Modeling of abnormal grain growth in textured materials

doi:10.1016/j.scriptamat.2004.01.036

Scripta Materialia

Volume 50, Issue 9, May 2004, Pages 1241-1245

https://doi.org/10.1016/j.scriptamat.2004.01.036 Get rights and content

Abstract

The effect of initial texture on the occurrence of abnormal grain growth (AGG) was modeled via a 3D Monte-Carlo approach. A diagram of texture characteristics which give rise to AGG was derived. AGG was associated with periods of linear growth behaviour of the largest grain within the microstructure.

Introduction

Grain growth in polycrystalline solids such as that which occurs during annealing treatments is a process driven by the reduction of the overall grain-boundary energy, thus yielding an increase in the average grain-size D_av. Usually, two limits of this process can be distinguished––normal grain growth and AGG. If there is no anisotropy in the grain-boundary properties, normal grain growth occurs, and the grain-size distribution function remains uniform and self-similar. In the case of AGG, grain-boundary motion is restricted by one or several factors, and microstructure evolution proceeds nonuniformly by the growth of several ‘abnormal’ grains. A particular kind of AGG, sometimes called “catastrophic” AGG, results in the final volume of abnormal grains more than three orders of magnitude larger than that of the surrounding matrix grains [1]. Such heterogeneous microstructures may lead to poor mechanical properties and thus should be avoided during thermomechanical processing.

Following the initial fundamental work of Hillert [2] and Gladman [3], considerable theoretical attention has been focused on the problem of AGG [4], [5], [6], [7], [8], [9], [10]. Most of the models postulated that the initial grain-size distribution was not uniform, but contained at least one large grain. The possible growth of such larger grains was then analyzed. However, as shown recently by Rios [10], [11], AGG can develop even from a uniform grain-size distribution for the case in which grain growth is restricted by a pinning force which decreases slowly with time. The Monte-Carlo (MC) method has been successfully applied to simulate AGG for different starting conditions [12], [13], [14], [15].

Based on recent numerical (MC) and analytical simulations of the AGG phenomenon [6], [16], [17], [18], it appears natural to consider both normal and AGG as limiting cases within a unified framework in which different kinds of anisotropy and grain-boundary pinning associated with texture (i.e., spatial anisotropy of grain-boundary velocity) are included as factors. These factors define the place of any particular microstructure in an N-dimensional space. Hence, a processing map can be developed to characterize the expected system behaviour. The objective of the present paper was to establish the portion of such a map dealing with the effect of texture-component width and intensity on grain growth via 3D MC simulations. A method to define/recognize periods of AGG in MC simulations was also developed.

Section snippets

Theoretical aspects of abnormal grain growth

The theoretical model of AGG focuses on an isolated abnormal grain A surrounded by normally growing grains comprising the “matrix microstructure”. In general, the local grain-boundary velocity is proportional to grain-boundary curvature. Hence, the abnormal grain will grow faster than the surrounding grains because the motion of the abnormal grain-boundary is directed entirely outside the grain. Following Hundery [19], [20], the contact area of neighboring grains A and j (i.e., grain-boundary

Simulation technique

Grain growth was simulated using the MC (Potts) model described in Ref. [27]. Thus, only a brief description is given here. The model domain was formed by a 3D cubic array of model units (MU), each of which represented a point in a cubic lattice. The size of individual grains was taken to be equal to the diameter of a sphere containing the same volume. The length measure was assumed to be equal to 1 MU, and the time measure was 1 MCS. During one MCS, the number of elementary flip-simulation

Results and discussion

The main results of the present work consisted of a number of MC simulations used to establish the effects of texture on AGG. These simulations were also used to develop a map describing the effects of anisotropy on the occurrence of AGG. A relative GB mobility parameter M was introduced as a normalization factor for the dependence of the elementary orientation-flip probability on intergranular misorientation. M was assumed to be small (0.05) for low-angle boundaries and equal to unity for

Summary and conclusions

The transition between normal and AGG in textured materials was analyzed using a 3D Monte-Carlo (Potts) model in which initial texture intensity/halfwidth characteristics could be carefully quantified. It was demonstrated that abnormal grain growth and rapid growth of the average grain-size do not coincide. Periods of AGG are associated with periods of linear growth behaviour of the largest grain within the microstructure. Periods of normal grain growth are characterized by the similar

Acknowledgements

The present work was supported by the Air Force Office of Scientific Research (AFOSR) and the AFOSR European Office of Aerospace Research and Development (AFOSR/EOARD) within the framework of STCU Partner Project P-057A. The encouragement of the AFOSR program managers (Drs. C.H. Ward and C.S. Hartley) is greatly appreciated.

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Utilizing the data assimilation and multi-phase-field grain growth model, this study proposes a novel framework of measuring anisotropic (nonuniform) grain boundary energy and mobility. The framework can evaluate a large number of boundary properties from typical observations of grain growth without requiring specifically designed experiments or calculations. In this method, by optimizing the multi-phase-field model parameters such that the simulation results are in good agreement with the observation data, the energies and mobilities of multiple individual boundaries are directly and simultaneously estimated. To validate the method, numerical tests on boundary property estimation were performed using synthetic microstructure dataset generated from grain growth simulations with a priori assumed property values. Systematic tests on simple tricrystal systems confirmed that the proposed method accurately estimates each boundary energy and mobility within an error of only several % of their assumed true values even for conditions with strong property anisotropy and grain rotation. Further numerical tests were conducted on a more general multi-grain system, showing that our method can be successfully applied to complicated polycrystalline grain growth. The obtained results demonstrate the potential of the proposed method in extracting a large dataset of grain boundary properties for arbitrary boundaries from actual grain growth observations.
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In actual materials, these properties are usually strongly anisotropic, with their variations depending primarily on the misorientation angle between adjacent grains [1,4–10]. Several studies have suggested that such anisotropy in grain boundary properties could be a dominant factor in important grain growth-related phenomena, e.g., nucleation of recrystallized grains [11,12], abnormal grain growth [11–14], texture development [15,16], and deviation of grain growth kinetics from the ideal parabolic law [17,18]. However, it is difficult to explicitly take these anisotropic properties into account in analytical grain growth theories.
Three-dimensional grain growth behaviors under anisotropic (misorientation-dependent) grain boundary energy and mobility are investigated via phase-field simulations. Based on a multi-phase-field model and parallel graphics-processing unit computing on a supercomputer, very large-scale simulations with more than three million grains are achieved, enabling reliable statistical evaluation of anisotropic grain growth. The anisotropic boundary properties are introduced by the classical Read-Shockley and sigmoidal models; the threshold misorientation angle, Δθ_h, included in these models is used as a quantity to determine the anisotropy strength of the system. Systematic simulations are performed for different Δθ_h values, through which the correlations between the anisotropy strength and grain growth characteristics such as grain size and misorientation distributions are examined. The obtained results show that anisotropic grain growth reaches the steady-state regime irrespective of the Δθ_h value. However, the kinetics and microstructural morphology during the steady-state growth are largely dependent on Δθ_h. Furthermore, by comparison with the simulated results, the applicability of analytical grain growth theories to anisotropic systems are tested. The tests reveal that the steady-state microstructure in anisotropic growth cannot be well captured by the existing theories, which is likely because the basic assumptions of the theories do not hold for anisotropic systems.
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Grain boundary migration and grain growth are prominent factors influencing microstructure-property-relationships in polycrystalline materials like metals, alloys, and biogenic composites. The motion of grain boundaries during grain growth is strongly controlled not only by the curvature of the boundaries but also by the grain boundary mobility and energy per unit area, where the latter two factors depend on the crystallographic misorientation of two adjacent grains. In the present work, the influence of crystallographic misorientation on grain growth kinetics is analysed qualitatively and quantitatively with respect to classical grain growth predictions in terms of the average growth law, size distribution functions, and von Neumann-Mullins-law.
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Modeling of abnormal grain growth in textured materials

Abstract

Introduction

Section snippets

Theoretical aspects of abnormal grain growth

Simulation technique

Results and discussion

Summary and conclusions

Acknowledgements

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