Dynamic fragmentation of ceramics, signature of defects and scaling of fragment sizes

Abstract

a b s t r a c tDefects play a critical role in the dynamic fragmentation process of structural ceramics. Cracks initiate at seemingly random locations, propagate and coalesce to form fragments. The process is accompanied by stress release waves, whose influence is difficult to account for without numerical analysis. In this paper, we use a finite-element program with a cohesive fracture capability, to relate a defect distribution contained in a material with the resulting number of fragments. We show how the distribution tail, e.g. the number of large defects, and the rate at which cracks can be initiated at these sites have a critical influence on the generation of stress release waves and thus on the fragmentation process. Our numerical calculations yield a new factor, which we label communication factor, that we use to normalize the average fragment size and to define a new scaling function of material properties, defect statistics and loading rate.

Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled?

“…Recently, using expanding ring numerical tests, Levy and Molinari [10] generalized these expressions to heterogenous materials:…”

“…Therefore, similarly as the fragment size s ch , which is inverse proportional to the number of fragments, f 1 is a decreasing function of the left tail's slope of the cohesive strength distribution. Empirical arguments have shown that f 1 is comprised between 1 and √ 2 [10]. The second function f 2 is a decreasing function of the ratio between σ c,aver − σ c,min and σ c,aver , and is comprised between 0 and 1.…”

“…In section five, the evolution of the average fragment size with strain rate and material parameters is investigated. We compare our results to prior one-dimensional numerical results [10], as well as analytical energy models [5,6] in order to underline their limitations. Finally, in section six, we expose the reasons for these limitations, and provide a discussion summarizing the physical mechanisms that operate during dynamic fragmentation.…”

“…For more general fragmentation events and for a full consideration of the physics of the problem, it has become customary to resort to computer simulation, [2,22,19,23,24,10]. Numerical approaches aim to describe all the relevant physical mechanisms of the fragmentation event, which remain not well understood.…”

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

“…Recently, the small-scale 2D-MD simulations were also used by Sator and his collaborators (Sator et al, 2008, Sator andHietala, 2010) to investigate generic behaviors and damage evolution in the instantaneous point fragmentation of the LJ brittle solid colliding with a wall. In addition to MD, examples of computational techniques utilized recently in the dynamic fracture and fragmentation investigations include particle models (Baker and Warner, 2012;Kumar and Ghosh, 2015), discrete element models (Wittel et al, 2008;Iturrioz et al, 2009;Timar et al, 2010Timar et al, , 2012Paluszny et al, 2014), finite element methods (Levy and Molinari, 2010;Ugrcic, 2013), and meshfree methods (Wu et al, 2014;Li et al, 2012Li et al, , 2015.…”