Multiscale effects in crystal grain growth and physical properties of metals

A multiscale approach for the simulation of physical properties of metals is suggested and discussed. Grain growth in metals involves interactions at three distinct scale levels: the atomic scale (length of crystal lattice spacing), microscale (grain length) and macroscale. A simulation scheme should include these three levels. The crystalline microstructure is simulated by the Monte Carlo method. The average grain radius is then used to determine the yield strength from the Hall-Petch relationship for large grains and the inverse Hall-Petch relationship for submicron-sized grains. The yield strength is then supplied to a continuum macroscale model. The normal grain growth, which has a theoretical solution for grain size as a function of time, is discussed in detail as a case study and conclusions are drawn with regard to more complex situations such as dynamic recrystallization.