Many pervasive construction materials, including wood, paper, plastics and concrete, exhibit creep when subjected to stresses below the yield stress. This can lead to catastrophic failure at prolonged, moderate loads. Remarkably, the creep response of these dissimilar materials shares at least two important features: First, the average time-to-failure decreases exponentially with the applied stress. This suggests that a stress-enhanced, thermally-activated process governs the creep. Secondly, the variability of the time-to-failure between samples is huge, which is usually attributed to their stochastic microstructures. Owing to the strong molecular bonds between the constituents of typical construction materials, they creep slowly, and the time-to-failure under typical loading conditions can be very long, which is experimentally challenging. Therefore, we consider an experimental model system for studying the thermally-activated, delayed failure. Weakly attractive colloidal particles in suspension form a sample-spanning network with the low-frequency mechanical response of an elastic solid. This material is a statistically homogeneous, hierarchically structured solid, with two distinct length-scales: that of the particles and that of the filaments. The interaction potential between the particles is controlled in this system, so that the thermally-activated remodeling of the material operates on experimental time-scales. The creep response of the colloidal gel is investigated in simple shear, using a stress-controlled rheometer. For each constant shear stress, the shear strain is measured as a function of time. After an initial elastic deformation, the material deforms slowly at an essentially constant rate. After a time-delay, the material fails abruptly. This delay time decreases exponentially with the applied stress. Moreover, if the gel is made anisotropic by applying a high rate pre-shear, the delay time is reduced, and two regimes appear with different exponential factors. It is hypothesized that the initial creep is governed by a distributed, stochastic failure process, which preserves the statistical homogeneity of the sample. This slow process is followed by avalanching critical crack growth and failure. The time-to-failure is dominated by the initial process, which can be model using mean-field theory, by virtue of the assumed statistical homogeneity. In this model, the stress-enhanced dissociation dynamics of individual particle bonds are related to the stochastic fracture of strands, which, in turn, are govern the delay time of the macroscopic failure.
2013.