How the Slow Propagation of Wing Cracks Can Control Creep

Abstract:

The slow growth of micro-scale wing cracks weakens rock by forming linked zones of damage that eventually lead to failure at stresses below that of the short-term failure strength. The displacement accumulated on systems of micro-fractures is termed brittle creep. An existing brittle creep flow law is based on the growth of wing cracks from pre-existing flaws. This flow law suggests that the strain rate of the brittle creep is heavily influenced by the length of the pre-existing initial flaws, a, where small variations in a can produce orders of magnitude variation in strain rate. The value of a is usually taken to equal grain size though it is difficult to test what governs a and thus brittle creep. While rock physics experiments are capable of using acoustic emissions to track fracture propagation, direct observation of key fracture parameters such as the initial flaw length is a major challenge. Here, we conduct physical experiments using a semi-brittle gel-polymer (Carbopol) to investigate the impact of a single wing crack set on creep. The fracture propagation in Carbopol is phenomenologically similar to sub-critical fracture growth in natural rock. The combination of the brittle phase of the polymer, which allows it to fracture, with the ductile component that dampens fracture growth, serves as an analog for stress-corrosion creep. We find that the smallest initial flaw sizes need to accumulate more shear strain to propagate wing cracks. Additionally, the propagation of wing cracks controls the strain rate on the initial flaw. The experiments show a typical creep curve where the measured pulling force increases to a maximum as fracture growth slows and ceases (secondary creep). Besides their potential impact on brittle creep, wing cracks are also observed in semi-brittle mid-crustal rocks and have been postulated to impact seismicity in regions that generate slow-slip events. Understanding what governs their propagation and arrest has the potential to shed light on the complex interplay between brittle and ductile deformation mechanisms.