Determination of the Macroscopic Elastic Constants of a Phase Embedded in a Multiphase Polycrystal-Application to the β-Phase of a Ti-17 Titanium Based Alloy

A one-site elastic self-consistent model following the mathematical formalism introduced by Kroner and Eshelby (KE) has been developed in order to solve the case of multiphase materials. This model has been applied to duplex steels and aluminium - silicium carbide Metal Matrix Composites (MMC) in the aim to study the evolution of their stiffness at pseudomacroscopic scale. Simulations justify the usually implicit hypothesis of the identity of the elastic moduli of a given phase, at macroscopic and pseudomacroscopic scales. The implementation of KE model by this hypothesis yields a new implicit formulation for the stiffness of a given unknown phase embedded in a two-phase material. This original characterization method will be applied to the beta -phase of Ti-17 alloy. The singular behaviour in terms of residual pseudomacrostress of each phase after uniaxial loadings will be deduced from these data.