Ice is a complex heterogeneous medium. Its behavior depends on many factors and changes in different processes. Thus, the problem of the determination of the correct rheological model is still unsolved. In this work low-speed impact on ice by the ball striker is considered. The main focus of the research is the development of the method of the correct model selection based on the computer simulation of the laboratory experiment. The simulation was conducted using the following rheology models: isotropic linear elasticity model, elastoplasticity model with the von Mises and the von Mises-Schleicher yield criteria, elasticity model with elastoplastic inclusion. The governing system of equations is solved using grid-characteristic method. Models’ comparison is performed based on the ball’s velocity and depth of ball’s immersion into the ice. The model parameters’ influence on the results is surveyed. As a result, the parameters that reconstruct the solution close to the experimental results are chosen.

Ice plays the central role in many processes in the Arctic region. However, the problem of the determination of the correct rheological model that can define its behavior is still unsolved. Thus, this work is a part of a series of works dedicated towards the creation of the method that allows to select ice model based on the laboratory and numerical experiments. The process of the low-speed impact on the artificially frozen ice plate by the ball striker is examined. The isotropic linear elasticity model serves as the governing system of equations. It is solved using grid-characteristic method on structured grids. Plasticity is introduced as a corrector of the elasticity with the von Mises yield criteria. Finally, ice is divided into two zones, the plasticity zone in the form of a hemisphere with the center in the first contacting point of the plate and the ball, and the elasticity zone in the rest part of the medium. The radius of the hemisphere is considered to be a function of the depth of the ball immersion into the ice. As a result of the simulation, wave and stress tensor patterns are obtained. The comparison with the laboratory experiment is conducted based on the analysis of the ball's coordinate and velocity. The influence of the model's parameters on the simulation results is analyzed.

Ice is a complex heterogeneous medium that can be described using different mathematical models, for instance, elasticity, viscosity, plasticity, and viscoplasticity models. This work is aimed at the ice properties investigation based on the data of laboratory experiments. The dependencies between instantaneous force on the ball in the impact point and the depth of ball immersion into ice for different striking velocities were obtained experimentally by other scientists. In this work, linear elasticity, elastoplasticity, and Kukudzhanov elastoviscoplasticity models with different parameters were applied to the collision process simulation. The governing system of equations was solved using grid-characteristic method on structured moving meshes. The results of numerical experiments were compared with the dependencies from the laboratory experiments. Qualitative evaluation of the relation between the chosen model parameters and the calculated dependencies was performed.

Experimental data and results of theoretical modeling of the bending of a viscoelastic floating ice plate formed under constrained deformation are analyzed. When a thin plate of ice is frozen on the water surface under conditions of constrained deformation, which may be caused, for example, by the rigid walls of the pool, periodic changes in physical properties occur in it, in particular, periodic penetration resistance. Experimental results confirming this fact were obtained during tests of a thin ice cover at the Krylov State Research Center (Saint-Petersburg, Russia). A characteristic feature of the test results is that their spatial distributions can be represented with sufficient accuracy as an overlap of two periodic functions with significantly different periods: long-wave and short-wave components. In this paper, a detailed analysis of experimental data is given, which makes it possible to isolate these components. Furthermore, the theoretical model that explains the physical causes for double periodicity is proposed. The model assumes viscoelastic quasi-static deformation of the ice plate caused by small fluctuations of the water level in the basin and random disturbances of its surface. An analytical solution for the model case of cylindrical bending is derived. The solution is presented in the form of an expansion in terms of eigenfunctions of differential operators generated by the boundary value problem under study. It has been established that when a thin plate of ice freezes under conditions of constrained deformation, there are at least two reasons for the appearance of a periodic structure: a general loss of stability as an elastic structure and a local loss of stability by a viscoelastic-plastic mechanism. The results obtained can be used in the development of the theory of ice compression, in assessing the causes of variation in the local strength of ice fields and the possibility of their artificial destruction.

The phenomenon of double periodicity of the mechanical properties of a thin ice field in a rigid pool is studied. A modal analysis of the experimental data was carried out, that makes it possible to identify two main periods in the spatial distribution of the reaction of ice to cross-cutting penetration. A new mathematical model for evolution of the properties of an ice field is developed. It is based on the ability of the viscoelastic mechanical system to emit perturbations with a certain spatial length and to accumulate them over time, which theoretically explains the effects observed in the experiment.

The paper gives the experimental data on wave metamorphism of ice. The conclusion about the presence of wave metamorphism relies on the local hardness study of model ice sheet. Measurement results were used to obtain characteristic wave lengths. The presence of wave structures has been confirmed by independent tests with indentor, as well as by local hardness studies of full-scale river ice.

The influence of nonlinear wave structures on the local hardness of an ice field of a dynamic type of formation is studied. Wave structures are formed by the interference of flexural–gravitational and longitudinal waves. The source of oscillations is coherent radiation in the ice itself. The difference in the local hardness of ice in the nodes and antinodes of standing waves (up to 60%) is explained by the dynamic metamorphism of ice. The dependences of the local ice hardness on the coordinates in the longitudinal and transverse profiles of the ice field have the form of periodic curves. The texture scales were determined, and the phase surface of the wave structures was constructed, which is not monochrome and reflects the spatial heterogeneity of the strength properties of the ice field. The effect of the wave action depends on the conditions at the interface between the ice and the pool walls. The influence of wave structures on the strength properties of the ice field as one of the possible factors of the spatial variability of ice under various modes of occurrence in situ is quantified.

The heterogeneity of the strength of the ice field of the dynamic type of formation with an area of 800 m2 was investigated in time and space. It is shown that stationary periodic wave structures are formed in a closed volume of an ice field lying on the surface of a liquid in a rectangular basin. In a case of absence of any external influences, the dominant source of elastic waves in the ice is the coherent radiation of them on freezing of water, i.e. the ice field itself. Another wave structures, i.e. standing waves, form secondary ice textures in the ice field with diminished strength. Local hardness of ice was chosen as the criterion of strength. The recurrence of local hardness values as a function of coordinates of the measurement points in the longitudinal and transverse profiles of the ice field was determined. The hardness values vary from 40 to 60% with an axial force measurement error of 5%. The experimental relations are approximated by periodic curves, in which the maxima and minima of local hardness correlate with the nodes and antinodes of standing waves, respectively. The decrease in local ice hardness in the secondary textures is explained by high-frequency dynamic metamorphism. The wavelengths corresponding to bending-gravitational and longitudinal waves are identified, with the interference of which stationary periodic wave structures are formed. A similar regularity of changes in local hardness was revealed also in a river ice. The results obtained allow us to consider nonlinear wave phenomena as one of the factors controlling the spatial-temporal variability of the ice strength characteristics.

The heterogeneity of the strength of the ice field of the dynamic type of formation with an area of 800 m2 was investigated in time and space. It is shown that stationary periodic wave structures are formed in a closed volume of an ice field lying on the surface of a liquid in a rectangular basin. In a case of absence of any external influences, the dominant source of elastic waves in the ice is the coherent radiation of them on freezing of water, i.e. the ice field itself. Another wave structures, i.e. standing waves, form secondary ice textures in the ice field with diminished strength. Local hardness of ice was chosen as the criterion of strength. The recurrence of local hardness values as a function of coordinates of the measurement points in the longitudinal and transverse profiles of the ice field was determined. The hardness values vary from 40 to 60% with an axial force measurement error of 5%. The experimental relations are approximated by periodic curves, in which the maxima and minima of local hardness correlate with the nodes and antinodes of standing waves, respectively. The decrease in local ice hardness in the secondary textures is explained by high-frequency dynamic metamorphism. The wavelengths corresponding to bending-gravitational and longitudinal waves are identified, with the interference of which stationary periodic wave structures are formed. A similar regularity of changes in local hardness was revealed also in a river ice. The results obtained allow us to consider nonlinear wave phenomena as one of the factors controlling the spatial-temporal variability of the ice strength characteristics.

The formation of an intermediate layer under hydrostatic compression at a shear appearing due to the action of converging and diverging fronts of stress momentums (pulses) is considered. Continuous monitoring of deformational changes in the structure of ice was carried out using acoustic methods. The features of contact ice breaking in the diverging fronts of stress pulses are considered by the example of the slow impact of a rigid spherical indenter on an ice plate simulating half-space. Using the piezoelectric accelerometer, an oscillogram of the impact was recorded and a generalized dependence of the reduced stress on the reduced instantaneous velocity of the impact (semi-cubic parabola) was obtained. It is established that under conditions of the experiment (smooth convex indenter surface and icy half-space) a thin intermediate layer is formed, the properties of which determine the physical similarity in the family of curves "instantaneous force-instantaneous velocity". A rheological model with due regard for the change in the microstructure of ice during the impact is proposed. Quantitative determinations of the deformation changes in structure of solid ice samples were performed under intensive plastic deformation in a matrix with a profile similar to the Laval nozzle. The deformations created by the piston caused forced vibrations in the ice. The working surface of the piston in the form of an ellipsoid together with the smooth walls of the matrix and the reverse cone created conditions for parametric resonance and the formation of fronts of high-frequency stress pulses. Under influence of these pulses, zones with a superplastic fine-crystalline structure of ice (cumulative effect) were formed in ice. In the outlet cylindrical channel, a flow around an obstacle of the ice with the structure of an intermediate layer (dynamic viscosity 20 MPa s) and the distribution of velocities of motion over the channel cross section were studied. The obtained results can be used to simulate the processes of contact destruction of deep rocks by a support or an ice-resistant platform loaded with an ice field.

The formation of an intermediate layer under hydrostatic compression at a shear appearing due to the action of converging and diverging fronts of stress momentums (pulses) is considered. Continuous monitoring of deformational changes in the structure of ice was carried out using acoustic methods. The features of contact ice breaking in the diverging fronts of stress pulses are considered by the example of the slow impact of a rigid spherical indenter on an ice plate simulating half-space. Using the piezoelectric accelerometer, an oscillogram of the impact was recorded and a generalized dependence of the reduced stress on the reduced instantaneous velocity of the impact (semi-cubic parabola) was obtained. It is established that under conditions of the experiment (smooth convex indenter surface and icy half-space) a thin intermediate layer is formed, the properties of which determine the physical similarity in the family of curves «instantaneous force-instantaneous velocity». A rheological model with due regard for the change in the microstructure of ice during the impact is proposed. Quantitative determinations of the deformation changes in structure of solid ice samples were performed under intensive plastic deformation in a matrix with a profile similar to the Laval nozzle. The deformations created by the piston caused forced vibrations in the ice. The working surface of the piston in the form of an ellipsoid together with the smooth walls of the matrix and the reverse cone created conditions for parametric resonance and the formation of fronts of highfrequency stress pulses. Under influence of these pulses, zones with a superplastic fine-crystalline structure of ice (cumulative effect) were formed in ice. In the outlet cylindrical channel, a flow around an obstacle of the ice with the structure of an intermediate layer (dynamic viscosity 20 MPa s) and the distribution of velocities of motion over the channel cross section were studied. The obtained results can be used to simulate the processes of contact destruction of deep rocks by a support or an ice-resistant platform loaded with an ice field.

Two scenarios of the influence of standing waves on the strength properties of ice lying on a liquid surface are considered: one during freezing of the ice field and one resulting from instability, which is caused by compression at the pool walls due to expansion of the water during freezing. The experimental hardness profiles of the ice field indicate the formation of periodic structures characteristic for the wave process. It is shown that the standing waves arising in the basin change the strength characteristics of the ice cover in both cases.

Рассматриваются два сценария влияния стоячих волн на прочностные свойства льда, лежащего на поверхности жидкости: в процессе намораживания ледяного поля и в результате потери устойчивости, которая вызвана обжатием по стенкам бассейна из-за расширения воды при замораживании. Полученные экспериментальные профили твёрдости ледяного поля свидетельствуют о формировании периодических структур, характерных для волнового процесса. Показано, что в обоих случаях возникающие в бассейне стоячие волны изменяют прочностные характеристики ледяного покрова.

The effect of stress pulses on the formation of an intermediate layer in freshwater ice under an impact and in the ice bulk at a shear under conditions of quasi-static compression is considered when applying finite-amplitude elastic waves and when the fronts of these waves collapse.

К 80-ЛЕТИЮ СО ДНЯ РОЖДЕНИЯ Н.К. РЯЗАНЦЕВА Генерального конструктора, ученого, создателя танковых двигателей, почетного доктора НТУ «ХПИ» выпускника кафедры двигателей внутреннего сгорания ХПИ