Size effect on the punch performance of brittle porous ceramics : theoretical analysis and numerical simulation

This work provides a multi-scale investigation on the punch performance of brittle porous ceramics with a flat, square-ended die. The micro discrete representation of porous ceramics is built by imitating the natural formation process. The macro effective model is established based on continuum mechanics. The effects of thickness and relative density of the porous ceramic layer on the indentation depth and the stress field are predicted. Results from the micro and macro models are in good agreement. The stress singularity at the punch tips is characterized by the stress intensity factor (SIF). The values of SIF increase with the rising thickness and finally level at a constant. A punch toughness concept is proposed by combining the developed micro discrete representation and the macro continuum model to evaluate the indentation resistance of the porous ceramics. The punch toughness varying with the relative density of porous ceramics is provided. Besides, size effect investigation proves that the brittle porous ceramics with larger cell size generally possess a greater punch toughness. The responsible physical mechanisms are revealed by the deformation analysis of individual cells. Meanwhile, when the ratio of specimen length to punch width is less than 3.0, the edge effect in indentation tests cannot be neglected and the punch toughness of the specimen will be underestimated.