基于扩展有限元的混凝土三点弯曲梁断裂性能数值模拟研究

基于扩展有限元法,模拟了不同宽度混凝土三点弯曲梁的断裂破坏过程,得到了荷载-裂缝口位移曲线;对不同宽度、缝高比、跨高比的三点弯曲梁断裂过程进行模拟并利用双K断裂准则得出了不同宽度、缝高比、跨高比等条件下的应力强度因子,研究了这三种参数的变化对应力强度因子的影响。研究结果表明:当跨高比、缝高比等于0.4,梁宽在100~250 mm范围内变化时,其起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un基本保持不变;当梁宽不变,跨高比等于4,缝高比从0.2增大到0.5时,起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un呈现先增大后减小的趋势;当梁宽不变,缝高比等于0.4,跨高比从2.5增大到3.5时,起裂断裂韧度K_Icⁱⁿⁱ保持不变,失稳断裂韧度K_Ic^un将逐渐增大但幅度很小;当跨高比不变,缝高比等于0.4,梁宽在100~250 mm的范围内变化时,起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un均呈现先增大后减小的趋势,表明小跨高比的K_Icⁱⁿⁱ、K_Ic^un在梁宽度方向存在一定的尺寸效应。

Numerical Simulation of Fracture Performance of Concrete Three-Point Bending Beam Based on Extended Finite Element Method

Based on the extended finite element method (XFEM), the fracture failure process of concrete three-point bending beams with different widths was simulated, and the load-crack mouth displacement curve (P-CMOD) was obtained. The fracture process of three-point bending beam with different width, crack height ratio and span height ratio was simulated, and the stress intensity factor under different width, crack height ratio and span ratio was obtained by using the double K fracture criterion. The influence of these three parameters on the stress intensity factor was studied. The results show that the initiation fracture toughness K_Icⁱⁿⁱ and unstable fracture toughness K_Ic^un of three-point bending beam with span-depth ratio and crack-depth ratio equal to 0.4 basically remain unchanged when the beam width changes from 100 mm to 250 mm. When the beam width was constant, the span-depth ratio was 4 and the crack-depth ratio increases from 0.2 to 0.5, the initiation fracture toughness K_Icⁱⁿⁱ and the unstable fracture toughness K_Ic^un increase first and then decrease. When the beam width was constant, the crack height ratio was equal to 0.4, and the span height ratio increases from 2.5 to 3.5, the initial fracture toughness K_Icⁱⁿⁱ remains unchanged, and the unstable fracture toughness K_Ic^un will gradually increase but the amplitude was small. When the span-to-height ratio was constant, the crack-to-height ratio was equal to 0.4, and the beam width changes in the range of 100~250 mm, the initial fracture toughness K_Icⁱⁿⁱ and the unstable fracture toughness K_Ic^un all increase first and then decrease, indicating that K_Icⁱⁿⁱ and K_Ic^un with small span-to-height ratio have a certain size effect in the beam width direction.