Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass, and the notch radius rho. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age-and history-dependent, plastic relaxation time scale tau(pl)(0) and an effective loading time scale tau(ext) ((K) over dot(I), rho), where (K) over dot(I) is the tensile stress-intensity-factor rate. The toughness is predicted to scale with root rho independently of xi equivalent to tau(ext)/tau(pl)(0) for xi << 1, to scale as T root rho log(xi) for xi >> 1 (related to thermal activation, where T is the temperature), and to feature a nonmonotonic behavior in the crossover region xi similar to O(1) (related to plastic yielding dynamics). These predictions are verified using 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of time-scale competition and far-from-steady-state elasto-viscoplastic dynamics for understanding the toughness and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented, and possible implications for applications are discussed.