Study The Stress Intensity Factor Of HCCD Specimens Under Mixed Loading Conditions By Numerical Simulation

Concrete materials are more and more widely used in the field of modern civil engineering.However,there are a large number of primary cracks in concrete.Because of the expansion of cracks,structural members will be damaged when they do not reach the bearing capacity,which poses a huge threat to people’s life and safety.Therefore,the study of fracture toughness of brittle materials such as concrete has very important practical significanceIn this paper,the finite element method is used to simulate the composite fracture of the Hollow Center Cracked Disc（HCCD）specimen under static and dynamic loading conditions.Interaction integral method and displacement extrapolation method are used to calculate the stress intensity factors of standard thin plate examples respectively,compared with the stress intensity factors manual,the difference is less than 3%.The interaction integral method is used to calculate the stress intensity factors(K_Ⅰ and K_Ⅱ)of the crack tips of HCCD specimens.Based on the results of a large number of examples and dimensional analysis,the fitting formulas of K_Ⅰ and K_Ⅱ of the crack tips of HCCD specimens under combined loading conditions are obtained.This set of formulas include three parameters of specimen inner diameter r,crack length a,crack inclination angleθ,and has high precision.For K_Ⅰ fitting formula,when theθwas from 0°to 15°,the r/R was from 0.05 to 0.5,and a/（R-r）was in the 0.1 to 0.6 range,the calculation difference does not exceed 8%.when theθwas from 15°to 30°,the r/R was from 0.05 to 0.5,and a/（R-r）was in the 0.1 to 0.4 range,the calculation difference does not exceed 9%.For K_ⅡI fitting formula,when theθwas from 0°to 30°,the r/R was from 0.1 to 0.5,and a/（R-r）was in the 0.1 to 0.6 range,the calculation difference does not exceed 10%.In the dynamic simulation,the SHPB device is used to load the specimen,and the results of contact force curves at both ends of the specimen under different velocity pulses are compared,trapezoidal velocity pulses with a width of 600μs and a rise time of 200μs were selected as the dynamic loading conditions.When theθwas from 0°to15°,the r/R was from 0.1 to 0.5,and a/（R-r）was in the 0.1 to 0.6 range,the difference of K_Ⅰ value calculated by displacement extrapolation method and static stress intensity factor formula is not more than 6%.When theθwas from 15°to 20°,the r/R was from0.1 to 0.5,and a/（R-r）was in the 0.1 to 0.4 range,the difference of K_Ⅰ value calculated by the two methods is not more than 10%.When theθwas greater than 7°,r/R was 0.1to 0.5,and a/（R-r）was in the 0.1 to 0.6 range,the difference of K_Ⅱ value calculated by the two methods is not more than 10%.It is indicated that the stress intensity factor formula can be extended to dynamic experiments in this range.