Effects of material properties on the fragmentation of brittle materials

Abstract

We present a fundamental investigation of the influence of material and structural parameters on the mechanics of fragmentation of brittle materials. First, we conduct a theoretical analysis (similar to Drugan's single wave problem, Drugan, W..) and obtain closed form solutions for a problem coupling stress wave propagation and single cohesive crack growth. Expressions for a characteristic fragment size s 0 and a characteristic strain-rateε 0 are given. Next, we use a numerical approach to analyze a realistic fragmentation process that involves multiple crack interactions. The average fragment size s is calculated for a wide variety of strain-ratesε and a broad range of material parameters. Finally, we derive an empirical function that relates the normalized fragment size s/s 0 to the normalized strain-rateε/ε 0 and that fits all of the numerical results with a single master curve.

The cohesive element approach to dynamic fragmentation: the question of energy convergence

“…We have shown in previous work [23] that the shape of the unloading curve does not change significantly the fragmentation results. Therefore, we use a simple irreversible linear decaying cohesive law:…”

“…A first item that will be briefly discussed in the paper is the choice of the cohesive law. We have shown in a different work that the shape of the cohesive-law softening curve has little effect on the fragmentation results [20,23]. This paper illustrates that initially rigid cohesive laws can successfully model the 'side-branching' fracture mechanism [24,25].…”

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

“…Therefore, we only describe the theory derived by Grady (1982), extended by Glenn and Chudnovsky (1986), and the recent numerical results of Zhou et al (2006c). They all propose a law relating the number of fragments and the strain rate in the case of the fragmentation of a homogeneous material.…”

“…Employing the cohesive methodology, Zhou et al (2006c) detailed the effect of wave interactions and normalized their results, making implicit the dependence on material parameters in a simple equation. The normalization involves three relevant parameters: s 0 , t 0 and _ e 0 .…”

Explosive fragmentations of alumina (Al2O3) under quasistatic compressive loading

“…We have proposed a model that linked the non-dimensional fragment size to the nondimensional strain rate [11]:…”