No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Mesoscale simulation of discontinuous dynamic recrystallization using the cellular automaton method
Abstract
A dynamic recrystallization (DRX) cellular automaton (CA) model that can mark the microstructure with DRX circle was developed. The effects of initial grain size on the stress-strain curve, mean grain size and DRX fraction were mainly investigated, and the simulated results were compared with those obtained from previous researches. The results show that the shape of the stress-strain curve is sensitive, while the stress and mean grain size at the steady state are insensitive to the initial grain size. The transition from a multiple-peak stress-strain curve to a single-peak one can be explained by variations in DRX circle fraction, and the initial grain size to make this transition is between 70 and 80 µm.
In order to probe the virtual experiment for studying the dynamic recrystallization behavior of steel, a two dimensions model of dynamic recrystallization was established by cellular automata(CA) method, related theories and thermal simulation experiment. The processes of dynamic recrystallization in the HPS485wf steel hot-compressed at the different conditions were simulated using the model, and the simulated results were compared with the hot-compressed tests and dynamic recrystallization theory. The results show that the dynamic recrystallization behaviors of the steel not only have the same change laws as the experimental results and the dynamic recrystallization theory, but also show the characteristics with the phenomenon of multi-rounds dynamic recrystallization and the single peak type of stress-strain curve. The accuracies of microstructure evolution, recrystallization area fraction, average grain size and stress-strain curve simulated by the model are better.
Based on the theory of dynamic recrystallization (DRX) simulation and the principle of closed loop control, a new method that the golden section search combines with the closed loop control of the difference between the values of simulated and experimental flow stress was proposed to identify the transient nucleation rate of dynamic recrystallization, which aimed to improve the simulation accuracy of the conventional model with constant nucleation rate. Compared with the dynamic recrystallization of HPS485wf steel simulated by the conventional cellular automata (CA) model, the reasonability and application efficiency of this method were verified. The results show that the method can effectively identify the transient nucleation rate and significantly improve the accuracy and its stability of the simulated flow stress, and enhances the accuracy of the simulated area fraction of dynamic recrystallization. ©, 2015, Editorial Office of Transactions of Materials and Heat Treatment. All right reserved.
Substructure evolution significantly influences the flow behavior of titanium alloys in isothermal hot compression. This paper presents a physical experiment (isothermal hot compression and electron backscatter diffraction, EBSD) and a cellular automaton (CA) method to investigate the substructure evolution of a near-α titanium alloy Ti-6Al-2Zr-1Mo-1V (TA15) isothermally compressed in the α + β two-phase region. In the CA model, the subgrain growth, the transformation of low angle boundaries (LABs) to high angle boundaries (HABs) and the dislocation density evolution were considered. The dislocation density accumulating around the subgrain boundaries provided a driving force and made the transformation of the LABs to HABs. The CA model was employed to predict the substructure evolution, dislocation density evolution and flow stress. In addition, the effects of strain, strain rate and temperature on the relative frequency of the HABs were analyzed and discussed. To verify the CA model, the predicted results including the relative frequency of the HABs and the flow stress were compared with the experimental values.
A numerical model to simulate microstructure evolution and macroscopic mechanical behavior during hot working was developed. In this model, we employed a multi-phase-field model to Simulate the growth of dynamically recrystallized grains with high accuracy and the Kocks-Meehing model to calculate the evolution of dislocation density due to plastic deformation and dynamic recovery. Furthermore, an efficient computational algorithm was introduced to perform the multi-phase-field simulation efficiently. The accuracy of the developed model was confirmed by comparing the migration rate of grain boundaries with the theoretical value. Also, the numerical results for a polycrystalline material are compared with those obtained from a cellular automaton simulation. Furthermore, the effects of the initial grain size, grain boundary mobility and nucleation rate on the dynamic recrystallization behavior were investigated using the developed model. [doi: 10.2320/matertrans.MB200805]
The cellular automaton computer simulation technique has been applied to the problem of dynamic recrystallization. The model is composed of simple microstructural mechanisms - such as evolution of dislocation density, grain boundary movement and nucleation - that acting together result in complex macrostructural response expressed by evolution of flow stress and grain size. A strong sensitivity of the flow stress curves to the initial grain size and nucleation rate is observed. Simulations lead to the conclusion that model of a dynamically recrystallizing material has a strong structural memory resulting in wide variety of experimentally observed responses.
A cellular automaton algorithm with probabilistic cell switches is employed in the simulation of dynamic discontinuous recrystallization. Recrystallization kinetics are formulated on a microlevel where, once nucleated, new grains grow under the driving pressure available from the competing processes of stored energy minimization and boundary energy reduction. Simulations of the microstructural changes in pure Cu under hot compression are performed where the influence of different thermal conditions are studied. The model is shown to capture both the microstructural evolution in terms of grain size and grain shape changes and also the macroscopic flow stress behavior of the material. The latter gives the expected transition from single- to multiple-peak serrated flow with increasing temperature. Further, the effects on macroscopic flow stress by varying the initial grain size is analyzed and the model is found to replicate the shift towards more serrated flow as the initial grain size is reduced. Conversely, the flow stress is stabilized by larger initial grain sizes. The extent of recrystallization as obtained from simulations are compared to classical JMAK theory and proper agreement with theory is established. In addition, by tracing the strain state during the simulations, a post-processing step is devised to obtain the macroscopic deformation of the cellular automaton domain, giving the expected deformation of the equiaxed recrystallized grains due to the macroscopic compression.
Along with the work hardening and dynamic recovery, the dynamic recrystallization of pure copper at 673 K is simulated with Monte Carlo (MC) method. By investigating the evolution of the plastic strain energy and the morphology of the simulated microstructure, the physical process of the system during the continuous loading procedure is studied. When the strain is small enough, nothing happens in the system. Once the strain reaches a critical value, the dynamic recrystallization occurs by the nonuniform nucleation. As the strain increase, the nucleation mechanism transforms to uniform nucleation. After some MC steps, the plastic strain energy drops from its maximum value. Ever since then, the plastic strain energy fluctuates around a fixed value.
In order to set up a CA model that has a better physical significance, a new second criterion, considering the effects of the thermodynamic mechanism and the activation energy, was appended for the transition of cellular state. The grain growth processes were investigated for different temperatures and activation energies, respectively. The results are in accordance with the normal grain growth kinetics and reflect the both effects of temperature and the activation energy.
Based on the metallurgical principles of hot working process, a two-dimensional cellular automata model for the dynamic recrystallization (DRX) was built up to simulate a series of processes such as the work hardening, dynamic recovery, nucleation and growth of recrystallization grains (R-grains). By using the model, the variations of the flow stress, the morphology, orientation, and size of R-grains during the whole hot working process can be obtained. The flow stress can be calculated from the average dislocation densities in the matrix and the R-grains. The DRX processes of pure copper under different strains, strain rates, and temperatures were simulated, and the simulated results agree well with experimental results.
A cellular automaton (CA) model is established to simulate dynamic recrystallization (DRX) in the β single-phase field of Ti6Al4V alloy, and the kinetics during DRX processing has been analyzed. The model employed considers the influences of dynamic recovery, nucleation rate, strain rate and dislocation density on DRX, and practical deformation parameters, such as temperature, strain and strain rate on DRX have been considered in the simulation. The simulated DRX grain size and DRX grain shape agree well with the experimental results, which shows the availability and feasibility of the cellular automaton method for the simulation of DRX. The result of kinetics analysis of DRX reveals that the Avrami exponent is variable ranging from 2.4 to 2.9, which increases with the increase of strain rate.
A quasi-synchronous integration model is constructed in this paper by coupling a cellular automaton (CA) model with a topology deformation technique for simulating the microstructure evolution of dynamic recrystallization (DRX). The uniform topology deformation technique based on vector operation can track the change of grain topology effectively during DRX simulation. The effects of topology deformation on the kinetics of DRX, mean grain size and effective nucleation sites are discussed in detail. This flexible simulation technique provides a novel way for investigating the dynamic microstructure evolution accompanied with plastic deformation on a mesoscale.
The kinetics of the restoration processes that take place during the isothermal annealing of metals for the case when the critical strain for the onset of dynamic recrystallization is reached and exceeded were modeled using the Cellular Automata approach. The model enables both quantitative and topographic simulations of microstructural evolution before and during metadynamic recrystallization. It allows the simulation of multi-stage deformation. It was observed that two kinds of transition between the strain-dependent and strain-independent range are possible: the first is smooth, whereas the second is oscillatory. The post-dynamic softening is shown to be weakly dependent on strain and temperature, but strongly dependent on strain rate, as has been observed in published experimental work.
A dynamic recrystallization multi-phase-field (MPF-DRX) model that can approximately take into account grain deformation during dynamic recrystallization (DRX) has been developed, where the grain deformation was introduced by changing the size of a finite difference grid so as to keep the volume constant. The accuracy of the developed model was confirmed by simulating a single DRX grain growth. As a result of MPF-DRX simulations with grain deformation, it was clarified that, from microstructure evolutions, the appropriate deformation during DRX can be reproduced by the developed model. However, it was also concluded that the macroscopic stress–strain relationship and variations in grain size are not affected by the grain deformation introduced here. Furthermore, the DRX cycle was defined and the relationship between the DRX cycle fraction and the stress–strain curve was discussed. As a result, it was concluded that the stress–strain curve with multiple peaks is observed when the strain at the first valley of the stress–strain curve is smaller than that corresponding to the maximum first DRX cycle fraction.
Recently, simulational procedure that models dynamic recrystallization and recovery in polycrystals has been proposed. The combined effects of deformation and elevated temperatures, which are interrelated by the Zener—Hollomon parameter, Z=∈exp(Qact/RT, are simulated by adding stored energy and recrystallization nuclei continuously with time. The experimentally observed spatial inhomogeneity of the dislocation density within grains is represented by a probabilistic expression for the stored energy distribution. The simulated transient and steady-state recrystallization parameters' relationships agree very well with experimental observations. The microstructures obtained in the simulations at Z = const and their properties are almost identical. The observations vindicate the description of dynamic recrystallization as a “simultaneous static recrystallization”. A careful analysis of simulational data demonstrates very good quantitative agreement between our results and those found in experiment.
Dynamic recrystallization (DRX) and dynamic recovery (DR) are two competing processes by which metals and alloys undergo a reduction in the density of accumulated dislocations during plastic deformation at elevated temperatures. The objective of the present work was to model DRX under isothermal and constant strain rate conditions using the cellular automata (CA) technique. CA is similar to the MC method. However, fundamental differences exist due to the use of different phenomenological relationships, MC`s probabilistic method of grain boundary motion, and its use of the Potts model. This study is a sequel to the authors work on static recrystallization at grain boundaries using CA. The application of CA to DRX was practicable because DRX also occurs through grain boundary nucleation. The model will be used to examine the effect of initial grain size on the transition from single to multi-peak flow curves, nucleation density, recrystallization kinetics, and the strain hardening rate.
The prediction of microstructure evolution plays an important role in the design of forging process. In the present work,
the cellular automaton (CA) program was developed to simulate the process of dynamic recrystallization (DRX) for aluminium
alloy 7050. The material constants in CA models, including dislocation density, nucleation rate and grain growth, were determined
by the isothermal compress tests on Gleeble 1500 machine. The model of dislocation density was obtained by linear regression
method based on the experimental results. The influences of the deformation parameters on the percentage of DRX and the mean
grain size for aluminium alloy 7050 were investigated in details by means of CA simulation. The simulation results show that,
as temperature increases from 350 to 450 °C at a strain rate of 0.01 s−1, the percentage of DRX also increases greatly and the mean grain size decreases from 50 to 39.3 μm. The mean size of the
recrystallied grains (R-grains) mainly depends on the Zener-Hollomon parameter. To obtain fine grain, the desired deformation
temperature is determined from 400 to 450 °C.
A new modelling approach that couples fundamental metallurgical principles of dynamical recrystallization (DRX) with the cellular automaton (CA) method has been developed to simulate the microstructural evolution and the plastic flow behaviour during thermomechanical processing with DRX. It provides an essential link for multiscale modelling to bridge mesostructural dislocation activities with microstructural grain boundary dynamics, allowing accurate predictions of microstructure, plastic flow behaviour, and property attributes. Variations of dislocation density and growth kinetics of each dynamically recrystallizing grain (R-grain) were determined by metallurgical relationships of DRX, and the flow stress was evaluated from the average dislocation density of the matrix and all the R-grains. The growth direction and the shape of each R-grain were simulated using the CA method. The predictions of microstructural evolution and the flow behaviour at various hot working conditions agree well with the experimental results for an oxygen free high conductivity (OFHC) copper. It is identified that the oscillation of the flow stress–strain curve not only depends on thermomechanical processing parameters (strain rate and temperature) but also the initial microstructure. The mean size of R-grains is only a function of the Zener–Hollomon parameter. However, the percentage of DRX is not only related with the Zener–Hollomon parameter, but also influenced by the nucleation rate and the initial microstructure.
A criterion for the initiation of dynamic recrystallization during hot working is proposed. This is based on the contention that the reduced driving force due to concurrent deformation modifies the normal energy balance which defines the conditions for nucleation of new grains. A principal conclusion from the analysis is that the initiation of dynamic recrystallization requires a critical dislocation density irrespective of whether dynamic recovery is occurring simultaneously or not. The theory forecasts behaviour in reasonable accord with experiment particularly as regards the temperature and strain rate dependence of the stress maximum which characterizes hot working stress-strain curves from materials undergoing dynamic recrystallization. In addition, the present predictions, combined with a treatment of grain boundary nucleated reactions due to Cahn, may be used to calculate the dynamically recrystallized grain size.
This paper reports on work in developing a cellular automaton (CA) model coupling with a topology deformation technique to simulate the microstructural evolution of 30Cr2Ni4MoV rotor steel during the high-temperature austenitizing and dynamic recrystallization (DRX). The state transition rules for simulating the normal grain growth was established based on the curvature-driven mechanism, thermodynamic driving mechanism and established based on the curvature-driven mechanism, thermodynamic driving mechanism and the lowest energy principle. To describe the compression effect on the topology of grain deformation more accurately, the update topology deformation model was proposed in which a cellular coordinate system and a material coordinate system were established separately. The cellular coordinate system remains unchangeable, but the material coordinate system and the corresponding grain boundary shape will change with deformation in the update topology deformation model. The effects of a wide range of thermomechanical parameters (e.g., temperature and strain rate) on the DRX kinetics and mean grain size were investigated. It was found that increasing the temperature and/or decreasing the strain rate can reduce the incubation period, and decreasing the temperature and/or increasing the strain rate can refine the DRX grain size. The simulation results are validated by comparing the experimental results.
A Monte Carlo simulation technique has been used to study dynamic recrystallization in a polycrystalline matrix. The model employed, maps the microstructure onto a discrete, two dimensional lattice with use of a magnetic analog, the Q-state Potts model. The response of the material to hot deformation is simulated by adding recrystallization nuclei and stored energy continuously with time. The simulations presented in this work use an energy storage rate procedure that models stage III hardening in metals and thereby incorporates both work hardening and dynamic recovery. This model reproduces many features found recently by Rollett et al. in a more simple model that did not include an explicit dynamic softening mechanism. It is found, that the type of work hardening law assumed results in relationships between transient and steady state recrystallization parameters which more closely approach those observed in physical experiments. In this view, the roles of the controlling mechanisms of dynamic recrystallization in real polycrystalline materials are discussed.
The characteristics of high temperature flow curves and evolution of new grain structures under conditions of dynamic recrystallization (DRX) are reviewed, together with the associated development of dislocation substructures. It is shown that the type of DRX taking place depends on the relative grain size Do/Ds, where and Do and Ds are the initial and stable dynamic grain sizes, and also on the nature of dispersion particles. These can be attributed to that dynamic nucleation occurs mainly at or near existing grain boundaries, and dynamic growth is controlled by not only the temperature corrected strain rate Z, but also dispersion particles. The work softening accompanied with DRX results from a change in the substructural nature from homogeneous. The dislocation substructures under full DRX are classified into the three categories: (i) DRX nuclei, (ii) growing DRX grains containing a dislocation density gradient, and (iii) large DRX grains with fairly homogeneous substructure. Finally, the metadynamic or post-dynamic restoration processes taking place in the DRX matrices are reviewed. The static softening-annealing time curve observed after DRX consists of three distinct stages with the respective inflection plateaus, followed by incomplete softening (stage 1,2 and 3). The rate of grain growth at stage 3 is much lower than that of normal grain growth. These can be caused by the stable existence of growing DRX grains having many-sided irregular shapes as well as high density dislocations.
A Monte Carlo model for dynamic recrystallization has been developed from earlier models used to simulate static recrystallization and grain growth. The model simulates dynamic recrystallization by adding recrystallization nuclei and stored energy continuously with time. The simulations reproduce many of the essential features of dynamic recrystallization. The stored energy of the system, which may be interpreted as a measure of the flow stress, goes through a maximum and then decays, monotonically under some conditions and in an oscillatory manner under others. The principle parameters that were studied were the rate of adding stored energy, ΔH, and the rate of adding nuclei, ΔN. As ΔH increases, for fixed ΔN, the oscillations decay more rapidly and the asymptotic energy rises. As ΔN increases again the oscillations decay more rapidly but the asymptotic stored energy decreases. The mean grain size of' the system also oscillates in a similar manner to the stored energy but out of phase by 90°. The flow stress oscillations occurred for conditions which lead to both coarsening and refinement of the initial grain size. Necklacing of the prior grain structure by new grains were observed for low ΔH and high ΔN; it is, however, not an invariable feature of grain refinement. The initial grain size has a profound influence on the microstructure that evolves during the first cycle of recrystallization but at long times, a mean grain size is established which depends on the values of ΔH and ΔN alone. Comparison of the relationships between the energy storage rate, maximum and asymptotic stored energy and the grain size suggest that in physical systems the energy storage rate and the nucleation rate are coupled. Comparison of the simulation results with experimental trends suggests that the dependence of nucleation rate on storage should be positive but weak. All of these results were obtained without the addition of special parameters to the model.
The paper is about cellular automaton models in materials science. It gives an introduction to the fundamentals of cellular automata and reviews applications, particularly for those that predict recrystallization phenomena. Cellular automata for recrystallization are typically discrete in time, physical space, and orientation space and often use quantities such as dislocation density and crystal orientation as state variables. Cellular automata can be defined on a regular or nonregular two- or three-dimensional lattice considering the first, second, and third neighbor shell for the calculation of the local driving forces. The kinetic transformation rules are usually formulated to map a linearized symmetric rate equation for sharp grain boundary segment motion. While deterministic cellular automata directly perform cell switches by sweeping the corresponding set of neighbor cells in accord with the underlying rate equation, probabilistic cellular automata calculate the switching probability of each lattice point and make the actual decision about a switching event by evaluating the local switching probability using a Monte Carlo step. Switches are in a cellular automaton algorithm generally performed as a function of the previous state of a lattice point and the state of the neighboring lattice points. The transformation rules can be scaled in terms of time and space using, for instance, the ratio of the local and the maximum possible grain boundary mobility, the local crystallographic texture, the ratio of the local and the maximum-occurring driving forces, or appropriate scaling measures derived from a real initial specimen. The cell state update in a cellular automaton is made in synchrony for all cells. The review deals, in particular, with the prediction of the kinetics, microstructure, and texture of recrystallization. Couplings between cellular automata and crystal plasticity finite element models are also discussed.
- P Peczak
- M J Luton
P. Peczak and M.J. Luton, Acta Metall Mater 41(1) (1993) 59.
- M M Tong
- C L Mo
- D Z Li
- Y Y Li
M.M. Tong, C.L. Mo, D.Z. Li and Y.Y. Li, Acta Metall Sin 38(7) (2002) 745 (in Chinese).
- T Takaki
- T Hirouchi
- Y Hisakuni
- A Yamanaka
- Y Tomita
T. Takaki, T. Hirouchi, Y. Hisakuni, A. Yamanaka and Y. Tomita, Mater Trans 49(11) (2008) 2559.
- T Takaki
- Y Hisakuni
- T Hirouchi
- A Yamanaka
- Y Tomita
T. Takaki, Y. Hisakuni, T. Hirouchi, A. Yamanaka and Y. Tomita, Comput Mater Sci 45(4) (2009)
881.
- R L Goetz
- V Seetharaman
R.L. Goetz and V. Seetharaman, Scr Mater 38(3) (1998) 405.
- J W Zhao
- H Ding
- W J Zhao
- F R Cao
- H L Hou
- Z Q Li
J.W. Zhao, H. Ding, W.J. Zhao, F.R. Cao, H.L. Hou and Z.Q. Li, Acta Metall Sin (Engl Lett) 21(4)
(2008) 260.
- Y Lu
- L W Zhang
- X H Deng
- J B Pei
- S Wang
- G L Zhang
Y. Lu, L.W. Zhang, X.H. Deng, J.B. Pei, S. Wang and G.L. Zhang, Acta Metall Sin 44(3) (2008) 292
(in Chinese).
- N M Xiao
- C W Zheng
- D Z Li
- Y Y Li
N.M. Xiao, C.W. Zheng, D.Z. Li and Y.Y. Li, Comput Mater Sci 41(3) (2008) 366.
- F Chen
- Z S Cui
- J Liu
- W Chen
- S J Chen
F. Chen, Z.S. Cui, J. Liu, W. Chen and S.J. Chen, Mater Sci Eng A 527(21-22) (2010) 5539.
- H Hallberg
- M Wallin
- M Ristinmaa
H. Hallberg, M. Wallin and M. Ristinmaa, Comput Mater Sci 49(1) (2010) 25.
- S Q Huang
- Y P Yi
- C Liu
S.Q. Huang, Y.P. Yi and C. Liu, J Cent South Univ Technol 16(1) (2009) 18.
- K Janssens
- D Raabe
- E Kozeschnik
- M Miodownik
- B Nestler
K. Janssens, D. Raabe, E. Kozeschnik, M. Miodownik and B. Nestler, Computational Materials Engineering (Elsevier Academic Press, Burlington, 2007) p.117.
- X F Ma
- X Guan
- Y T Liu
- X M Shen
- L J Wang
- S T Song
- Q K Zeng
X.F. Ma, X.J Guan, Y.T. Liu, X.M. Shen, L.J. Wang, S.T. Song and Q.K. Zeng, Chin J Nonferrous
Met 18(1) (2008) 138.
- L Blaz
- T Sakai
- J J Jonas
L. Blaz, T. Sakai and J.J. Jonas, Met Sci 17(12) (1983) 609.
- B Derby
B. Derby, Scr Metall Mater 27(11) (1992) 1581.
- T Sakai
T. Sakai, J Mater Process Technol 53(1-2) (1995) 349.
- J Kroc
J. Kroc, LNCS 2329 (2002) 773.