Modeling and simulation of recrystallization and microstructure evolution
The following sections give a brief overview of the importance of the grain microstructure in metallic materials and how it evolves due to recrystallization. In particular, on-going and published research on numerical modeling and simulation of recrystallization and related issues is discussed.
The importance of the grain microstructure in metallic materials
Several properties of metallic materials depend to a large extent on the grain structure of the material microstructure. Properties that are influenced by the grain structure include such important quantities as strength, ductility and resistance to creep deformation. Also the strain rate dependence of the material is influenced by the grain size.
One of the most important aspects of the grain microstructure is the presence of grain boundaries. As the grain size is reduced, an increasing amount of grain boundaries will be present in the microstructure.
Plastic deformation raises the internally stored energy in the material, mostly due to the creation and rearrangement of dislocations. Grain boundaries pose obstacles to dislocation motion and dislocation accumulation will take place at the grain boundaries, contributing to the macroscopic deformation hardening of the material.
The perhaps most well-known, macroscopic, observation of grain size influence on material behavior is the Hall-Petch relation, indicating a proportionality between the yield stress and the inverse of the square-root of the average grain size in the material. The existence of this proportionality is, however, a manifestation of processes taking place in the grain microstructure .
Recognizing the importance of the grain microstructure, great possibilities lie in being able to control and take advantage of designed microstructures in practical applications. Such applications include production of metallic materials of superior strength and the development of functionally graded materials, having different properties in different regions, appropriate for a certain product or application.
Being able to control aspects of the grain microstructure can also be vital in miniaturization of products, e.g. in the production of micro-electro-mechanical systems (MEMS) and in biomedical applications.
Tailoring material properties is further important as it permits lowered weight of products while maintaining the appropriate weight-to-strength ratios, leading to reduced emissions and less negative environmental impact.
Microstructure evolution through recrystallization
The main mechanism for the development of grain microstructures is recrystallization. This might be a relatively slow and static process or fast-proceeding dynamic process, driven by plastic slip deformation of the material. In either case, recrystallization occurs by growth of new grains of low dislocation density which consume the surrounding cold-worked microstructure, effectively lowering the level of stored energy in the material. Grain growth occurs mainly by migration of high-angle grain boundaries (HAGB) although also low-angle boundaries (LAGB) may partake in some situations.
The nature of the recrystallization process is dependent on the extent of recovery, the rate of which is determined by the stacking-fault energy (SFE) of the material.
The progression of recrystallization is strongly influenced by processing temperature and by the rate of deformation. In addition, the presence of particles in the material can affect the process. Such particles, being deliberately added or being impurities, can either retard recrystallization through particle pinning (also referred to as Zener pinning) or facilitate nucleation by particle stimulated nucleation (PSN). The type of particle influence depends largely on the size of the particles.
Since processing conditions and material purity influences the recrystallization process – and thereby also the grain size of the material – possibilities are given to exert some control over the development of the material microstructure. This is of great interest in practical applications and reliable simulation models can provide the means for optimal design and processing of materials and products, considering recrystallization and grain size.
Production of fine-grained materials through severe plastic deformation
Dynamic recrystallization is driven by plastic slip deformation of the material and the resulting grain size is directly related to the amount of deformation imposed onto the work piece. This knowledge has led to the development of material processing techniques based on severe plastic deformation (SPD). Such processes include high pressure torsion (HPT), accumulated roll bonding (ARB), asymmetric rolling (AR) and equal channel angular pressure/extrusion (ECAP/ECAE).
A typical ECAP setup is shown in the figure to the right. The deformation imposed onto the work piece in a single ECAP pass can be estimated from the expression.
Note the dependence on the channel geometry. ECAP processing is modeled and further discussed in .
By processes as these, materials can be produced with grain sizes reduced down to the nanometer scale. The SPD techniques are therefore of great industrial importance and accurate modeling of such processes can help in optimizing the techniques as well as the resulting product .
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Modeling and simulation of recrystallization and microstructure evolution
Recrystallization modeling is interesting in several aspects, not least since it bridges materials science and computational mechanics. Although the importance of the grain size for material behavior has been recognized for several decades, understanding of the related microstructure processes is still developing. This is also true for numerical modeling and simulation of microstructure evolution through recrystallization, being a very vital field of research.
Recrystallization has in recent years been approached by several different simulation techniques and algorithms. A review of the most influential approaches is given in .
Adopting a continuum mechanical approach, recrystallization can be modeled using an internal variable representation of the pertaining quantities, such as the average grain size and the dislocation density. The macro-scale material behavior will in this way be based on parameters related to the evolving microstructure [1,3].
An example of continuum-scale modeling and simulation of ECAP-processing of Aluminum is given in . Some results on the distributions of grain size and dislocation density in the work piece are shown in the figure below.
Recrystallization modeling with explicit representation of grain boundaries as well as nucleation and growth of recrystallized grains can be achieved by meso-scale models [2,3,4].
Classically Monte Carlo Potts (MCP) and cellular automata (CA) algorithms have been used by the computational materials science community to model the development of grain microstructures. Especially cellular automata are attractive since high spatial and temporal resolution can be achieved at the grain-scale. In addition, the CA algorithm is computationally efficient and lends itself to computer parallelization.
Examples from 3D cellular automaton simulations of dynamic recrystallization in Copper at different temperatures are shown in the figure below.
Modeling of dislocation/grain boundary interaction
Meso-scale models of microstructure evolution also allow studying of heterogeneous dislocation density distributions and gradient effects. In  a hybrid finite difference/cellular automaton model is established where dislocation density gradient are modeled in a reaction-diffusion system. This approach results in the expected Hall-Petch behavior of the macroscopic flow stress – without including an explicit dependence on the grain size – in addition to providing a physically sound dislocation density distribution, shown in the figure below.
By this modeling approach, the dislocation density will be concentrated at grain boundaries and particularly at triple junctions, directly providing the sites for nucleation of recrystallization. This is in contrast to the common modeling approach where nuclei are placed manually at appropriate sites in the microstructure.
- Modeling of continuous dynamic recrystallization in commercial-purity Aluminum, H. Hallberg, M. Wallin and M. Ristinmaa, Materials Science and Engineering A (2010), vol. 572, pp. 1126-1134.
- Simulation of discontinuous dynamic recrystallization in pure Cu using a probabilistic cellular automaton, H. Hallberg, M. Wallin and M. Ristinmaa, Computational Materials Science (2010), vol. 49, pp. 25-34.
- Approaches to modeling of recrystallization, H. Hallberg, Metals (2011), special issue on Processing and Properties of Bulk Nanostructured Materials, vol. 1, pp. 16-48.
- Microstructure evolution influenced by dislocation density gradients modeled in a reaction-diffusion system, H. Hallberg and M. Ristinmaa, Computational Materials Science, vol. 67, pp. 373-383.