Stress-strain behavior

Figure 3 shows the compressive stress-strain curves for both horizontally and vertically oriented specimens deformed at −10°C. The shape of the curves and the trends apparent were similar for the other three

Fig. 3. Stress strain curves of laboratory-grown saline ice at 10°C of horizontal and vertical orientations at a range of strain rates from 8.9 x 10 ⁻⁷ to 1.8 x 10⁻³s⁻¹ The “X” on curves A, D and E denotes fracture. The trends that the curves show are also typical of the other temperatures, −40°, −20° and −5°.

temperatures. At high strain rates the ice was brittle and the curves (A and D) were nearly linear, terminating in fracture. As the strain rate decreased and approached the brittle-to-ductilc transition, the curves for samples which failed in the brittle regime showed some curvature as well as an abbreviated peak before fracture (sec curve E). At low strain rates, the ice was ductile: the stress first increased, reached a peak and then decreased to almost a constant stress level, i.e to nearly a plateau (curves B, C, F and G).

Tests within the ductile regime were terminated after roughly 3% shortening through an operator-controlled unloading of the specimens. It is possible that a plateau would have been seen in all cases of ductile behavior had some of the specimens been deformed further. The strain softening occurred more rapidly in the vertical orientation than in the horizontal orientation for a given strain rate (compare curves B and F). The ratio of the plateau strengths from the vertical to the horizontal orientations was smaller than the ratio of the peak strengths from the vertical to the horizontal orientations. This suggests thai, for a given strain rate, some form of steady-stale was developing, independent of the loading direction. Also, the stress reduction decreased as the strain rate decreased, to a point where little if any peak was observed (curves C and G). It is likely that the peak reflects the onset of dynamic restorative processes such as recovery and recrystallization and that the plateau reflects a more or less steady-state microstructure. This is discussed farther under ‘Ductile regime’ below.

Ductile-to-brittle transition

As will become apparent, the transition from ductile to brittle failure marks the point of greatest compressive strength. Figure 4 shows the transition strain rate venus temperature for both vertical and horizontal orientations. The transition rate was obtained from both the transition in the shape of the stress-strain curve (i.e. from one showing only a rising branch (AD; Fig. 3) to one showing both rising and descending branches (B, C, F, G; Fig. 3)) and from the failure mode (described in the next section). Generally, a range of strain rates marked the transition, and not one particular value. Hence a range of values is shown. The transition strain rate was generally higher by approximately an order of magnitude in horizontally oriented ice than in vertically oriented ice. The effect of temperature is less clear, but two possible patterns could be discerned: either there is little change in the transition strain rate from about −5° to −20°C followed by a decrease at −40°C; or the transition strain rale decreases continuously with decreasing temperature over the whole range.

The ductile-to-brittle transition strain rate is roughly an order of magnitude greater in columnar saline ice than in fresh-water columnar ice of the same grain-size (Reference Batto and SchulsonBatto and Schulson, 1993). The origin of this difference as well as the transition itself can be understood within the context of the micromcchanical model proposed by Reference SchulsonSchulson (1990). Accordingly, the transition from ductile to brittle behavior is attributed to the suppression of time-dependent (i.e. creep) deformation at the tips of internal microcraeks and, thus, to the onset of crack propagation.

Fig. 4. The ductile-to-brittle transition strain rate of horizontally and vertically oriented LGSI vs temperature.

The transition strain rate, , can then be expressed in terms of a set of parameters which incorporate creep deformation, fracture toughness, ice/ice friction and microslructural size. Specifically,

where A is the constant in the power law expression for creep , K_1c, μ is the fracture toughness, μ is ice/ ice friction coefficient and λ is the microstructural size that sets the length of the parent, internal crack; Z is a dimensionless experimental parameter which relates the brittle fracture strength to K_1C, μ and λ. and f is a dimensionless constant which relates the diameter of the crack-tip creep zone to the microstructural size. Of these parameters the one most likely to differ for the saline ice is A, being about one order of magnitude higher lor this material than for fresh-water ice. (This difference is based upon a comparison of the B-parameter for both materials, where B relates the ductile failure strength to the strain rate (see ‘Ductile failure strength’ below); and the comparison is with Sinha’s data (Reference Sinha1981) for fresh-water columnar ice.) Hence the greater ductile-to-brittlc transition strain rate. Interestingly, the transition strain rate (personal communication from H. Eicken, J. A. Richter-Menge and M. Lange) for more finely grained saline ice (albeit, granular sea ice) is higher than that reported here (~10⁻³ to 10⁻² s⁻¹ vs 8 x 10⁻⁴s⁻¹ for horizontal orientation), in qualitative accord with the model. Parametric values lor horizontally oriented ice at −10°C are as follows: A = B^−1/m = 1.1 x 10 ⁻⁵MPa⁻³s⁻¹ (where B and m are given under ‘Ductile failure strength’ below), K_lc ~ 0.1 MPa -m^l/2 (Reference Parsons, Snellen, Hill, Lunardini, Wang, Ayorinde and SodhiParsons and others, 1986, for sea ice), μ≃ 0.5 (Reference Jones, Kennedy and SchulsonJones and others, 1991), λ≃3 mm (from the length of parent, sliding cracks shown in Reference Smith and SchulsonSmith and Schulson, 1994), Z ≃ 2.5 (Reference SchulsonSchulson, 1990, albeit for fresh-water ice) and f ≃ 0.02 (Reference Batto and SchulsonBatto and Schulson, 1993); these values lead to a predicted transition strain rate of which is in rough agreement with the present observations.

Failure characteristics

Table 2 summarizes the failure characteristics for the samples tested using the brush platens. We focus on the brush platens because, as noted above, they were the ones which produced the most truly uniaxial loading and so were the ones used to investigate the behavior at all temperatures. The characteristics depended upon sample orientation and strain rate, but not upon temperature. Synthane end-caps(which impart a laterally confining

stress) caused barreling of both horizontally and vertically oriented ductile samples and caused shear faulting of horizontally oriented brittle samples. Barreling was not seen with the brush platens, even when specimens were shortened by as much as 8% (Reference Lasonde, Gies, Schulson, Saeki and –HirayamaLasonde and others, 1988). Although the different boundary conditions produced different failure characteristics, they produced no discernible difference in the strength, for a given strain rate.

Ductile regime

Figure 5a and b illustrates the characteristics of ductile deformation for ice slowly loaded perpendicular to the columns. Voids were seen ai higher Strains, i.e. beyond the peak and near to the plateau l Fig. 5a). The deformation of the horizontally oriented ice was probably caused principally by intragranular crystallographic slip on favorably oriented basal planes. Grain (column), boundary sliding may also have contributed, but its relative contribution was noi ascertained. The voids may

Fig. 5. Photographs of ductile specimens, a. horizontal orientation; the long axis of the columnar grains run in and out of plane of paper. Note the void and the displacement across the columnar grains (T= −5°C, , ∊ = 0.031 ). b, as a. rotated 90° about axis of spiri men. Note absence of displacement along the columnar grains, c, Vertical orientation. Note the bulge or “foot” near the bottom of the specimen (T = −5°C, ∊= 0.031. d, vertical thin section of c. Note the recrystallized grains in the “fool”.

Fig. 6. Thin sections of a. vertically ( T= −10°C, ∊ = 3 x 10⁻⁶ s⁻¹, ∊ = 0.037) and b. horizontally (T = −10°C ∊= 3 x 10⁵s⁻¹, ∊= 0.038) oriented LGSI compressed about 3% in the ductile regime. Both sections show a few columns ( longitudinal (a) and cross sections (b) ) similar to those of undefarmed ice bordered by regions of banding and recrystallization.

reflect different basal plane orientations in adjacent columns with one grain being favorably oriented to slip and ihe other not.

The ductile deformation of the vertically oriented ice (Fig. 5c, d) occurred preferentially in localized areas. With the synthane end-caps the deformation was localized to either a shear band which bulged out at the surface (similar to the one apparent for the horizontally oriented ice, Fig. 5a) or a displacement of the columns through bending outward. When the brush platens were used, the deformation appeared like a “foot” or bulge (Fig. 5c) at the sample ends; this feature occurred most often at the bottom end of the sample which corresponded to the lower part of the parent ice puck. Regardless of platen type, in every case the localized area of deformation was recrystallized, whether within a shear band or within a “foot”. This feature can be seen in Figure 5d.

Every ductile specimen of both orientations, even those deformed at −40°C, showed bands and recrystallized grains in post-test thin sections. These sections were made as soon as possible within about 30 min) from specimens strained beyond the peak, and are assumed to display the actual deformation structure and not some post-test features which arc irrelevant to the mechanical behavior of the material, Figure 6a and b shows typical microstructures, from vertically and horizontally oriented samples, respectively. Note that the grains which contain the bands border the recrystallized regions. The bands were similar to those seen by Reference Steinmann S.Steinmann (1958) in warm (−1.9°C) granular fresh-water ice slowly deformed at 10 ⁻⁵s ⁻¹ and by Reference KnightKnight (1962) and by Nathanson (reponed by Reference KnightKnight. 1962) in arctic sea ice. They are also similar to the kink bands which form in fresh-water columnar ice during creep deformation at −9.5°C (Reference Gold and KingeryGold. 1963).

The bands in the sea ice were attributed to the formation of sub-grains under thermal stress (Knight) and to uniaxial compressive deformation (Nathanson). In the columnar, fresh-water ice they were explained in terms of the formation of sub-grain boundaries through a dislocation process (Gold). In the present work, many thin sections were examined. In every case the bands were oriented more or less normal to the platelet-like array of brine pockets, analogous to their being perpendicular to the basal slip lines in the fresh-water ice (Gold). Since the brine-pocket array lies along the basal planes, this alignment means that the walls separating the bands are roughly normal to the basal planes. In view of their orientation, the bands are probably sub-grains which resulted from the development during straining of a polygonized microstructure, as commonly seen in hot-worked metals. In this regard, therefore, the salt-water and fresh-water materials are similar. Polygonization and

Fig. 7. Photographs of brittle failure specimens, a and b. horizontally oriented LGSI which failed through axial cracking (a. T = −40°C, ). The arrows point to inclined steps. The cracks within other horizontally oriented samples linked to produce shear failure planes (b, T = −40°C, ) the columns run in and out of the page, c and d, shards of a vertical oriented LGSI sample (c, T =−40°C, ) and a sample still intact (d, T = −40°C, ) show evidence of axial cracking. Both the edges of the shards (c) and central regions of the intact sample (d) show evidence of cross-column cracking. Note the steps on the fracture surface in 7c (arrows).

dynamic recrystallization often occur together in metals (Reference Cahn and CahnCahn, 1970) deformed at high temperatures and so it is not surprising to see evidence for both features in ice slowly deformed at temperatures above 80% of the melting point. Although evidence for their occurrence near the peak of the stress-strain curve has not been obtained, polygonization and recrystallization are probably important elements in the strain softening of saline ice.

Brittle regime

The brittle failure of horizontally oriented samples occurred through either axial splitting (i.e. along the loading direction) or macroscopic shear faulting, Figure 7. It is likely that the shear zones observed in some specimens are a result of the linking of flaws such as brine channels and/or short axial cracks created during the loading. Both failure modes have been described by Reference Smith and SchulsonSmith and Schulson (1994) in their study on the failure of saline ice plates loaded biaxially across the columns under small degrees of confinement. It is interesting to note the inclined steps on the fracture surface (arrows, Fig. 7a). Reference Smith and SchulsonSmith and Schulson (1994) observed similar features and attributed them to the development of wing cracks through the operation of the frictional crack sliding mechanism analyzed by Reference Nemat–Nasser and HoriiNemat-Nasser and Horii (1982) and by Reference Ashby and HallamAshby and Hallam (1986).

The brittle failure of vertically oriented ice also occurred by axial splitting, i.e. parallel to the loading direction, Figure 7c and d. The splits appeared to be a combination of intra- and inter-granular cracking. Often the axial cracks were linked together by cross-column cracks, which were usually perpendicular but sometimes inclined at about 45° to the loading direction (see arrows, Fig. 7c). The perpendicular cracks probably formed as the result of rapid unloadling (see Reference Couture and SchulsonCouture and Schulson, 1994) once the specimen split, while the inclined cracks may have acted as parent cracks upon which sliding occurred and from the tips of which axial wings sprouted and grew into full-length splits.

Mechanical properties

Failure strain

Figure 8 shows the failure strain versus strain rate and orientation for each temperature. For ductile behavior, the strains correspond to the peak stress while for brittle behavior they correspond to the strain at specimen collapse. Within the ductile regime (to the left of the broken vertical lines) the failure strain rises with decreasing strain rate, while within the brittle regime it is lower and roughly independent of strain rate. To a first approximation, temperature appears to have little effect for a given strain rate and orientation. Similarly, orientation appears to have little effect, although the data are too scattered to allow a firm conclusion on this point.

Compressive strength

The strength of the ductile ice was taken as the peak stress. The strength of the brittle ice was taken as the brittle failure stress. The strength varied markedly with the strain rate, temperature, and sample orientation,

Fig. 8. The failure strain (strain at peak or fracture) vs strain rate for LGSI of horizontal and vertical orientations tested with brush platens at −5°, −10°, −20° and −40°C. The ductile-to-brittle transition regions of the vertical and horizontal orientations are between the broken vertical lines.

(Fig. 9). Although earlier work by Butkovich (Reference Butkovich1956, Reference Butkovich1959), Reference PeytonPeyton (1966), Reference SchwarzSchwarz (1970), Reference WangWang (1979), Frederking and Timco (Reference Frederking and Timco1980, Reference Frederking and Timco1983, Reference Frederking and Timco1984), Sinha (Reference Sinha1983,Reference Sinha1984) and Reference Richeter–MengeRichter-Menge (1986) has shown the importance of these variables, the present study perhaps shows the effects more comprehensively using one kind of ice. It is interesting to note that the data for the laboratory ice are similar to those for first-year sea ice (Reference WangWang, 1979), at least at −10°C loaded across the columns. (Wang’s data are plotted in Fig. 9b.) The behavior is described below.

Fig. 9. Peak of fracture stress vs strain rate for LGSI of horizontal and vertical orientations at −5°, −10°, −20° and −40°C. Data from Reference WangWang (1979) at −10°C for sea ice with 45° c-axis alignment are included for comparison. The ductile-to-brittle transition regime of the vertical and horizontal orientations lies between the broken vertical lines.

Ductile failure strength

For both orientations and at all temperatures, the strength, σ_d within the ductile regime increased with increasing strain rate, The dependence can be described by the relationship

where B is a temperature-sensitive constant. The strain-rate sensitivity exponent, m, was computed using least-squares analyses from the data for each temperature and orientation, Table 3. No consistent trend in m is evident with either temperature or ice orientation, suggesting that the strength-limiting process is independent of these parameters over the ranges investigated. The average value is m = 0.26 ± 0.05, which is close to the value of 0.3 found for fresh-water columnar ice (Reference SinhaSinha, 1981) and Tor columnar sea ice (Sinha, Reference Sinha1983, Reference Sinha1984).

Concerning the effect of temperature, Figure 10 shows the ductile compressive strength at different strain rates. The values plotted are averages and were obtained from the data in Figure 9. For both orientations the strength increases with decreasing temperature, the effect being greater as the strain rate increases. Butkovich (Reference Butkovich1956, Reference Butkovich1959) and Frederking and Timco (Reference Frederking and Timco1980, Reference Frederking and Timco1984) previously reported this same trend from studies over a smaller range of temperature than used here.

Brittle failure strength

In the brittle regime the strength appeared either to be constant or to decrease slightly with increasing strain

(Fig. 9). Also, it increased with decreasing temperature (Fig. 10c, d). Since strain rate had only a small effect, the average strength from tests at all strain rates was plotted versus temperature for both orientations to illustrate the effect of temperature. Similar effects were reported by Reference Richeter–MengeRichter-Mcnge (1986) in laboratory-grown ice and in first-year sea ice, by Reference CoxCox and others (1985) in multi-year sea ice and by Reference SchulsonSchulson (1990) in fresh-water ice. That similar patterns are seen in both salt-water and freshwater ice implies that the behavior noted here is more a reflection of the ice per se than of an effect of the entrapped air and brine.

Vertical versus horizontal orientation

As apparent from Figure 9, in both the ductile and the brittle regimes the strength was greater along the columns than across the columns. Specifically, from the averages of the values shown in Figure 9, the ratio of the strength of

Fig. 10. Average peak (ductile regime) or fracture stress (brittle regime) vs temperature for horizontally and vertically oriented LGSI. In the ductile regime, for each temperature and orientation, peak stress values were taken from a least-squares line of the ductile test results from a separate log stress vs log strain-rate plot. In the brittle regime, for each temperature and orientation, the average fracture stress of all of the brittle test results was plotted.

the vertically oriented ice to that of the horizontally oriented ice, σ_v/σ_h, for the ductile and for the brittle regimes was 3.6 ± 1.7 and 2.0 ± 0.7. respectively, Table 4. The ratio for the ductile strength is similar to that noted for columnar sea ice (Reference ButkovichButkovich, 1959; Reference PeytonPeyton, 1966; Reference Frederking and TimcoFrederking and Timeo, 1984; Reference Richeter–MengeRichter-Menge, 1986). No consistent variation with either temperature or strain rate is evident.

The origin of the greater strength along the columns than across the columns is different for the two regimes. Within the ductile regime, the difference can be explained in terms of the difference in the orientation of the basal planes on which cristallographic slip occurs. For the horizontal orientation there is always a high resolved shear stress on the basal planes in the slip direction in at least some grains so that, to a first approximation, the ductile failure strength across the columns, σ_h, is about 2T where T is the shear stress on the basal planes at failure. For the vertically oriented samples the basal planes are inclined to the loading direction by a small angle, γ, owing to the fact (as noted under ‘Experimental procedures and ice structure’) that the c-axes were oriented up to 15 out of the horizontal plane of the parent ice puck. As a result, there is a much smaller shear stress resolved on to the slip planes when the ice is loaded along the columns, In this case it can be shown that for small γ the shear stress on the basal plane is given by the produci of the applied compressive stress and γ,i.e. . Then, by equating the shear stress at failure for both orientations and writing that it follows that the ratio of the ductile failure strengths for the vertical to the horizontal orientations is given as σ_v/σ_h, = 1/2γ. For an average value of γ, say γ= 8 ± 2° (which is within the extremes measured), σ_v/σ_h = 3.6 ± 1.0, which agrees with the observations.

The origin of the difference in strength with orientation within the brittle regime is less dear. Possibly, it relates to an effect of orientation on the parameters which control the brittle compressive strength of ice (Reference SchulsonSchulson, 1990), such as fracture toughness, the ice/ice friction coefficient or the appropriate microstructural scale.