硅酸盐学报

钢纤维取向对超高性能混凝土(UHPC)力学性能有显著影响，传统实验方法较难直接控制纤维取向和分布，且缺乏可同时反映UHPC裂缝演化与纤维作用等复杂机理的三维细观模型，造成了定量分析和模拟验证纤维取向影响的困难。为此，首先开展了UHPC直接拉伸实验，采用外置磁场实现纤维定向并利用图像分析获得纤维倾角分布密度，通过数字图像相关技术(DIC)研究了纤维取向对断裂过程、应力–应变曲线的影响。其次建立了可显式考虑纤维取向和分布、不同倾角的纤维拉拔力本构以及基体离散粘性断裂的三维UHPC细观数值模型，并通过开展的直拉实验获得验证。结果表明：建立的细观模型能有效描述UHPC材料复杂的三维断裂过程；UHPC的应变硬化特性、裂缝发展与最终形态、纤维桥连作用等均受到纤维分布和取向等细观因素的影响。

Extended Abstract Introduction The orientation of steel fibres has an impact on the mechanical properties of ultra-high performance concrete(UHPC). It is difficult for the conventional experimental methods to maintain the same fibre orientation and distribution characteristics even under identical conditions, and there is a lack of mesoscale model that can simultaneously capture the complex mechanisms of crack evolution and fibre-mortar interaction in UHPC. This impedes the quantitative analysis and simulation validation. This paper thus conducted direct tensile tests of UHPC in an external magnetic field to achieve a certain fibre orientation, and the distribution density of fibre inclination angles was obtained via image analysis. The influence of fibre orientation on the fracture processes and stress-strain curves was investigated by a digital image correlation(DIC) technique. Also, a 3D microscale numerical model of UHPC was established to explicitly consider fibre orientation and distribution, single fibre pullout force-slip relations based on inclination angles, and discrete cohesive cracking of mortar. The model was validated by the experiments, the complex 3D fracture process of UHPC was quantified, and the influences of mesoscale factors(i.e., fibre distribution and orientation) on the strain hardening characteristics, crack evolution and final morphology, and fibre bridging effects were investigated. Methods In the experiments, steel fibre orientation was controlled through an external magnetic field, which was created by direct current in a coil loop. The dog-bone specimens were vibrated in the magnetic field during the sample preparation. As a result, the fibres were subjected to the electromagnetic force and underwent a directional distribution, i.e., along the magnetic field direction. Three fibre orientations were a) parallel to the tensile direction, b) perpendicular to the tensile direction, and c) no magnetic field applied. This resulted in three groups of specimens termed aligned-UHPC(AUHPC), perpendicular-UHPC(PUHPC), and UHPC, respectively. A tensile testing device for dog-bone specimens was used to investigate the fibre orientation-dependent mechanical properties of UHPC for subsequent validation of simulations. The loading process was recorded by a high-speed camera, providing data for the fracture process analysis based on the DIC technique. In addition, the cut-off sections were analyzed on specimens AUHPC, UHPC, and PUHPC to obtain the orientation distribution characteristics of fibres for later simulations. In the mesoscale simulation, cohesive elements were pre-inserted in the mortar to simulate the energy dissipation in the fracture process zone and the opening/closing of discrete cracks. Different fibre orientation distributions in specimens AUHPC, UHPC, and PUHPC were generated by a random algorithm. The fibre-mortar interaction was equivalently simulated through fibre constitutive laws, which were curve-fitted from the pullout force-slip relations extracted from single fibre pullout tests for various inclination angles. The mesoscale model was validated via single fibre pullout tests and direct tensile tests. In addition, the mesoscale influencing factors on the complex multiple cracking and fibre bridging mechanisms were also quantified. Results and discussion The experimental results reveal that the specimen AUHPC exhibits the most pronounced strain-hardening behavior and maximum peak stress, which are 2.3 times and 1.4 times greater than those of specimens PUHPC and UHPC, respectively. The first cracking stress of specimen AUHPC is also the maximum, while there is no obvious change in the elastic modulus. The increase in peak stress can be explained by the fracture process using DIC: when fibres are more aligned with the tensile direction, there are more microcracks in the specimen. This is because when the fibre orientation follows the tensile direction, the fibre bridging effect is the more intense, thus having the maximum crack resistance. When the fibre orientation is perpendicular to the tensile direction, the fibre bridging effect is the minium. The final crack patterns of specimens AUHPC and UHPC are complex and tortuous, while the crack paths in specimen PUHPC are smoother and mostly perpendicular to the tensile direction. The distinct crack patterns also indicate the differences in the stress-strain curves. Moreover, from the cur-off sections of specimen AUHPC determined by optical microscopy, the fibres after the test have obvious pullout scratching on the fibre surfaces with spalled mortar clinging to them. In addition, there is no obvious necking at the fibre ends, indicating that the fibre failure is pullout rather than yield fracture. The mesoscale mechanisms(i.e., interfacial failure, mortar detachment, and fibre pullout) indicate a much energy dissipation, which improves the material ductility. The mesoscale simulations predict the fracture patterns and stress-strain curves, which are in reasonable agreement with the experimental results. Based on the analysis of fibre stress evolution, this work can quantify the process of microcrack initiation, multiple cracking, strain hardening, localized major cracks or macrocracks, and gradual closure of other microcracks with increasing the displacement. The stresses of fibres far away from the localization zones decrease, while the stresses of fibres crossing the major cracks continue to increase(i.e., 2 000 MPa) due to fibre bridging. Afterwards, the specimen gradually enters the softening stage until complete failure. The specimen AUHPC exhibits three macrocracks, while specimens UHPC and PUHPC have only one macrocrack each. Besides, the quantities of microcracks in specimen AUHPC are much larger than those in specimen PUHPC, and the fibre average stress level in specimen AUHPC is much higher. This is because when the fibre is aligned with the tensile direction, more stresses can be transferred into the mortar, causing re-cracking, which is a repeated process, leading to multiple cracking in specimen AUHPC. As a result, the stresses of bridging fibres consistently increase. On the contrary, the efficiency of stress transfer for the fibres perpendicular to the tensile direction is the lowest, with the minimum fibre average stress of 94 MPa in specimen PUHPC, while AUHPC and UHPC have 328 MPa and 188 MPa, respectively. It is evident that the fibre orientation has an impact on the fibre utilization level. The simulated stress-strain curves demonstrate that specimen AUHPC has the most pronounced strain hardening and the maximum ductility, while specimen PUHPC is relatively brittle and shows no strain-hardening characteristics. This indicates that aligning the fibres with the tensile direction is an effective way to enhance the strength and ductility of specimen UHPC. Conclusions When the fibre orientation was consistent with the principal stress direction, the fibre had a bridging effect on cracks. Therefore, specimen AUHPC had more microcracks, more tortuous paths, higher peak stress, more pronounced strain hardening, and more energy dissipation. specimen PUHPC had only one single, much smoother crack and showed no strain hardening. In addition, specimen AUHPC had the maximum fibre utilization level with the maximum fibre average stress, thus having the most intense bridging effect. The fibre average stress in specimen PUHPC was the minimum with insufficient ductility and significant brittleness. Therefore, optimizing the fibre orientation could be an effective way to improve the strength and ductility of specimen UHPC. Although the fibre-mortar interfaces were not simulated directly, the proposed mesoscale model with rigid embedment of fibres and equivalent fibre stress-strain constitutive relation could prove computationally efficient in simulating the bridging effects from massive random fibres. Therefore, the model could be used for the optimization of material parameters such as fibre dimensions, shape, distribution and volume fraction.