Kinetic Monte Carlo algorithm for thermally induced breakdown of fiber bundles

Fiber bundle models are one of the most fundamental modeling approaches for the investigation of the fracture of heterogeneous materials being able to capture a broad spectrum of damage mechanisms, loading conditions, and types of load sharing. In the framework of the fiber bundle model we introduce a kinetic Monte Carlo algorithm to investigate the thermally induced creep rupture of materials occurring under a constant external load. We demonstrate that the method overcomes several limitations of previous techniques and provides an efficient numerical framework at any load and temperature values. We show for both equal and localized load sharing that the computational time does not depend on the temperature; it is solely determined by the external load and the system size. In the limit of low load where the lifetime of the system diverges, the computational time saturates to a constant value. The method takes into account the secondary failures induced by subsequent load redistributions after breaking events, with the additional advantage that breaking avalanches always start from a single broken fiber.

Figure 1

Comparison of the CPU time for simulations with the traditional approach and with the kinetic Monte Carlo (KMC). Equal load-sharing simulations were carried out with a bundle of $N_0={10}^5$ fibers. For the quenched disorder of fiber strength Weibull distributions with $m=2$ and 3 are considered. Results of the KMC algorithm are indicated by the open symbols, while their filled counterparts represent the results of the traditional method.

Figure 2

Comparison of the CPU time for simulations with the traditional approach and with the kinetic Monte Carlo (KMC). Local load-sharing simulations were carried out on a square lattice of side length $L=256$. For the quenched disorder of fiber strength Weibull distributions with $m=2$ and 3 and a uniform distribution between 0 and 1 are considered. Results of the KMC algorithm are indicated by the open symbols, while their filled counterparts represent the results of the traditional method.

Figure 3

Size dependence of the CPU time of kinetic Monte Carlo simulations for ELS and LLS at several load and temperature values with two Weibull exponents. For both ELS and LLS simulations a power-law dependence on the number of fibers $N_0$ is evidenced for load values which fall in the plateau regime in Figs. 1 and 2. Straight lines represent power laws of exponent 2.