PSI - Issue 61

Igor Gribanov et al. / Procedia Structural Integrity 61 (2024) 89–97 I.Gribanov et al. / Structural Integrity Procedia 00 (2024) 000–000

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Table 1. Parameters of the simulation common to all examples (Sanderson (1988); Gribanov et al. (2019)). Parameter Notation Value Young’s modulus E 3.7GPa Poisson’s ratio ν .3 Initial time step ∆ t .02 s HHT-alpha α .3 Damping coe ffi cient k d .1 Gravitational acceleration g 9.81m / s 2 Density of ice ρ ice 910kg / m 3 Density of water ρ w 997kg / m 3 Tensile strength σ max 100kPa

Fig. 7. (a) Intact irregular ice floe at t = .32 s. The color indicates the distribution of the tensile stress along the x -axis in Pascals. (b) The same floe after the fragmentation due to stretching, t = 14.00 s. The colors indicate disconnected fragments.

Fig. 8. The fracture pattern at t = 10 s. (a) Top view; (b) side view shows the vertical displacement of the fragments floating in the waves. The colors indicate disconnected fragments.

tension may be created, for example, by a force field applied at all points of the object away from the center. This test uses an irregular floe measuring 20 m across and 10 cm thick (Figure 7a). A radial in-plane load is gradually applied during a 20-second interval. The result of the fragmentation is shown in Figure 7b. The cracks develop one at a time as the stretching force is applied. The first crack appears at the stress concentration point in the bottom notch and splits the floe along a nearly straight vertical line. The second crack separates the small region in the bottom-left corner. The curvatures of the cracks are formed by the stress distribution, which is a ff ected by the shapes of the fragments. Standing wave test is inspired by the Hamburg Ship Model Basin (Hamburgische Schi ff bau-Versuchsanstalt, HSVA) experiments, where a relatively thin ice sheet was subjected to standing waves (Herman et al. (2018)). In a similar set of experiments at the same location, the formation of fragments was observed (Marchenko et al. (2019)). At first, the ice broke up into elongated strips, from which smaller floes formed. The smaller floes rotated and became rounded. Some water spilled through the cracks onto the surface of the ice, which led to wave dissipation. This work does not take into account hydrodynamic e ff ects, but attempts to reproduce the fracture patterns as sociated with bending-type fracture. A rectangular sheet is selected for this test measuring 20 × 5 m. In three sep arate tests, plate thickness is set to 3 cm, 10 cm, and 50 cm. The buoyancy force is modeled by a spring force that depends on the z-coordinate of the mesh nodes. The standing wave is described by the equation L w ( x , t ) = A w cos(2 π x /λ )sin(2 π t / T w )min( t /τ, 1) , where x is the horizontal position, t is the elapsed time, A w is the wave am plitude, λ is the wavelength, T w is the wave period, and τ is the initial attenuation delay. To match one of the HSVA experiments, λ is set to 3.99 m, T w is 1.6 s, and τ is 2 s. The resulting fracture pattern, shown in Figure 8, is consistent 4.2. Standing wave