What happens to fracture energy in brittle fracture? Revisiting the Griffith assumption

Abstract

Abstract. Laboratory experiments involving unconfined compressive failure of borosilicate glass cylinders quantified the elastic strain energy released at failure and the size distribution of the resulting fragments. The data were carefully assessed for potential inaccuracies in surface-area calculation, the contribution of energy from the compression machine relaxation during specimen failure, and possible variations in the specific fracture energy of the specimens. The data showed that more new surface area was created during the failures than would be possible if the long-standing assumption, which is that all the energy involved in creating new rock surface area in brittle material is taken up by the newly created surfaces as surface potential energy and is not available to do further work, were valid. We therefore conclude that the assumption is false. This conclusion is supported by independent data from a previous investigation whose authors did not pursue this particular application. Our result does not affect the validity of Griffith fracture mechanics and is significant only when large numbers of very fine fragments are created by brittle fracture, as in rock-avalanche motion and earthquake rupture, and are identified in particle-size distributions. In such situations our result is very significant to understanding fracture energetics.

Contributions of Rock Mass Structure to the Emplacement of Fragmenting Rockfalls and Rockslides: Insights From Laboratory Experiments

“…The energy consumption efficiency of fragmentation is the core issue in rock fracture dynamics (Davies, McSaveney, & Reznichenko, 2019; Grady & Kipp, 1987; Zhang et al, 2000; Zhang & Zhao, 2014). However, the proportion of kinetic energy dissipated during rock fracture is controversial (Bowman et al, 2012; Crosta et al, 2007; Davies, McSaveney, & Reznichenko, 2019; Haug et al, 2016; Locat et al, 2006). Zhang et al (2000) calculated that only about 5% of energy absorbed by a rock specimen is transformed into kinetic energy of fragments, while most of the energy is dissipated through the fracture process.…”

“…Ghaffari et al (2019) also calculated that more than 94% of absorbed energy is dissipated from a pulverized rock specimen. However, Davies, McSaveney, & Reznichenko (2019) and Davies, Reznichenko, & McSaveney (2019) inferred that only very small part of input energy is taken up as surface free energy in a newly created fragment surface (Savvova et al, 2015; Zdziennicka et al, 2009). For practicality, De Blasio et al (2018) proposed a semiexperimental method by which to obtain the fragmentation energy loss from the fragment size distribution, which indicated that, typically, 0.2–18% of the potential energy is consumed by fragmentation.…”

“…This energy sink caused by fragmentation is due to the generation of a new fragment surface (Chester et al, 2005; Grady, 2008; Hungr, 2006; Livne et al, 2010; Miller et al, 1999). Davies, McSaveney, and Reznichenko (2019) stated that only a very small proportion of the energy is converted to surface potential energy while the main part of energy is released as an elastic body wave. The energy calculation of one rock avalanche event in New Zealand also proved this point of view (Davies, McSaveney, & Reznichenko, 2019).…”

“…Given the lack of knowledge about the comminution limit in our experiments, we chose 0.074 mm, the same value used by Bowman et al (2012), as a limitation. There may be a grain size limit that represents the different mechanisms of fragmentation in rock mass (e.g., 500 μm, Perinotto et al, 2015), but it is unknown under which grain size limit the comminution or fragmentation process can be ignored (Davies, McSaveney, & Reznichenko, 2019). Therefore, this comminution limit is dubious and arbitrary, but we can still capture the characteristics of fragmentation because the relative results of each experiment remain the same.…”

“…Haug et al (2016) proved that the displacement of the center of mass decreases with the degree of fragmentation, suggesting an energy sink during fragmentation in rockfalls and rockslides. However, Davies et al (2019) stated that only a small portion of energy is consumed as fracture surface energy in creating new surface area following fragmentation, and the main part of the energy is possibly converted into an elastic body wave. This theory has also been supported by preparing an approximated energy budget for a real rock avalanche (Davies et al, 2019).…”