Elastic properties of polycrystalline microcomponents

The statistics of Young’s modulus of microspecimens subjected to a tensile load is examined experimentally, numerically and analytically. The material considered is Stabilor®G, a dental alloy, mainly consisting of gold. Tensile tests with microspecimens produced by vacuum pressure casting have been performed using a self-designed universal micro-testing machine. The numerical approach is based on the finite element method with the microstructure being described by a periodic Voronoi tessellation with randomly oriented grains. The analytical approach uses an explicit formulation of the singular approximation in terms of texture coefficients and is valid for arbitrary sample symmetries. It is found that the finite element approach and the analytical approach reproduce the experimental findings. Furthermore, it is shown that the mean value and the standard deviation of Young’s modulus of microspecimens made of cubic crystals subjected to tensile loads can be described by a unified scaling law. The results imply that the statistics of apparent properties of cubic crystal aggregates can be determined using anisotropic effective medium approximations.