Size effect model of nominal tensile strength with competing mechanisms between maximum defect and fracture process zone (CDF model) for quasi-brittle materials

Abstract

Developing a physics-based model to describe the different types of size effects is one of the most challenging problems in materials science. In this work, the variations of the maximum defect and fracture process zone (FPZ) with respect to the specimen size are comprehensively analyzed, and then the size effect models of the maximum defect and FPZ are developed and demonstrated by collected data. On this basis, a new size effect model of nominal tensile strength (NTS) is developed by considering competing mechanisms between maximum defect and FPZ, referred to as the CDF model. The effect of the parameters on the CDF model is investigated to gain a deep understanding. The size effect curves of NTS are constructed by the CDF model to evaluate its performance on the prediction of the different types of size effects. The results indicate that the CDF model can successfully predict different types of size effects, and determined parameters are located in the pre-specified range. Furtherly, the CDF model is compared with the boundary effect model (BEM). It is found that the CDF model gives a better prediction than the BEM. Nevertheless, the BEM is closer to the experimental data than the CDF model for the Type 1 size effect of notched specimens, and can capture the basic features of Type 2 and 3 size effects. Moreover, the determination coefficients R2 are also determined to quantitatively assess the prediction accuracy of the CDF model and BEM. It is noted that there are six maximum R2 for the CDF model and only one maximum R2 for BEM. This means that the forecast accuracy of the CDF model is higher than that of the BEM. This study gives new insight into the contribution of the maximum defect and FPZ to the size effect of NTS.