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[SCG74-04] On ductile-to-brittle transition of ice-silica mixtures under compressive loading
Keywords:ductile-to-brittle transition, ice-silica mixtures, silica volume fraction, stress-strain curve, compressive strength
On the bodies in the solar system such as Earth, Mars, and icy satellites, various landforms related to the flow and the fracture of ice-rock mixtures are found; for examples, glaciers on Earth, fretted terrains on Mars, relaxed craters and trough terrains on Europa and Ganymede. To clarify the formation processes and structures of these features, it is necessary to understand the rheological properties of ice-rock mixtures.
Ductile-to-brittle (D/B) transition is one of the most important rheological properties to determine the tectonic style on the bodies, flow features and fracture patterns. The D/B transition of water ice has been studied by some researchers and a theoretical model for the strain rate corresponding to the D/B transition was proposed [Schulson, 1990; Renshaw and Schulson, 2001]. This model indicates that the transitional strain rate depends on ice grain size, temperature, confining pressure, and degree of pre-cracks. However, the D/B transition of ice-rock mixtures has not been studied yet. In this study, we carried out compression experiments on ice-rock mixtures to examine the D/B transition. One of the parameters which is expected to affect the D/B transition of ice-rock mixture is a rock content. So we examined the effect of rock content on D/B transition and compared the experimentally observed transitional strain rates to predictions of the model proposed earlier.
The samples were prepared by mixing ice seeds (diameter < 850 μm) and amorphous silica beads with a diameter of 0.25 μm. To fill spaces and to reduce porosity of sample as soon as possible, the distilled water at 0° C was filled. The samples were frozen over a period of one day in a cold room set at -10° C. We made samples with silica volume fraction f of 0, 0.06, and 0.18. The sample has a cylindrical shape with a diameter of 30 mm and a height of 30 or 60 mm. We performed unconfined compression experiments under constant strain rate from 10-5 to 0.6 s-1 in a cold room at Ice Research Laboratory, Dartmouth College. The room temperature was set to be -10° C.
The deformation behavior, ductile or brittle, under compressive loading is characterized by the shape of stress-strain curve and by the relationship between peak stress on the stress-strain curve and strain rate. In the case of water ice, the peak stress increased exponentially with increasing strain rate in the ductile regime while it decreased with increasing strain rate in the brittle regime. In the case of ice-silica mixture with f=0.06, the peak stress change with strain rate was similar to that with pure ice (f=0), that is, the peak stress reached a maximum at the D/B transition. However, in the case of ice-silica mixture with f=0.18, the peak stress continued to increase with increasing strain rate. The stress-strain curves for f=0.18 remained ductile-like for all strain rates, so the D/B transition for f=0.18 was expected to be greater than the maximum strain rate (0.6 s-1) explored in this study. Consequently, the transitional strain rates for pure ice and ice-silica mixtures were determined; 10-3-10-2 s-1 for pure ice, 10-2-10-1 s-1 for f=0.06 and > 0.6 s-1 for f=0.18. We found that the transitional strain rate increased with increasing silica volume fraction.
Finally, we compared the theoretical value predicted from the model by Schulson [1990] to the experimental value. In the case of pure ice, the theoretical transitional strain rate was in good agreement with the measured value. On the other hand, in the case of ice-silica mixtures the theoretical value was larger than the measured value. This might be caused by high sensitivity of the transitional strain rate to the stress exponent n, in the power law relationship between peak stress and strain rate (dε/dt=Bσpeakn).
Schulson [1990], Acta Metall. Mater. 38, 1963-1976.
Renshaw and Schulson [2001], Nature 412, 897-900, doi:10.1038/35091045.
Ductile-to-brittle (D/B) transition is one of the most important rheological properties to determine the tectonic style on the bodies, flow features and fracture patterns. The D/B transition of water ice has been studied by some researchers and a theoretical model for the strain rate corresponding to the D/B transition was proposed [Schulson, 1990; Renshaw and Schulson, 2001]. This model indicates that the transitional strain rate depends on ice grain size, temperature, confining pressure, and degree of pre-cracks. However, the D/B transition of ice-rock mixtures has not been studied yet. In this study, we carried out compression experiments on ice-rock mixtures to examine the D/B transition. One of the parameters which is expected to affect the D/B transition of ice-rock mixture is a rock content. So we examined the effect of rock content on D/B transition and compared the experimentally observed transitional strain rates to predictions of the model proposed earlier.
The samples were prepared by mixing ice seeds (diameter < 850 μm) and amorphous silica beads with a diameter of 0.25 μm. To fill spaces and to reduce porosity of sample as soon as possible, the distilled water at 0° C was filled. The samples were frozen over a period of one day in a cold room set at -10° C. We made samples with silica volume fraction f of 0, 0.06, and 0.18. The sample has a cylindrical shape with a diameter of 30 mm and a height of 30 or 60 mm. We performed unconfined compression experiments under constant strain rate from 10-5 to 0.6 s-1 in a cold room at Ice Research Laboratory, Dartmouth College. The room temperature was set to be -10° C.
The deformation behavior, ductile or brittle, under compressive loading is characterized by the shape of stress-strain curve and by the relationship between peak stress on the stress-strain curve and strain rate. In the case of water ice, the peak stress increased exponentially with increasing strain rate in the ductile regime while it decreased with increasing strain rate in the brittle regime. In the case of ice-silica mixture with f=0.06, the peak stress change with strain rate was similar to that with pure ice (f=0), that is, the peak stress reached a maximum at the D/B transition. However, in the case of ice-silica mixture with f=0.18, the peak stress continued to increase with increasing strain rate. The stress-strain curves for f=0.18 remained ductile-like for all strain rates, so the D/B transition for f=0.18 was expected to be greater than the maximum strain rate (0.6 s-1) explored in this study. Consequently, the transitional strain rates for pure ice and ice-silica mixtures were determined; 10-3-10-2 s-1 for pure ice, 10-2-10-1 s-1 for f=0.06 and > 0.6 s-1 for f=0.18. We found that the transitional strain rate increased with increasing silica volume fraction.
Finally, we compared the theoretical value predicted from the model by Schulson [1990] to the experimental value. In the case of pure ice, the theoretical transitional strain rate was in good agreement with the measured value. On the other hand, in the case of ice-silica mixtures the theoretical value was larger than the measured value. This might be caused by high sensitivity of the transitional strain rate to the stress exponent n, in the power law relationship between peak stress and strain rate (dε/dt=Bσpeakn).
Schulson [1990], Acta Metall. Mater. 38, 1963-1976.
Renshaw and Schulson [2001], Nature 412, 897-900, doi:10.1038/35091045.