Study On Size Effect Of Fracture Performance Of Concrete Beams Under Three-point Bending

In the research on the fracture performance of concrete for more than half a century,the size effect has always been the key issue.Only by solving the size effect of the fracture performance of concrete,can we accurately reflect the fracture performance of the actual structure through the experimental results of small-scale reduced-scale specimens.This paper first briefly introduces Weibull’s statistical size effect theory,Bazant’s size effect law,and Hu and Duan’s boundary effect models.In order to study the size effect of the fracture performance of concrete beams,three-point bending tests were carried out on five groups of 20 concrete beams with similar geometry and different sizes.The load-crack mouth opening displacement（P-CMOD）and load deflection（P-δ）curves of the whole loading process of the concrete beam are recorded by the data acquisition instrument,and some mechanical properties of the material are tested.The fracture energy of concrete is calculated by p-δcurve,and the existing method of calculating fracture energy by P-CMOD curve is simplified.The advantages and disadvantages of the two methods are compared,and the size effect of fracture energy is discussed.Based on the experimental results,the size effects of critical crack mouth opening displacement（CMOD_c）,critical deflection（δ_c）,nominal fracture strength（σ_N）and fracture toughness(K_IC)are analyzed.The results show that the ratio of CMOD_c,δ_c,σ_N to the height H（or span S）of the specimen decreases with the increase of specimen size,and all of them have obvious size effect.According to the simple rigid body displacement assumption at the time of concrete beam fracture,it is believed that the critical crack length a_c can be obtained by combining the span（S）of the specimen beam with CMOD_c andδ_c.The ratio of a_c to specimen span has no size effect,so it can be used as the criterion of crack development state under certain conditions.Based on experiments,the extended finite element method（XFEM）in Abaqus was used to numerically simulate the fracture behavior of concrete beams.The fracture process of nine concrete beams with the same geometry size and different crack-to-height ratio was simulated by using the material mechanical parameters measured in the laboratory.The simulation results were processed by Python script.According to the results of the simulation it is believed that the fracture process zone（FPZ）had three distinct stages of growth,necking and stabilization on the fracture ligament.Based on the change of the width of the fracture process zone,a trilinear distribution model of the local fracture energy along the fracture ligament was proposed.With the extreme value of the local fracture energy in the trilinear model,the change range of the critical fracture opening displacement（ω_c）in the tensile softening curve is explored.The similarities and differences between the trilinear model and the bilinear model of local fracture energy are compared.The results show that the bilinear model is a degradation of the trilinear model under specific conditions,and the trilinear model is closer to the real distribution of the local fracture along the ligament.Based on the simulation results,the size effects of CMOD_c,δ_c,a_c,critical crack tip opening displacement（CTOD_c）,and fracture toughness were discussed again,and compared with the experimental results.Finally,the main contents and results of the study on the size effect of concrete fracture performance are summarized,and suggestions for further research are put forward.