Behavior Under Cyclic Loading of Freshwater Ice and Sea Ice With Thermal Microcracks

The combination of thinning ice, larger waves, and damage due to diurnal thermal cycling motivate the need to better understand the impact of flexing under the action of oceanic waves on the strength of thermally cracked ice. To that end, new experiments were performed on freshwater, lab‐grown ice and first‐year natural sea ice. Both materials were cracked by thermal shocking and then subsequently cyclically flexed. Initially, the thermal cracks weakened both materials. When the cracked ice of either origin was cyclically flexed under fully reversed loading, its flexural strength, initially reduced by the stress‐concentrating action of the cracks, recovered to the strength of non‐cracked, non‐flexed ice. When the cracked ice was cyclically flexed non‐reversely, its strength recovered only partially. During reversed cyclic flexing, the cracked region experienced alternately compressive and tensile stresses. We suggest compression resulted in contact of opposing crack faces followed by sintering leading to strength recovery. During non‐reversed cyclic flexing, contact and sintering were reduced and ice strength did not fully recover. The tendency for cracks to heal during cyclic flexing may lessen their threat to the structural integrity of an ice cover.

to several kilometers (Evans & Untersteiner, 1971), and their depth can reach tens of centimeters (Milne, 1972) can serve as the initiators of failure via fatigue, evidence for which is the relatively sudden breakup of the arctic ice cover on at least two occasions (Asplin et al., 2012;Collins et al., 2015). The strength of thermally damaged ice was investigated earlier by Murdza et al. (2022a). In that study, Murdza et al. (2022a) thermally shocked laboratory-grown freshwater and saline ice as well as natural first-year sea ice and they investigated the change in flexural strength at different time intervals after the shocking/cracking. Initially, the cracks weakened the materials in accordance with the expectations from fracture mechanics theory. However, within tens to hundreds of seconds, the cracks healed and the strength recovered completely.
The aim of the present work was to investigate the behavior of thermally cracked ice under flexing. Given the consequences of breakup and the unknown contribution of thermal microcracks on fatigue, new experiments were performed in the laboratory to gain some insight into the mechanical behavior of thermally cracked ice under cyclic loading. With that idea in mind, a set of thermal cracks was introduced into specimens either before or during flexing. As will become apparent, when the ice was cycled under reversed loading, the cracked material strengthened, while when the ice was cycled non-reversely such that the cracked region was always under the tension, the ice weakened. To our knowledge, this is the first report on the cyclic loading of thermally damaged ice.

Materials and Methods
We studied the same kind of S2 freshwater ice (i.e., salt-free) and natural first-year sea ice that we studied earlier (Murdza, Polojärvi, et al., 2021;Murdza, et al., 2022a;Schulson et al., 2022). Freshwater ice was produced in the laboratory through unidirectional solidification of local tap-water, following a standard procedure (Golding et al., 2014;Smith & Schulson, 1993). We measured salinity of this tap-water to be less than 0.1 ppt. During freezing, all salts, if any, are expelled from the ice due to very low segregation coefficient for most impurities in ice. The sea ice was harvested in the form of a submeter size block from the ice cover on the Beaufort Sea during the winter 2020 and then stored at −30°C in a cold room at Dartmouth's Ice Research Laboratory. Both types of ice were polycrystalline and characterized by columnar-shaped grains whose long axis was parallel to the direction of growth. Each type possessed the S2 crystallographic growth texture in which the c-axes of the grains were confined more or less to the horizontal plane, but randomly oriented within that plane. The grain size (column diameter) of the freshwater ice so produced was 5.5 ± 1.3 mm and its density was 914.1 ± 1.6 kg · m −3 . Grain size, density, and salinity of first-year sea ice were 2.7 ± 0.4 mm, 906 ± 4 kg · m −3 and 3.0 ± 0.3 ppt, respectively. From such materials, test specimens were machined in the form of beams that were milled to final dimensions: thickness h = 13 mm (along the columns), width w = 75 mm, and length l = 300 mm.
All the experiments were conducted at −10°C. The specimens were allowed to reach thermal equilibrium at this temperature prior to testing. The thermal shock and subsequent damage were introduced to all ice specimens through spraying with either liquid nitrogen (−196°C) or medical spray (−52°C, this spray contains pure 1,1,1,2-tetrafluoroethane HFC 134a) for ∼1-2 s across a narrow (∼20 mm) band in the middle of one of the largest faces or by placing a cold (−30°C) steel plate directly on the ice (similarly to Gold (1961Gold ( , 1963). Results from the experiments showed that the different types of thermal cracking had no significant effect on the flexural strength (Murdza et al., 2022a). The thermal shock was introduced only to one surface of the specimen and created a network of randomly oriented grain-sized cracks, both inter-granular and trans-granular. Within the freshwater ice, the cracks were clearly visible to the unaided eye and penetrated ∼4 ± 1 mm into the ice (see Figure 1a of (Murdza et al., 2022a)). This is consistent with observations by Gold (1963) where the author reported that the crack depth in ice as a result of contact between ice plate and colder brass plate was between 0.24 and 0.39 cm. In sea ice, due to its opacity, cracks were less visible, and it was not possible to estimate their penetration depth. Although there is a wide variety of thermal cracks in nature, we believe that thermal shock that was introduced in our experiments resulted in a crack pattern in ice samples that mimicked the pattern in nature (cracks extend through multiple grains in length and ∼20%-30% of ice thickness in depth).
To investigate the effect of thermal shocking on the behavior of ice under reversed and non-reversed cyclic flexing, we introduced the thermal shock, either 24 hr before cycling, or immediately before cycling, or, to minimize microstructural changes, during initial cycling when specimens were sprayed during the first cycle.
Cycling of cracked specimens was done by flexing under 4-point loading using a custom-built frame was attached to a servo-hydraulic loading system housed within the same cold room in which the specimens were thermally shocked (Murdza et al., 2018(Murdza et al., , 2019(Murdza et al., , 2021b. The specimens were cycled at the same temperature of −10°C at which they had been equilibrated. The samples were loaded across the columns at a constant outer-fiber center-point strain rate of ∼10 −4 s −1 which resulted in frequency of ∼0.1 Hz (∼10 s period) which is approximately the frequency of ocean swells (Collins et al., 2015). In order to reach higher outer-fiber stress amplitudes during cycling, the maximum outer-fiber stress was gradually increased, as described earlier (Iliescu et al., 2017;) to a pre-determined level and then held constant at that level while the ice was cycled for an additional number of cycles, typically ∼500. Stress amplitude is defined as one-half of the difference between the maximum and the minimum outer-fiber stress.
In order to reduce the potential for opposing crack surfaces to come into contact and potentially heal, additionally to reversed cycling, we also cycled specimens in a non-reversed manner such that the shocked region was always under tension; that is, we raised the mean stress from zero, where mean stress is defined as one-half the sum of the maximum stress and the minimum stress. During the non-reversed cycling we varied the minimum stress from 0 to 0.5 MPa. This means that for a given maximum outer-fiber stress the stress amplitude decreased as the mean stress increased.
The flexural strength was obtained from the load at failure, P, using the relationship: where L = 254 mm is the distance between the outer pair of load lines and b and h denote the width and thickness of the beam, respectively.

Results
In total, 40 measurements were made on cracked ice, including 27 on freshwater ice, and 13 on sea ice. Fewer tests were performed on sea ice owing to the limited availability of the material. Results for each experiment are available in the data repository. Figure 1 and Table 1 show the effect of cycling on the flexural strength of S2 freshwater ice and S2 sea ice, with and without thermal cracks. The data for crack-free freshwater ice (solid, black points) were obtained from  and are shown for comparison. A few points are noteworthy.
Freshwater ice (Figure 1): 1. Flexural strength of cracked freshwater ice (points filled in red) fully recovered upon fully reversed cyclic flexing for ∼500 times (i.e., under zero means stress) over the range of maximum outer-fiber stress explored from 0.4 to 1.5 MPa. The flexural strength of the thermally cracked ice upon cycling increased linearly as the maximum outer-fiber stress increased, which is similar to the behavior of non-cracked ice during cycling. The similarity in slopes of cracked and non-cracked ice may be attributed to the internal back-stress buildup suggested earlier . The only difference between non-cracked and cracked ice after cycling is that, for given cyclic flexing conditions, the cracked ice was slightly weaker than non-cracked ice (by ∼0.4 MPa), owing perhaps to some residual stress concentrating effects of the damage. 2. The interval of time between thermal shocking and reversed cycling (i.e., thermal shocking imposed either 24 hr before cycling, imposed right before cycling, or imposed at the beginning of cycling as load began to rise) appears not to affect the behavior of freshwater ice during fully reversed cycling nor to affect its ultimate strength. 3. Cracked ice that was cycled in a non-reversed manner with a minimum outer-fiber stress of 0 MPa but the same maximum outer-fiber stress as during reversed cycling (red triangles pointing downwards in Figure 1) had the same flexural strength after cycling as cracked ice that was cycled under fully reversed loading. These experiments were conducted at 0.5, 1.2, and 1.5 MPa maximum outer-fiber stress. 4. The flexural strength of cracked ice that was cycled under a non-reversed manner with a higher minimum outer-fiber stress of either 0.3 or 0.5 MPa recovered partially. The flexural strength measured after cycling was lower when compared to the strength of cracked ice that was cycled fully reversely. Moreover, the obtained strength values are lower than the flexural strength of pristine, non-cycled ice and cracked, non-cycled ice that was allowed to recover without cycling. 5. As well, the flexural strength of ice that was cracked and then strengthened by reverse cycling (red triangular points, Figure 1) relaxed when allowed to anneal at −10°C for 48 hr before bending to failure. During annealing its flexural strength decreased from 2.28 ± 0.13 MPa to 1.58 ± 0.05 MPa. This relaxation is essentially the same as that exhibited by pristine ice that was strengthened by cyclic loading and then annealed (Murdza et al., 2022b); it is attributed to the relaxation of an internal back stress induced by cycling.
Sea ice (Table 1): 1. Thermal cracking imposed at the beginning of reversed cycling does not affect the strength of sea ice after ∼500 cycles; that is, the strength of cracked ice after it was cycled for ∼500 times (1.47 ± 0.04 MPa) is about the same as the strength of pristine, non-cracked, non-cycled sea ice (1.40 ± 0.07 MPa). 2. The number of cycles matters. Thermal cracking imposed at the beginning of reversed cycling does affect the strength of sea ice after only 50 cycles. Specifically, the strength recovers partially. The strength of pristine non-cracked non-cycled ice (1.40 ± 0.07 MPa) is reduced immediately after thermal shocking to 0.91 ± 0.04 MPa. The strength partially recovers after the ice was cycled for 50 times to 1.19 ± 0.03 MPa.    . The solid pink line indicates the average flexural strength of non-cracked non-cycled freshwater ice plus and minus one standard deviation, that is, 1.73 ± 0.25 MPa (Timco & O'Brien, 1994). Red dashed line represents the trend for cracked freshwater ice that was cycled reversely.
10.1029/2023GL102889 5 of 7 3. The flexural strength of cracked ice that was loaded under non-reversed cycling between outer-fiber tensile stresses of 0.5 and 0.7 MPa for more than 500 cycles partially recovered to 1.16 ± 0.05 MPa. This strength is lower than the strength of cracked ice that was cycled reversely (1.47 ± 0.04 MPa) and that of pristine ice that was never cycled (1.40 ± 0.07 MPa).
The other point to note is the fracture path. When cycled reversely, the crack at failure generally did not pass through the pre-cracked region, but instead through pristine ice. In contrast, when cycled non-reversely where both minimum and maximum stresses are tensile, the crack at failure generally passed through the thermally cracked region. An implication is that when crack faces are not allowed to come together during cyclic flexing, healing may be impeded when compared to the case of fully reversed cyclic flexing during which crack surfaces are in contact for some time during each cycle.

Discussion
The question that motivated this work is whether thermal cracks that are introduced into ice affect behavior under cyclic loading, specifically whether the flexural strength of cracked ice changes upon cyclic flexing. The results show that in all experiments both freshwater ice and sea ice recover their strength either partially or fully when compared with the flexural strength of ice that is shocked and then bent to failure immediately. As shown earlier (Murdza et al., 2022a) the as-cracked strength is governed by fracture mechanics. When cyclically flexed reversely for ∼500 cycles, the flexural strength of both freshwater ice and sea ice recovers fully and is either about the same as or greater than the strength of non-cycled, non-cracked ice. When cycled non-reversely where both outer-fiber minimum and maximum stresses in the cracked region are tensile, the flexural strength recovers only partially.
As was discovered and discussed earlier (Murdza et al., 2022a), the ice that was thermally shocked but not cyclically flexed heals and completely recovers its strength relatively quickly (∼10-300 s). In those experiments, after thermal shocking the ice was allowed to rest in the cold room while opposing crack faces were able to come into contact, mainly due to the subsequent warming and expansion of the material around the shocked area. We suggested that the healing of cracks occurred primarily from sintering via surface diffusion and may have been assisted as well by the presence of a quasi-liquid layer on the crack faces (Murdza et al., 2022a). To ensure sintering and surface diffusion, the crack faces must be in contact. A similar process is thought to have occurred in the present experiments when cyclic flexing included a compression phase. Compression may even have enhanced healing by increasing the area of contact through creep. When the crack region was held under tension, contact of the crack surfaces was prevented and so was the recovery.
It is important to point out the time required for the recovery of ice strength. In the previous study (Murdza et al., 2022a), it was found that ∼300 s is enough to recover the strength of cracked (but not cyclically flexed) freshwater ice and that even less time (<10 s) is required for cracked (but not cyclically flexed) sea ice to fully heal. Given that period of a cycle in the present study is ∼20, 300 s is equivalent to 15 flexing cycles. However, here we observed that even after 50 cycles sea ice does not fully recover its strength. It is necessary to apply ∼500 cycles to recover the ice strength completely. This observation may be explained by the fact that during reversed cycling the cracked region experiences both tensile and compressive stresses and healing is impeded during the tensile part of a cycle. Local plasticity and crack tip blunting may have also contributed to the increase in strength upon cycling.
Should the behavior of ice on the larger scale reflect the behavior on the smaller scale, given that natural sea ice covers undergo reversed cyclic loading under the action of oceanic waves, it seems possible that these covers with thermal cracks may not weaken.

Conflict of Interest
The authors declare no conflicts of interest relevant to this study.

Data Availability Statement
The data presented in this paper are available at the Arctic Data Center website (Murdza et al., 2023).