experimental Investigation of Visible-Light and X-ray Emissions during Rock and Mineral Fracture: Role of Electrons Traveling between Fracture Surfaces

Radiation phenomena are usually observed during fracture of quartz-bearing rocks. Since quartz is a piezoelectric material, the associated electrical processes such as the electrification of fracture surface and the flight of electrons between fracture surfaces should be important for radiation during fractures. In this article, supposing that travelling electrons between crack surfaces cause the radiation, we experimentally investigate X-ray emission in a vacuum and visible-light emission in the atmosphere during rock and mineral fracture and verify the consistency of both emissions. The number of electrons in flight between surfaces during fracture that result in X-ray is estimated and the comparison with the number of photons in visible light suggests that one electron repeatedly collides with N2 molecules. The estimated number of collisions resulting in a visible-light emission is slightly less than the expected upper limit. This is reasonable because the collision would cause the light emission not always in the wavelengths of visible light. Moreover, the number of electrons resulting in X-rays is comparable with the number of electrons resulting in the emission of radio waves during fracture obtained in previous studies. Thus, we conclude that the radiations during fracture can be attributed to the flight of electrons between fracture surfaces. Finally, we evaluate the feasibility of observing the X-ray emission in planetary exploration and the radio waves and the visible light in natural earthquakes and find that these radiations are observable.

Curvature flows, scaling laws and the geometry of attrition under impacts

Impact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. Here we establish the first link between microscopic, particle-based models and the mean field theory for these processes. Based on realistic computer simulations of particle-wall collision sequences we first identify the well-known damage and fragmentation energy phases, then we show that the former is split into the abrasion phase with infinite sample lifetime (analogous to Sternberg's Law) at finite asymptotic mass and the cleavage phase with finite sample lifetime, decreasing as a power law of the impact velocity (analogous to Basquin's Law). This splitting establishes the link between mean field models (curvature-driven partial differential equations) and particle-based models: only in the abrasion phase does shape evolution emerging in the latter reproduce with startling accuracy the spatio-temporal patterns (two geometric phases) predicted by the former.

Emergence of energy dependence in the fragmentation of heterogeneous materials

The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of universality depending mainly on the dimensionality and on the brittle-ductile mechanical response of the system. Recently, experiments and computer simulations have reported an energy dependence of the exponent increasing with the imparted energy. These novel findings question the phase transition picture of fragmentation phenomena, and have also practical importance for industrial applications. Based on large scale computer simulations here we uncover a robust mechanism which leads to the emergence of energy dependence in fragmentation processes resolving controversial issues on the problem: studying the impact induced breakup of platelike objects with varying thickness in three dimensions we show that energy dependence occurs when a lower dimensional fragmenting object is embedded into a higher dimensional space. The reason is an underlying transition between two distinct fragmentation mechanisms controlled by the impact velocity at low plate thicknesses, while it is hindered for three-dimensional bulk systems. The mass distributions of the subsets of fragments dominated by the two cracking mechanisms proved to have an astonishing robustness at all plate thicknesses, which implies that the nonuniversality of the complete mass distribution is the consequence of blending the contributions of universal partial processes.

Mechanisms for fragment formation in brittle solids

A model for mode I fracture in brittle materials is used to elucidate the relationship between characteristics of the fracture process, such as crack roughness, fractal dimension, and fragment size distributions. It is shown that different roughness in local regions of the crack path leads to different mechanisms for the subsequent fracture of those regions. Formation of two robust power laws for the distribution of formed fragments is observed, governing the size distribution of smaller and larger fragments. We connect measurements in fragment size distribution with the local roughness of cracks in the region of fragment formation.