# Nucleation of Recrystallization

As a metallic material is plastically deformed, energy will be accumulated in the material through generation and rearrangement of defects, mainly dislocations. As dislocation networks develop they will tend to form entanglements that subsequently form dislocation cells which, in turn, eventually leads to the formation of subgrains in the grain interiors. These subgrains will be the birthplaces of the recrystallization nuclei. In order for the subgrains to become viable nuclei, however, two criteria need to be met locally in the microstructure. The first is a kinematic criterion requiring mobile high-angle grain boundaries to be formed by the nucleation event. The second is a thermodynamic criterion requiring a stored energy gradient to be present across the interface that is sufficient to provide enough positive driving pressure for grain growth to occur. These criteria are usually found to be met at grain boundary triple junctions and along grain boundaries. Such sites provide enough lattice curvature and sufficient stored energy differences for providing possible nucleation sites. Nucleation may also, but less common, take place in the grain interiors, for example along shear bands and near particle inclusions. The latter is often referred to as particle-stimulated nucleation. As nucleation preferentially takes place along pre-existing grain boundaries, it is common to observe so-called necklace patterns of recrystallized material along the boundaries.

The process of subgrain formation is in mesoscale models usually captured by considering an incubation time $t_{\mathrm{c}}$ or a threshold dislocation density $\rho_{\mathrm{c}}$, i.e. a threshold stored energy, that needs to be reached before nucleation is initiated. In macroscale models, the same process is usually formulated in terms of a critical strain $\varepsilon_{\mathrm{c}}$ that has to be achieved in order for nucleation to take place. Also the notion of a critical stress $\sigma_{\mathrm{c}}$ has been proposed to identify the onset of recrystallization.

During the formation of the subgrains, recovery processes very rapidly reduce the dislocation content in the subgrain interiors by annihilation of dislocations and by accumulation of dislocations at the subgrain boundaries. This increases the subgrain misorientation with respect to neighboring regions and eventually provide high-angle, mobile, boundaries. The same processes also provide subgrains with very low internal stored energy.

The crystallographic orientation of the nuclei will influence both the progression of recrystallization and also the evolution of any recrystallization texture in the material. Recrystallization nuclei are products of the cold worked parent material but they do not necessarily inherit their orientation from the parent grains although it is not uncommon that clear evidence of the texture present in the initial, cold worked, microstructure can be observed also in the recrystallized material. High-angle boundaries with respect to the surrounding material are also required in order to permit growth of the nuclei, causing differences to develop between the initial and recrystallized textures. It can be noted that the development of recrystallization texture is usually attributed to either orientated nucleation or oriented growth or possibly a combination of these processes.

Having defined the initiation of recrystallization, the next question is at what frequency new nucleation events take place. This issue has been approached in a number of ways in different studies. The two main trends is to consider either of  site-saturated nucleation where all nuclei are assumed to be present at the start of the simulation and no new nuclei are added over time or, alternatively, continuous nucleation where new nuclei are continuously added according to some expression of the rate of nucleation. In the latter scenario, both constant and non-constant rates of nucleation have been considered.

Although constant nucleation rates are often assumed, there are experimental studies indicating nucleation to be non-constant and continuous process. However, it is inherently difficult to experimentally determine the rate of nucleation as it is not easy to define through experimental observations if a region in the microstructure is a subgrain, a nucleus or an expanding grain and the exact time at which one changes into the other.

# New paper on recrystallization modeling

A new paper, titled ", was recently published in Modelling and Simulation in Materials Science and Engineering and can be found at the publisher's site following this link.

# Recrystallization and grain growth

Recrystallization (RX) is one of the main mechanism to control the evolution of grain microstructures. RX is generally accepted to be defined as the formation of a new grain structure in a cold-worked material and occurs through the formation and migration of high-angle boundaries. The grain boundary migrations are primarily driven by stored energy reduction and minimization of grain boundary surface energy.

As a metallic materials is deformed through plastic slip, energy will be accumulated in the material. This energy is to a large extent expended as heat while the remainder is stored in the material microstructure through the generation and redistribution of imperfections, mainly dislocations. By this process, the material becomes increasingly thermodynamically unstable. During subsequent annealing of the material, reduction of the stored energy can take place through relatively slow recovery or by more rapid static recrystallization (SRX). While the recovery proceeds as a continuous process, SRX is discontinuous. During thermomechanical processing of the material, i.e. when the material is exposed to plastic deformation at elevated temperatures, stored energy generation through dislocation accumulation and stored energy reduction through nucleation of new grains work in parallel. This process is commonly labeled dynamic recrystallization (DRX). The latter process of DRX may be further subdivided into a relatively slow continuous dynamic recrystallization (CDRX) or a more rapidly progressing discontinuous dynamic recrystallization (DDRX).

In materials of high stacking-fault energy, such as aluminum, dynamic recovery is significant and recrystallization occurs mainly by CDRX. In this case, subgrains with low-angle boundaries are formed from dislocation networks. With progressing plastic deformation, misorientation is increased until enough energy is achieved and the initially mobile subgrain walls have become immobilized, allowing new grains to be separated by subgrain growth. In materials of low stacking-fault energy, such as copper, dynamic recovery processes such as cross slip and climb are less influential and the recrystallization is dominated by DDRX during which new grains are nucleated as regions of low dislocation density grow to consume more dislocation-dense surroundings. RX nuclei are commonly accepted to form from subgrains and DDRX will be most significant in the microstructure regions having the highest dislocation density, primarily at grain boundary triple junctions, secondly along grain boundaries and at inclusions and with lesser probability in the grain interiors.

Processing conditions, such as temperature and strain rate, as well as material purity will influence the recrystallization process. This allows some control to be exerted over the resulting microstructure. Simulation models can provide the means for design and processing of materials through recrystallization.

# Animation showing a 2D level set simulation of Dynamic Discontinuous Recrystallization (DDRX)

A simple 2D simulation of dynamic discontinuous recrystallization (DDRX) in pure Cu at an elevated temperature. The simulation is based on level sets in a finite element setting. Adaptive remeshing is performed in each step. The animation speed is increased compared to actual time.