Size effect on the FPZ length in notched beams: Mesoscopic method and theoretical analytical

Abstract

A microscopic finite element model of three-point bending (TPB) notched lightweight concrete beams is established in this paper. The behavior of discrete crack initiation and propagation in notched beams is simulated based on the cohesive and interface frictional coupling model. The correctness of the microscopic model is verified by the experimental data from related literature, and the length evolution of the fracture process zone (FPZ) during the loading process of the microscopic notched beams is performed. Meanwhile, the evolution laws of macroscopic and mesoscopic characteristic parameters such as the crack-height ratio, porosity, lightweight aggregate strength, and the lightweight aggregate volume fraction on the FPZ length of the mesoscopic notched beams are studied. In addition, the size effect of the FPZ of the mesoscopic notched beams is analyzed. The size effect law based on the critical distance line criterion is derived and the effect of high-order terms of the stress field is considered. The functional relationship between the nominal strength, FPZ length, and notched beam height is obtained to explain the size effect phenomenon. The results show that the FPZ length obtained by the mesoscopic method is in good agreement with the FPZ length obtained by the critical distance line criterion.