Behavior of Saline Ice under Cyclic Flexural Loading

. New systematic experiments reveal that the flexural strength of saline S2 columnar-grained ice loaded 6 normal to the columns can be increased upon cyclic loading by about a factor of 1.5. The experiments were 7 conducted using reversed cyclic loading over ranges of frequencies from 0.1 to 0.6 Hz and at a temperature of -10 ºC 8 on saline ice of two salinities: 3.0±0.9 and 5.9±0.6 ‰. Acoustic emission hit rate during cycling increases with an 9 increase of stress amplitude of cycling. Flexural strength of saline ice of 3.0±0.9 ‰ salinity appears to increase 10 linearly with increasing stress amplitude, similar to the behavior of laboratory-grown freshwater ice (Murdza et al., 11 2020b) and to the behavior of lake ice (Murdza et al., 2021). The flexural strength of saline ice of 5.9±0.6 ‰ 12 depends on the vertical location of the sample within the thickness of an ice puck; i.e., the strength of the upper 13 layers, which have a lower brine content, was found to be as high as three times that of lower layers. The fatigue life 14 of saline ice is erratic. Cyclic strengthening is attributed to the development of an internal back stress that opposes 15 the applied stress and originates possibly from dislocation pileups.

.7 of Schulson and Duval (2009)). The grain size noted above is the averge diameter of the columnar-shaped 108 grains, ranging from about 2 to 7 mm in Figure 1. 109

Growth features 110
The ice contained both sub-mm sized brine pockets and supra-mm sized drainage channels, reminiscent of 111 natural sea ice. Figures 3 and 4 show examples. The ice of lower salinity (3.0±0.9 ppt) had fewer defects of both 112 kinds. Some of the ice of higher salinity (5.9±0.6 ppt) possessed channels whose size was almost as large as the 113 grain diameter. The defects scattered light to the degree that in bulk form the ice had an overall opaque appearance. 114 When observed in thin section (~1mm) the ice exhibited to the naked eye distinct linear whitish features which we 115 took to be sets of interconnected brine pockets that could possibly be filled with very fine-grained ice. The ice of 116 higher salinity possessed more of these features, especially near the bottom of the parent puck (which was the last 117 part to solidify). Our sense is that these features served as stress concentrators, particularly ones that traversed the 118 width of the test specimen (described below), thereby weakening the ice. Indeed, as will become apparent, samples 119 obtained from near the bottom of a puck of higher salinity (5.9±0.6 ppt) had relatively low flexural strength. 120 compression, and a linear variable differential transformer (LVDT) gauge were used for measurements of load and 140 displacement of the upper surface of the ice beam during cycling. 141 142 Acoustic emissions were recorded during cycling using a PCI-2 18-bit A/D system; its frequency response 143 was 3 kHz-3 MHz and its minimum acoustic emission (AE) amplitude detection threshold was set to 45 dB. We 144 used a micro 30STC sensor (9.5 mm diameter, 11 mm thickness) which was attached to the top surface of an ice 145 beam with a rubber band. Vacuum grease was used as the coupling agent between the sensor and the ice surface. 146

147
The experiments were performed in a cold room at a temperature of -10°C and at an outer-fiber center-148 point displacement rate of 0.1 mm s -1 (or outer-fiber strain rate of about 1.4 x 10 -4 s -1 ). This displacement rate 149 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 150 from 0.35 to 1.2 MPa, outer-fiber strain amplitude in the range from ~ 1 to 5 x 10 -4 and frequencies in the range 151 from 0.1 to 0.6 Hz (i.e. periods from ~10 to 1.5 sec). where P is the applied load and L is the distance between the outer-pair of loading cylinders (shown in Figure 5b) 158 and is set by the geometry of the apparatus to be L = 254 mm. 159 160 We used two different loading procedures, as we did earlier in our study of S2 freshwater ice. Type I 161 loading was a completely reversed stress cycle with constant stress amplitude and mean stress of zero. Type II was 162 similar to Type I but incorporated an increasing multi-level (or step-level) stress amplitude. This second type of 163 loading essentially consisted of several Type I steps of increasing stress amplitudes. In the present study for stress 164 amplitudes below 0.7 MPa we used Type I loading. To cycle ice samples at stress amplitudes above 0.7 MPa, we 165 first pre-conditioned specimens through step-loading Type II procedure at progressively higher stress amplitude 166 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 167 and so on either until failure occurred or until a specific value of stress amplitude set by the operator (see Iliescu et 168 al. (2017) and Murdza et al. (2018) for details). To change stress amplitude the loading was stopped for ~15 sec to 169 change settings. After pre-conditioning, the specimens were cyclically loaded according Type I loading at least 300 170 times and generally for ~2000 times, since no change in strength was observed beyond a few hundred cycles (see 171 below). 172 Figure 6 shows measurements of load and of displacement versus time at the beginning and near the end of increase of strain during cycling at constant stress amplitude during the tests). The absence of detectable softening 177 during cycling of the saline ice is reminiscent of the absence of softening during the cycling of freshwater ice

Flexural strength of non-cycled ice 181
The flexural strength of non-cycled saline ice of both salinities was measured at -10 ºC and at a nominal 182 outer-fiber center-point displacement of 0.1 mm s -1 . The results are listed in Table 2. Failure more often occurred at 183 random locations between the two inner loading cylinders and less often either below or slightly outside the loading 184 cylinders. The reason for the latter location was the presence prior to testing of a significant concentration of whitish to the data of Timco and O'Brien (1994), although scatter is significantly greater than is the scatter in the strength of 199 the ice of lower salinity (3.0±0.9 ppt). This may be explained by the greater degree of interconnectivity of brine 200 pockets at the bottom of an ice puck (discussed above and shown in Figures 3 and 4). Indeed, the flexural strength of 201 the higher-salinity specimens appears to depend on the depth of ice from which beams were prepared, Table 2 tensile strength lends confidence that our lab-grown saline ice is a reasonably faithful analogue of natural sea ice. 218

Flexural strength versus number of reversed cycles under constant low stress amplitude 219
To determine whether there is a relationship between flexural strength and number of cycles imposed under 220 a constant low stress amplitude, we performed via Type-I loading a series of experiments on saline ice of lower 221 salinity (3.0±0.9 ppt) at -10 ºC at an outer-fiber center-point displacement rate of 0.1 mm s -1 at a low stress 222 amplitude of 0.35 MPa; i.e., at an amplitude less than one-half the flexural strength of non-cycled ice. implying that a kind of saturation of strength developed. Given that result and the new resuts for saline ice, we 229 followed the practice in the present study of cycling more than 300 times, often as many as 2000 times, before 230 bending the ice to failure. 231

Flexural strength versus stress amplitude 232
The flexural strength increases with stress amplitude. Figure 9 shows measurements obtained from saline 233 ice of both salinities cycled at -10 º C at an outer-fiber displacement rate of 0.1 mm s -1 . For comparison, data from 234 laboratory grown freshwater ice (Murdza et al., 2020b) of S2 character and from lake ice of the same character 235 (Murdza et al., 2020a(Murdza et al., , 2021 are also shown. The relationship between the flexural strength, and cycled stress 236 amplitude, , for saline ice appears to be a linear one and, within experimental scatter, to have essentially the same 237 sensitivity to stress amplitude as freshwater ice; namely: 238 8 where = 0.68 is a constant. For freshwater ice the non-cycled flexural strength is 0 = 1.75 MPa compared with 241 about 0.4 MPa that must be exceeded to detect strengthening. Interestingly, this apparent threshold is similar in 243 magnitude to the stress that marks the onset of significant AE activity under cyclic loading of sea ice cores (Cole 244 and Dempsey, 2006). Although saline ice is weaker than freshwater ice, it appears that upon cycling its strength 245 increases at the same rate as freshwater ice. 246 247 Although the rate of strengthening with stress amplitude appears to be the same for sline ice and freshwater 248 ice, the maximum increase in strength in the case of saline ice of lower salinity (3.0±0.9 ppt) is significantly lower. 249 We were able to strengthen saline ice by about 50% of the non-cycled strength compared with about 100% for 250 freshwater ice (Murdza et al., 2020b). Another point is that we almost were not able to cycle specimens at stress 251 amplitudes greater than the flexural strength of non-cycled material, whereas in the case of freshwater ice we were 252 able to cycle at stress amplitudes significantly greater than flexural strength of non-cycled ice. Indeed, the maximum 253 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 254

Fatigue behavior 263
Although the specimens from which the data in Figure 9 were obtained did not fail during cycling, other 264 specimens cycled under similar consitions did fail while being cycled. Results from such tests (on of saline ice of 265 lower salinity (3.0±0.9 ppt) at -10ºC and 0.1 mm s -1 outer-fiber displacement rate) allowed us to construct S-N 266 fatigue curve , shown in Figure 11. The number of cycles here is the number of cycles to failure during cycling at 267 the last stress amplitude level and not the total number of cycles. At most the S-N curve showd only a weak 268 systematic dependence of the number of cycles to failure on stress amplitude. Indeed, for the same stress amplitude 269 of ~ 0.9 MPa, fatigue failure occurred after as few as <10 cycles and after as many as a few thousand cycles. 270 Statistical analyses to test the hypothesis that the slope in Figure 11 is zero resulted in a p-value equal ∼0.06. 271 Therefore, there is only a marginally significant effect of number of cycles on the stress at which failure occurred. 272 We attribute this variability in fatigue life to the variability in microstructure from specimen to specimen. 273 That said, a note of caution is appropriate. The data in Figure 11 should not be viewed as fatigue data in the 275 usual sense; i.e., in the way such data are viewed when obtained from other materials (e.g., metals and alloys) that 276 exhibit classical fatigue behavior. In those cases, before cycling, all specimens are assumed to have the same 277 thermal-mechanical history. That was not the case here for the saline ice, as most of the samples were pre-278 conditioned according to Type II procedure before they were cycled at the last stress level where they failed while 279 cycling. In other words, in order to get fatigue failure, we were increasing stress amplitude by small increments of 280 ~0.05 MPa and allowed a sufficient number of cycles at each stress level (~500-1000) before we reached a fatigue 281 failure. 282

283
The question to address here is why we did not obtain a classical S-N curve? We suggest that the classical 284 mechanism of fatigue, i.e. accumulation of damage, is not in play in our tests and some other process is controlling 285 fatigue life. 286

Microstructural observations of samples after fatigue failure 287
In an attempt to reveal deformation damage in the form of microscracks, we examined using thin-section 288 optical microscopy (up to 50x magnification) the microstructure of specimens of the lower salinity ice (3.0±0.9 ppt) 289 after they had failed during cycling; i.e., failed in fatigue. Three thin sections were prepared from four specimens in 290 order to ensure a greater probability of observing microcracks growing from brine pockets or brine channels, should 291 they be present. The plane of the thin section was parallel to the long axis of the columnar grains and parallel to the 292 direction of the greater normal stress. This plane was taken as the best plane to observe possible cracks. Thin 293 sections were observed using non-polarized light. We found no evidence of microcracks starting from brine pockets 294 or from other defects. In fact, we found no microcracks at all. It appears, therefore, that slow crack growth is not a 295 significant contribution to the fatigue life of the beams of the laboratory-grown saline ice that we studied.  Figure 12 shows the cummulative acoustic 304 emissions, or "hits", as a function of time for ice that was cycled reversely at a constant stress amplitude of 0.5 MPa. 305 As can be seen, the hit rate (or hits per unit time), which is the slope of the curve in Figure 12, is about the same for 306 the duration of the experiment. 307 greater is the stress amplitude, the greater is the hit rate. However, during cycling below about 0.2 MPa no hits were 310 detected. 311 312 Figure 13 also indicates that the hit rate is independent of the sequence of different stress amplitudes.The 313 numbers in Figure 13 show the order of cycling at different stress amplitudes; i.e., firstly we cycled ice at higher 314 stress amplitudes (0.5-0.8 MPa), then at lower stress amplitudes (0.2-0.4 MPa). The results showed an increase in 315 the hit rate as stress amplitude increases, regardless of the sequence of cycling. to do for freshwater ice. Indeed, this seems reasonable given the fact that freshwater ice comprises of ~95% by 325 volume of the saline ice we studied. Within the freshwater component, there is almost no solubility of salts (Weeks 326 and Ackley, 1986). The remainder of the saline ice is a mixture of air and brine. As was shown earlier, the 327 microstructure of saline ice that we grew is closely similar to the microstructure of sea ice. Pores lower the saline ice 328 strength (Sammis and Ashby, 1986). However, the behavior of S2 saline ice under cyclic loading is essentially the 329 same as the behavior of S2 freshwater ice (Murdza et al., 2020b), i.e. its strength increases at the same rate as 330 freshwater ice upon cycling under a given amplitude of the outer fiber stress. Hence, it is reasonable to assume that 331 the strengthening mechanism for the saline ice is similar to that for the freshwater ice. In our earlier work (Murdza 332 et al., 2020b) we proposed that strengthening might be due to the development of an internal back stress that 333 originates from either dislocation pileups or grain boundary sliding. However, one reviewer suggested the 334 possibility of a different strengthening mechanism. Due to the inherent weakness of the saline ice microstructure, the 335 microstructural stress relief may occur through localized damage via microcracking mentioned above. More 336 research, however, is needed to examine this hypothesis. 337

338
The maximum degree of strengthening in the case of saline ice is significantly lower than that for the 339 freshwater ice, although the slopes of the two data sets (rate of strength increase with increasing cyclic amplitude) in 340 Figure 9 are nearly equivalent. That difference may be explained by the structure of saline ice which limits 341 maximum possible strengthening. Given the significantly greater number of stress concentrators in saline ice, such Flexural experiments conducted on saline ice of higher salinity (5.9±0.6 ppt) showed the importance of 347 brine features. Samples that were manufactured from the bottom of the ice puck were characterized by more 348 frequent whitish interconnected features (taken to be interconnected brine pockets) that often were the path for easy 349 crack propagation. Often samples were so weak that they failed before testing simply by handling. Interestingly, 350 there were no interconnected features in samples prepared from the top of an ice puck, which resulted in a difference 351 of more than a factor of three in strength between samples from top and bottom. Samples produced from saline ice 352 of lower salinity (3.0±0.9 ppt) also had whitish features; however, these features were spread more uniformly (on a 353 macroscopic scale) across the sample, resulting in little difference in strength between the bottom and top samples. the ice sheet failed in the field, we expect that there are many micro and macro cracks in natural sea ice. Indeed, 382 thermally-induced tensile stresses can induce thermal cracking in floating ice sheets (Evans and Untersteiner, 1971). 383 Therefore, our sense is that the difference in ice behavior under cyclic loading in situ in the field (Bond and 384 Langhorne, 1997;Langhorne et al., 1998) and in the laboratory in the present study is due to other types of defects 385 other than brine channels and pockets that are generated in the field as a result of thermo-mechanical history of ice. 386