Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow.

Achille Capelli,Peter Lehmann,Jürg Schweizer,Ingrid Reiweger

doi:10.1103/physreve.98.023002

Abstract

Snow is a heterogeneous material with strain- and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the bvalue, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b≈2, a value higher than that of a classical FBM without healing (b=3/2). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

Highlights

Failure of heterogeneous materials by gradually increasing load is a progressive process which starts from damage at the microscale
We show that the combination of sintering and load relaxation significantly changes the character of the failure
We presented a version of a fiber-bundle model including a combination of two healing mechanisms: (a) sintering, which is equivalent to creating new fibers with a probability depending on time and the number of broken fibers, and (b) time-dependent relaxation of load inhomogeneities between fibers

Summary

Introduction

Failure of heterogeneous materials by gradually increasing load is a progressive process which starts from damage at the microscale. Fiber-bundle models (FBM) are widely used to study the failure process of heterogeneous materials [2]. In FBMs a complex behavior of the system arises from the interaction of multiple single elements (fibers) with heterogeneous properties (strength), which obey simple rules (e.g., elastic deformation). The FBM models allow investigating the influence of local microscopic mechanisms on the (global) failure of the whole system. FBMs are often used to study material failure in the context of statistical physics and the analogy to phase transitions and critical phenomena. A variety of modifications of FBMs have been proposed to study the failure of different types of heterogeneous materials (e.g., [2,3])

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