Fracturing of ice under compression creep as revealed by a multifractal analysis

Abstract

Abstract. Fracturing of freshwater granular ice up to failure under uniaxial compression creep was investigated from series of interrupted creep tests and from a multifractal analysis of the corresponding fracture patterns. At the early stages of damage corresponding to primary and secondary creep, the fracturing process is dominated by the nucleation of microcracks from stress concentrations within the material (unlike rocks, artificial freshwater ice does not contains starter flaws). Because of the crack nucleation mechanisms, the microstructure of the material (e.g., the nonfractal grain size distribution) strongly influences the organization of fracturing which is therefore nonfractal. As fracturing proceeds during tertiary creep, a hierarchical (fractal) organization of the fracturing emerges progressively over a wider scale range. At failure, this fractal organization is fully developed without detectable lower or upper bound, and the role of the initial microstructure has completely disappeared. Similarly, cracks are preferentially oriented along the compression axis at the early stages of damage, but this anisotropy vanishes as failure is approached. The simultaneity between the onset of tertiary creep and the emergence of fractal organization suggests that the acceleration of the deformation during tertiary creep is due to the cataclasis of a material which becomes granular. An important consequence of the fractal organization of fracturing is that homogenization procedures, as well as damage mechanics, developed to study the behavior of damaged materials, cannot be used to describe tertiary creep and failure. 1.IntroductionOffshore structures located in polar regions experience important forces when a moving sea-ice cover or icebergs crush against them. This problem has given rise, in the last 15th years, to an abundant literature about damage, fracturing and failure of ice under compressive loading. The dependence of the compressive failure stress on temperature, strain rate or confinement has been established for different kinds of ice (see e.g. Schulson [1990] On the other hand, the fracturing processes of other geomaterials (i.e., essentially rocks) have been largely studied from the laboratory scale to the Earth's crust scale, and one major preoccupation was to relate large-scale features to small-scale (laboratory) observations. The self-similar nature of fracturing and faulting (i.e. the appearance of identical features at different scales) has been claimed both for laboratory experiments and field observations. This scale invariance can be expressed by power law distributions of fracture or fault lengths (see, e.g., Main [1996], Grasso and Bachelery [1995] [1992] argued that the fractal properties of rock fracturing result "naturally" from basic mechanical mechanisms such as crack nucleation from initial flaws, buckling of slabs, spalling, and interactions between particles of different sizes in a granular medium. However, they considered the evolution of damage and fracturing within mater...

Dynamic damage model of crevasse opening and application to glacier calving

“…The zero-order fractal dimension associated to p f c is d 0 = 1.97 Turcotte [1986]. This value is close to the result d 0 = 2 measured on the fracture pattern and d 0 = 2.15 measured on the fragmentation [Weiss and Gay, 1998] of compression creep to failure test (at 3.1 MPa). This suggests that the fractal fracture pattern of ice controls the final failure of the ice and that the global failure at the mesoscale is a discontinuous response of a continuous damage accumulation at the microscale.…”

“…Note that a low bound of the scale invariance was observed in the fracture pattern of ice in compression by Weiss and Gay [1998]. They related this limit to the ice grain size.…”

“…Weiss and Gay [1998] found g % 0.05 during creep to failure for uniaxial compression at 3 MPa and À10°C. They quantified the orientation of the cracks by analyzing sample cross sections in a plane parallel to the axis of loading.…”

“…These inhomogeneities have been either related to the fractal pattern of the microstructure [Carpinteri et al, 1995] or to the spatial distribution of material properties. Since the microstructure of ice is not fractal (Weiss and Gay [1998] found that the grain size for granular ice follows a Weibull distribution), the size effect is assumed to be related to the material inhomogeneities of the ice. The influence of the size on the stress threshold can be accounted for, either by considering the size of the global system using a deterministic size effect law [Bažant, 1999] or by introducing stochastic inhomogeneities in the model [Herrmann and Roux, 1990].…”

“…No experimental results have been found for tension or shearing at low stresses. Because of insufficient data, g is set at the value found by Weiss and Gay [1998].…”