Improved size effect law (SEL) considering size-dependent fracture process zone (FPZ) for quasi-brittle materials

Establishing a mechanistic model to simultaneously capture the descending size effect (DSE) and the change from DSE to the ascending size effect (ASE) remains a challenging issue for quasibrittle materials. A size-dependent fracture process zone (FPZ) model is proposed and verified by experimental and simulative results. Subsequently, the size effect law (SEL) of unnotched specimens is improved by considering the size-dependent FPZ model, which is termed the improved SEL in this paper. Parametric studies are conducted for a better understanding of the improved SEL. It is found that the underlying mechanism of the DSE and the change from DSE to ASE is the competition between the relative rates of FPZ and specimen size change with respect to specimen size. The ASE is obtained when the relative rate of FPZ change is higher than that of specimen size. Conversely, the DSE is observed. No size effect exists when the relative rate of FPZ change is equal to that of specimen size. Experimental and simulative results are adopted to validate the improved SEL of unnotched specimens. The validation of the improved SEL indicates that the improved SEL not only accurately predicts the DSE, but also correctly captures the change from DSE to ASE. In addition, the size effect of nominal strength with different maximum aggregate size is well captured by the improved SEL. The fitting parameters of the improved SEL lie in the given interval. By comparing the determination coefficients R2 of the SEL, unified size effect law (USEL), and improved SEL, it is found that the R2 of the improved SEL is higher than that of the SEL for the DSE and is close to that of the IUSEL for the change from DSE to ASE. Therefore, it is recommended that engineers and researchers use the improved SEL to describe the DSE and the change from DSE to ASE of unnotched specimens.