Effect of Modulus Heterogeneity on the Equilibrium Shape and Stress Field of Precipitate in Ti-6Al-4V

For media with inclusions (e.g., precipitates, voids, reinforcements, and others), the difference in lattice parameter and the elastic modulus between the matrix and inclusions cause stress concentration at the interfaces. These stress fields depend on the inclusions' size, shape, and distribution and will respond instantly to the evolving microstructure. This study develops a phase-field model concerning modulus heterogeneity. The effect of modulus heterogeneity on the growth process and equilibrium state of the alpha plate in Ti-6Al-4V during precipitation is evaluated. The alpha precipitate exhibits strong anisotropy in shape upon cooling due to the interplay of the elastic strain and interfacial energy. The calculated orientation of the habit plane using the homogeneous modulus of alpha phase shows the smallest deviation from that of the habit plane observed in the experiment, compared to the case where the homogeneous modulus of beta phase is adopted. In addition, the equilibrium volume of alpha phase within the system using homogeneous beta modulus exhibits the largest dependency on the applied stresses. The stress fields across the alpha/beta interface are further calculated under the assumption of modulus heterogeneity and compared to those using homogeneous modulus of either alpha or beta phase. This study provides an essential theoretical basis for developing mechanics models concerning systems with heterogeneous structures.