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

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 b value, 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.

Numerical investigation of the mixed-mode failure of snow

“…Hence, our model successfully captures the so-called strain-rate dependency of snow [ 31 ]. This increase in snow strength with decreasing loading rate was also well captured by the fiber bundle model of Reiweger et al [ 28 ] and Capelli et al [ 4 ] (also including viscous stress relaxation), but they did not investigate the effect of the loading angle and sintering, simultaneously.…”

Shear failure of weak snow layers in the first hours after burial

“…Data are thus required to describe the mismatch between the weak layer and the slab or the softening behavior prior to failure (Gaume et al, 2018). During natural release, deformation in the snowpack takes place at longer times scales (>1 s), and Capelli et al (2018a) showed that healing of broken bonds or viscoelastic load redistribution are important processes for failure at lower rates. Hence, to model natural release, knowledge of the sintering behavior of different weak layer grain types is relevant.…”

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

“…The higher strength and the higher strain at equal stress for low loading rates observed for snow were reproduced by the FBM. The strain rate divergence is caused by a divergence of the number of intact fibers carrying load and the resulting increase of the load per fiber (see also the discussion about the order parameter in Capelli, Reiweger, Lehmann, et al, 2018). However, at low loading rates the model shows a divergence of the strain rate that was not observed in the experiments (Figure 1b).…”

“…The probability of sintering increases with the number of broken fibers N broken , since we assume that in order to form a new bond, a broken fiber needs to meet another broken one. The effects of sintering speed on the damage process are discussed in more detail in Capelli, Reiweger, Lehmann, et al (2018). The strength of a new ice bond increases with time.…”

“…The effects of relaxation speed on the damage process and failure behavior are discussed in more detail in Capelli, Reiweger, Lehmann, et al (2018). Increasing the relaxation speed leads to faster load transfer from older fibers to younger fibers, which initially carry less load.…”