How Fast Can Tensile Cracks Propagate in Rock?
Authors: Koul S. , Serati M. , Bahaaddini M. 
Published: September 2023

ABSTRACT
An important issue in rapid brittle fracture is the limiting speed of crack propagation. Continuum mechanics theories suggest that Mode I and Mode II brittle cracks cannot propagate faster than the speed of Rayleigh and Longitudinal waves, respectively. That is, the branching of a propagating crack occurs once the crack speed reaches these upper limits in a material. To verify this hypothesis, this paper presents the results of an experimental program aimed at studying the limit of tensile crack velocity in the Brazilian test using high-speed photography techniques, and combines these with the results found in the literature. Over 100 Brazilian tests with more than 10 different rock types were carried out according to the ASTM standard using either a servo-hydraulic machine or an electromagnetic load frame at wide ranges of load/displacement rates. The fracture process was captured at 130k+ frames per second (fps), and crack initiation, crack propagation and coalescence, as well as the failure mode were studied in each test. Results show that the tensile crack speed in rocks ranges between 50 to 3,000 m/s.

INTRODUCTION AND MOTIVATIONS
Rock dynamics is an interdisciplinary field that deals with rock behaviour under high-strain rates such as earthquakes, impact loads, blasting, and similar seismic events. Dynamic properties of rock and their measurements are, therefore, of critical importance to understanding the propagation of stress waves over time in a loaded rock sample. In particular, accurate measurement of fracture propagation speed can assist with estimating the time to rock disintegration before failure at a given loading/strain rate (Dai et al., 2011; Serati et al., 2014; Serati et al., 2015; Xing et al., 2017). In brittle rock fracturing disasters such as rock bursts and coal-gas outbursts, for instance, knowing the crack velocity can also help with choosing suitable equipment and safeguarding humans and machinery working on the site (Yang et al., 2016).
While crack/fracture propagation varies at various phases of the failure process, studies suggest that the terminal fracture velocity is a characteristic property of rock; the value for which has been suggested numerically and tested experimentally for many rock types (Bieniawski, 1968; Mott, 1948). The present study aims to verify the tensile crack speed in rock-like solids by conducting an extensive literature review supplemented by experiments on selected rock types using high-speed photography methods. Typical measurement techniques adopted in the literature to measure crack speed are first reviewed and their limitations are discussed. Next, over 100 Brazilian tests with more than 10 different rock-like materials – including various rock types, ceramic, brittle polymers, concrete, asphalt, and bricks – were prepared and the speed of crack in tested samples was measured using high recording frame rates of 130,000 Hz and above. Crack initiation, propagation, and coalescence were captured to study the crack speed and failure mode on the Brazilian test results. These results help to explore how fast tensile cracks can propagate in rock.