Plasticity more than (linear elastic crack) Propagation may govern standard Propagation Saw Test in snow: evidence from “Fracture toughness of mixed-mode anticracks in highly porous materials” experiments1

Nicola M Pugno, Hamed Haftbaradaran, Mahmood Heshmati

An extensive experimental campaign of propagation saw tests (PST) has recently been conducted, enabling systematic investigation of critical cut length vs. slope angle in snowpacks1. PST is considered crucial for understanding avalanche release. Using a linear elastic fracture mechanics (LEFM) framework built upon a linear elastic analysis, it was concluded that not a theoretical but a phenomenological mixed-mode fracture criterion governing fracture behavior of the weak layer can explain calculated energy release rates corresponding to experimental measurements.1 In spite of this, we noted that while experiments presented a clear trend, the application of LEFM dispersed them, thus nor the theoretical nor the phenomenological approaches may result and indeed resulted in a good experimental comparison. Intrigued by this discrepancy, we show that strains at crack tip are indeed not consistent with linear elasticity for snow and instead that a simple and classical quadratic cap failure envelope combined with static equilibrium can explain results of these experiments once plastic (thus nonlinear) behavior of the weak layer under combined loading is considered. This is a natural consequence of the brittle-to-ductile transition, which is predicted by classical mechanics for any material by reducing the size scale,2 thus failure of sufficiently “short” slabs of snow must be governed by plasticity rather than brittle fracture often considered in standard PST analyses. This finding builds on the original PST studies in snow suggesting such a transition at scales comparable to standard PST3, as we have verified also calculating in a self-consistent manner the size of the plastic/cohesive zone: thus it is not surprising to us that at the length scale of standard (1 m) PSTs plastic/cohesive zone may dominate resulting in plastic failure and in general necessitating elasto-plastic more than linear elastic fracture mechanics. Summarizing our analysis highlights the importance of these complex measurements,1 even if adopting a viewpoint different from the LEFM-based phenomenological interpretation,1 by showing that they are very robust and that can be much better understood as a result of a simple nonlinear plastic behavior of the weak layer. This new interpretation (P=Plasticity more than Propagation in short PST) allows a simple extraction of the cap failure envelope parameters (critical stresses) for the weak layer from short PST (P=Plasticity, and suggests longer PST for extracting snow fracture properties, where P=Propagation), as we will hopefully adopt soon in Italy for better related avalanches forecasting.