Homogenisation of micromechanical modelling results for the evaluation of macroscopic material properties of brittle ceramics. (15th April 2022) - Falco, S.; Fogell, N.; Kasinos, S.; Iannucci, L.
Abstract: This paper presents an approach to evaluate the macroscopic properties of ceramic materials based on the homogenisation of the results of micromechanical simulations performed on Representative Volume Elements (RVEs) of polycrystalline microstructures. The RVEs are defined using a bespoke algorithm to generate numerical model geometries statistically representative of the microstructure of polycrystalline ceramics. The material properties of single crystals and grain boundaries, obtained from direct experimental measurements at the relevant scales, are used for the generation of RVEs, which are then subjected to unit load cases. The results of the numerical simulations, performed using the explicit Finite Element Method (FEM), are used to calculate the macroscopic material parameters governing elastic deformation, and brittle failure due to initiation and propagation of cracks at the grain scale. The automated approach adopted to generate and analyse the response of RVEs under a specified set of loading conditions permits a statistically relevant number of simulations to be performed on different combinations of microstructural morphologies, distributions of crystallographic orientations, and defects, thus demonstrating a homogenisation and upscaling methodology that captures several important aspects of the stochastic variability typically exhibited by ceramic materials. The numerical simulations of elastic deformation and brittle failure of polycrystalline alumina ( A l 2 O 3 ) are compared against both experimental measurements and analytical calculations, showing good agreement for both elastic deformation - expressed in terms of homogenised elastic moduli - and failure strength - observed both as changes in the crack pattern at the microscale and when measured as the value of the stress at the onset of failure. Graphical abstract: Highlights: The use of structured meshes provides robust models for large parametric studies. A novel cohesive formulation is implemented to model interfaces in a raster model. Micromechanical models capture the stochastic variability of mechanical properties. The models show the importance of defects on failure strength mean value and variance.