Ceramics are considered as promising materials for multiple functional applications, such as batteries, solar and fuel cells, and thermal engines. However, their inherent brittleness restricts the use of ceramics for industrial implementations. To overcome this limitation, we first introduce two mechanisms into toughening ceramics at different length scales. A brick-and-mortar structure, resulting in crack deflection, is used to design the microscale layout of ceramics. In addition, the tetragonal-to-monoclinic phase transformation of zirconia in the mortar, leading to volume expansion and shear deformation, is adopted to decrease the stress intensification in the vicinity of cracks at the nanoscale. We then propose a multiscale modeling approach to capture the structural performance and the influence of toughening mechanisms at the macro-/micro-/nano-scales. More specifically, we use computational homogenization to evaluate the fracture toughness of the representative volume elements at micro- and nano-scales. Finally, we adopt a gradient-free optimization algorithm to update the nano- and micro-structures to maximize fracture resistance while not compromising on strength.
 
As both the phase transformation and fracture occur at the nanoscale, we implement a multiphysics model to catch their interactions and effects on the overall mechanical behavior. The phase field method is adopted to represent the material states (tetragonal/monoclinic and intact/broken). It is demonstrated that the phase transformation results in more energy dissipation until the final fracture. The critical energy release rate is then evaluated from load-displacement curves. The corresponding value is set as the fracture toughness of the mortar in the microscale model, where a three-point bending test is used to investigate the effect of the brick-and-mortar structure. As in the nanoscale model, the resulting fracture toughness at the microscale is finally used in the macroscale model, consisting of a homogenized material. The numerical results are compared with experimental ones. To enhance the fracture performance at the macroscale, we apply the particle swarm optimization method to optimize both the grain size at the nanoscale and the geometry of the brick and mortar at the microscale.
 
We thus propose a computational design framework for toughened ceramics that includes multiscale modelling and optimization across three length scales. The brick-and-mortar structure and the tetragonal-to-monoclinic phase transformation of zirconia are employed at the microscale and nanoscale, respectively, and optimal material designs are identified. Such a computational platform enables the tailored development of “double-tough” ceramics.