Strain energy limitations in Monte Carlo Potts modeling of grain growth

• Linearity between grain boundary velocity and strain energy within Monte Carlo Potts is examined.
• Linearity occurs over a limited ranged depending on the lattice used.
• Simulation temperature will influence linearity slope and range limits.
• For square 2D lattices, an upper limit for linearity is approximately 3.5 n.d.
• For cubic 3D lattices, linearity is dependent on included grain boundary curvature.

Previous 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.

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