Laboratory-scale mixed-mode I/II fracture tests on columnar saline ice
Introduction
Interest in ice-covered seas is continuously increasing due to the warming climate. To meet the growing need for clean energy and other natural resources, offshore wind power parks and drilling platforms are built higher up north. Increased access to ice-covered sea areas has also led to a search for more efficient marine transit routes and even an increase in tourism. Operations on ice-covered sea areas face more severe challenges due to ice loads on vessels and offshore structures. Ice loads are caused by ice-structure interaction processes, where ice comes into contact with a structure, deforms, fails and piles up against it. The safety and sustainability of the above-described operations require in-depth insight into sea ice failure.
Sea ice always contains numerous defects, such as brine channel networks, voids and cracks, with sizes ranging from micrometers to kilometers [1]. The size, density and orientation of the defects influence the mechanical behavior of ice, and consequently the magnitude of ice loads [2]. The failure of sea ice is often due to crack initiation and propagation or coalescence of cracks; cracks often have a crucial role in sea ice failure [3], [4]. Fracture mechanics has thus been applied in many ice-related studies [5], [6], [7], [8] and as a basis for numerical modeling of ice loads on ice-breaking ships [9].
Laboratory-scale fracture experiments on freshwater and saline ice have been performed since the late 1970s [10], [11]. Stehn et al. [2] applied chevron-notched short rod (SR) specimens to measure the R-curve of large-grained freshwater ice and found the specimen geometry favorable for studying the crack growth resistance. Stehn [10] determined of brackish sea ice using SR and the chevron-notched and semi-circular bend specimens [11], [12]. They found that was higher for the cracks perpendicular to the columnar grains than for the cracks parallel to them. Sammonds et al. [13] measured of multi- and first-year sea ice at the temperature −20 °C using SR specimens. Dempsey and co-researchers [14], [15] conducted laboratory and field fracture experiments using ice specimens of sizes ranging from 10−1 m to 102 m to investigate the effect of scale on ice fracture. Schulson and collaborators [16], [17] presented experimental work and discussion on the impact of grain size, temperature and loading rate on ice fracture toughness.
While the earlier work has yielded considerable insight on ice behavior, it has mostly focused on mode I fracture of ice, or in other words, on fracture under purely tensile mode [5], [7], [8], [10], [13], [18], [19]. Mixed-mode loads are, however, common in nature and engineering [20], [21], [22], and studies on mode II or mixed-mode I/II fracture of ice are rare; to our best knowledge, they have been explored only by Shen et al. [23], [24] and DeFranco and Dempsey [25].
Further, the earlier work on ice fracture has focused on isothermal, often relatively cold, ice specimens. Natural sea ice floating on seawater is often relatively warm (compared to its freezing point) and has a through-thickness temperature gradient, which may affect its mechanical properties. While in-situ experiments [7], [18] have the appropriate ice temperature and its gradient guaranteed to be accounted for, the costs of such operations are high. It is, therefore, useful to develop techniques for laboratory-scale fracture experiments on floating ice. A known limitation of usual laboratory-scale studies on ice fracture, applying to the experiments performed here as well, is that the specimen sizes are often not large enough to yield size-independent results [14], [15]. Laboratory ice fracture experiments with specimens ensured to be of adequate size are very challenging and performed only recently on freshwater ice by Gharamti et al. [19].
This paper focuses on laboratory-scale experiments on mode II and mixed-mode I/II fracture of ice. The focus is not on size-independent fracture toughness of ice, but rather on increasing the understanding of mixed-mode fracture of ice and of the role of T-stresses in ice fracture. The paper describes the experiments, reports their results and presents a theoretical analysis based on brittle fracture and generalized maximum tangential stress criterion. It also introduces the equipment and methods developed for conducting such experiments on floating ice. The experiments were performed using obliquely notched beam (ONB) specimens [26], which have also been applied to study the fracture behavior of other materials such as bitumen [27] and bone [28]. The reason for selecting this fracture specimen geometry is because the molds and fixtures required to produce and test the ONB ice specimens are relatively easy to make or relatively common in the laboratory, compared with other fracture specimen geometries such as the anti-symmetric four-point bend specimen [29] and the obliquely notched semi-circular specimen [30], [31]. During the tests, the crack propagated horizontally, and the crack front was vertical and through-the-ice-thickness, similarly to the cracks in Ref. [9]. Two types of ice specimens were used: isothermal specimens at the temperature of −10 °C and relatively warm specimens floating on water, with a through-thickness temperature gradient and an average temperature of −2.5 °C. The results demonstrated that a fracture-mechanics-based method coupled with the critical distance theory [32] predicted the failure loads of laboratory-scale cracked ice specimens under mixed-mode I/II loading well. This was the case, even if the small-scale specimen failure was likely dominated by its strength, since the notch sensitivity parameter, calculated using the approach adopted by Mulmule and Dempsey [14], [15], was ≈1 in our mode I tests.
Section 2 introduces approaches for producing non-oriented columnar ice specimens and performing fracture experiments on floating ice. Section 3 compares the experimental results, including fracture loads and crack initiation angles, with the theoretical predictions. The results are then discussed in Section 4, which also presents observations on trans- or intergranular crack propagation. Section 5 concludes the paper.
Section snippets
Ice preparation and microstructure characterization
This study focused on non-oriented columnar-grained saline ice because it was one of the most extensively occurring ice types on northern ice-covered seas. The ice specimens were produced using the approach introduced in detail by Wei et al. [33]. The ice was grown in a cold room using a plywood tank insulated with rigid foam (Fig. 1). Insulation inhibited the freezing from the structural members of the tank and ensured the vertical heat flux leading to columnar grains. The bottom of the tank
Results and analysis
This section first presents the results of the experiments. The theory for the analysis is then introduced. After this, the fracture loads and crack initiation angles from the experiments are compared to those predicted by the theory.
Strength and apparent fracture toughness
In Fig. 11, Fig. 12, the scatter of the results looks relatively large compared to that of other brittle materials in the literature, such as PMMA in Ref. [43]. Note that saline ice usually has numerous defects (including brine channel networks, voids and cracks), relatively irregular grains (Fig. 3), and consequently significant heterogeneity. By contrast, man-made PMMA and the rock materials selected for conducting laboratory fracture tests are usually much more homogeneous. These are why our
Conclusions
Mixed-mode I/II fracture experiments were conducted on non-oriented, columnar saline ice. The specimens were tested under two conditions: (i) being relatively cold and dry, and (ii) floating on water. The fracture initiation angles and fracture loads of the specimens were compared with the theoretical predictions based on the traditional MTS and the GMTS criteria. The main conclusions are as follows.
- 1.
The obliquely notched specimen under three-point bending is viable for achieving mixed-mode I/II
CRediT authorship contribution statement
Mingdong Wei: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Visualization. Feng Dai: Methodology, Validation, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors thank Prof. Arttu Polojärvi (Aalto University) for providing the experimental setup and language editing, Prof. Jukka Tuhkuri (Aalto University) for providing valuable comments, and Dr. Malith Prasanna (Aalto University) for his help in the experiments.
References (60)
- et al.
Orientation effects on the fracture of pond (S1) ice
Eng. Fract. Mech.
(1995) Research trends in ice mechanics
Int. J. Solids Struct.
(2000)- et al.
A large scale simulation of floe-ice fractures and validation against full-scale scenario
Int. J. Nav. Arch. Oceang.
(2018) - et al.
In-plane fracture of an ice floe: a theoretical study on the splitting failure mode
Cold Reg. Sci. Technol.
(2015) - et al.
Fracture of S2 columnar freshwater ice: size and rate effects
Acta Mater.
(2021) - et al.
DEM simulations of direct shear box experiments of ice rubble: Force chains and peak loads
Cold Reg. Sci. Technol.
(2015) - et al.
Low temperature fracture toughness study for bitumen under mixed mode I+II loading condition
Eng. Fract. Mech.
(2019) - et al.
Fracture and microstructural study of bovine bone under mixed mode I/II loading
Procedia Struct. Integr.
(2018) - et al.
Fracture loads prediction of the modified 3D-printed ABS specimens under mixed-mode I/II loading
Eng. Fract. Mech.
(2020) - et al.
A review of the engineering properties of sea ice
Cold Reg. Sci. Technol.
(2010)