Papers by Keyword: Phase Mixture Model

Abstract: In nanocrystalline materials the grain boundaries must be considered as regions of finite thickness with properties different from the crystalline bulk material present in the crystallite cores. Thus, dense (i.e. pore-free) single-phase nanocrystalline materials can be considered as quasi-twophase systems whose effective properties can be calculated when quantitative thickness information is available and the property value of the grain boundary phase can be reliably estimated. Similarly, dense two-phase nanocomposites may be considered as quasi-three-phase systems and their effective properties can be predicted using an analogous phase mixture modeling approach. In this contribution this is done for the thermal conductivity of alumina-zirconia nanocomposites. A twostage homogenization procedure is applied, consisting of a first step in which the alumina-zirconia composite is treated as a symmetric-cell material, and a second step in which the highly disordered grain boundary phase is treated as a matrix-phase, coating the crystallite cores. The individual averaging steps are discussed with respect to the two- and three-point bounds, and the resulting grain size dependence is compared with that of pure alumina and zirconia, and literature data.

Abstract: In this study, a deformation mechanism map of metallic nanocrystalline materials (NCMs) using the phase mixture model is proposed. It is based on recent modelling that appears to provide a conclusive description of the phenomenology and the mechanisms underlying the mechanical properties of NCMs. The proposed models adopted the concept of a ‘phase mixture’ in which the grain interior and the grain boundaries are treated as separate phases. The volume fraction of this grain boundary ‘phase’ may be quite appreciable in a NCM. Based on the theoretical model that provides an adequate description of the grain size dependence of plasticity covering all grain size range from coarse down to the nanoscale, the tensile deformation response of NCMs, especially focusing on the deformation mechanisms was investigated. The deformation mechanism map is newly proposed with axes of strain rate, grain size and temperature.

Abstract: A phase mixture model (PMM) was considered in which materials are treated as a mixture of grain interior phase, grain boundary phase and pores (if the material is porous) for the elasticity and plasticity of nanostructured materials (NSMs). In order to investigate the effects of grain size and porosity on the elastic modulus, a self-consistent method in conjunction with PMM was employed. The calculated results are compared with the experimental measurements in the literature. The elastic modulus of NSMs decreases with a decrease of the grain size and the decrement is relatively large at grain sizes below about 10 nm. The effect of porosity, however, is substantially greater than the grain size effect. For the plasticity of NSMs, grain size effects were introduced both via the dislocation glide mechanism and through the diffusion mechanisms providing mass transfer via grain boundaries. A good agreement between the calculated deformation behavior and experiment was found. The quality of the above predictions with regard to strength, strain hardening, strain sensitivity and ductility behavior testify the adequacy of the model. It is concluded that the model can be used as a convenient tool for simulating the deformation behavior of NSMs.