Mathematical law of size effect on the flexural property of ceramics

Brittle materials generally exhibit size effects, and the mechanical properties of these materials degrade significantly with an increase in size. However, the mathematical law governing the attenuation degree of mechanical properties with the increase in size is still unknown. In this study, maximum loads of differently sized ceramic test strips were subjected to three point bending tests under two working conditions of equal spans and span amplifications, respectively. Subsequently, the theoretical maximum loads of materials were calculated using the finite element method (FEM). By calculating the difference between the calculated values and the actual maximum loads, the attenuation of mechanical properties of ceramic samples were observed. The results show that the theoretical mechanical properties and the performance attenuation caused by the size effect tend to increase according to the following equation: y=ax³+bx²+cx+d. Therefore, mechanical properties and performance attenuation of any sample exhibiting a size within the experimental range can be predicted by a mathematical law, which was obtained through mechanical tests results of four samples with different sizes. The obtained mathematical law holds great significance for predicting the mechanical properties of materials under size effects.