Cellular Automaton Method Research Articles

Research on Thermal Topology Design Method of Spindle Based on HCAM

Spindle thermal error is one of the key factors in the machining accuracy of CNC machine tool. In order to reduce the thermal error of the spindle and improve the machining precision of the CNC machine tool, the idea of the thermal topology design based on the hybrid cellular automaton method (HCAM) is proposed. In this paper, the existing research results of hybrid cellular automaton are summarized, and the main achievements of domestic and foreign research work are analysed and reviewed from the aspects of structural topology optimization. Finally, the realization and prospect of HCAM self-optimizing thermal topology design method for spindle are presented.

Multiscale Simulation of Porous Ceramics Based on Movable Cellular Automaton Method

The paper presents a model for simulating mechanical behaviour of multiscale porous ceramics based on movable cellular automaton method, which is a novel particle method in computational mechanics of solid. The initial scale of the proposed approach corresponds to the characteristic size of the smallest pores in the ceramics. At this scale, we model uniaxial compression of several representative samples with an explicit account of pores of the same size but with the random unique position in space. As a result, we get the average values of Young’s modulus and strength, as well as the parameters of the Weibull distribution of these properties at the current scale level. These data allow us to describe the material behaviour at the next scale level were only the larger pores are considered explicitly, while the influence of small pores is included via the effective properties determined at the previous scale level. If the pore size distribution function of the material has N maxima we need to perform computations for N − 1 levels in order to get the properties from the lowest scale up to the macroscale step by step. The proposed approach was applied to modelling zirconia ceramics with bimodal pore size distribution. The obtained results show correct behaviour of the model sample at the macroscale.

Modeling and simulation of dynamic recrystallization behavior for 42CrMo steel by an extended cellular automaton method

The dynamic recrystallization (DRX) behavior of 42CrMo steel was studied by hot compressive tests and cellular automaton (CA) simulation. The experimental results showed that initial grain size besides deformation parameters has an obvious influence on dynamic recrystallization (DRX) behavior. It is found that the initial grain size not only influences the number of DRX nucleation site, but also the work-hardening (WH) coefficient, dynamic recovery (DRV) coefficient, DRX nucleation rate and grain boundary (GB) mobility. Moreover, the relationships between the WH coefficient, DRV coefficient, DRX nucleation rate, GB mobility and initial grain size can be well described by the power function. Based on the findings, the traditional CA model was extended to describe the effect of initial grain size on DRX behavior. The comparison between experimental and simulated results showed that the microstructural evolution of 42CrMo steel with different initial grain sizes during hot deformation can be accurately simulated by the extended CA model.

Continuous-discontinuous cellular automaton method for cohesive crack growth in rock

A group of nonsingular enrichment functions is proposed for an exact representation of the cohesive stresses, which are consistent with a nonsingular asymptotic stress field around a crack tip. An improvement in the adaptive crack tip polar coordinate is proposed for treating the local polar coordinate error. Finally, a discontinuous cellular automation model was developed, including a cell model, cell state, and updating rules. Combined with these developments and the cohesive rock model, a continuous-discontinuous cellular automaton method (CDCA) for a cohesive crack analysis is proposed, through which the calculation is only limited to the cell locality without re-meshing, and therefore, no assembled global stiffness matrix is required. Numerical simulations reveal the accuracy and efficiency of the presented method.

Numerical simulation of microstructure evolution on near eutectic spheroidal graphite cast iron

A multiphase cellular automaton model was developed to simulate microstructure evolution of near eutectic spheroidal graphite cast iron (SGI) during its solidification process, and both dendritic austenite and spheroidal graphite growth models were adopted. To deduce the mesh anisotropy of cellular automaton method, the composition averaging and geometrical parameter were introduced to simulate the spheroidal graphite growth. Solute balance method and decentered square algorithms were employed to simulate austenite dendrites growth with different crystallographic orientations. The simulated results indicate that the graphite nodule grows in a spherical morphology when the surrounding environment of a single graphite nodule is same. However, for two adjacent graphite nodules, the environment is different. The higher the carbon concentration, the faster the growth of graphite. By comparison with experimental results, it is found that the microstructure evolution of near eutectic spheroidal graphite cast iron during solidification process can be reproduced quantitatively by numerical simulation with this model.

Investigation of primary static recrystallization in a NiTiFe shape memory alloy subjected to cold canning compression using the coupling crystal plasticity finite element method with cellular automaton

The behavior of primary static recrystallization (SRX) in a NiTiFe shape memory alloy (SMA) subjected to cold canning compression was investigated using the coupling crystal plasticity finite element method (CPFEM) with the cellular automaton (CA) method, where the distribution of the dislocation density and the deformed grain topology quantified by CPFEM were used as the input for the subsequent SRX simulation performed using the CA method. The simulation results were confirmed by the experimental ones in terms of microstructures, average grain size and recrystallization fraction, which indicates that the proposed coupling method is well able to describe the SRX behavior of the NiTiFe SMA. The results show that the dislocation density exhibits an inhomogeneous distribution in the deformed sample and the recrystallization nuclei mainly concentrate on zones where the dislocation density is relatively higher. An increase in the compressive deformation degree leads to an increase in nucleation rate and a decrease in grain boundary spaces in the compression direction, which reduces the growth spaces for the SRX nuclei and impedes their further growth. In addition, both the mechanisms of local grain refinement in the incomplete SRX and the influence of compressive deformation degree on the grain size of SRX were vividly illustrated by the corresponding physical models.

A cellular automaton – finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid–liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid–liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton–Glicksman–Kurz model for the steady growth of a dendrite tip and the Jackson–Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

Multiscale modeling of localized resistive heating in nanocrystalline metals subjected to electropulsing

Many electrically assisted processes have been reported to induce changes in microstructure and metal plasticity. To understand the physics-based mechanisms behind these interesting phenomena, however, requires an understanding of the interaction between the electric current and heterogeneous microstructure. In this work, multiscale modeling of the electric current flow in a nanocrystalline material is reported. The cellular automata method was used to track the nanoscale grain boundaries in the matrix. Maxwell's electromagnetic equations were solved to obtain the electrical potential distribution at the macro scale. Kirchhoff's circuit equation was solved to obtain the electric current flow at the micro/nano scale. The electric current distribution at two representative locations was investigated. A significant electric current concentration was observed near the grain boundaries, particularly near the triple junctions. This higher localized electric current leads to localized resistive heating near the grain boundaries. The electric current distribution could be used to obtain critical information such as localized resistive heating rate and extra system free energy, which are critical for explaining many interesting phenomena, including microstructure evolution and plasticity enhancement in many electrically assisted processes.

Dynamic recrystallization and texture modeling of IN718 superalloy

In the present study, dynamic recrystallization (DRX) of IN718 superalloy was modeled based on the experimental data as well as modified cellular automaton (CA) methods. To verify the ability of the presented models for predicting the microstructural features, the electron backscattered diffraction technique was used. Results showed that both models are capable of estimating the mean grain size and volume fraction of DRX grains. Furthermore, the macroscopic flow behavior of the material, and texture evolution of the structure were simulated using the proposed CA model. In this model, the lattice rotation of grains was determined assuming that each grain obeys the rules of single crystal deformation, and the morphological texture was obtained using a topological module in the CA approach.

Effect of Temperature and Fluid Flow on Dendrite Growth During Solidification of Al-3 Wt Pct Cu Alloy by the Two-Dimensional Cellular Automaton Method

A two-dimensional cellular automaton–finite volume model was developed to simulate dendrite growth of Al-3 wt pct Cu alloy during solidification to investigate the effect of temperature and fluid flow on dendrite morphology, solute concentration distribution, and dendrite growth velocity. Different calculation conditions that may influence the results of the simulation, including temperature and flow, were considered. The model was also employed to study the effect of different undercoolings, applied temperature fields, and forced flow velocities on solute segregation and dendrite growth. The initial temperature and fluid flow have a significant impact on the dendrite morphologies and solute profiles during solidification. The release of energy is operated with solidification and results in the increase of temperature. A larger undercooling leads to larger solute concentration near the solid/liquid interface and solute concentration gradient at the same time-step. Solute concentration in the solid region tends to increase with the increase of undercooling. Four vortexes appear under the condition when natural flow exists: the two on the right of the dendrite rotate clockwise, and those on the left of the dendrite rotate counterclockwise. With the increase of forced flow velocity, the rejected solute in the upstream region becomes easier to be washed away and enriched in the downstream region, resulting in acceleration of the growth of the dendrite in the upstream and inhibiting the downstream dendrite growth. The dendrite perpendicular to fluid flow shows a coarser morphology in the upstream region than that of the downstream. Almost no secondary dendrite appears during the calculation process.

Клеточно-автоматные методы решения классических задач математической физики на гексагональной сетке. Часть 2

Клеточно-автоматные методы решения классических задач математической физики на гексагональной сетке. Часть 2

A hybrid cellular automata-finite element model for the simulation of the grind-hardening process

Grind-hardening process is a hybrid process for the simultaneous finishing and heat treatment of the workpiece material. Several studies have been presented for the simulation of the process, using either analytical or finite element-based models. In the present paper, the cellular automata method is used for simulating the metallurgical changes in the workpiece material. The method is coupled with a finite element model for the macro-modelling of the process, allowing the prediction of the microstructure of the material as a function of the macro-process parameters.

Effect of Structural Heterogeneity of 17Mn1Si Steel on the Temperature Dependence of Impact Deformation and Fracture

The paper deals with a theoretical and experimental study of the relationship between the microstructural parameters, mechanical properties, and impact deformation and fracture of steels using the example of 17Mn1Si pipe steel. A model for the behavior of a polycrystalline grain conglomerate under impact loading at different temperatures was proposed within a cellular automata framework. It was shown that the intensity of dissipation processes explicitly depends on temperature and these processes play an important role in stress relaxation at the boundaries of structural elements. The Experimental study reveals the relationship between pendulum impact test temperature and the deformation/fracture energy of the steel. The impact toughness was shown to decrease almost linearly with the decreasing test temperature, which agrees with the fractographic analysis data confirming the increase in the fraction of brittle fracture in this case. It was shown with the aid of the proposed model and numerical simulations that the use of the excitable cellular automata method and an explicit account of test temperature through the possibility of energy release at internal interfaces help to explain the experimentally observed features of impact failure at different temperatures.

Reliability-based operation of reservoirs: a hybrid genetic algorithm and cellular automata method

A novel hybrid genetic algorithm and cellular automata method is presented here for solving reliability-based reservoir operation problems. The method uses a decomposition approach in which the reliability part of the problem is handled with a GA, while the operational side of the problem is solved by a CA method. In the proposed method, a binary genetic algorithm is employed to determine success/failure periods of the operation. A period is considered as a success period if the corresponding gene value is one, and failure period if otherwise. The success/failure pattern suggested by the genetic algorithm is used to explicitly rewrite the reliability constraints of the operation problem in terms of the reservoir releases. A CA method is then used to solve the resulting problem in which the two types of the constraints, namely operational constraints and reliability constraints, are dealt with differently. Operational constraints are applied to all periods, while reliability constraints are only applied to the success periods determined by genetic algorithm. The proposed method is used for monthly water supply and hydropower operation of Dez reservoir in Iran, and the results are presented and compared with those of a GA model. The efficiency and effectiveness of the method are tested for the short-, medium- and long-term operation periods assuming different target reliabilities. Comparison of the results with those of a GA model shows that the proposed method is both more effective and efficient compared to GA.

Research on microstructure evolution of austenitization in grinding hardening by cellular automata simulation and experiment

Heat generated within the grinding zone is used to generate a hardened layer in grinding hardening. The phase fraction and carbon content of the hardened layer have significant effects on its mechanical properties. Specially, the heating rate is extremely high and the duration time beyond A c1 (austenitization starting temperature) is short in grinding hardening, so the austenitization is sometimes incompleted and the carbon content is always non-uniform. In the present paper, three-dimensional finite element method (FE) incorporating a regular triangle heat source is used for computing temperature histories of the specimen. Microstructure evolution model of austenitization of AISI 1045 steel considering the heating rate in grinding hardening is developed by using the cellular automata method (CA). In the CA model, austenite nucleation, pearlite dissolution, austenite growth in proeutectoid ferrite, and carbon diffusion are considered and simulated based on their respective theories. A new variable t d (duration time beyond A c1) is defined to describe the temperature history characteristic. The effects of grinding parameters on the temperature characteristic variables are studied. Meanwhile, austenitization are simulated under different grinding parameters. The microstructure of the hardened layer is observed in grinding hardening experiment to validate the CA model. The results show that, firstly, the CA model can effectively simulate the microstructure evolution. Secondly, both peak temperature and t d have significant effects on the austenitization in grinding hardening. Thirdly, better microstructure and mechanical properties can be obtained by optimizing grinding parameters.

Numerical simulation of non-dendritic structure formation in Mg-Al alloy solidified with ultrasonic field

The formation of non-dendritic structure of Mg alloy solidified with ultrasonic treatment was investigated by numerical simulation and experiment. The models of nucleation and crystal growth involved the effects of ultrasonic cavitation and acoustic streaming were built. Based on the models, the grain refinement and the microstructure change from dendrite to non-dendritic structure of a Mg-Al alloy were numerically simulated by cellular automata method. The simulation and experimental results indicated that the ultrasonic cavitation strongly contributes to the grain refinement by improving nucleation, while the acoustic streaming is mainly responsible for the formation of non-dendritic structure.

Effects of plastic distortion in the lattice curvature zone of a crack tip

The paper proposes a discrete-continual method of excitable cellular automata for simulating the stress-strain state at crack tips and in notches with account of lattice curvature and plastic distortion through ion motion from lattice sites to interstices. The proposed nonlinear method allows one to determine the crack type and the character of fracture, to predict the possibility of dynamic rotations and structural turbulence, and to describe the processes of nonlinear wave structural transformations in strain localization bands involved in microporosity and tearing mode cracking.

Adaptive Hybrid Genetic Algorithm and Cellular Automata Method for Reliability-Based Reservoir Operation

AbstractAn adaptive hybrid genetic algorithm (GA) and cellular automata (CA) method is proposed for solving implicit stochastic optimization of reservoir operation problems. The method is based on ...

Modeling of the static recrystallization for 7055 aluminum alloy by cellular automaton

In order to simulate the flow behavior and microstructure evolution during the pass interval period of the multi-pass deformation process, models of static recovery (SR) and static recrystallization (SRX) by the cellular automaton (CA) method for the 7055 aluminum alloy were established. Double-pass hot compression tests were conducted to acquire flow stress and microstructure variation during the pass interval period. With the basis of the material constants obtained from the compression tests, models of the SR, incubation period, nucleation rate and grain growth were fitted by least square method. A model of the grain topology and a statistical computation of the CA results were also introduced. The effects of the pass interval time, temperature, strain, strain rate and initial grain size on the microstructure variation for the SRX of the 7055 aluminum alloy were studied. The results show that a long pass interval time, large strain, high temperature and large strain rate are beneficial for finer grains during the pass interval period. The stable size of the static recrystallized grain is not concerned with the initial grain size, but mainly depends on the strain rate and temperature. The SRX plays a vital role in grain refinement, while the SR has no effect on the variation of microstructure morphology. Using flow stress and microstructure comparisons of the simulated and experimental CA results, the established CA models can accurately predict the flow stress and microstructure evolution during the pass interval period, and provide guidance for the selection of optimized parameters for the multi-pass deformation process.

Simulation of Corrosion Process for Structure with the Cellular Automata Method

In this paper, from the mesoscopic point of view, under the assumption of metal corrosion damage evolution being a diffusive process, the cellular automata (CA) method was proposed to simulate numerically the uniform corrosion damage evolution of outer steel tube of concrete filled steel tubular columns subjected to corrosive environment, and the effects of corrosive agent concentration, dissolution probability and elapsed etching time on the corrosion damage evolution were also investigated. It was shown that corrosion damage increases nonlinearly with increasing elapsed etching time, and the longer the etching time, the more serious the corrosion damage; different concentration of corrosive agents had different impacts on the corrosion damage degree of the outer steel tube, but the difference between the impacts was very small; the heavier the concentration, the more serious the influence. The greater the dissolution probability, the more serious the corrosion damage of the outer steel tube, but with the increase of dissolution probability, the difference between its impacts on the corrosion damage became smaller and smaller. To validate present method, corrosion damage measurements for concrete filled square steel tubular columns (CFSSTCs) sealed at both their ends and immersed fully in a simulating acid rain solution were conducted, and Faraday’s law was used to predict their theoretical values. Meanwhile, the proposed CA mode was applied for the simulation of corrosion damage evolution of the CFSSTCs. It was shown by the comparisons of results from the three methods aforementioned that they were in good agreement, implying that the proposed method used for the simulation of corrosion damage evolution of concrete filled steel tubular columns is feasible and effective. It will open a new approach to study and evaluate further the corrosion damage, loading capacity and lifetime prediction of concrete filled steel tubular structures.