A mean-field model of static recrystallization considering orientation spreads and their time-evolution

Abstract

In this paper, we develop a mean-field model for simulating the microstructure evolution of crystalline materials during static recrystallization. The model considers a population of individual cells (i.e. grains and subgrains) growing in a homogeneous medium representing the average microstructure properties. The average boundary properties of the individual cells and of the medium, required to compute growth rates, are estimated statistically as a function of the microstructure topology and of the distribution of crystallographic orientations. Recrystallized grains arise from the competitive growth between cells. After a presentation of the algorithm, the model is compared to full-field simulations of recrystallization performed with a 2D Vertex model. It is shown that the mean-field model predicts accurately the evolution of boundary properties with time, as well as several recrystallization parameters including kinetics and grain orientations. The results allow one to investigate the role of orientation spreads on the determination of boundary properties, the formation of recrystallized grains and recrystallization kinetics. The model can be used with experimentally obtained inputs to investigate the relationship between deformation and recrystallization microstructures.

Introduction

In most models of static and dynamic recrystallization, recrystallized grains arise from a competitive growth of subgrains or cells pre-existing in the deformed microstructure [1], [2], [3], [4], [5], [6], [7], [8], [9]. In high stacking fault energy materials, the force driving the growth of subgrains comes almost entirely from the interfacial tension of the subgrain network (e.g. aluminium alloys [5]), while the energy stored in tangled dislocations plays a more important role as the stacking fault energy decreases (e.g. silver and nickel [2], copper [2], [6], [8]). While the micro-mechanisms at the origin of recrystallization are well known, the conditions leading to the development of recrystallized grains of particular orientations, and their incidence on the kinetics, remain difficult to identify.

This challenge is to a great extent due to the large number of features involved in recrystallization. Deformed grains contain of the order of 10⁵ subgrains [5], out of which a handful turn into recrystallized grains during annealing. State-of-the-art full-field models (e.g. phase field, Vertex dynamics, level-set) can simulate this many subgrains [10], [11], but this is still insufficient to confidently predict recrystallization kinetics, grain size and crystallographic texture. As a result, the most significant applications of full-field models to recrystallization remain restricted to comparison with analytical model predictions [4], [7] or to parametric studies on the role of some initial microstructure parameters [3], [12].

Mean-field models are computationally more efficient than full-field models, but are limited by additional assumptions. In the early model of Bailey and Hirsch [1], [2], a subgrain is considered as a potential recrystallized grain when its radius exceeds the value where its inward capillary pressure is overcome by the outwards pressure induced by its neighbours. This model was extended by Zurob et al. [6] to predict the incubation period during which future recrystallized grains grow normally compared to the rest of the microstructure. This approach, however, misses the fact that every growing subgrain satisfies the Bailey-Hirsch criterion [1], [2]. Meeting the Bailey-Hirsch criterion is necessary but insufficient for a subgrain to become a grain in the recrystallized state. In two separate publications, Humphreys [13], and Rollett and Mullins [14] proposed an approach that considers that a recrystallized grain forms when the growth rate of a subgrain relative to the average is positive. Notably, the model highlights the role of heterogeneous subgrain size and boundary properties on the onset of recrystallization. Despite a few interesting applications to experimental cases [5], [15], and comparisons to full-field simulations [4], [16], this approach remains much less popular than those relying on the Bailey-Hirsch criterion (e.g. [8], [9], [17], [18]).

As the microstructural heterogeneities giving rise to recrystallization develop during prior deformation, substantial efforts have also been made to simulate recrystallization from outputs of crystal plasticity models. In these cases, heterogeneities of subgrain size and disorientation have been attributed to inter-granular contrast of slip activity (estimated by Taylor factors) [19], resolved shear stress [20], and intragranular disorientation levels [21]. These approaches generally focus on predicting the texture out of these heterogeneities while ignoring the recrystallization kinetics.

In this paper, we propose an extended mean-field model that builds on the approaches described above. In our approach, a discrete population of subgrains evolves according to classic cellular growth laws, with a time-integration scheme implemented to update the microstructural parameters. The recrystallized grains are identified based on a size threshold. The model extends beyond classic mean-field approaches by accounting for the variation of subgrain properties with crystallographic orientation by tracking the moments of several boundary property distributions. As a result, recrystallization kinetics and recrystallized grain orientations are predicted together. This model is tested against full-field vertex simulations of subgrain growth and its extension to predicting experimental results is discussed.

The paper starts by briefly introducing the methodology used for Vertex simulations. This serves to also familiarize the reader with the topology of the microstructures investigated. Next, the mean-field model is introduced. In the following sections, the ability of the mean-field model to reproduce the full-field simulations is shown, with a discussion on the strengths, weaknesses and areas for further improvement.