Creep rupture due to thermally induced cracking

Abstract

ABSTRACTWe study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization.