Design of strain tolerant porous microstructures – A case for controlled imperfection

Porous materials, especially ceramics, are used in an ever-expanding range of functional applications. In most cases there are minimum mechanical requirements which limit the porosity level and thus the functional performance provided by the pore surface or volume. In order to design porous materials with the best compromise between functional and mechanical performance, a sound understanding of microstructure-mechanical properties relationships is required. In the current work, discrete simulations are used to assessed the Young's modulus and fracture toughness of various realistic porous microstructures obtained via partial sintering of powders. Scaling laws relating these quantities to microstructural parameters are derived and it is demonstrated that the proportionality between Young's modulus and fracture toughness, often claimed for partially sintered materials, is actually an approximation of a more general relationship. The proposed scaling laws suggest new strategies to build microstructurally tougher and strain tolerant porous materials. It is shown that strain tolerant microstructures can be designed by introducing controlled heterogeneity and hierarchy. Finally, the proposed scaling relationship between Young's modulus and fracture toughness is simplified to give it a practical use and verified for a wide range of porous microstructures, including hierarchical ones.