Elsevier

Materials Science and Engineering: A

Volume 711, 10 January 2018, Pages 268-283
Materials Science and Engineering: A

Modeling of dynamic recrystallization of magnesium alloy using cellular automata considering initial topology of grains

https://doi.org/10.1016/j.msea.2017.11.024Get rights and content

Abstract

A two-dimensional cellular automaton (CA) model was established on MATLAB platform for quantitative and topographic simulation of the microstructure evolution of magnesium alloy ZM21 during hot deformation. A probabilistic approach was employed to improve the grain topology accuracy of discrete simulation method. Not only the average grain size but also more details including the grain size distribution of the measured microstructure were reflected in the initial conditions of CA simulation. Quantitative relationship between the parameters defined in the CA model and actual deformation condition was built to increase the applicability of the established model. The dynamic recrystallization (DRX) of magnesium alloy ZM21 was predicted using the CA model. Simulation results, including grain topology, average grain size, grain size distribution and DRX fraction were obtained and compared with experimental results. The good agreement between simulated and experimental results indicated that the established CA model is reliable to predict the microstructure evolution during the hot deformation of magnesium alloy. The influences of initial grain size and its distribution on the microstructure evolution were investigated. It indicated that fine and homogeneous microstructure at initial stage is favorable for the DRX process in hot deformation of magnesium alloy.

Introduction

In order to study the recrystallization kinetics and the microstructure evolution during DRX, a lot of empirical and semi-theoretical models were proposed by metallurgical researchers [1]. Most of them are phenomenological models which describe the relationship of DRX kinetics and average grain size with temperature, strain and strain rate based on empirical observations. Others consider metallurgy theory and take subgrain size and dislocation density as internal variables based on microscopic mechanism [2]. These empirical models have been proved effective and even practically used in predicting the primary kinetics of DRX and microstructure characters during hot working of various metals and alloys. However, the empirical models based on the assumption of material homogeneity ignore local effect of microstructure evolution. Although the description of DRX process by average behavior and characteristics can be sufficient in some low-required cases, a further topological and local description of microstructure evolution during DRX process is not available through empirical models.

With the advance of computation ability, some time and space discretized simulation methods considering inhomogeneous behavior during microstructure evolution in mesoscale are gaining increasing attentions. They mainly include Monte Carlo (MC) method, Cellular automata (CA) method and phase field (PF) method. MC models employed by Rollett et al. [3] and Peczak et al. [4] to simulate the microstructure evolution during DRX can reproduce many features of the DRX process. However, these models were unable to describe grain growth kinetics because of the intrinsic limitations of the lack of physical length and time scales. While PF models focus on a continuous description of grain boundary. The diffuse transition regions can simulate the DRX process from a more theoretical way where the topological transformation is resulting from energy minimization and no rule is required. However, PF models are quite computationally intensive and inefficient compared with other discrete methods [1]. On the contrast, the CA algorithm is high spatial resolution and provide excellent scalability for computer code parallelization. In addition, in CA method arbitrary constitutive relations and cell state switching rules can be used, which makes it a versatile tool in computational materials science [1]. Thus, the CA method, which possesses the advantage of consideration of actual deformation condition and computational efficiency, is recently extensively used in DRX process simulation by several researchers for various materials.

At early stage, researchers focused on the simulation of DRX behavior without considering specific materials. Hesselbarth [5] first introduced a CA model for recrystallization prediction and studied the kinetics of nucleation and growth of recrystallizing grains under different parameters. Goetz and Seetharaman [6] proposed a CA model and successfully reproduced the typical DRX features such as necklace type microstructures at high strain rates and a transition from single to multi-peak flow curves under various initial conditions. However, these initial models were not associated with actual process parameters and cannot be applied into realistic microstructural evolution.

Ding and Guo [7], [8] proposed a 2-D DRX model based on CA method in which the models of nucleation and grain-growth were all based on metallurgical theories and the parameters were derived from experimental results. Based on this model, the DRX behaviors of various materials, including HY-100 steel [9], low carbon steel [10], Ti-alloy Ti-10V-2Fe-3V [11], NiTi shape memory alloy [12] and Mg alloy AZ91 [13], were simulated and investigated, respectively, by proposing new definitions of local radius or adding grain-size related parameters into the dislocation density evolution model. Kugler and Turk [14] studied the DRX under multi-stage hot deformation using a similar CA method. Chen et al. [15], [16] coupled an updated topology deformation technique with the CA model and studied the DRX behavior in austenitic stainless steel. Sitko et al. [17] employed a multi-space CA method, in which a typically defined cell was additionally described by a set of sub-cells, and studied the influences of time and length scale on the accuracy of the DRX simulation results. More and more works were focused on the modification of the CA method by coupling with other methods, such as crystal plasticity method [18], [19] and finite element method [20], to expand the simulation scale and optimize the simulation accuracy.

However, the practicability is another significant prospect for the development of a CA method. In conventional CA models, a lot of parameters are deformation condition dependent and most of them are derived from experimental results under specific deformation conditions. Liu et al. [21] studied the DRX process of a Ni-based superalloy using CA method. In their CA model, the values of important material parameters C and M0 were listed at limited strain rates. Lin et al. [22] studied the static recrystallization behavior of Ni-based superalloy using CA method, in which the parameters of grain boundary mobility were listed respectively under only three temperatures. The lack of quantitative description of the relationship between these specific parameters and deformation conditions makes the CA model inapplicable at universal deformation conditions. Therefore, such existing CA models are good at reproducing experimental results under specific deformation conditions while weak in predicting the microstructure evolutions under extensive deformation conditions, which makes these models restricted in practical application.

In order to ensure the accuracy of the simulation, the initial microstructure of a simulation model must be set as close as the experimental one. However, most researchers take the average grain size as the only factor when judging the similarity of the experimental and simulation initial microstructures [23]. The lack of consideration about grain size distribution in initial microstructure set-up of CA simulation makes the results less convincing.

In the present work, a 2-D CA model with probabilistic switching rules of cell state was developed to simulate the microstructural evolution of DRX process of the as-extruded magnesium alloy ZM21 under hot-working conditions. The models of multi-step nucleation and growth of grain were proposed to make the initial microstructure a better match with the experimental microstructure from both average grain size and grain size distribution. Parameters of the CA model were calibrated on the basis of the experimental results of flow stress and strain data by hot compression tests of the studied material at various deformation conditions. The relationship between these parameters and the deformation conditions were established to make the CA model suitable in arbitrary deformation conditions. The accuracy of the established model was verified by comparison with the experimental result on quantitative and topological aspects. Finally, the DRX behavior of the studied alloy was investigated from mechanical and topological prospects using this established CA model.

Section snippets

Experiment procedures

As-extruded magnesium alloy ZM21 was used to investigate the DRX behavior during hot deformation process, whose chemical components are listed in Table 1.

The compression tests were carried out to determine the material parameters in CA model. Cylindrical specimens with a diameter of 8 mm and a height of 12 mm were machined. Hot compression tests were performed on a Gleeble-1500D thermal mechanical simulator under temperatures of 350, 400, 425, 450 and 480 °C and strain rates of 0.001, 0.01, 0.1

General description of CA models

The CA method is time and space discretized in which lattice elements called cells are the basic components. The evolution of each cell's state is determined by the states of its neighboring cells and its previous state according to a certain transformation rule. The rule could be either deterministic or probabilistic. All of the above features make the method suitable for simulating the evolution of complex and dynamic systems which can be simplified into tremendous similar components with

Microstructure evolution with increasing strain

Simulation of microstructure evolution during DRX of magnesium alloy ZM21 was carried out using the CA model described above. Fig. 10 shows the simulated microstructure evolution as well as the flow stress at different strains for the as-extruded magnesium alloy ZM21. Varying colors of the grains denote different crystal orientations of the DRX grains while the white region means the unrecrystallized matrix. The black lines represent grain boundaries with a crystal misorientations over 15

Conclusions

A two-dimensional CA model combined with a probabilistic grain growing approach was established to investigate the DRX behaviors of the as-extruded magnesium alloy. The CA models was programmed on the MATLAB platform. The DRX behaviors of the magnesium alloy were thoroughly investigated using the CA model. The reliability and accuracy of the model were validated through comparison between experiment and simulation results in terms of flow stress, average grain size and grain size distribution

Acknowledgements

The authors (Lixiao Wang and Gang Fang) greatly acknowledge the financial support by the National Natural Science Foundation of China (No. 51675300).

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