Modeling Static Recrystallization in Al-Mg Alloys

ORIGINAL RESEARCH ARTICLE Modeling Static Recrystallization in Al-Mg Alloys HEINRICH BUKEN and ERNST KOZESCHNIK In the present work, the influence of Mg on recrystallization kinetics in Al is analyzed by computer simulation. A comprehensive state parameter-based microstructure model is developed, which describes recrystallization in terms of nucleation and growth. The mechanism of solute drag is fully incorporated, thus accounting for the decrease of grain boundary mobility in the presence of impurity atoms. On the basis of the present approach, the solute binding energy between Mg atoms and grain boundaries is assessed and compared to experimentally measured values. Furthermore, the influence of Mg on dislocation production during strain hardening is modeled. The simulations of the composition and temperature-dependent recrystallization kinetics are verified on experimental studies where excellent agreement is achieved. Both simulation and experiment show that increasing Mg content first decelerates and, later on, accelerates recrystallization kinetics. https://doi.org/10.1007/s11661-020-06100-9 Ó The Author(s) 2020 I. INTRODUCTION THE control of microstructure evolution during processing of Mg-alloyed Al materials is a key factor for determining the final mechanical–technological properties of the material. Mg is a widely used element in Al alloys, especially in the 5xxx and 6xxx series. On the one hand, Mg segregates into grain boundaries and reduces the mobility of the moving boundary by several orders of magnitude in comparison to pure Al.[1] This so-called solute drag effect[2] is caused by solute atoms being dragged along with the moving grain boundary, thus exerting a restraining force against the movement of the grain boundary. As a result, microstructural processes involving the motion of high-angle grain boundaries (HAGB) and low-angle grain boundaries (LAGB) can be severely slowed down by the presence of impurity atoms.[1,3] On the other hand, an increased Mg content promotes a higher strain-hardening rate, which, at identical strain, induces a higher dislocation density.[4,5] As a result, the driving pressure for recrystallization increases, thus accelerating the observed recrystallization kinetics. Koizumi et al.[6] have performed recrystallization experiments in Al-Mg alloys, observing that an increase of the Mg content first leads HEINRICH BUKEN is with the Primetals Technologies Austria GmbH, Turmstrasse 44, 4031 Linz, Austria and also with the Institute of Materials Science and Technology, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria. ERNST KOZESCHNIK is with the Institute of Materials Science and Technology, TU Wien and also with the MatCalc Engineering GmbH, Getreidemarkt 9, 1060 Vienna, Austria. Contact e-mail: Manuscript submitted August 21, 2020; accepted November 6, 2020. METALLURGICAL AND MATERIALS TRANSACTIONS A to a deceleration of the rate of recrystallization, followed by an acceleration at further increasing Mg content. These results will form the basis of experimental verification of the present model. In literature, several approaches are available describing recrystallization phenomena in metallic materials. With particular focus on Al alloys, earlier models[7,8] mostly utilize JMAK-based equations[9] for describing the kinetics of static recrystallization. In these models, several semi-empirical parameters are commonly utilized to adjust the simulated recrystallizing kinetics to experimentally measured recrystallized fractions. Since JMAK-based models do not incorporate explicit mechanism-based descriptions for nucleation and growth of recrystallizing grains, they can only take limited account of basic physical phenomena such as the solute drag effect, precipitate–dislocation interactions in precipitation hardening alloys or the influence of impurities on dislocation generation during strain hardening. Recently, Zurob et al.[10,11] presented a physically based model describing recrystallization with explicit expressions for nucleation and growth. In their work, the nucleation rate for recrystallization is evaluated from microstructural state parameters such as the subgrain size and the dislocation density, which, in combination with growth equations, delivers information on the recrystallized fraction within the deformed microstructure. The solute drag impact is included in the grain boundary mobility within the Cahn approach.[2] When applying the model to Al, however, Zurob et al.[10] utilized experimentally determined mobilities taken from literature instead of calculating composition-dependent mobilities based on physical relationships. Furthermore, this work does not take into account that the alloy composition has an important impact on the dislocation evolution during and after deformation. Consequently, no variation in the alloy composition of various Al alloys is elaborated in this work and recrystallization kinetics is evaluated only for a single Mg content of 1 wt pct. In the present work, a state parameter-based model is developed, in which all relevant microstructural parameters are numerically integrated forward in time. The evolution equations incorporate full composition and temperature dependence for grain boundary mobilities as well as dislocation generation during strain hardening. The calculated grain boundary mobilities are compared to experimentally measured values to illustrate the predictive potential of the present grain boundary mobility approach. In addition, relations, by which the driving pressure for recrystallization is described as a function of the Mg content through a composition-dependent dislocation generation term, are introduced. Furthermore, the previous version of the model, which has been reported in References 12 and 13 is substantially improved in terms of the introduction of the Rayleigh distribution for the rate of supercritical subgrain formation (Section II–A) instead of a sharp limit corresponding to the comparison of the mean and critical subgrain sizes, as well as a dynamic treatment of the subgrain size with growth and shrinkage terms (Section II–B). The predictions of the recrystallization model are finally compared with experimentally measured values from literature. The entire model and input parameters are explained in detail, subsequently. II. THE RECRYSTALLIZATION MODEL A. Nucleation and Growth The nucleation rate of newly formed recrystallized grains, N_ rx , is formulated as the product of the number density of potential nucleation sites, Npot , a site saturation factor, Bnuc , which accounts for the grain area that is already covered by recrystallized grains and which is, therefore, no longer available for further nucleation, as well as the flux of subgrains reaching supercritical size, F_ sub , as N_ rx ¼ Npot Bnuc F_ sub : ½1 Bailey and Hirsch[14] suggested that the main nucleation mechanism for recrystallization is given by the process of strain-induced boundary migrat (...truncated)