We studied saline ice of two meltwater salinities: 3.0 ± 0.9 and 5.9 ± 0.6 ppt, where ± sign indicates standard deviation. We produced the ice in the laboratory in an 800 L circular polycarbonate tank in the manner described previously (Golding et al., 2014). Briefly, solutions containing 17.5 ± 0.2 ppt and 35 ± 0.2 ppt (parts per thousand, or ‰) of the commercial product “Instant Ocean” salt mixture were prepared and then frozen unidirectionally downward over a period of about 7 d by using a top-placed cold plate maintained at a temperature T=-20 ± 0.1 ∘C. Before bringing the cold plate into contact with the salt-water solution, the top surface of the solution was seeded with freshwater ice fragments of ∼ 0.3–1 mm in diameter. This procedure produced pucks ∼ 1 m in diameter and ∼ 0.3 m thick. For practical considerations, the bottom, skeletal layer of ice of about 7–10 cm was discarded as it was slushy and weak; we also believe that the skeletal layer does not play a significant role in supporting load. The top layer of ice of a few centimeters was also discarded because it was seeded and its grain size was considerably smaller and its microstructure thus different from the rest of the ice puck. Meltwater salinity was measured using a calibrated YSI Pro30 conductivity and salinity probe.

Figure 1 shows the microstructure of the ice. Table 1 lists its density and the average grain size of the test specimens described below. Figure 2 shows stereographic projections of the orientation of the crystallographic c axes. The ice is characterized by columnar-shaped grains whose growth texture is marked by c axes confined within about 15∘ of the horizontal plane of the parent ice puck and randomly oriented within that plane. In other words, the ice is termed S2, after Michel and Ramseier (1971), and is similar to natural first-year sea ice (for comparison, see Fig. 3.7 of Schulson and Duval, 2009). The grain size noted above is the average diameter of the columnar-shaped grains, ranging from about 2 to 7 mm in Fig. 1.

The ice contained both sub-millimeter-sized brine pockets and supra-millimeter-sized drainage channels, reminiscent of natural sea ice. Figures 3 and 4 show examples. The ice of lower salinity (3.0 ± 0.9 ppt) had fewer defects of both kinds. Some of the ice of higher salinity (5.9 ± 0.6 ppt) possessed channels whose size was almost as large as the grain diameter. The defects scattered light to the degree that in bulk form the ice had an overall opaque appearance. When observed in thin section (∼ 1 mm) the ice exhibited to the naked eye distinct linear whitish features which we took to be sets of interconnected brine pockets that could possibly be filled with very fine-grained ice. The ice of higher salinity possessed more of these features, especially near the bottom of the parent puck (which was the last part to solidify). Our sense is that these features served as stress concentrators, particularly ones that traversed the width of the test specimen (described below), thereby weakening the ice. Indeed, as will become apparent, samples obtained from near the bottom of a puck of higher salinity (5.9 ± 0.6 ppt) had relatively low flexural strength.

Because the ice of both salinities exhibited a different appearance from the top and bottom of the parent puck, in preparing test specimens for flexing we distinguished them by their position (depth from top surface) within the ice puck from which they were prepared, Table 2.

Once the ice had been grown, it was cut into blocks of dimensions ∼ 10×30×20 cm3, where the longest and the shortest dimensions are in the horizontal plane of the original ice puck, perpendicular to the direction of growth. The blocks were stored in a cooler (at -10 ± 0.5 ∘C) on their side (such that columnar-shaped grains were oriented horizontally) to reduce brine drainage for periods of time of about 1–10 weeks.

Specimens for flexing were manufactured from the ice blocks in the form of thin beams of dimensions h∼ 16 mm in thickness (parallel to the long axis of the grains), b∼ 85 mm in width, and l∼ 300 mm in length. The test specimens were allowed to equilibrate to the test temperature of -10 ± 0.5 ∘C for at least 24 h before testing.

A detailed description of the specimens' preparation and loading can be found elsewhere (Iliescu et al., 2017; Murdza et al., 2018, 2019, 2020b). To summarize, the ice beams were flexed up and down under four-point loading under constant displacement rate using a servo-hydraulic loading system (MTS model 810.14) to which we attached a custom-built four-point loading frame, Fig. 5. The hydraulic actuator was driven up and down under displacement control with the load limited in both directions. A load cell, calibrated for both tension and compression, and a linear variable differential transformer (LVDT) gauge were used for measurements of load and displacement of the upper surface of the ice beam during cycling.

Acoustic emissions were recorded during cycling using a PCI-2 18-bit A/D system; its frequency response was 3 kHz–3 MHz and its minimum acoustic emission (AE) amplitude detection threshold was set to 45 dB. We used a micro 30STC sensor (9.5 mm diameter, 11 mm thickness), which was attached to the top surface of an ice beam with a rubber band. Vacuum grease was used as the coupling agent between the sensor and the ice surface.

The experiments were performed in a cold room at a temperature of -10 ∘C and at an outer-fiber center-point displacement rate of 0.1 mm s-1 (or outer-fiber strain rate of about 1.4×10-4 s-1). This displacement rate resulted in an outer-fiber stress rate in the range from ∼ 0.3 to 0.5 MPa s-1, outer-fiber stress amplitude in the range from 0.35 to 1.2 MPa, outer-fiber strain amplitude in the range from ∼ 1 to 5×10-4, and frequencies in the range from 0.1 to 0.6 Hz (i.e., periods from ∼ 10 to 1.5 s). The period, as already noted, is similar to the period of ocean swells (Collins et al., 2015). The major outer-fiber stress σf was calculated from the relationship (the loading span is one-half of the support span) 1σf=3PL4bh2, where P is the applied load and L is the distance between the outer pair of loading cylinders (shown in Fig. 5b) and is set by the geometry of the apparatus to be L=254 mm.

We used two different loading procedures, as we did earlier in our study of S2 freshwater ice. Type I loading was a completely reversed stress cycle with constant stress amplitude and mean stress of zero. Type II was similar to Type I but incorporated an increasing multi-level (or step-level) stress amplitude. This second type of loading essentially consisted of several Type I steps of increasing stress amplitudes. In the present study for stress amplitudes below 0.7 MPa, we used Type I loading. To cycle ice samples at stress amplitudes above 0.7 MPa, we first pre-conditioned specimens through step-loading the Type II procedure at progressively higher stress amplitude levels; i.e., we cycled specimens for ∼ 300 times at each of the following stress amplitudes: 0.7, 0.75, 0.8, 0.85 MPa, and so on either until failure occurred or until a specific value of stress amplitude set by the operator (see Iliescu et al., 2017, and Murdza et al., 2018, for details). To change stress amplitude the loading was stopped for ∼ 15 s to change settings. After pre-conditioning, the specimens were cyclically loaded according to Type I loading at least 300 times and generally for ∼ 2000 times, since no change in strength was observed beyond a few hundred cycles (see below).

Figure 6 shows measurements of load and of displacement versus time at the beginning and near the end of cycling before specimen failure of a lower-salinity specimen (3.0 ± 0.9 ppt). The measurements detected no softening. According to Bažant et al. (1984) softening is a decline of stress at increasing strain or, in our case, an increase in strain during cycling at constant stress amplitude during the tests. The absence of detectable softening during cycling of the saline ice is reminiscent of the absence of softening during the cycling of freshwater ice (Iliescu et al., 2017; Murdza et al., 2020b).

The flexural strength of non-cycled saline ice of both salinities was measured at -10 ∘C and at a nominal outer-fiber center-point displacement of 0.1 mm s-1. The results are listed in Table 2. Failure more often occurred at random locations between the two inner loading cylinders and less often either below or slightly outside the loading cylinders. The reason for the latter location was the presence prior to testing of a significant concentration of whitish features at loading cylinders which served as stress concentrators and along which the failure ultimately occurred (similar to Fig. 4). The average and standard deviation of the measured flexural strength of saline ice of lower salinity (3.0 ± 0.9 ppt) are 0.96 ± 0.13 MPa. The strength of the lower-salinity ice did not correlate systematically with the depth of the parent puck from which ice beams were prepared. The measured strength compares favorably with the value of 0.85 ± 0.20 MPa reported by Timco and O'Brien (1994) for sea ice of similar salinity, as can be seen in Fig. 7. Brine volume fraction νb was calculated according to Frankenstein and Garner (1967): 2νb=0.001×S49.185T+0.532, where T is temperature in degrees Celsius between -0.5 and -22.9 ∘C, and S is meltwater salinity (in parts per thousand) of the ice.

The average and standard deviation of the measured flexural strength of saline ice of higher salinity (5.9 ± 0.6 ppt) are 0.98 ± 0.36 MPa. The measured values (Fig. 7) deviate slightly towards higher values compared to the data of Timco and O'Brien (1994), although scatter is significantly greater than the scatter in the strength of the ice of lower salinity (3.0 ± 0.9 ppt). This may be explained by the greater degree of interconnectivity of brine pockets at the bottom of an ice puck (discussed above and shown in Figs. 3 and 4). Indeed, the flexural strength of the higher-salinity specimens appears to depend on the depth of ice from which beams were prepared, Table 2. This result shows how much the strength of ice is sensitive to flaws and defects. Given that larger bodies usually contain larger defects, the flexural strength of sea ice on the medium and large scales, in the field (Karulina et al., 2013, 2019; Murdza et al., 2016) for instance, is expected to be lower than on the smaller scale of the present experiments.

We also compare our measurements of flexural strength with the tensile strength of sea ice. For this purpose, and as we did in our previous work on freshwater ice (Iliescu et al., 2017; Murdza et al., 2020b), flexural strength is divided by 1.7 (Ashby and Jones, 2012). This factor reflects the fact that the volume of the material which is subjected to the highest stress in bending is smaller than in uniaxial tension; thus, the largest defect which governs the failure may not be near the surface of a bent specimen. Upon dividing the flexural strength of the non-cycled saline ice of lower salinity by 1.7, we found the average across-column tensile strength from our experiments to be 0.96 ± 0.13 MPa / 1.7 = 0.56 ± 0.08 MPa. This value compares favorably with the values 0.56 ± 0.06 MPa and 0.63 ± 0.12 MPa reported by Richter-Menge and Jones (1993) for the tensile strength of columnar-grained first-year sea ice of 4.1 ± 0.3 ppt salinity loaded uniaxially across the columns at a temperature of -10 ∘C and strain rates of 10-5 and 10-3 s-1. Recall that in the present experiments the outer-fiber strain rate was about 1.4×10-4 s-1, which is within the range reported by Richter-Menge and Jones (1993). This agreement between direct and indirect measurements of tensile strength lends confidence that our lab-grown saline ice is a reasonably faithful analogue of natural sea ice.

To determine whether there is a relationship between flexural strength and number of cycles imposed under a constant low stress amplitude, we performed via Type I loading a series of experiments on saline ice of lower salinity (3.0 ± 0.9 ppt) at -10 ∘C at an outer-fiber center-point displacement rate of 0.1 mm s-1 at a low stress amplitude of 0.35 MPa, i.e., at an amplitude less than one-half the flexural strength of non-cycled ice. Figure 8 shows the results. The number of cycles varied from about 100 to 14 000. The average strength and standard deviation of all data from Fig. 8 are 0.96 ± 0.23 MPa. As noted above, the strength and standard deviation of non-cycled ice are 0.96 ± 0.13 MPa. In other words, no strengthening was detected upon cycling up to 14 000 times at a stress amplitude of 0.35 MPa. For freshwater ice (Murdza et al., 2020b), we found that once the number of cycles at a given low stress amplitude exceeded 300, the number of cycles had no significant effect on the flexural strength, implying that a kind of saturation of strength developed. Given that result and the new results for saline ice, we followed the practice in the present study of cycling more than 300 times, often as many as 2000 times, before bending the ice to failure.

The flexural strength increases with stress amplitude. Figure 9 shows measurements obtained from saline ice of both salinities cycled at -10 ∘C at an outer-fiber displacement rate of 0.1 mm s-1. For comparison, data from laboratory grown freshwater ice (Murdza et al., 2020b) of S2 character and from lake ice of the same character (Murdza et al., 2020a, 2021) are also shown. The relationship between the flexural strength, σfc, and cycled stress amplitude, σa, for saline ice appears to be a linear one and, within experimental scatter, to have essentially the same sensitivity to stress amplitude as freshwater ice, namely 3σfc=σf0+kσa, where k=0.68 is a constant. For freshwater ice the non-cycled flexural strength is σf0=1.75 MPa compared with σf0= 0.96 MPa for the saline ice. There is, perhaps, in Fig. 9 a hint that for saline ice there is a threshold of about 0.4 MPa that must be exceeded to detect strengthening. Interestingly, this apparent threshold is similar in magnitude to the stress that marks the onset of significant AE activity under cyclic loading of sea ice cores (Cole and Dempsey, 2006). Although saline ice is weaker than freshwater ice, it appears that upon cycling its strength increases at the same rate as freshwater ice.

Although the rate of strengthening with stress amplitude appears to be the same for saline ice and freshwater ice, the maximum increase in strength in the case of saline ice of lower salinity (3.0 ± 0.9 ppt) is significantly lower. We were able to strengthen saline ice by about 50 % of the non-cycled strength compared with about 100 % for freshwater ice (Murdza et al., 2020b). Another point is that we almost were not able to cycle specimens at stress amplitudes greater than the flexural strength of non-cycled material, whereas in the case of freshwater ice we were able to cycle at stress amplitudes significantly greater than flexural strength of non-cycled ice. Indeed, the maximum cycled stress amplitude we were able to reach in the case of saline ice of lower salinity (3.0 ± 0.9 ppt) during all tests was 1.1 MPa, which is not statistically different from the non-cycled flexural strength of 0.96 ± 0.13 MPa.

For saline ice of lower salinity (3.0 ± 0.9 ppt), there is no evidence that the flexural strength of both non-cycled and cycled ice is significantly affected by the depth of ice from which ice beams were harvested. For saline ice of higher salinity (5.9 ± 0.6 ppt), however, the flexural strength of both non-cycled and cycled ice appears to depend on the depth of ice from which beams were prepared, Fig. 10. Indeed, the flexural strength of specimens from the bottom and from the top of an ice puck of higher salinity (5.9 ± 0.6 ppt) differs by a factor of ∼ 3 (∼ 0.4 MPa vs. ∼ 1.4 MPa).

Although the specimens from which the data in Fig. 9 were obtained did not fail during cycling, other specimens cycled under similar conditions did fail while being cycled. Results from such tests (on saline ice of lower salinity (3.0 ± 0.9 ppt) at -10 ∘C and 0.1 mm s-1 outer-fiber displacement rate) allowed us to construct a S–N fatigue curve, shown in Fig. 11. The number of cycles here is the number of cycles to failure during cycling at the last stress amplitude level and not the total number of cycles. At most the S–N curve showed only a weak systematic dependence of the number of cycles to failure on stress amplitude. Indeed, for the same stress amplitude of ∼ 0.9 MPa, fatigue failure occurred after as few as < 10 cycles and after as many as a few thousand cycles. Statistical analyses to test the hypothesis that the slope in Fig. 11 is zero resulted in a p value equal ∼ 0.06. Therefore, there is only a marginally significant effect of number of cycles on the stress at which failure occurred. We attribute this variability in fatigue life to the variability in microstructure from specimen to specimen.

That said, a note of caution is appropriate. The data in Fig. 11 should not be viewed as fatigue data in the usual sense, i.e., in the way such data are viewed when obtained from other materials (e.g., metals and alloys) that exhibit classical fatigue behavior. In those cases, before cycling, all specimens are assumed to have the same thermal–mechanical history. That was not the case here for the saline ice, as most of the samples were pre-conditioned according to the Type II procedure before they were cycled at the last stress level where they failed while cycling. In other words, in order to get fatigue failure, we were increasing stress amplitude by small increments of ∼ 0.05 MPa and allowed a sufficient number of cycles at each stress level (∼ 500–1000) before we reached a fatigue failure.

The question to address here is why we did not obtain a classical S–N curve. We suggest that the classical mechanism of fatigue, i.e., accumulation of damage, is not in play in our tests, and some other process is controlling fatigue life.

In an attempt to reveal deformation damage in the form of microcracks, we examined using thin-section optical microscopy (up to 50× magnification) the microstructure of specimens of the lower-salinity ice (3.0 ± 0.9 ppt) after they had failed during cycling, i.e., failed in fatigue. Three thin sections were prepared from four specimens in order to ensure a greater probability of observing microcracks growing from brine pockets or brine channels, should they be present. The plane of the thin section was parallel to the long axis of the columnar grains and parallel to the direction of the greater normal stress. This plane was taken as the best plane to observe possible cracks. Thin sections were observed using non-polarized light. We found no evidence of microcracks starting from brine pockets or from other defects. In fact, we found no microcracks at all. It appears, therefore, that slow crack growth is not a significant contribution to the fatigue life of the beams of the laboratory-grown saline ice that we studied.

Acoustic emissions (AE) during repetitive loading of ice have been previously recorded and analyzed in laboratory and in situ (Langhorne and Haskell, 1996; Cole and Dempsey, 2006, 2004; Lishman et al., 2020; Murdza et al., 2020b). Langhorne and Haskell (1996) suggested that the emissions originate either from dislocation breakaway or from microcracking associated with dislocation motion.

In contrast to freshwater ice, where no sound was detected until failure (Murdza et al., 2020b), continuous emission was detected while cycling at constant stress amplitude. Figure 12 shows the cumulative acoustic emissions, or “hits”, as a function of time for ice that was cycled reversely at a constant stress amplitude of 0.5 MPa. As can be seen, the hit rate (or hits per unit time), which is the slope of the curve in Fig. 12, is about the same for the duration of the experiment.

Interestingly, the hit rate depends on stress amplitude during cycling. Figure 13 shows this behavior. The greater the stress amplitude, the greater the hit rate. However, during cycling below about 0.2 MPa no hits were detected.

Figure 13 also indicates that the hit rate is independent of the sequence of different stress amplitudes. The numbers in Fig. 13 show the order of cycling at different stress amplitudes; i.e., firstly we cycled ice at higher stress amplitudes (0.5–0.8 MPa) and then at lower stress amplitudes (0.2–0.4 MPa). The results showed an increase in the hit rate as stress amplitude increases, regardless of the sequence of cycling.