Annotation of the results obtained in 2020
1) On the basis of the model developed at the second stage of the project, a refined computer model was proposed that describes the deformation of monolithic nanoceramic MgAl2O4 spinel. The “stress-strain” curves were calculated by the method of discrete dislocation dynamics and the dependence of the yield stress on the grain size was found. Within the framework of the model, the plastic deformation of nanoceramics is described through either the combined action of grain boundary (GB) sliding and the emission of lattice dislocations from GB triple junctions, or (for materials with a sufficiently large grain size) the standard slip of lattice dislocations nucleating on Frank-Read sources. The calculation results demonstrated the presence of both an inverse Hall-Petch relation (a decrease in the yield stress with a decrease in grain size) in the range of small grain sizes, and a normal Hall-Petch relation for larger grain sizes. The results of model calculations show good agreement with the available experimental data. 2) An analytical model is developed that describes both direct and inverse Hall-Petch dependences observed in nanocrystalline ceramics as well as the low strain rate sensitivity of such ceramics. The model predicts that the transition from the direct to the inverse Hall-Petch dependence is associated with an increase in the number density of triple junctions with a decrease in grain size. It is demonstrated that the critical grain size for this transition depends on the fraction of triple junctions that can emit lattice or grain boundary dislocations at a given stress, which, in turn, can depend on the structure, energy and chemical composition of grain boundaries. 3) An analytical model is suggested that describes the mechanical properties of ceramic/graphene composites. Within the model, the dependence of the porosity of the ceramic/graphene composites on the volume fraction of graphene is obtained. Based on this dependence, the dependences of hardness and fracture toughness of ceramic/graphene composites on the volume fraction of graphene are calculated. The existence of an optimal graphene volume fraction corresponding to the maximum values of hardness and fracture toughness is demonstrated. The calculated dependences of porosity, hardness, and fracture toughness on the volume fraction of graphene for ceramic/graphene composites are compared with the corresponding experimental data for an Al2O3-WC-TiC ceramic composite reinforced with graphene platelets. It is shown that the calculation results are in good agreement with the experimental data. 4) The finite element method is employed for investigating the fracture in the "YSZ-ceramic-graphene" nanocomposites through the mode I crack generation inside the graphene inhomogeneity placed at a three-fold junction of grain boundaries. To this aim, the finite element model of an elastic body containing an almost triangle inhomogeneity is developed. The distribution of stresses in the vicinity of the inhomogeneity and the stress intensity factor of the crack are determined. It is shown that, in the case of a rigid inhomogeneity, the stress intensity factor of the crack is 1.5 times bigger than in the case of a homogeneous material. 5) The new methodology for the design of ceramic nanocomposites based on their representation by combinatorial discrete cell complexes has been developed. The used three-dimensional discrete complexes contained several thousand cells each and were created by space tessellation with Voronoi polyhedra. Furthermore, we extensively employed the tools of modern graph theory for rGO network characterisation. The concept of configurational (structural) entropy in a system of triple junctions made it possible to characterise and study high-entropy structures of rGO, which are far from the random spatial distributions of inclusions. To characterise the density of local concentration of rGO inclusions associated with porosity and cracking of nanocomposites, new structural indices were proposed. Modelling of various structures of rGO inclusions clearly showed that their spatial distribution could have a more substantial effect on the structural indices comparing with increasing of rGO fraction. Therefore, the only changes in the fraction of inclusions (that is usual practice in experimental studies) or a change in the grain size of the nanocomposite, obviously, cannot provide the best possible values of porosity, strength, and electrical conductivity. According to our simulations, the best possible strategy to obtain ceramic/rGO nanocomposites possessing the superior physical and mechanical characteristics is the increase in rGO fraction slightly above 1 mass percent with simultaneous increase in the introduced parameter of normalized configurational entropy up to its medium values of about 0.3-0.4. The random distribution of inclusions can be an optimal choice only for their small mass fractions, usually below 1 mass per cent. Numerical simulations of various textures and mass fractions of rGO inclusions have shown that the specific choice of rGO patterns can increase grain boundary conductivity of nanocomposite by almost an order of magnitude. 6) The study of electrical and mechanical characteristics of ZrO2-Y2O3-rGO composites obtained by spark plasma sintering (SPS) and sintering in a closed volume (without oxygen access) was continued. For the sample with 2 wt. percentage of rGO obtained by SPS, the mixed electron-ion conductivity was obtained. Thermal evolution of conductivity under heating in both the "oxidizing" nitrogen atmosphere (with a residual partial pressure of 10-3 atm.) and inert argon atmosphere (with a residual partial pressure of 10-5 atm.) was studied. It was shown that, due to the lack of the phase equilibrium during the SPS process, even in an inert atmosphere, there is a gradual loss of electronic conductivity due to grain growth. A model of the process was proposed, which takes into account the formation of semiconductor (for electron conductivity) rGO|YSZ|rGO sites. When sintered in a closed volume, a competition between SiC (the middle layer of the garnish) and the introduced graphene takes place in the intergranular space. Based on microstructural studies, the optimum rGO content was determined near one weight percent. The microhardness of the resulting composites (HV0.3), as well as the previous series of ceramics sintered on air and in high vacuum, was determined. It was shown that the key factor affecting microhardness is the lack of achieving phase equilibrium and homogeneity. The largest values (with the smallest errors) for all compositions were observed for samples obtained by spark plasma sintering. A record value of 14.19 GPa was obtained for a sample with 1 wt. percentage of rGO, which slightly exceeds the data available in the literature for composites based on cubic ZrO2. With a further increase in the rGO content to 2-2.5 wt. percent, the microhardness reduced by 10-15 percent. Thus, the creation of a nanocomposite based on YSZ ceramics with an rGO filler makes it possible to maintain an acceptable hardness of the obtained functional material with improved electrical conductivity. 7) A data set of computer molecular dynamics modeling of tension, compression, and shear of a fragment of the YSZ-ceramic-graphene composite for different values of temperature and strain rate is obtained. Stress maps are constructed for a cross section of the model sample. It is shown that, within the framework of the model under study, at small and medium strains, no fracture or stratification of the graphene nanoinclusion is observed. Upon the nucleation of a pore about 5 angstroms in size in a graphene nanoinclusion under tensile strain, a crack is formed, which propagates perpendicular to the applied load, moving between graphene layers, which ultimately leads to the separation of the inclusion into two parts. An increase in temperature reduces the interaction between graphene sheets, which leads to crack initiation when smaller pores are formed. 8) Based on the theoretical and experimental studies of YSZ-ceramics-graphene nanocomposites carried out within the framework of this project, it is possible to make a general conclusion about the need to select such a technology for obtaining a composite that provides the optimal (close to uniform) distribution of rGO in the matrix and to search for a corresponding optimal concentration of rGO which would provide a balanced combination of the required structural, functional and mechanical properties. 9) Further development of bulk functional YSZ-ceramics-graphene nanocomposites is quite promising and should be continued. Research on improving the technology of their synthesis should be aimed at eliminating such harmful factors as burnout of carbon additives during sintering and during electrochemical studies, possible diffusion of the skull material into the bulk of ceramics, lack of phase equilibrium, differences in the initial characteristics of precursor powders, etc.

 

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Annotation of the results obtained in 2018
1) A model is suggested describing both direct and inverse Hall-Petch dependences observed in nanocrystalline ceramic MgAl2O4 spinels. Within the model, plastic deformation in nanocrystalline ceramics is realized via lattice dislocation slip combined with thermally activated grain boundary sliding (GBS). The first mechanism dominates in the larger grains, while the second mechanism in the smaller grains. It is shown that depending on the GBS activation energy, the yield strength can be related to the grain size via either direct or inverse Hall-Petch dependence. Thus, plastic deformation realized through the thermally activated GBS combined with intragrain plasticity can explain the observations of both direct and inverse Hall-Petch dependences in nanocrystalline MgAl2O4 spinels. 2) Some theoretical models are developed to describe the fracture toughness of YSZ-ceramics-graphene nanocomposites and some related phenomena. In particular, a model is proposed describing the effect of crack bridging on the fracture toughness of ceramic-graphene composites. The dependences of the fracture toughness on the graphene content and the sizes of the graphene platelets are calculated in the exemplary case of yttria stabilized zirconia (YSZ)-graphene composites. The calculations predict that if crack bridging is the dominating mechanism of fracture toughness improvement, the maximum toughening can be achieved in the case of long graphene platelets provided that the latter do not rupture and adhere well to the matrix. The model shows good correlation with the experimental data at low graphene concentrations. An elastic model is proposed for one of the main stress concentrators in ceramics and ceramic nanocomposites that are pores in triple junctions (TJs) of grain boundaries (GBs), which have the shape of a rounded convex or concave triangle with three-fold symmetry axes. For the solution, we used numerical simulation by the finite element method within the ANSYS software. The case of uniaxial tension was studied in detail, the stress concentration on the pore surface and stress distribution near the pore along the axes of its symmetry were calculated. It is shown that the maximum value of the tangential stress concentration on the pore surface increases as its shape deviates from a circular one and reaches the values of ~ 3.7 for a convex and ~ 4.3 for a concave pore. The effect of stress concentration along the pore symmetry axes increases with the deviation of the shape of the pore from the round one and is quite noticeable in the region not exceeding 3 radii of the round pore. Outside this area, the effect of stress concentration becomes negligible. Comparison of the obtained results with the known numerical results of the first approximation analytical solution revealed the need to take into account the next approximation orders in analytical expressions for the stress field around the pore. A model of dislocations-GBs interaction is developed for nanocrystalline materials (NCMs), where dislocation generation, gliding and GBS take place. Based on the new model coupled both direct and inverse grain rotation processes, the interrelations between dislocation mechanism of plasticity and GBS in NCMs are discussed with special attention to high-strain-rate deformation. It is shown that the stored energy concept allows one to describe by natural way the transition between intragranular and GB mediated mechanisms of plasticity at grain size increasing. For extremely high strain rates 108-109s-1, the diffusion processes related with GB energy only occur for grains larger than 5 nm. This leads to appearance of a critical grain size below which grains remain their initial form during deformation. The obtained value of 3-5 nm is close to the well-known value of 6 nm for quasi-static loading. For larger grains, the kinetics of the emergence of new dislocations completely determines the angles of rotation and inclination of GBs. A computer model based on 3D discrete complex is preliminary developed to simulate the electrical conductivity and the fracture toughness of YSZ/rGO ceramics. The combinatorial 3-complex representing a polycrystalline microstructure of the ceramics, is obtained by a constrained Voronoi tessellation around a given set of points distributed randomly in a given container. Free software Voro++ (math.lbl.gov/voro++) is used for the tessellation. The Voro++ output is a list of nodes forming the Voronoi cells (polytops) together with the nodal coordinates. This allows to visualize the assembly and to obtain the statistical information on the number of vertices contained in each grain. It is shown that for large complexes containing more than 200 grains all relationships between variables defined on its elements become quite smooth. This gives a possibility to define the electrical conductivity of the complex, separately accounting the contribution of grains, GBs and network of graphene sheets. Moreover, a preliminary simulation of cracking along the GBs depending on the initial concentration of rGO was carried out and its effect on the conductivity of the whole complex was determined. 3) Synthesis methods have been developed and experimental studies of ceramic-graphene nanocomposites based on zirconium oxide CaO-ZrO2-Gr (rGO) and ZrO2-Y2O3-Gr (rGO) synthesized by these methods have been carried out. Ceramics of the composition 0.12CaO-0.88ZrO2 (mol. fractions) was obtained from a composite nanopowder 0.12CaO-0.88ZrO2 + 0.25 weight. percent of the reduced graphene oxide (rGO) by sintering in air at 1823 K. Ceramics were shown to consist of cubic grains separated by phase boundaries. The structure of ceramics has a high degree of formation. The use of a composite precursor leads to a significant refinement of the microstructure of ceramics in comparison with traditional methods for its preparation. The rGO additive segregates at the grain boundaries and effectively blocks the growth of ceramic grains during sintering, as indicated by a larger number of grains 1-2 microns in size. The phase composition of all ceramics corresponds to a well-formed cubic solid solution without CaO impurities or CaZr4O9 compound, as indicated by high crystallinity (98 percent), as well as crystallite size 60 nm. rGO acts as a lubricant which facilitates the pressing of the sample and its subsequent removal from the mold, which allows for a more perfect structure of the solid solution during sintering. The spectra of Raman scattering contain lines at 146, 260, and 610 cm-1, corresponding to the cubic modification of zirconia. The lines ~1368 and 1578 cm-1 which are characteristic of rGO are absent, which indicates that rGO was completely retired during the firing process. The Arrhenius dependence of the electrical conductivity of ceramics on temperature in the entire studied interval is shown. The conductivity is purely ionic. The value of conductivity at 973 K (700 degrees Celsius) is ~10-2 S/cm, the calculated total activation energy of conductivity is 1.14 eV. It is also shown that the addition of rGO to the ceramic composition reduces the Vickers microhardness from 10.09 ± 0.91 to 7.85 ± 0.84 GPa. The maximum compressive strength of ceramics was 472 MPa, which is ~1.7 times higher than for ceramics based on cubic solid solutions of calcium oxide stabilized zirconium dioxide (CSZ, 300 MPa), as well as ~2.5 times higher than for solid electrolytes based on the system MgO-ZrO2. Thus, as a result, zirconium dioxide-based ceramics with high electrophysical and sufficient mechanical characteristics for obtaining solid electrolytes with improved characteristics was obtained. For the synthesis of composite ceramics ZrO2-Y2O3-Gr(rGO), rGO obtained by the Hammers method was used as a carbon component. The ceramic powder precursor was obtained by the method of sol-gel synthesis in the option of reverse coprecipitation from solutions of ZrO (NO3)2 and Y(NO3)3 salts with the total concentration of dissolved salts 0.1 M; a 1M solution of ammonia in water was used as a precipitator. The precursor powder and rGO were mixed and mechanically activated for 6 hours at a rotation speed of 420 rpm using the Pulverizette 4 planetary mill. The resulting powders were converted into ceramic composites by various compactification and roasting methods. The first series of samples of ceramics with different contents of the carbon component, YSZ + 0; 0.25; 0.6; 2.5 wt. percent rGO, was sintered in air at a temperature of 1550 degrees Celsius in a chromitlantan furnace for 3 hours. The phase composition, the presence of a carbon additive after synthesis, density, Vickers microhardness and electrical characteristics were studied on the obtained samples. It is shown that during the synthesis, well-sintered samples were obtained, consisting only of the phase of cubic ZrO2 with a crystallinity of >95 percent. The presence of the carbon phase is not detected. It is concluded that the graphene additive burns out at a given temperature during sintering in air. For compositions with 0, 0.25, 0.6 and 2.5 mass. percent of rGO, a decrease in the average hardness with an increase in the addition of graphene within the framework of measurement error is obtained. The smallest addition leads to a decrease in hardness and to the smallest measurement error. At 0.6 percent and higher of graphene, the hardness remains constant, but the deviation from the average value increases. At 2.5 percent of graphene, the hardness decreases, and the deviation from the average value significantly increases. To obtain ceramics with preserved graphene phase, we have carried out the experiments on the synthesis of samples of composition YSZ + 0.25 wt. percent of rGO in the following different conditions: (1) in silicon carbide lining slag in a mixture with graphite at the temperature of 1550 degrees Celsius for 1 hour and (2) in a high vacuum (10-8 atm.) with an exposure of 1 hour and without exposure. Similarly to samples sintered in air, the samples were examined by SEM, XRD, Raman spectroscopy and impedance spectroscopy. It is shown that during the synthesis on route (1), graphene does remain in ceramics, however, it does not have such an effect on the electrical properties as in the previous case. The hardness of ceramics with 0.25 percent of rGO is on the same level for sintering in air and in the lining slag, but the spread of values is greater in the second case, which indicates a greater heterogeneity of these samples. In case (2), there is a visual difference in the peripheral and central parts of the samples. For sample III, obtained without exposure, this does not affect the values of hardness. For sample I, obtained with an exposure, the hardness values in the peripheral region are higher. The hardness of sample I in both the peripheral and central regions is higher than that of sample III. Samples of YSZ (91ZrO2-9Y2O3) without and with the addition of 0.25 wt. percent of rGO were also obtained by plasma spark sintering in vacuum at the temperature of 1400 degrees Celsius and an applied pressure of 50 MPa for 3 minutes. The density values were 5.757 g/cm3 for YSZ-rGO and 5.832 g/cm3 for pure YSZ, that is, 96.6-97.9 percent of the theoretical density of 5.96 g/cm3. A high degree of crystallinity indicates that well-sintered samples were obtained. The measured microhardness values were 14.09 GPa for YSZ-rGO and 14.05 GPa for pure YSZ. The SEM data also showed that the samples were well sintered, the grains of the resulting ceramics had clear boundaries, the number of pores in the ceramics was minimal. The presence of dispersed carbon phase was also shown. Thus, it is established that the presence of graphene in the composition of composites significantly affects the electrical and mechanical properties. This influence is determined by the method of synthesis of composites, namely the conditions and method of firing. The concentration of the carbon component also affects the properties of the composites, and has a concentration optimum, in the region of which graphene does not recombine into graphite.

 

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Annotation of the results obtained in 2019
1) Discrete dislocation dynamics simulations of plastic deformation of MgAl2O4 monolithic nanoceramics A computer model of the plastic deformation of nanocrystalline ceramics with small grain sizes is proposed. Within the model, deformation is described as the combined effect of grain boundary sliding and the emission of lattice dislocations from triple junctions of grain boundaries (GBs). Using the method of discrete dislocation dynamics, the stress-strain curves were calculated, and the yield strength as a function of grain size was found. Within the model, the applied load activates the source of grain-boundary dislocations in the center of a GB, causing GB sliding resulting from successive emission of GB dislocation dipoles. GB dislocations are accumulated near the triple junction, which leads to a stress concentration in the vicinity of the triple junction. If the applied load is sufficiently high, this stress concentration can activate the source of lattice dislocations and lead to the nucleation of a dipole of lattice dislocations near the triple junction and the emission of one of the dipole dislocations into the grain interior. The results of the calculation demonstrated the presence of an inverse Hall-Petch relationship (a decrease in the yield strength with a decrease in grain size) in the range of grain sizes from 10 to 50 nm. The results of the model calculations show qualitative agreement with experimental data. 2) Theoretical models of strength and fracture toughness of ceramic-graphene nanocomposites 2.1. A theoretical model is proposed that describes the effect of GB sliding on the fracture toughness of ceramic/graphene composites. Within the model, GB sliding near the tip of a mode I crack initiates the formation of a new nano- or microcrack in an adjacent GB. A new crack merges with the existing main crack, thereby leading to its propagation. For the case where the proposed crack growth mechanism limits the fracture toughness of the ceramic/graphene composites, the dependence of the fracture toughness on the grain size and lateral dimensions of graphene platelets is calculated. It is shown that GB sliding near the crack tip reduces fracture toughness, and this effect is strongest in the case where grain size is small and the lateral sizes of graphene plates are close to GB dimensions. The results of the calculations are consistent with experimental data on the fracture toughness of Al2O3/graphene composites. Thus, graphene additives can not only increase the fracture toughness of ceramics (due to the effects of cracks bridging, bending and branching) but also reduce it under certain conditions. In the case of small lateral sizes of graphene platelets, grain size begins to strongly affect the fracture toughness of ceramic/graphene composites. In this case, the grain size of the composites with high fracture toughness should be not too small (at least several micrometers for Al2O3/graphene composites). http://www.rscf.ru/en/node/v-kompozitakh-iz-keramiki-i-grafena 2.2. A finite element model of an elastic inhomogeneity in the triple junction of GBs is proposed. It is assumed that this inhomogeneity has the shape of a round convex or concave triangle with the third-order symmetry axes lying in the GB planes forming the triple junction. In general, the elastic moduli of the inhomogeneity differ from the elastic moduli of the surrounding matrix. A remote load corresponding to the plane strain condition is applied to such an inhomogeneity. To solve the posed boundary-value problem of the theory of elasticity, a numerical finite element simulation using the ANSYS software package is carried out. The case of uniaxial tension of a solid with such an inhomogeneity is investigated in detail, and the stress concentration at the matrix/inhomogeneity interface and the stress distribution near the inhomogeneity along its symmetry axes are calculated. The stress intensity factor (SIF) is also determined at the tip of a mode I crack, which nucleates at the matrix/inhomogeneity interface and propagates along one of the GBs. The dependences of the SIF on the ratio of the elastic moduli of the matrix and the inhomogeneity, as well as on the shape of the inhomogeneity, are investigated. It is shown that for a “soft” inhomogeneity whose shear modulus is, for example, 3 times as small as that of the surrounding matrix, the highest concentration of circumferential stresses is reached at the point of contact of the GB, oriented perpendicular to the tension direction, with the matrix/inhomogeneity interface and reaches ~ 2.0 for the convex inhomogeneity and ~ 2.1 for the concave one. For a “rigid” inhomogeneity whose shear modulus is, for example, 3 times as large as that of the surrounding matrix, the highest concentration of circumferential stresses is reached at the intersection of the imaginary extension of the same GB and the interphase boundary and reaches ~ 1.6 for the convex inhomogeneity and ~ 1.9 for the concave one. The general dependences of the concentration coefficients of circumferential stresses at the indicated points on the ratio of the shear moduli of the inhomogeneity and the matrix are calculated. The study of the effect of stress concentration on the distance from the interphase boundary has shown that along the inhomogeneity symmetry axis, this effect becomes stronger with the deviation of the inhomogeneity shape from the circle and is quite noticeable in the region not exceeding two radii of the circular inhomogeneity. Outside this region, the effect of stress concentration becomes negligible. As a result of the analysis of the SIF at the tip of a mode I crack, which nucleates at the interphase boundary of a concave inhomogeneity and advances along one of the GBs, it is shown that in the case of a homogeneous material, the calculated SIF coincides with the known value, and for the case of the inhomogeneity in the form of a cavity, it exceeds the value known for round pores ~1.81 times. For rigid inhomogeneities (with the ratio of the shear modulus of the heterogeneity to that of the matrix exceeding 5), the contribution of the difference in the elastic moduli saturates, and the calibration coefficient takes a constant value of ~0.80. 2.3. Theoretical studies of the distribution of reduced graphene oxide (rGO) inclusions in ceramics depending on the initial mass fractions of rGO are carried out. The cases of 0.25, 0.6 and 2.5 per cent rGO mass fractions that have been studied in experimental part of the project are specially considered. Two situations have been investigated: a random spatial distribution of small inclusions, whose lateral size is comparable with the GB dimensions, and an inhomogeneous distribution of rGO platelets, which also comprises the case of inclusions with the sizes exceeding the grain size of the ceramic matrix. The ranges of the optimal mass fraction of rGO providing the smallest number of stress concentrators are investigated. The planes connecting adjacent junctions of rGO inclusions are considered as the main nucleation sites of large pores. The dependence of their fraction on the grain size of the ceramic matrix is theoretically investigated. Using the three-dimensional complex of Voronoi polyhedra, the role of the inhomogeneity in the rGO distribution in the formation of stress concentrators is studied. It is shown that this inhomogeneity is one of the main factors affecting the number of stress concentrators. For its quantitative characteristics, a structural entropy parameter is proposed. It is shown that the small size of inclusions and their random distribution create significantly more possibilities for controlling the properties of the material by changing the mass fraction of inclusions than a much more inhomogeneous distribution of sufficiently large inclusions. In the case of inhomogeneous distribution of large inclusions, despite the large spatial inhomogeneity, the fractions of triple junctions with different numbers of adjacent rGO platelets are close to each other for any mass fraction of rGO. In this situation, local rGO accumulations occur even at small fractions of rGO inclusions, and the strength and toughness of the material should monotonously degrade with an increase in the mass fraction of inclusions. 3) Synthesis and experimental studies of ceramic-graphene nanocomposites The experiments on the synthesis of ZrO2-Y2O3-rGO nanocomposites by various methods have been continued in order to select the optimal method. Using two chosen methods – spark plasma sintering and skull sintering – a series of YSZ-rGO ceramic samples has been synthesized with 9 various compositions. It has been confirmed that spark plasma sintering allows one to obtain composites with a preserved carbon phase for all the proposed compositions. The microstructure and electrical characteristics of the obtained ceramic composites have been investigated. It has been confirmed that rGO additives significantly affect the growth of ceramic grains. The effect of a significant decrease in the electrical conductivity of composites upon reaching 2 wt. percent of rGO has been revealed. For the system sintered by the skull method, it was shown that the introduction of rGO significantly changes the mechanical characteristics, in contrast to the ceramic-rGO composites with similar compositions, sintered in air. 4) Development and testing of a computer code for molecular dynamics simulations of the structure evolution and mechanical behavior of an individual graphene nanoinclusion A program code for the MatLab software package is proposed, which enables one to determine the atomic configurations corresponding to the YSZ-ceramic-graphene model for subsequent calculations. A program has been developed for the LAMMPS software package, which allows one to simulate the process of compression or tension of the YSZ-ceramic-graphene system under external loads. A test model is developed. The process of deformation of the YSZ-ceramic-graphene system under external loads is investigated. The stress-strain maps of the YSZ-ceramic-graphene system are obtained. The process of nucleation and propagation of cracks inside a graphene inclusion in the YSZ-ceramic-graphene system is described. It is shown that upon tension of the YSZ-ceramic-graphene system, a crack forms inside the graphene inclusion, which propagates normally to the applied load, moving between graphene layers, which ultimately leads to the separation of the inclusion into two parts. Based on the performed test calculations, it is concluded that it is necessary to refine the model, in particular, to adjust the interatomic interaction potentials between the ceramic matrix and the graphene inclusion to quantitatively evaluate the critical parameters that influence the development of a defect structure in the YSZ-ceramic-graphene system.

 

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