New Universality Class for the Fragmentation of Plastic Materials

Abstract

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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