Toughening mechanism and meso-scale fracture simulation of concrete with different aggregate volume fractions
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摘要: 研究了不同骨料体积分数下的混凝土增韧机制,建立了II型断裂韧度KIIC的细观力学模型。对含有4种骨料体积分数(19vol%、25vol%、31vol%、37vol%)的混凝土试件,分别进行了楔入劈拉试验和无切口试件的II型断裂试验,并利用内聚力模型及点阵法对相关II型断裂试验开展了细观模拟。结果表明:随着骨料体积分数的增加,混凝土I型断裂韧度KIC和II型断裂韧度KIIC均明显提高,KIIC/KIC逐渐增大且与骨料体积分数之间存在对数函数关系;骨料的圈闭-桥联对混凝土增韧起着主导作用,其增韧效应远大于裂纹路径偏转或裂尖屏蔽引起的;给出了II型断裂韧度KIIC和骨料体积分数Va之间的细观力学关系,其预测值和试验值的符合性较好;混凝土II型断裂细观模拟的力学响应、断裂形态和试验结果表现出良好的一致性;内聚力单元的标量刚度退化(Scalar stiffness degradation,SDEG)值的变化,可用来表征混凝土在细观水平上的损伤演化,且对宏观断裂响应的预测有着重要作用。Abstract: The toughening mechanism of concrete with different aggregate volume fractions was investigated, and the meso-mechanical model of mode II fracture toughness KIIC was developed. The wedge splitting tests and mode II fracture tests for non-notched specimens were carried out simultaneously for concrete specimens which were prepared with aggregates in different volume fractions of 19vol%, 25vol%, 31vol% and 37vol%. The meso-scale simulations of corresponding mode II fracture tests were also performed by the cohesive zone model combined with the dot matrix method. The results show that as the aggregate volume fraction increases, the mode I fracture toughness KIC, mode II fracture toughness KIIC and the values of KIIC/KIC increase significantly. It was further found that the relationship between the values of KIIC/KIC and aggregate volume fraction can be described by a logarithmic function. The trapping-bridging of aggregate plays a leading role in the toughening of concrete, and its toughening effect is much greater than that caused by crack deflection or crack shielding. The meso-mechanical relation between KIIC and aggregate volume fraction was developed, and its prediction agrees well with the experimental data. The mechanical response and fracture morphology from meso-scale simulation of mode II fracture of concrete are in good agreement with those of experimental tests. Furthermore, the scalar stiffness degradation (SDEG) development of the cohesive element can be utilized to characterize the damage evolution of concrete at meso-level, which is valuable to the prediction of macro performance.
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图 2 楔入劈拉试验(WST)试件、无切口试件的几何形状
Figure 2. Geometries of wedge splitting tests (WST) specimen and non-notched specimen
D1—Depth of WST specimen; D—Effective depth of WST specimen; B—Thickness of WST specimen; a0—Length of precast crack; σ—External loads on non-notched specimen; a—Half length of ligament on non-notched specimen; h—Half depth of non-notched specimen; w—Half thickness of non-notched specimen
图 17 试验和模拟的混凝土试件荷载-位移曲线
Figure 17. Load-displacement curves of the concrete specimens from experimental and numerical results
a1-a3, b1-b3, c1-c3, d1-d3—The characteristic loads corresponding to the crack initiation, crack propagation and crack basically penetrating ligament on the specimen with aggregate volume fraction of 19vol%, 25vol%, 31vol%, 37vol%, respectively
表 1 混凝土配合比
Table 1. Compositions of concretes
kg/m3 Va/vol% Cement Sand Coarse aggregate Limestone powder Water Superplasticizer 19 490 1167 500 96 179.3 5 25 490 1000 667 96 179.3 5.5 31 490 834 833 96 179.3 6.1 37 490 667 1000 96 179.3 7.4 Note:Va—Aggregate volume fraction. 表 2 试验测得的混凝土断裂参数
Table 2. Fracture parameters of concrete by the experimental tests
Va/vol% fc/MPa ft/MPa E/GPa Pv,max/kN PIIC/kN KIC/(MPa·m1/2) KIIC/(MPa·m1/2) KIIC/KIC 19 44.79 3.80 33.23 8.53 279.35 1.03 2.21 2.15 25 51.96 3.59 32.3 9.49 368.21 1.09 2.91 2.67 31 50.08 4.41 34.01 11.35 401.22 1.17 3.17 2.72 37 58.36 4.85 35.26 13.05 431.56 1.20 3.41 2.84 Notes: fc—Compressive strength; ft—Tensile strength; E—Modulus of elasticity; Pv,max—Peak vertical load of WST specimens; PIIC—Critical fracture load of non-notched specimens; KIC—Mode I fracture toughness; KIIC—Mode II fracture toughness. 表 3 混凝土I型断裂韧度KIC的细观力学模型预测值
Table 3. Predicted value of mode I fracture toughness of concrete KIC by the meso-mechanical model
Va/vol% Km IC/(MPa·m1/2) Kdef IC/Km IC Kdic IC/Km IC Kbri IC/Km IC KIC/(MPa·m1/2) Model Experiment 19 0.559 1.080 1.062 1.553 0.996 1.03 25 0.559 1.103 1.083 1.623 1.086 1.09 31 0.559 1.127 1.107 1.684 1.176 1.17 37 0.559 1.150 1.132 1.739 1.267 1.20 Notes: Km IC—Mode I fracture toughness of matrix; Kdef IC—Effective toughness due to crack deflection; Kdic IC—Effective toughness due to crack shielding; Kbri IC—Effective toughness due to trapping-bridging. 表 4 混凝土模拟所需的计算参数
Table 4. Parameters used in the simulations of concrete
Solid elements Constant Coarse aggregate Mortar E/GPa 70 27.5 ν 0.2 0.2 Cohesive elements ITZ Interface elements
within mortarEn/(N·mm−3) 4000 5000 Es/(N·mm−3) 4800 6000 Tnmax/MPa 1 2 Tsmax/MPa 2 4 GIC/(N·mm−1) 0.05 0.1 GIIC/(N·mm−1) 0.5 1 Notes: ν—Poisson's ratio; En and Es—Normal and tangential stiffness, respectively; Tnmax and Tsmax—Normal and shear strength, respectively; GIC and GIIC—Fracture energies from mode I to mode II, respectively. -
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