Normal Grain Growth Mediated by Microstructural Heterogeneity

Grain size is a characteristic of crystalline solids that controls material properties with cross-disciplinary interest. In the geodynamic context, grain size influences rheology and permeability. Heterogeneity in grain size is empirically known to promote strain localisation. We present a new theory for normal grain growth that accounts for grain-size heterogeneity and thereby provides a better fit to observed grain-size distributions.

Normal grain growth is the most fundamental process acting on grain size and is driven by the surface curvature of the grains themselves. It is known empirically that the grain-size distribution produced by normal grain growth is quasi-steady: although the mean grain-size changes with time, the mean-normalized distribution is fixed.

The classical mean-field model of normal grain growth is the Hillert model, the basic assumptions of which are validated and broadly accepted. However, the Hillert model fails to predict the grain-size distribution that is observed in experiments and numerical simulations. This represents a gap in our theoretical understanding of normal grain growth. The Hillert model is rooted in a mean field formalism that assumes each grain responds to the global ensemble of grains. In real systems, however, individual grains interact with their near neighbours. Due to microstructural heterogeneity, these neighbours may present a different grain-size distribution than the global set. We hypothesise that the disparity between local and global environments plays a key role in the development of the global grain-size distribution.

To test this hypothesis, we develop a statistical model for the local environment of a grain as a function of the size of the local neighbourhood. By coupling this statistical model to the canonical mean-field model of normal grain growth, we simulate the time-evolution of both the size of a grain and its local environment. Building on this, we model the evolution of a large ensemble of such grains with a Monte Carlo approach. The resulting grain-size distribution is quantitatively consistent with observations.

The mathematical framework developed here can be extended to include other processes that drive grain-size evolution.