Calculation of whisker Poisson’s ratio and hardnessprediction of whisker-reinforced ceramic composites

Whisker is able to enhance remarkably the hardness of ceramics while strengthening their strength and toughness, and has outstanding advantages in solving the lack of hardness. Aiming at the problems of high blindness of component design and time-consuming of specimen preparation in the current experimental method to investigate whisker-reinforced ceramics, a bidirectional stochastic modeling method to calculate the whisker Poisson’s ratio was proposed taking β-Si₃N_4w-reinforced Si₃N₄ ceramic as the object. Based on the plane super-soft pseudopotential method under the framework of density functional theory (DFT) and Perdew-Wang 91 (PW-91) function in the generalized gradient approximation (GGA), the β-Si₃N₄ supercell Poisson’s ratio was calculated. Further, an approach to establish the two-dimensional microstructure of β-Si₃N_4w-reinforced Si₃N₄ ceramics was presented by using Delaunay triangulation rule and pseudo-random function method. Then, the model hardness was predicted and the hardening mechanism of β-Si₃N_4w was discussed. Results show that the Poisson’s ratio of β-Si₃N_4w is about 0.27. The predicted hardness values of β-Si₃N_4w-reinforced Si₃N₄ ceramics are in good consistent with the related experimental test values, which demonstrates the validity of whisker Poisson’s ratio calculation model and whisker-reinforced ceramic microstructure modeling method. The hardness of Si₃N₄-based ceramics reaches the maximum value of 22.80 GPa at 3wt% β-Si₃N_4w content. Stress analysis shows that the anisotropic distribution of β-Si₃N_4w disperses the stress concentration area and with stands a large amount of stress depending on its high strength characteristics, which is the main reason for the increase in hardness.