Where curling stones collide with rock physics: Cyclical damage accumulation and fatigue in granitoids
Authors: Leung Derek , Fusseis Florian , Butler Ian 
Published: February 2023

Fatigue and damage accumulation in granitoids are classical, but poorly characterised, rock mechanics problems. In order to explore these phenomena, we consider colliding curling stones as a rock physics experiment. Curling stones are made using granitoids from either Ailsa Craig (Scotland) or Trevor (North Wales), which are chosen for their uniformity, strength, and durability. During a curling game, stones are slid over an ice sheet and made to collide along a circumferential striking band. From a rock physics perspective, the collision of curling stones can be modelled as unconfined uniaxial compression of two convex surfaces under well defined boundary conditions. A curling stone experiences about 2900 collisions per season and is played for 10-15 years before refurbishment, which provides a unique long-term opportunity to study fatigue and damage accumulation under cyclic loading.Here, we first determine the stress magnitudes and strain rates of head-on curling stone impacts using a series of on-ice experiments involving a high speed camera and pressure-sensitive films. We then characterise the observed damage that these collisions produce on the centimetre and micrometre scale using photogrammetry, synchrotron microtomography, optical microscopy, and backscattered electron imaging. We show that during each impact, a curling stone is stressed to at least 300-680 MPa (for a maximum-velocity scenario of 2.9&#177;0.1 ms-1), which exceeds the unconfined compressive strength of the rocks (232-395 MPa; Nichol, 2001, J. Gemm. 27/5). Over its lifetime, a curling stone thus experiences thousands of impacts that will cause damage. The strain rates of these impacts (24&#177;4 s-1) most closely resemble seismic magnitudes, suggesting that the impacts are dynamic in nature. This is supported by the type of damage observed in aged curling stones: (1) Hertzian cone fractures, (2) ejection of rock powder during collisions, and (3) minor spalling microcracks. Most samples show damage being confined to macroscopic Hertzian cone fractures and their immediate collet zones in the relatively narrow striking band. Within the striking band, the circumferential density of cone fractures is limited to about 2-2.5 fractures/cm. Surprisingly, damage does not appear to extend beyond about 3-5 cm into the stones along a radial direction.Our observations allow us to formulate a model for damage evolution in curling stones. We infer that high-velocity/high-stress impacts initiate cone fractures up to a specific spatial density. As they mature over repeated impacts in the same regions of the striking band, cone fractures progressively propagate and coarsen with subsequent collisions, concentrating and channelling the accumulating damage. This damage geometry is surprisingly effective in shielding the rest of the stones from the reaching critical stress levels for damage. Our findings are significant for applications where rocks are exposed to large numbers of high-stress impacts and suggest that a relatively narrow damage zone can dampen even high-impact stresses over a relatively moderate network of fractures.