A computational study of recrystallisation and grain growth using a 3D Potts Monte Carlo model
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The ever increasing capability of computer systems and the advances in theoretical understanding of the underlying physics and chemistry of materials have, over the last couple of decades, provided the basis for mathematical models and associated software codes. These models and codes have become valuable tools in the prediction of materials nano- and microstructure, and associated properties and behaviour. Since materials science and engineering involves reactions and processes on many time- and length scales, many different computational techniques are required, spanning from quantum mechanical atomistic simulations to macroscopic continuum modelling. The ultimate aim is to provide virtual tools which can be used to optimise production processes and to improve and ”tailor-make” materials properties and component performance. The aim of this thesis has been to investigate a small part of this ”big picture”, i.e. the ability to predict microstructure and texture evolution in aluminium alloys through the use of a 3D Potts Monte Carlo model, together with a thorough parameter study of the same model. Two main types of models have been used in these investigations: 1. A 3D Potts Monte Carlo code with full anisotropy, i.e. a Read-Shockley grain boundary energy with a Σ7 coincident site lattice and a step function in the mobility at the transition between a low and high angle grain boundary, with a peak around Σ7 misorientations. 2. A 3D parallel Monte Carlo code to account for second phase particles with application to aluminium alloys. These models have been used to investigate the following aspects: 1. Recrystallisation kinetics. 2. Recrystallisation texture evolution. 3. Grain size distribution, both in cases with recrystallisation and grain Growth 4. Abnormal grain growth. The main findings of these investigations are summarised below. First of all, the predictive power with respect to recrystallisation texture and the ability to simulate recrystallisation kinetics giving results in accordance with theory have been investigated. It is demonstrated that the Avrami plots exhibit a curvature in the graphs both for small and large volume fractions recrystallised. However, by introducing an incubation time, t0, the kinetics are improved by a straightening of the Avrami plots at lower volume fractions, and its introduction is shown to enable Avrami exponents in accordance with theory. The incubation time, t0, is shown to depend both on the initial grain size, nucleus size and the amount of stored energy, although, no simple analytical expression can be given for this quantity. Still there is a curvature at volume fractions recrystallised close to 1, but as this is believed to originate from the discretisation of the lattice, not much can be done, and this aspect has therefore not been paid any further attention. When it comes to texture predictions, which in the present work was based on an initially calculated deformation texture as the main input, there is a problem getting a recrystallisation texture close to what is predicted by other recrystallisation texture simulations from well verified simulation codes. In an attempt to improve the texture predictions, a thorough model parameter study was carried out, including various grain boundary energy and mobility functions, without any significant influence on the recrystallisation texture. The sensitivity to the misorientation distribution function and the spatial distribution of the nuclei was also tested out, again with limited effect on the final recrystallisation texture. The most pronounced effect was obtained when artificially adding a small fraction of Cube to the nucleation texture, although the expected recrystallisation texture was still not well reproduced. The simulation results point to the importance of the nucleation part of the recrystallisation process and a correct orientation spectrum of nuclei to give good texture predictions by 3D MC simulations. The evolution of grain size distributions during and after recrystallisation and during grain growth has also been extensively investigated. The motivation for this part is the origin of the log-normal like size distributions commonly observed experimentally, and the fact that most simulation methods do not reproduce this log-normal behaviour very well. In the present work it is shown that with the presence of inert second phase particles, there is a clear tendency towards log-normal grain size distributions, a tendency which is strengthened with increasing volume fraction of particles (at least at lower and moderate volume factions). However, only a weak shift towards log-normality is seen with increasing anisotropy in the grain boundary energy and mobility functions. Various aspects of abnormal grain growth, or more precisely possible causes of abnormal grain growth, have also been investigated. This includes the effect of high mobility Σ7 boundaries in an initially uniform grain assembly with a γ-fibre texture, and the possibility of two types of abnormal grain growth occurring at the same time in thin films, due to a high mobility of certain boundaries and due to a low surface free energy. However, in the first case no indications of abnormal grain growth were found. Although the high mobility Σ7 boundaries provided an initial growth advantage for some grains, it was not preserved during coarsening, and on average the grain assembly coarsened uniformly. For the latter case each of the two types of abnormal grain growth was individually successfully simulated, however, it was not possible to make both types of abnormal grains occur in the microstructure at the same time. Also the effects of particles on abnormal (sub-)grain growth have been investigated. This is an extension of previous work considering abnormal subgrain growth as possible mechanisms for nucleation of recrystallisation. For a vol% of particles less than or equal to 5 it can be argued that the number of abnormal grains is constant, while a small decrease is seen when a vol% of particles of 10 is added. However, this only resulted in a small reduction in the number of and a slower growth of the abnormal grains, for the conditions investigated abnormal growth was never totally inhibited.