Numerical Simulation on Size Effect of Fracture Toughness of Concrete Based on Mesomechanics

Abstract

The fracture performance of concrete is size-dependent within a certain size range. A four-phase composite material numerical model of mesofracture considering a mortar matrix, coarse aggregates, an interfacial transition zone (ITZ) at the meso level and the initial defects of concrete was established. The initial defects were assumed to be distributed randomly in the ITZ of concrete. The numerical model of concrete mesofracture was established to simulate the fracture process of wedge splitting (WS) concrete specimens with widths of 200-2000 mm and three-point bending (3-p-b) concrete specimens with heights of 200-800 mm. The fracture process of concrete was simulated, and the peak load (P max ) of concrete was predicted using the numerical model. Based on the simulating results, the influence of specimen size of WS and 3-p-b tests on the fracture parameters was analyzed. It was demonstrated that when the specimen size was large enough, the fracture toughness (K IC ) value obtained by the linear elastic fracture mechanics formula was independent of the specimen size. Meanwhile, the improved boundary effect model (BEM) was employed to study the tensile strength (f t ) and fracture toughness of concrete using the mesofracture numerical model. A discrete value of β = 1.0-1.4 was a sufficient approximation to determine the f t and K IC values of concrete.Materials 2020, 13, 1370 2 of 16 considered that when the height of the specimen reaches 800 mm, the measured fracture toughness K IC value no longer has size effects [4]. The similar conclusion drawn by Bazant [5] is that the mechanical parameters measured for specimens in a certain size range had size effects. That is to say, when the size of the specimens was small enough or large enough, the mechanical properties and fracture parameters remained unchanged. In view of this experimental phenomenon, Weibull [8,9] considered that the size dependence was due to the increase in the probability of encountering low-strength material elements with increasing structure sizes. Based on the law of extreme strength distribution, a size effect statistical theory was proposed. However, this theory was limited to structures that fail at the beginning of macro-cracks and small structures that only cause negligible stress redistribution in the fracture process zone when they fail. Subsequently, based on the energy theory, Bazant et al. [5] proposed a size effect theory of fracture mechanics for geometrically similar specimens with a size range of approximately 1:20 notches. Based on the concept of fractals, Carpinteri et al.[6] established a multi-fractal size effect law that reflected the unstable cracking of structures when the size range was approximately 1:10. Hu [7] concluded that the initial crack and ligament depth should be far from the specimen boundary to reflect the true mechanical parameters of a material, independent of size. Based on this, the boundary effect theory was established. In addition to this basic theory, indirect size effects such as the boundary layer ...

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