Universal Dynamic Fragmentation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>Dimensions

Åström, Jan; Ouchterlony, Finn; Linna, Riku; Timonen, J.

doi:10.1103/physrevlett.92.245506

Cited by 92 publications

(69 citation statements)

References 24 publications

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“…At lower impact velocities the power law regime of the distribution is followed by a hump for the largest fragments which gradually disappears and the cutoff becomes exponential as v 0 increases. The most astonishing feature of the experimental results is that the value of the exponent τ pl = 1.2 ± 0.06 of the power law regime is significantly lower than the values τ br ≈ 1.8 − 2.1 typically found in the fragmentation of threedimensional bulk objects consisting of disordered brittle materials [3][4][5][6]12]. The anomalously low value of τ pl is the consequence of the breakup mechanism of plastic materials which has not been considered by the usual theoretical approaches [6,12].…”

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“…The most astonishing feature of the experimental results is that the value of the exponent τ pl = 1.2 ± 0.06 of the power law regime is significantly lower than the values τ br ≈ 1.8 − 2.1 typically found in the fragmentation of threedimensional bulk objects consisting of disordered brittle materials [3][4][5][6]12]. The anomalously low value of τ pl is the consequence of the breakup mechanism of plastic materials which has not been considered by the usual theoretical approaches [6,12]. In order to reveal the underlying physical mechanisms of the fragmentation of plastic materials, we used a Discrete Element Model (DEM) to simulate the fragmentation of polymeric particles of spherical shape when they impact a hard wall.…”

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“…Several possible mechanisms have been put forward to understand the emergence of the universal power law behavior. For rapid break-up of heterogeneous bulk solids with a high degree of brittleness, the self-similar branching-merging scenario of propagating unstable cracks governed by tensile stresses can explain the main features of the fragment mass distribution [5,[11][12][13], while for shell systems an additional sequential binary breakup mechanism has to be taken into account [7,8]. It is an important question of broad scientific and technological interest how plasticity, and the emergence of complicated stress states like shear affect the fragmentation process.…”

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New Universality Class for the Fragmentation of Plastic Materials

et al. 2010

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We present an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene particles of spherical shape against a hard wall. Experiments reveal a power law mass distribution of fragments with an exponent close to 1.2, which is significantly different from the known exponents of three-dimensional bulk materials. A 3D discrete element model is introduced which reproduces both the large permanent deformation of the polymer during impact, and the novel value of the mass distribution exponent. We demonstrate that the dominance of shear in the crack formation and the plastic response of the material are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena. PACS numbers: 62.20.Mk; 46.50.+a; Fragmentation phenomena are ubiquitous in nature and play a crucial role in numerous industrial processes related to mining and ore processing [1]. A large variety of measurements starting from the breakup of heavy nuclei through the usage of explosives in mining or fragmenting asteroids revealed the existence of a striking universality in fragmentation phenomena [1-10]: fragment mass distributions exhibit a power law decay, independent on the type of energy input (impact, explosion, ...), the relevant length scales or the dominating microscopic interactions involved. Detailed laboratory experiments on the breakup of disordered solids have revealed that mainly the effective dimensionality of the system determines the value of the exponent, according to which universality classes of fragmentation phenomena can be distinguished. Several possible mechanisms have been put forward to understand the emergence of the universal power law behavior. For rapid break-up of heterogeneous bulk solids with a high degree of brittleness, the self-similar branching-merging scenario of propagating unstable cracks governed by tensile stresses can explain the main features of the fragment mass distribution [5,[11][12][13], while for shell systems an additional sequential binary breakup mechanism has to be taken into account [7,8]. It is an important question of broad scientific and technological interest how plasticity, and the emergence of complicated stress states like shear affect the fragmentation process. The fundamental questions of how robust the universality classes are with respect to mechanical properties and whether there exist further universality classes of fragmentation of solids, still remain open.In the present Letter we investigate the fragmentation process of plastic materials by impacting spherical particles made of polypropylene (PP) against a hard wall. Our experiments show that the mass distribution of plastic fragments exhibits a power law behavior with an exponent close to 1.2, which is substantially different from the one of bulk brittle materials in three-dimensions. In order to understand the physical origin of the low exponent, a three-dimensional discrete element model is developed where the sample is discretized in terms of ...

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New Universality Class for the Fragmentation of Plastic Materials

et al. 2010

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“…Note that the value of the exponent τ = 1.7 of p(m) falls close to the theoretical prediction of Refs. [41,42] based on the branching-merging scenario of dynamic cracks: if fragments are formed by the merging of branches of splitting unstable cracks a universal exponent of the fragment mass distribution τ = (2D − 1)/D was predicted depending solely on the dimensionality D of the embedding space. For D = 3 the formula yields τ = 5/3 in the vicinity of our numerical result, although, in our case simulations did not reveal a branching-merging sequence of cracks.…”

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Emergence of energy dependence in the fragmentation of heterogeneous materials

2014

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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.

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“…Importantly, branching models of fragmentation predict that the exponent of the power law is universal and depends only on the dimension D in which the process takes place: Åström et al, 2004;Kekäläinen et al, 2007). In two dimensions, relevant for sea ice breaking at scales larger than ice thickness, this value relates to pdf of surface areas, p s (s):…”

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