Polycrystalline Materials Using the Johnson-Mehl Model
Z. Chu (zxc9@po.cwru.edu)
Robert. L. Mullen, Professor (rlm@po.cwru.edu)
and
Roberto Ballarini, Professor (rxb7@po.cwru.edu)
Department of Civil Engineering,
Case Western Reserve University
Cleveland, OH 44106-7201
In earlier work, the authors have investigated the statistical properties of elastic moduli and local stress intensity factors for two-dimensional microstructures based on random anisotropic grain orientation and a grain structure approximated as a Poisson-Voronoi tessellation (Ballarini et al. Int. J. of Fracture, 95, 1999 and Mullen et al. Acta Meterialia, 45, 1997). The Poisson-Voronoi tessellation assumes simultaneous nucleation (rapid site saturation) followed by uniform grain growth. Allowing continuous nucleation and growth can generate a more realistic grain structure (Johnson-Mehl grain structure), which was found to have significantly different distributions of grain areas compared to Poisson-Voronoi models.
In current work, polycrystalline material microstructure is simulated by Johnson-Mehl model. Finite element analysis is implemented on unit volumes of Johnson-Mehl grain structures, which are aggregates of anisotropic grains orientated by a uniform-random distribution. Monte Carlo techniques are utilized in obtaining the statistical properties of elastic moduli of the ensemble from finite element solutions. Polysilicon is studied specifically highlighting the effect of material texture and different calculation assumptions. The statistical properties of the nominal Young’s modulus and Poisson’s ratio are expressed as functions of average number of grains within a unit volume and the level of crystal anisotropy. Differences in the corresponding computational results between Poisson-Voronoi and Johnson-Mehl models are discussed.