Transition from damage to fragmentation in collision of solids

Abstract

We investigate fracture and fragmentation of solids due to impact at low energies using a twodimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged and a fragmented state with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition. PACS number(s): 64.60.Ak, 46.30.Nz

Analyzing fragmentation of simple fluids with percolation theory

“…Moreover, experimental data [2][3][4][5] are rather sparse and often the experimental conditions are ill defined. As a consequence, the question of the possible existence of universal fragmentation mechanisms remains an open problem [6].…”

“…In many fragmentation processes the experimental observation, over many orders of magnitude, of power law (scale invariant) fragment size distributions is another possible indication of universal classes. In this case, the value of the power law exponent would be the corresponding fingerprint [2,6].…”

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

“…First, the analysis of the onset of the damage-fragmentation transition for slender projectiles, based on the maximum and average fragment mass, is refined to identify more transparently this continuous phase transition (Kun and Herrmann, 1999;Timar et al, 2012). Second, an attempt is made to capture so-called shattering transition (Kun and Herrmann, 1999) -the elusive terminal fragmentation defined by the uniformly monatomic debris (mmax ≡ 1) and predicted by the piecewise-linear model to correspond to the impact velocity of approximately 45 km/s. Most importantly, emerging unifying features of the nonlinear and saturable dependence of the maximum fragment mass upon the set of impact parameters and ballistic state variables are captured by a single reverse-sigmoid phenomenological model.…”

Emergence of energy dependence in the fragmentation of heterogeneous materials

“…During the past decades research on fragmentation mainly focused on the statistics of fragment masses (sizes) obtained by the breakup of heterogeneous materials [1,9,10]. A large number of experimental [1,[5][6][7][8][9][10][11][12][13][14][15][16][17] and theoretical studies [13,[18][19][20][21][22][23][24] have confirmed that the mass distribution of fragments is described by a power law functional form. The exponent of the distribution was found to show a high degree of robustness, i.e., investigations revealed that the value of the exponent does not depend on the type of materials, amount of input energy, and on the way the energy is imparted to the system until materials of a high degree of heterogeneity are fragmented [1,9,10].…”

“…The value of the exponent is mainly determined by the dimensionality of the system [13,15,18,19,21,23,[25][26][27] and by the brittle or ductile mechanical response of the material [28]. The universality of fragmenting has been shown to be the fingerprint of an underlying phase transition from the damaged to the fragmented phase of the breakup process [5,6,14,18].…”