Abstract:

This paper presents experiments showing that the nominal tensile strength of granite specimens measured in three-point bending tests increases with the logarithm of the loading rate. Based on these experiments, we propose a criterion for macroscopic breakage wherein failure occurs when a given proportion of available atomic-scale bonds are broken. Consistent with the experiments, this theory predicts that a linearly increasing applied load is expected to result in a linear relationship between the load at the time of macroscopic breakage and the logarithm of the loading rate. Furthermore, the parameters ascertained from the results of the increased load experiments give a lower bound prediction with the same slope for the time to failure under constant loading

Introduction

Static fatigue is a phenomenon that describes a material's tendency to fail under subcritical loads after a period of time (Zhurkov, 1984). Static fatigue is a ubiquitous property of materials and is typically expressed as either an exponential or a power-law relationship between the time to failure (i.e., life of the structure) and the nominal applied stress (Gy, 2003).

According to Zhurkov's 1984 experiments on over 50 materials, the relationship between the lifetime of a specimen under uniaxial load, tf, and the induced tensile stress, s, can be determined by an Arrhenius-type law:

(equation)

where k and T are Boltzmann's constant and absolute temperature, respectively. The characteristic time t0 is found to have the same order of magnitude as the period of thermal oscillation of atoms. U0 is interpreted as the interatomic binding energy. The coefficient ? is related to the characteristic of a solid that translates an applied stress into energy available for breaking interatomic bonds. Zhurkov (1984) concluded that the behavior of static fatigue in solids can be represented by this experimentally determined correlation.

The experiments of Zhurkov (1984) included over 50 materials spanning metals, alloys, non-metallic crystals, and polymers. Other experiments have been conducted which applied his theory to experimental results specifically testing rocks (e.g. experiments reviewed by Cruden, 1974, Scholtz, 1972 & 2002). Static fatigue of rocks has been connected in past research to initiation and aftershocks associated with earthquakes (Scholz, 2002) and failure of rocks due to mining-induced stresses (Cruden, 1974). Our present research is mainly motivated by recent investigation showing that characterization of static fatigue properties of a rock can help to interpret subcritical breakdown pressures observed in hydraulic fracture laboratory experiments (Bunger and Lu, 2014; Lu et al., 2015).

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