Strain energy limitations in Monte Carlo Potts modeling of grain growth

Abstract

a b s t r a c tPrevious literature reports that the Monte Carlo Potts (MCP) method can only reproduce the linear relationship between grain boundary velocity and strain energy driving force expected under ideal grain growth conditions for small values of strain energy. The exact range of strain energy values for which linearity can be reflected in MCP are not defined. To determine this range, a series of simulations are performed using Monte Carlo Potts in both square 2D and cubic 3D geometries using the Moore neighborhood. These simulations consider cases in which strain energy is either the sole driving force for grain growth or coupled with grain boundary curvature. The 2D results show that the strain energy upper bound is approximately 3.5 non-dimensional units. The 3D simulations show that the relationship between grain boundary velocity and strain energy is dependent on grain boundary curvature. Grain boundary curvature can affect the upper bound of the range of strain energy and can impose a lower bound as well, below which grain growth is discontinuous or stagnate. Both 2D and 3D results are dependent on simulation temperature, with simulation temperature capable of altering the lower and upper bounds in 3D. Increasing simulation temperature in 3D decreases both the upper and lower linearity bounds. MCP simulations using simulation temperatures of zero are not suitable for modeling strain energy driving forces, as grain boundary velocity becomes discontinuous with strain energy.

Non-self-similar grain growth by zero-temperature Potts model

“…Among those methods the Monte Carlo Potts model is known for its comparative simplicity regarding its basic algorithm. At the same time, it can be tailored to complex problems allowing the simulation of the influence of texture on grain growth, of junction-controlled grain growth as it may appear in nanocrystalline materials or of grain growth in thin films [10][11][12][13][14][15][16][17][18][19].…”

“…The introduction of the so-called simulation temperature, about which more information is provided in section 2, cf also [13], was one of the main improvement aspects. The traditional zero-temperature Potts model approach is still in use today, despite the fact that this particular improvement enables much more realistic simulations of, for example, anisotropic or abnormal grain growth, texture-controlled grain growth, coarsening under the influence of second phase particles [14][15][16][17][18][19], as well as ideal grain growth [8] that does indeed follow self-similarity as theoretically predicted.…”