Emergence of energy dependence in the fragmentation of heterogeneous materials

TL;DR

This study reveals that energy dependence in material fragmentation arises when lower-dimensional objects are embedded in higher-dimensional spaces, due to a transition between different cracking mechanisms influenced by impact velocity.

Contribution

It uncovers a robust mechanism explaining energy dependence in fragmentation, resolving controversies and highlighting the role of dimensionality and impact velocity.

Findings

Energy dependence occurs with lower-dimensional objects in higher-dimensional space.

Two distinct fragmentation mechanisms are controlled by impact velocity.

Mass distributions of different cracking mechanisms are robust across thicknesses.

Abstract

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 plate-like 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 non-universality of the complete mass distribution is the consequence of blending the contributions of universal partial processes.