Monte Carlo Simulation of Three-Dimensional Nonisothermal Grain-Microstructure Evolution: Application to LENS Rapid Fabrication

Abstract

A stochastic three-dimensional (3-D) model for grain-microstructure evolution during transient nonisothermal annealing of metallic materials is developed, validated, and applied to the LENS (Laser-Engineered Net Shaping) advanced rapid fabrication process. The model is based on the assumption that the main driving force for microstructure evolution is the reduction in energy contribution arising from the grain boundaries. A temperature-dependent grain-boundary mobility factor is introduced into the expression for the transition probability in order to account for nonisothermal effects, such as those induced by the rastering laser during LENS-based manufacturing. The grain-boundary mobility factor and its temperature dependence are determined using the available experimental isothermal-annealing data. The simulation of grain growth (under nonisothermal annealing conditions encountered in the LENS process) is carried out by coupling a Monte Carlo method for microstructure evolution with a finite difference-based solution to the three-dimensional (3-D) transient energy equation. In response to the computational challenges of the simulations, a highly efficient interprocessor communications methodology is developed, which greatly reduces the simulation time on parallel computers. The results obtained show that under isothermal annealing conditions, the kinetics of grain growth is governed by a temporal power-law behavior and that, after an initial transition period, the grain-size distribution (normalized with respect to the average grain size) becomes time invariant. Furthermore, the application of the model to the LENS process is found to enable establishment of the relationships between process parameters (the laser power, beam rastering velocity, etc.) and the microstructure (grain size distribution, depth of the heat-affected region, etc.) of the deposited material.