Discrete element modelling of the size-dependent mechanical behavior of Al2O3 ceramic under quasi-static uniaxial compression

The size-dependent mechanical behavior of Al2O3 ceramic under quasit-static uniaxial compression was simulated via two-dimensional discrete element method. The numerical sample of Al2O3 ceramic was established by adopting the linear parallel bond contact model, and the inherent defects was further generated by randomly removing a subset of elementary discs. The uniaxial compressive strength of Al2O3 ceramic samples with different sizes follows the Weibull distribution. With an increase in sample size, the magnitude of the uniaxial compressive strength decreases, while its variability increases. Additionally, with sample size increases, both the Young's modulus and Poisson's ratio decrease. Meanwhile, the variability in Young's modulus and Poisson's ratio is more pronounced in larger samples than in smaller ones. The progressive fracture process of Al2O3 ceramic sample can be categorized into four typical stages, namely linear-elastic stage, crack initiation stage, crack propagation stage and complete failure stage. The final fragment size distributions of Al2O3 ceramic samples of different sizes can be accurately described by the fractal model. Notably, smaller samples tend to exhibit a greater breakage extent compared to larger samples. Finally, a size-dependent statistical equation of uniaxial compressive strength of Al2O3 ceramic is proposed based on the numerical results and the inverse function of the Weibull distribution, which can provide a theoretical basis for the design and production of ceramic materials.