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The influence of defects on strength of ceramics modeled with Movable Cellular Automata
Abstract
Ceramics is widely used material in engineering practice because of its great strength, high heat resistance and low density. The strength is a subject of our investigations. It can be significantly decreased by small defects, such as scratches, inclusions, pores, and surface roughness. The aim of this article is to demonstrate an application of the Movable Cellular Automata (MCA) method in 3D to simulate static compression test of ceramic material with various type of defects. As results we can observe damage evolution and cracks propagation leading to sample failure.
... At the same time, novel computational techniques allow a correct simulation of the material behavior from atomic up to macroscale. Taking into account all the aspects mentioned above, one might conclude that, for predicting the properties of the advanced ceramics, it is promising to use computer simulation [2][3][4][5][6][7][8][9][10]. ...
... At present, finite element analysis, which is based on solving numerically the equations of continuum mechanics, is mainly used for simulating the mechanical behavior of materials at the meso-and macroscale [8][9][10]. However, recently, methods based on discrete material representation have been successfully developed and widely used [2][3][4][5][6][7]. One of them is the method of movable cellular automata (MCA), which assumes that the material consists of a set of elementary objects (automata), interacting with the forces determined in accordance with the rules of the many-particle approach. ...
... A number of previously published studies proved that the MCA method is very promising for modeling the fracture of ceramics. Aniszewska et al. showed that this method allows correct simulation of strength and its uncertainty of ceramics macrospecimens of different porosity both in compression and torsion [2,3]. Smolin et al. proposed to use uncertainty estimates obtained from simulation of model specimens with an explicit account for pores for multiscale simulation of ceramics [4,5]. ...
The paper presents a computational model for the numerical study of the mechanical behavior of ceramics with an explicit account of its internal structure, namely, cylindrical pores differently oriented in space. The model utilizes the movable cellular automaton method for modeling deformation and fracture as dynamic processes occurring in the material under loading. We model uniaxial compression of several representative 3D cubic specimens with an explicit account of pores of the same size but with a unique position and orientation in space. As a result, we get the average values of Young’s modulus, Poisson’s ratio, and strength, as well as the parameters of the Weibull distribution of these properties of the model material. The analysis of the modeling results shows that the minimum values of mechanical properties is exhibited by the specimens with all cylindrical pores inclined at the angle of 45° to the loading direction. The randomization of the elongated pore orientation leads to higher mechanical properties.
... At present, finite element analysis, which is based on numerical solving the equations of continuum mechanics, is mainly used for simulating the mechanical behavior of materials at meso and macroscale, for example, Eremin (2016) and Acton et al. (2018). However, recently methods based on the discrete representation of material have been successfully developed and widely used (Aniszewska, 2012, Czopor et al., 2012, Smolin et al., 2014, 2017. One of them is the method of movable cellular automata (MCA), which assumes that the material consists of a set of elementary objects (automata), interacting with the forces determined in accordance with the rules of many-particle approach. ...
... A number of previously published studies have proved that MCA is very promising for modeling fracture of ceramics and ceramic composites. Aniszewska (2012) and Czopor et al. (2012) showed that this method allows correct simulation of strength and its uncertainty of ceramics macrospecimens of different porosity both in compression and torsion. Smolin et al. (2016Smolin et al. ( , 2017 proposed to use uncertainty estimates obtained from simulation of the model specimens with an explicit account for pores and inclusions for multiscale simulation of ceramics. ...
In this paper, movable cellular automaton method (MCA) is applied to the multiscale simulation of 3D samples of ceramics composite with soft matter filler. MCA is an efficient numerical method in particle mechanics, which assumes many-particle interaction among discrete elements and makes a feasible simulation of solid behavior including deformation, crack initiation and propagation, and further fragmentation of the material at different scales. The lowest scale of the proposed model corresponds to the characteristic size of the smallest pores/inclusions. Herein we start with modeling uniaxial compression of several representative ceramics samples with an explicit account of small pores randomly distributed in space. The results are the average values of Young’s modulus, Poisson’s ratio, and strength, as well as the parameters of the Weibull distribution of these properties at the current scale. The data obtained allow us to describe the material behavior at the next scale were large cylindrical inclusions are considered explicitly, while the influence of small pores is accounted via the effective properties determined at the previous scale. The simulation results show that for each value of volume fraction of cylindrical soft inclusions there is no scattering of elastic modulus values while the scatter of strength and Poisson’s ratio values is significant. Random orientation of soft elongated inclusions results in higher strength value and does not change Young’s modulus of the model composites.
... A model of a local contact of polymer-based hybrid nanocomposite was developed within the method of the movable cellular automaton (MCA) [13][14][15][16][17]. In the MCA method the modeled objects are considered as a system of finite size bodies interacting with each other. ...
In the paper a model of a local contact of a polymer-based nanocomposite was developed within the method of a movable cellular automaton. The features of mechanical behavior of nanocomposite at the mesoscale level under dry sliding were studied with explicit account for the microprofile of the counterbody surface and the characteristic sizes of nanofiller. Factors that contribute to the conditions for the formation of a stable tribofilm of silica nanoparticles are analyzed. Two other parameters like sample geometry and the value of relative sliding velocity are also examined. It is shown that the thickness of tribofilm depends on stress conditions at the contact, and the friction coefficient decreases with increasing sliding velocity similar to one observed experimentally. To ensure the low friction properties of polymer nanocomposite, particles whose sizes are comparable with the characteristic size of the substrate microprofile are preferred. Results of numerical simulation are in good correlation with available experimental data.
... The aim of the study was to develop numerical models for the process of shooting through, using own software written in C for numerical calculations [5]. The tests were conducted using ballistic laminate Lim of domestic production and shot through with a pistol bullet with a hemispherical tip [6]. ...
Materials used for the construction of ballistic shields are characterized by a variety of behaviours under the influence of external loads. Ballistic impact (by a bullet) in armour (ballistic shield) is an example of the phenomena that could be considered in the category of a dynamic load caused by the strike of the mass. Computer simulations are commonly used in such situations. It is especially important to adopt a proper model of the behaviour of the material. This paper presents the results obtained by simulating free 3D points and using the application developed by the authors for the purpose of this research. The made calculations include the translational motion and rotary motion of the projectile as well as the stiffness of the material, the damping of the material, friction at the points of contacting surfaces, viscous friction and plastic deformation (the material beyond the plastic yield point is perfectly plastic). The results of simulations were validated with experimental research.
... The aim of the studies was to develop the numerical models of the process of shooting through, using own software written in C for numerical calculations [12]. Tests were conducted using the ballistic laminate Lim3 of domestic production, shot through with pistol bullet. ...
The paper presents the puncture resistance of the material, that is under the influence of highly deformable projectile, depending on changes of material’s yield strength. The simulation has been conducted using mobile cellular automata (MCA) with authors’ own software. The simulation took into account the elasto-plasto-viscous properties of the material as well as surface and internal friction. The selected results are illustrated in terms of piercing the multilayer material with chosen projectiles of kinetic influence in the range of impact velocity between 300 and 1000 m/s.
... The movable cellular automata method has been developed for elastic and brittle materials, such as ceramics, and presented in [8]. The rules of interaction between cellular automata have been complemented to provide plastic behaviour of material. ...
The Movable Cellular Automata (MCA) method is usually applied for
modelling behaviour of elastic, brittle and granular material under
various modes of mechanical loading. This paper presents principles and
results of numerical simulations experiments of elastic and plastic
material behaviour with this method.
In this paper the mechanical properties of silica aerogels are studied by simulations with the usage of the Movable Cellular Automata (MCA) method. In the MCA approach a sample is considered as a set of interacting cellular automata. The procedure to prepare porous samples is based on random spheres method. The resulting structures have densities in the range from 111 to 2200 kg/m3 and porosity up to 95%. The structures of the samples are studied by obtaining the fractal dimension using the FD3 program. The Young's modulus is examined in the simulation of a compression test. The elastic modulus relate to density by a power law characterized by exponent 3.83 ± 0.18 for samples with densities from 111 to 568 kg/m3 and 3.17 ± 0.11 for samples with densities from 350 to 2200 kg/m3. A comparison to previously published data from experiments and comparable computer simulations is included. The results prove that the Movable Cellular Automata method is suitable to investigate the mechanical properties of silica aerogels.
Peculiarities in the dependences of the elastic and strength properties of ceramics with a hierarchically organized pore structure on the porosity are revealed. To exclude the influence of other microstructural factors, such as, for example, grain size, the study was carried out on the basis of multilevel computer modeling using movable cellular automata and a probabilistic approach. A special computer model of the mechanical behavior of porous ceramics with a bimodal pore size distribution has been developed. At the lower level of the model, small isolated pores are explicitly taken into account and series of calculations are carried out for the representative samples with individual pore arrangement in space. The values of the elastic and strength characteristics of these samples obtained as a result of Weibull analysis serve as effective properties of the porous material matrix at the mesoscale. At the mesoscale, large pores of both equiaxial and elongated shapes are considered explicitly. At the macrolevel, the heterogeneity of the material is described implicitly by setting to the automata the unique elastic and strength properties obtained from the Weibull analysis of the calculation results obtained at the mesoscale.
Peculiarities in the dependences of the elastic and strength properties of ceramics with a hierarchically organized pore structure on the porosity are revealed. To exclude the influence of other microstructural factors, such as, for example, grain size, the study was carried out on the basis of multilevel computer modeling using movable cellular automata and a probabilistic approach. A special computer model of the mechanical behavior of porous ceramics with a bimodal pore size distribution has been developed. At the lower level of the model, small isolated pores are explicitly taken into account and series of calculations are carried out for the representative samples with individual pore arrangement in space. The values of the elastic and strength characteristics of these samples obtained as a result of Weibull analysis serve as effective properties of the porous material matrix at the mesoscale. At the mesoscale, large pores of both equiaxial and elongated shapes are considered explicitly. At the macrolevel, the heterogeneity of the material is described implicitly by setting to the automata the unique elastic and strength properties obtained from the Weibull analysis of the calculation results obtained at the mesoscale.
Highly porous brittle materials have many advantages. In this paper we describe method of generating highly porous structure based on the procedure of the overlapping spheres method. The improvement was added to this algorithm: linked state between spheres (cells) was used to speed up the process. Generated porous ceramic specimens were tested with using the Movable Cellular Automata method. Mechanical strength of specimens and the results of compression tests are given.
In this paper Movable Cellular Automata and fractal geometry are applied to examine defects growth in porous ceramic specimens.
The Movable Cellular Automata method is applied in numerical simulations of compression loading of ceramic specimens. It allows a continuous monitoring material processes and gives physical picture of defects over the meso- and macroscopic range of scales, at any stage of evolution.
The entire structure of defects enclosed in macroscopic volume is treated as a single fractal and described by means of fractals with fractal dimension and measure.
The Movable Cellular Automata (MCA) method is used to modelling a
behaviour of ceramics under various modes of mechanical loading.
Ceramics have many advantages, such as high strength, chemical stability
and low density, which are accompanied with low fracture toughness
compared to metallic materials. The majority of ceramic strength and
fracture investigations take place under uniaxial loading, but according
to engineering practice ceramic materials are subjected to the
multiaxial loading. Therefore it is important to investigate fracture
behaviour of ceramics under multiaxial loading. The paper presents
results of simulations of ceramic samples under compression, torsion and
combined compression/torsion.
In this paper numerical investigations of the ceramics behaviour have been conducted under quasi-static various loading conditions by application of the Movable Cellular Automata (MCA) method. The paper presents results of simulations of ceramic specimens with and without pores under compression, torsion and torsion of compressed specimens. Weibull analysis has been performed and values of Weibull modulus for all kind of specimens and mechanical loading are given.
We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with the timescale separation between particle diffusion and momentum diffusion (viscosity).
Basic concepts of methods of discrete simulation of physical systems based on the microscopic dynamics of a certain model medium are discussed. This medium is of the same macroscopic but rougher microscopic dynamics as compared to the system under review. Examples of modeling the behavior of hydrodynamic systems, elastic media, and diffusion processes show that the model medium can have much lower spatial symmetry than the model macroscopic system and essentially simpler microscopic interaction laws than real media. This, however, leaves the correctness of the description of the macroscopic dynamics unaffected. In particular, macroscopically isotropic systems can be described using discrete models. The application of discrete simulation concepts is discussed, considering the elastoplastic medium modeling by the movable cellular automata method as an example. The method is a hybrid model, proposed in 1995 by Psakhie and co-workers, that combines ideas and advantages of molecular dynamics and cellular automaton methods. In the present paper, we will restrict ourselves to the description of macroscopically homogeneous media. The modeling principles for heterogeneous media will be examined in Part II.
We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill’s formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.
Mathematical formalism and applications of the movable cellular automata (MCA) method are presented for solving problems of physical mesomechanics. Since the MCA is a discrete approach, it has advantages over that of the ®nite element method (FEM). Simulation results agree closely with the experimental data. The MCA approach cab solves mechanical engineering problems ranging from those in material science to those in structures and constructions. Computer simulation using MCA can also provide useful information in situations where direct measurements are not possible. Ó 2001 Published by Elsevier Science Ltd.
The basic principles of the physical mesomechanics of materials are formulated. This new scientific discipline relates the physics of plasticity (the micro level), the mechanics of a deformable solid (the macro level), and physical materials science. Plastic deformation and subsequent failure of a loaded solid develops as the successive evolution of shear-stability loss at the micro, meso, and macro levels. The deformation laws at the different scale levels are scale-invariant. To study the deformation mechanisms at the meso level, engineering viewing methods may be used. It is shown that, in deformable materials, a basic stress concentrator always appears at the point of application of an external load; this plays the fundamental role in the meso-level development of deformation. The basic carriers of plastic flow at the meso level are volume elements of various sizes; their motion occurs by a shear+rotation mechanism. In a structurally inhomogeneous medium, stress mesoconcentrators arise at internal boundaries; these form dissipative substructures and result in fragmentation of the material at the meso level. Electron-microscopic data on the basic types of meso-level substructures for high-strength materials indicate that, at the substructure boundaries, high-energy states that are in structural disequilibrium are formed at the substructure boundaries; these states are characterized by crystal-lattice curvature of up to 1 deg/mum and a high disclination density. A new structural state is observed: a substructure with a continuum disclination density, characterized by crystal-lattice curvature of up to 40 deg/mum. The methodological aspects of a unified theory of a deformable solid are discussed, and a theoretical approach that may be used to model the deformation and failure of materials with a complex internal structure at different scale levels, on the basis of continuum-mechanics methods, is proposed. This approach allows defining equations for the description of plastic deformation at the micro, meso, and macro levels to be written, taking account of the contribution of the accumulated strain at the lower levels to the strain at the upper levels. The theoretical results are in good agreement with experimental data.
Method called movable cellular automata (MCA) is used to modelling a process of defects growth in elastic‐brittle material.
Fractures is one of the main problem in the strength material research. Chosen elastic‐brittle material is Beryllium Oxide BeO. Simulations of samples containing hundreds of thousands cellular automata may generate problem in obtaining a high accuracy therefore different numerical methods of solving equations of motion are investigated.
This paper discusses the applicability of statistics to a wide field of problems. Examples of simple and complex distributions are given.
A general expression for the failure probability of a brittle material is developed by using the properties of flaw size distribution and the stress necessary to fracture an inclined crack. A comparison is made with Weibull analysis and an expression for the Weibull modulus, which is known to be an empirical material constant, is related to the properties of the flaw size distribution of a material. Limitations in the application of Weibull analysis are also discussed.
The paper presents the application of the Movable Cellular Automata (MCA) method for a simulation of 2D crack propagation
in ceramic materials. The MCA method let us to simulate a movement of formation and cracks course for impossible to observe
during an experiment. Ceramic sample was chosen to the research as an elastic-brittle material. During the study the simulation
was done and the experiment was carried out with the same guidelines. The MCA model was correlated with experimental data.
The simulation program generates data which allow to compute quantities such as an ultimate compressive strength and to show
in the graphic form the moment of cracks initiation. Comparison of experimental and simulated results proves that Movable
Cellular Automata method is suitable for modeling crack propagation in ceramic materials in two-dimensional system.