Equivalent Properties Prediction of the Composite Ceramics with an Arbitrary-Shaped Inclusion

Analysis of the effective properties in composite ceramics as mechanical properties analyzer can be a daunting task to handle. Here, we address two of its most prominent hurdles, namely, (i) solving the Eshelby tensor of an arbitrary-shaped inclusion (in this work, we separately consider the interaction tensor outside the inclusion and the Eshelby tensor inside the inclusion), while (ii) effective properties prediction of composite ceramics with arbitrary-shaped inclusion. To overcome the first issue, we derived analytical solution of the Eshelby tensor by Green’s function method for the Eshelby problem with an arbitrary-shaped inclusion and analyzed the influence of particle shape (particles with sharp angle and with edge angle) on the Eshelby tensor via numerical method. To approach the second issue, we adopted a recently popular IDD estimate, making changes to calculate the stiffness tensor of composites with inclusions. If the inclusions are randomly distributed in space, the equivalent stiffness of the composite materials is obtained via the direction probability density function and the Voigt method. Experiments on the related finite element analysis show the accuracy of numerical results with regard to the analytical solution of the Eshelby tensor and predict the effective properties of TiC-TiB₂ ceramics containing hexagonal prism particles.