Particularities of ductile crevassing

Ductile fracture is characterized by a large fracture process zone (FPZ, a zone where microcracks are active because of stress concentration at the crevasse tip) and a subcritical crevassing (a crevasse that propagates below the fracture toughness; more generally called subcritical crack growth, SCCG).

The size of the FPZ is associated with the stress relaxation at the crevasse tip due to viscoplastic deformations (creep), which are related to dislocation kinetics, and also to microcrack growth (Kachanov, 1999). The stress concentration at the tip is thus attenuated and the stress is redistributed in a zone around the tip. In that zone, microcracks grow. Some microcracks dominate and extend the crevasse. The FPZ influences the ice flow, because the microcracks reduce the mechanical properties of ice. In order to evaluate the size of the FPZ, crevasse patterns observed in nature can be considered. Weiss (2003) analysed the crevasses of a temperate alpine glacier (Glacier d'Argentiere, France). He found that the size of the crevasse length follows an exponential distribution, with a minimum crevasse size of 10 m. The spacing between crevasses could be approximated well using a log-normal distribution with a mode of 12.6m. These results suggest that the size of the FPZ is in the order of magnitude of 10 m in the case of ductile crevassing. This is confirmed by direct simulations of crevasse growth (see below).

Observations of subcritical crevassing are numerous, but the SCCG process has not yet been studied in the case of ice. Figure 62.1 presents a simplified pattern of crack velocity reported as a function of the stress intensity factor K, as observed in ceramics or glass. At the fracture toughness Kc, the crack propagates at a speed close to the body wave speed (critical crack growth). Under the threshold Kth, the crack does not progress. For ice, Kth can be related to the crack nucleation stress observed at low stress. Between Kth and Kc the crack grows with a controlled velocity. This mode of fracture corresponds to the SCCG. For rocks, ceramics or glass, SCCG is usually associated with diffusion processes, chemical reactions and plastic flow (Weiss, 2004). For ice, diffusion processes are known to be very slow. They can,

K stress intensity factor K

th c

Figure 62.1 Schematic crack velocity versus stress intensity factor. Critical crack growth (CCG) occurs for K > Kc, where K is the stress intensity factor and Kc is the fracture toughness. Subcritical crack growth (SCCG) arises for Kth < K < Kc, with Kth being the threshold of the stress intensity factor.

K stress intensity factor K

th c

Figure 62.1 Schematic crack velocity versus stress intensity factor. Critical crack growth (CCG) occurs for K > Kc, where K is the stress intensity factor and Kc is the fracture toughness. Subcritical crack growth (SCCG) arises for Kth < K < Kc, with Kth being the threshold of the stress intensity factor.

however, influence the SCCG at a low deformation rate. Chemical reactions due to ice impurities are not required for SCCG, as laboratory experiments performed with pure ice show subcritical effects (Mahrenholtz & Wu, 1992). As asserted above, viscoplas-tic flow is responsible for the formation of the FPZ. In the FPZ, the development of microcracks is not homogeneous because of the heterogeneity of the ice. In such conditions (e.g. Amitrano et al., 1999), some microcracks progressively dominate and extend the crevasse. As revealed by creep to failure measurements performed in the laboratory (Mahrenholtz & Wu, 1992), the duration of the microcrack accumulation process (until the formation of a crack) depends strongly on the applied load. At low stress (<1 MPa), it is in the order of weeks. Thus, SCCG could be interpreted as a discontinuous process of microcrack nucleation and propagation. At the macroscale, the organization of these microcracks can be regarded as a continuous process of crevasse growth.

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