On boundary misorientation distribution functions and how to incorporate them into three-dimensional models of microstructural evolution

The fundamental difficulties of incorporating experimentally obtained boundary misorientation distributions (BMDs) into three-dimensional microstructural models are discussed. An algorithm is described which overcomes these difficulties. The boundary misorientations are treated as a statistical ensemble which is evolved toward the desired BMD using a Monte Carlo method. The application of this algorithm to a number of complex arbitrary BMDs shows that the approach is effective for both conserved and non-conserved textures. The algorithm is successfully used to create the BMDs observed in deformation microstructures containing both incidental dislocation boundaries (IDBs) and geometrically necessary boundaries (GNBs). The application of an algorithm to grain boundary engineering is discussed.