Size effect model with competing mechanism for quasi-brittle materials under uniaxial compression

Although researchers have proposed various size effect models, it is still one of the most challenging problems in mechanics and materials science to establish a model that can capture different types of size effect trends. In this work, the size effect models of the maximum flaw and fracture process zone (FPZ) are defined and verified. Then, these models are incorporated into the fracture mechanics model to establish a new size effect model of uniaxial compressive strength (UCS) for quasi-brittle materials. The new size effect model reveals that the mechanism behind the size effect of UCS is attributed to the competition between the relative rate of change of FPZ and maximum flaw, the geometrical parameter with sample sizes. So, the new size effect model is called as size effect model with competing mechanism (CMSE model). Parametric analysis shows that six types of size effect trends can be reflected by the CMSE model. Moreover, this study also reveals that the fluctuation in size effect of type 5 is attributed to the competing mechanism, rather than the experimental errors believed by previous studies. To validate the performance of the CMSE model, the predictions of the CMSE model are compared with experimental and simulated results. The results indicate that the CMSE model can successfully predict six types of size effect trends, and determined parameters are located in the pre-specified range. It is noted that the minimum and mean determination coefficients R2 of the CMSE model are more than 0.91 and 0.97 for different quasi-brittle materials, respectively, which indicates high accuracy of the CMSE model. This study gives new insight into the contribution of the maximum flaw and FPZ to the size effect of UCS, and provide valuable guidance for predicting the strength of quasi-brittle materials with different size.