On critical exponents for impact fragmentation of spherical solids

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

“…Figure 2, illustrating the phase diagram of impact induced attrition processes, shows that, depending on the velocity, single impacts give rise either to damage or fragmentation of the sample with a sharp transition at the critical velocity v f . The damage -fragmentation transition has already been studied in experiments and computer simulations of impacting spherical samples against a hard wall, using heterogeneous brittle materials [29,31,33,36], plastics spheres [37], and liquid droplets [38]. In these studies, the same qualitative behavior was obtained for the largest fragment masses m 1st , m 2nd as in Fig.…”

“…Over the past decades, detailed knowledge has been accumulated in geology [1,2,18,24], physics [25-28, 28, 29, 29-32], and engineering [19,23,[33][34][35] on single impact breakage phenomena, however, a comprehensive understanding of low velocity impact sequences responsible for the gradual mass reduction and global rounding of solid particles is still lacking. In the physics literature the existence of two distinct energy phases (the damage phase and the fragmentation phase) has been established not only for brittle materials [29,31,33,36], and plastics spheres [37], but also for liquid droplets [38]. Moreover, the same two energy phases have also been reported in the geophysics literature [8] for the collisional attrition of sedimentary particles.…”

Critical behavior for impact fragmentation of spherical solid bodies sensitive to strain rate

“…the mass of the minimum fragment that can be formed as a result of the fragmentation). More detailed information about the simulation method and the algorithm for searching fragments are given in [10,13,15].…”

“…Later, these methods were applied to studying fragmentation in mechanical systems [5,6,[10][11][12][13][14]. The existence of the damage-fragmentation phase transition was confirmed for mechanical systems of various types both experimental studies [11,14] and computer simulations [5,15]. Despite the large amount of experimental and theoretical works, many questions of the critical behavior remain open.…”

“…Molecular dynamics (MD) [12,16], discrete element models (DEM) [5,6,17,18], and SPH method [10,13,15] are used to simulate fragmentation numerically. The choice of the particlebased MD and DEM simulations to analyze the high-velocity impact fragmentation is motivated by lack of reliable models and complexity of describing effects from the continuum point of view, namely plasticity, fracture and phase transitions.…”