超高性能纤维增强混凝土单轴本构关系和钢纤维增强作用对其影响

邓金岚; 杨简; 陈宝春; 徐港; 李洋

doi:10.13801/j.cnki.fhclxb.20230613.001

超高性能纤维增强混凝土单轴本构关系和钢纤维增强作用对其影响

邓金岚^{1, 2},
杨简^{1, 2, ,},
陈宝春^{3, 4},
徐港^{1, 2},
李洋^{1, 2}

1.
三峡大学　防灾减灾湖北省重点实验室，宜昌 443002
2.
三峡大学　土木与建筑学院，宜昌 443002
3.
福建理工大学　土木工程学院，福州 350118
4.
福州大学　土木工程学院，福州 350108

基金项目: 磷石膏基高性能水泥基材料制备研究(2022 KJZ09)；基于声发射特征的轻质超高性能混凝土单轴损伤本构关系研究(291219)；国家级地方高校能源和环境材料化学学科创新引智基地(D20015)；土木工程防灾减灾湖北省引智创新示范基地(2021 EJD026)

详细信息

通讯作者:
杨简，博士，讲师，硕士生导师，研究方向为超高性能混凝土、固废资源化利用和钢管节点　E-mail: 845175145@qq.com

中图分类号: TU528.31；TB332
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出版历程
- 收稿日期: 2023-04-16
- 修回日期: 2023-05-24
- 录用日期: 2023-05-25
- 网络出版日期: 2023-06-12
- 刊出日期: 2024-01-31

Uniaxial constitutive relation of ultra-high performance fiber reinforced concrete and the effect of steel fiber reinforcement on it

DENG Jinlan^{1, 2},
YANG Jian^{1, 2, ,},
CHEN Baochun^{3, 4},
XU Gang^{1, 2},
LI Yang^{1, 2}

1.
Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University, Yichang 443002, China
2.
College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, China
3.
College of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China
4.
College of Civil Engineering, Fuzhou University, Fuzhou 350108, China

Funds: Research on Phosphogypsum-based High-performance Cement-based Materials (2022 KJZ09); Research on Uniaxial Damage Constitutive Relation of Lightweight Ultra-high Performance Concrete Based on Acoustic Emission Characteristics (291219); The 111 Project of China (D20015); The 111 Project of Hubei Province (2021 EJD026)

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摘要

摘要: 超高性能纤维增强混凝土的单轴本构关系是认识其材料特性和非线性结构设计的基础。本文从本构方程函数模型建立的角度梳理了现有超高性能纤维增强混凝土单轴本构关系的相关研究；发现本构关系经验模型适用于结构设计计算，其中轴拉和轴压本构方程式均宜采用有理分式；本构关系简化模型适用于简化受力分析和数值模拟，其中轴拉宜采用三折线模型，轴压宜采用双折线模型；本构关系损伤模型适用于材料特性研究，其损伤演化函数较多采用Weibull分布。此外，还发现现有各种研究所得的本构方程中均不包含纤维相关参数，不能充分体现钢纤维的重要影响。因此，针对3种长径比、6种体积率的超高性能纤维增强混凝土进行轴拉和轴压试验，分析纤维对本构关系的影响。结果表明：超高性能纤维增强混凝土的轴拉和轴压本构关系经验模型均采用有理分式更适合，结合试验与收集的文献数据分析了纤维对经验模型本构方程系数的影响，提出了单轴本构关系经验模型的方程式；还探究了钢纤维参数对单轴损伤本构关系的影响，试验结果表明，钢纤维增强因子与损伤模型的控制系数间存在较强相关性，以试验数据为基础，数值分析得到钢纤维参数与本构方程控制系数间的关系式，进而提出包含钢纤维参数的轴拉和轴压损伤本构方程；并收集文献数据进行验证和修正，结果表明本文提出的本构方程与试验结果更吻合。
- 超高性能纤维增强混凝土 /
- 本构关系 /
- 轴拉 /
- 轴压 /
- 钢纤维 /
- 体积率 /
- 长径比
Abstract: The uniaxial constitutive relation of ultra-high performance fiber reinforced concrete (UHPFRC) is the basis for under-standing its material properties and nonlinear structural design. From the perspective of the constitutive equation function model, this paper reviews the existing research on the uniaxial constitutive relationship of UHPFRC. It was found that the empirical model of constitutive relation is suitable for structural design calculation, and the constitutive equations of uniaxial tension and compression should adopt rational fractions. The simplified model of constitutive relation is suitable for simplified force analysis and numerical simulation. The three-fold line model is suitable for uniaxial tension, and the double-fold line model is suitable for uniaxial compression. The damage model of constitutive relation is suitable for the study of material properties, and the damage evolution function is mostly Weibull distribution. In addition, it is found that the constitutive equations obtained by various existing studies do not contain fiber parameters, which cannot fully reflect the influence of steel fibers. Therefore, uniaxial tension and compression tests were carried out on UHPFRC with three aspect ratios and six volume fractions to analyze the influence of fibers on the constitutive relationship. The results show that the rational fraction is more suitable for the empirical model function of the uniaxial tension and compression constitutive model of UHPFRC. Combined with the test and the collected literature data, the influence of fiber on the coefficient of the empirical model equation was analyzed, and the equation of the empirical model of the uniaxial constitutive relationship was proposed. The influence of steel fiber parameters on the uniaxial damage constitutive relation was also explored. The experimental results show that there is a strong correlation between the steel fiber enhancement factor and the control coefficient of the damage model. Based on the experimental data, the relationship between the parameters of steel fiber and the control coefficient of constitutive equation is obtained by numerical analysis, and then the damage constitutive equations of uniaxial tension and compression including steel fiber variables are proposed. The literature data are collected for verification and correction, indicating that the constitutive relation proposed in this paper is in better agreement with the experimental results.
- ultra-high performance fiber reinforced concrete /
- constitutive relation /
- uniaxial tension /
- uniaxial compression /
- steel fiber /
- volume fraction /
- aspect ratio

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猪笼草口缘区表面有纹理，可用水溶液润滑使其有利于捕捉滑入猪笼草的昆虫^[1-2]。根据猪笼草的工作机制，研究人员提出了一种新型疏水表面：润滑剂注入型光滑多孔表面(SLIPS)。由于陷在多孔结构上的润滑剂与水相或其他液体不相溶，因此SLIPS结构不易损坏，具有良好的耐高温、耐高压性^[3-4]。此外，陷在粗糙结构表面润滑剂流动性强，使润滑表面在受到外界干扰时能够完成自修复^[5]。这些优势使SLIPS在液滴微流体^[6-7]、防冰^[8-9]、自清洁^[10-11]、抗生物污染^[12-13]、相变热传递^[14-15]、减阻^[16-17]等方面具有广阔的应用前景。

在SLIPS中加入刺激响应性材料，可在外界刺激下实现目标液滴动态操控，这种精准控制液滴运输的智能润滑表面因在生物芯片和微流控等领域的巨大应用潜力，引起了科研人员的广泛研究兴趣。目前，已通过机械力^[18-19]、热^[20-21]、电^[22-23]、磁^[24-25]和光诱导^[26-27]等外界刺激改变SLIPS界面润湿性，从而控制液滴运动状态。Pu等^[28]将磁性响应的铁/聚二甲基硅氧烷(Fe/PDMS)凝胶膜与硅油结合在一起，在脉冲磁场作用下利用Fe/PDMS凝胶膜上磁锥的可逆形成/消失，实现了水/气两用光滑凝胶表面分别对液滴和气泡的磁诱导操控。Zhao等^[18]通过模拟蚯蚓的自适应液体释放和表面结构固定润滑剂的特性，描述了一种外部机械刺激下能够快速释放储存在纹理中润滑油的软聚合物涂层，从而在固态环境下保持自适应性减摩、耐磨和自清洁性能。Han等^[29]展示了一种基于氧化锌纳米多孔复合材料的光电协同响应润滑面，在光电协同刺激下，可实现液滴的可控运动和图形化书写应用。

在以上所述外界刺激中，光响应润滑表面因其具有远距离、非接触操控和低接触角滞后等显著优势，被视为一种有竞争力的操控界面^[30]。一般来说，添加的光响应材料(例如石墨烯、Fe₃O₄)赋予新表面光热响应功能，引发的润湿性梯度力(F_wet-grad)可作为强大的驱动力，同时注入的润滑剂使原本的疏水表面形成气/液/液/固体系统，进而可进行精准无损液滴操控。例如，Wang等^[31]通过在光热响应石墨烯海绵中灌注石蜡，同时利用掩模对近红外光路进行图案化规划，能够实现材料表面的可编程液滴滑动路径。虽然这项工作具有良好的可重复性及高效的可调控性，但是石蜡润滑剂的高滞后阻力仍然是影响液滴响应速度的极大阻碍。后来，Gao等^[30]利用液滴非对称变形和内部马兰格尼流之间的协同效应，开发了一种掺杂Fe₃O₄的光响应有机凝胶光滑表面，近红外诱导的动态温度梯度衍生出润湿梯度力、马兰格尼力，可作为驱动力实现液滴高效传输。尽管上述方法已经证明了液滴滑动路径和速度是可控的，但仍有一些问题有待解决：(1)为了防止与润滑剂不相溶的目标液体侵入SLIPS界面，需制备超疏水多孔基底，而采用模板转移法和化学氟化相结合的传统方法过于繁琐，且并不环保；(2)虽然目前已经有对液滴操控性能影响因素的研究，但不同润滑剂流变性能(黏度和表面张力)与滑动速度之间的定量关系还有待探究。因此，有必要对基于光热材料的多孔润滑表面展开一种更简便、更环保的制备方法，并从流体力学定量分析的角度深入了解其内在机制。

在此，本文用飞秒激光交叉扫描制备了一种基于Fe₃O₄纳米颗粒的光响应SLIPS，在单侧近红外光刺激下，不对称的近红外负载导致基底形成温度梯度，引起液滴润湿梯度和内部马兰格尼流，驱使多种类型液滴以较高的速度向任意方向滑动。利用简单加载/撤离近红外负载，可以选择性地控制液滴滑动/钉扎状态，液滴运动方向和路线可以通过调谐近红外光照射位置进行实时更新。此外，基于液滴流体动力学分析，通过定量分析Fe₃O₄含量、润滑剂流变性能、液滴表面张力与液滴移动速率、响应时间之间的关系，进而实现液滴操控性能优化。

1. 实验材料及方法

1.1 原材料

实验用聚二甲基硅氧烷(PDMS)为道康宁SYLGARD184，Fe₃O₄颗粒直径为10 nm(纯度≥99.9%)；驱使液滴运动的近红外光照源为深圳台住激光公司的808 nm近红外点状激光器，功率为300 mW，照射面积为2.3 mm×1.4 mm点区域；近红外光激光器的辐射距离可以由一个专用万能支架在10~50 cm范围进行调整，实验中近红外辐射距离默认为10 cm。5 cSt矿物油、10 cSt二甲基硅油、10 cSt矿物油、100 cSt二甲基硅油、蓖麻油、无水乙醇、乙二醇、丙三醇、NaCl溶液均购于成都瑞思试剂公司，实验用水均为去离子水。

1.2 加工及表征设备

实验用飞秒激光器加工系统由美国Coherent公司Chameleon Vision-S种子激光和Legend Elite F HE-1K钛蓝宝石啁啾脉冲放大系统组成，激光波长为800 nm，脉冲宽度为104 fs，频率为1 kHz，加工过程中激光功率、扫描间距和速度分别设置为250 mW、100 μm和4 mm·s⁻¹。

在样品性能表征中，用日本电子公司JSM-7500F冷场发射扫描电子显微镜观察样品表面形貌，用德国Dataphysics公司OCA20视频光学接触角测量仪测量加工样品界面上的液滴接触角。在室温条件下(10%RH湿度、20℃)将5.0 μL去离子水滴用悬滴法滴到样品上测其接触角，每组样品均在不同区域进行至少5次重复测试，然后取其平均值作为静态接触角。同时，接触角测量仪配有分辨率为1 280×1 024的屏幕截图软件bandicam，可拍摄操控不同液滴运动过程的视频和图片。

1.3 光热响应SLIPS的制备及表征

图1(a)为SLIPS简易制备过程。将Fe₃O₄纳米颗粒、PDMS预聚体和固化剂(预聚物与固化剂的比例为10∶1)手动混合，通过磁力搅拌器以2 000 r/min转速搅拌5 min；将均匀混合物倒入培养皿中，抽真空30 min后放置在100℃恒温箱中1 h，待固化后将其从培养皿中剥离得到Fe₃O₄/PDMS复合材料。利用飞秒激光对Fe₃O₄/PDMS复合薄膜进行交叉扫描，制备形成三维微柱阵列结构。如图1(b)和图1(d)所示，柱状结构的平均周期、柱宽、柱高分别为92、40、68 μm，生成的超疏水表面接触角为150°。通过图1(c)中局部放大电镜图观察可知，激光诱导的柱状结构由复合多级微纳米结构组成，包括微纳米颗粒、微纳米多孔和微柱，有助于减少润滑油的损失及防止目标液滴侵入界面。与其他激光加工方式相比，飞秒激光具有超快加工速度和超低热效应等优势，能够在不改变材料的本征晶相的情况下诱导分层微纳米结构，并且材料表面无飞溅熔渣，在改善液滴滑动性能方面更有效^[32-34]；随后，将制备的柱状结构Fe₃O₄/PDMS薄膜浸入10 cSt二甲基硅油中24 h进行键合，硅油在毛细力的作用下会在柱状粗糙界面形成一层油膜；最后，将润滑处理过的光滑多孔表面垂直静置5 min去除多余的硅油，制备出掺杂Fe₃O₄的光热响应SLIPS。

图 1 掺杂Fe₃O₄纳米颗粒的润滑剂注入型光滑多孔表面(SLIPS)制备过程 (a) 和飞秒激光刻蚀制备的超疏水微柱阵列薄膜电镜图((b)~(d))

Figure 1. Facile fabrication of Fe₃O₄NPs-doped slippery lubricant-infused porous surface (SLIPS) (a) and SEM images of the as-prepared superhydrophobic micropillar-arrayed film by femtosecond laser cross-scanning ((b)-(d))

PDMS—Polydimethylsiloxane

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2. 结果与讨论

2.1 光热响应SLIPS液滴操控原理

为实现液滴在SLIPS上的稳定滑动，目标液滴、润滑剂和原始粗糙界面的组合表面张力应满足以下标准^[35]：

$\Delta \gamma = {\gamma _2}\cos {\theta _2} - {\gamma _1}\cos {\theta _1} - {\gamma _{12}} > 0$

(1)

其中：γ₁、γ₂、γ₁₂分别为目标液滴的表面张力(水，γ₁=72.7 mN·m⁻¹)、润滑剂的表面张力(10 cSt二甲基硅油，γ₂=19.7 mN·m⁻¹)和他们之间的界面张力(γ₁₂=56.5 mN·m⁻¹)；θ₁和θ₂为目标液滴(θ₁=150°)和润滑剂(θ₂=0°)在原始粗糙界面的水接触角。对于该系统，∆γ=26.2>0符合标准，水滴在SLIPS上能进行稳定无损滑动。如图2(a)所示，通过施加单侧近红外刺激，SLIPS中Fe₃O₄纳米颗粒的光热效应引起温度梯度，液滴两端润湿梯度和内部拉普拉斯压差分别衍生润湿梯度力和马兰格尼力，驱使液滴由钉扎状态开始滑动；撤离近红外光时，液滴逐渐停止滑动直至恢复钉扎状态。图2(b)为10 μL水滴在Fe₃O₄含量为5wt%的SLIPS界面受近红外驱使的智能运动控制过程。

图 2 基于近红外响应(NIR)在SLIPS界面进行液滴操控

Figure 2. Droplet manipulation on night-time ozone profile (NIR)-responsive SLIPS

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图3为有无单侧近红外刺激下液滴润湿性变化的机制模型。根据经典杨氏方程^[36]：

图 3 无外界近红外刺激 (a) 和有外界近红外刺激时 (b) 润湿梯度差异原理

Figure 3. Mechanism illustration for the wettability gradient variation without (a) and with (b) a unilateral NIR-stimuli

下载: 全尺寸图片幻灯片

$\cos \theta = ({\gamma _{{\rm{og}}}} - {\gamma _{{\rm{ol}}}})/{\gamma _{lg}}$

(2)

其中，γ_lg、γ_og和γ_ol分别为液-气、油-气及油-液界面的张力。润滑剂表面张力γ_og与温度成反比，近红外触发端SLIPS区域温度升高将导致触发端γ_og减小，液滴接触角增大。如图3(a)所示，无近红外刺激下，γ_og(A)=γ_og(R)，θ_A=θ_R，其中A端为近红外触发端，R端为未触发端。如若施加单侧近红外辐射，如图3(b)所示，触发端A处SLIPS温度升高，γ_og(A)<γ_og(R)，θ_A>θ_R，液滴发生明显变形。在含5wt% Fe₃O₄的SLIPS上，在无近红外单侧辐照下，10 μL水滴的θ_A=θ_R =87°，而存在近红外单侧辐照A端时，前进角大于后退角，θ_A=92°>θ_R=85°。

在光热响应SLIPS施加非对称近红外负载，照射SLIPS区域Fe₃O₄纳米颗粒的光热效应导致基底存在温度梯度，液滴两端形成的润湿梯度衍生润湿梯度力F_wet-grad^[37]：

${F_{{\rm{wet}}}}_{{\rm{ - grad}}}{\rm{ = }}{\gamma _{{\rm{lg}}}}{\rm{(cos}}{\theta _{\rm{R}}}{\rm{ - cos}}{\theta _{\rm{A}}}{{)d}}$

(3)

其中，d是液滴接触界面的特征长度，F_wet-grad方向由触发端A指向非触发端R。其次，由于液滴内部存在热传递和表面张力梯度，引发内部拉普拉斯压差，形成马兰格尼力F_M ^[38]：

${F_{\rm{M}}} = {\rm{\text{π}}} \frac{{{{{d}}^{\rm{2}}}}}{4}\frac{{{\rm{d}}{\gamma _{\lg }}}}{{{\rm{d}}T}}\frac{{{\rm{d}}T}}{{{\rm{d}}x}}$

(4)

其中：dγ_lg/dT是液-气界面张力随温度的变化；dT/dx是沿液滴运动方向的表面热梯度。F_M在运动平面上的方向是由热端指向冷端，即由A端指向R端。此外，由于液滴和润滑剂都具有黏度，因此液滴滑动时会产生与液滴运动方向相反的阻力F_H^[39]：

${F_{\rm{H}}} = \alpha ({\eta _{\lg }} + {\eta _{{\rm{og}}}})\nu \text{π} \frac{{{d}}}{{\rm{2}}}$

(5)

其中：α是数值因子；η_lg是液滴黏度；η_og是润滑剂黏度；ν为液滴的滑动速度。F_H方向与液滴运动方向相反，即与前两种驱动力方向相反。在近红外驱动液滴运动过程中，F_M远小于F_wet-grad^[40-41]，因此在分析中忽略F_M，将F_wet-grad视为主驱动力。

基于以上近红外驱动液滴的动力学分析，可以推断，在光诱导液滴运动的初始阶段，光热响应SLIPS产生的热量与表面润滑剂进行缓慢的热传递和热交换，液滴润湿梯度不足以克服润滑界面黏附力作用，F_wet-grad<F_H，液滴保持钉扎状态；待表面温度升高至液滴两端形成足够大的润湿梯度，F_wet-grad>F_H，液滴将由钉扎状态开始加速运动；与此同时，F_H随着运动速度加快而不断增大，液滴所受合力逐渐达到平衡，当F_wet-grad=F_H时，液滴以稳定的速度运动；当近红外刺激被撤离，剩余温度梯度因向周围冷源传播而减小，此时F_wet-grad小于F_H但不等于0，液滴会减速，但由于施加近红外刺激时基底的升温速度小于撤走红外时基底的降温速度，液滴的减速快于之前施加刺激时的加速过程^[30]；在残余温度梯度消失时，F_H=0，液滴会在没有近红外干扰的情况下恢复钉扎状态。

2.2 Fe₃O₄含量对液滴运动的影响

考虑到F_wet-grad大小主要由同一液滴的θ_A和θ_R之差决定，即由温度响应的润湿梯度决定，因此，Fe₃O₄质量分数通过对近红外辐射SLIPS区域温度变化造成影响，进而改变液滴滑动速度。从图4(a)可以看出，当SLIPS中Fe₃O₄质量分数从1wt%增加到5wt%时，液滴滑动速度逐渐增大，但当浓度大于5wt%时，液滴滑动速度几乎不变。以10 μL液滴为例，在含1wt%~7wt% Fe₃O₄的SLIPS上液滴的平均滑动速度分别测量为220、387、599、698、785、793和818 μm·s⁻¹。在单侧近红外刺激下，随着SLIPS中光热响应材料含量越高，局域化温度越高，γ_og(A)越小，θ_A越大，液滴所受驱动力F_wet-grad也就越大。在初始阶段，液滴的流体动力学受Fe₃O₄相对含量增加引起的局部化温度升高的影响较大，然而随着掺杂量的进一步增加，温度达到饱和，液滴滑动速度也趋于饱和状态^[42]。另外，可以通过改变液滴体积控制液滴运动，如图4(a)所示，随着液滴尺寸增大，滑移速度呈下降趋势。以含5wt%Fe₃O₄为例，5~40 μL水微滴的平均滑动速度分别为865、785、592、518、491和380 μm·s⁻¹。液滴越大，与基底接触的特征长度越大，液滴与润滑剂之间逐渐增大的黏附力阻碍液滴运动。以上变化趋势分析也适用于图4(b)所示的调整近红外辐射距离控制液滴速度过程，在Fe₃O₄质量分数不变的情况下，随着光源距SLIPS辐射距离增加，液滴滑动速度下降；然而在距离上升到30 cm后，液滴滑动速率下降趋势渐缓，也达到饱和值。以含5wt% Fe₃O₄为例，10~60 cm辐射距离的水微滴(10 μL)平均滑动速度分别为785、547、482、456、440和413 μm·s⁻¹。

图 4 Fe₃O₄含量和液滴体积 (a) 及近红外光辐射距离 (b) 对液滴运动的影响

Figure 4. Effect of Fe₃O₄-doped content and droplet volume (a) and irradiation distance (b) on droplet’s motion

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除了滑动速度，响应时间也是光响应操控液滴效率的关键，在此响应时间可以定义为近红外刺激下使液滴在SLIPS上开始运动的辐照时间，光接触液滴边缘的时间设置为0 ms。如图5(a)所示，在Fe₃O₄含量大于2wt%的SLIPS上，驱动液滴的响应时间小于1 s，随着Fe₃O₄含量的增加，反应时间缩短且变化趋势渐缓。由此可见，Fe₃O₄含量越高，SLIPS照射区域温度升高，导致F_wet-grad增长速度越快，从而缩短了光驱动响应时间。此外，图5(b)表明液滴体积的变化对运动响应时间影响不大。

图 5 Fe₃O₄含量 (a) 及液滴体积 (b) 对液滴响应时间的影响

Figure 5. Influence of Fe₃O₄NPs content (a) and droplet volume (b) on droplet’s response time

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2.3 润滑剂流变性能对液滴运动的影响

润滑剂的流变参数，包括表面张力(γ_og)和黏度(η_og)对液滴流体动力学的影响，前者影响F_wet-grad，后者影响F_H。选择利用5种黏度越来越大的润滑剂润滑处理过的SLIPS，进行液滴滑动速度差异性研究，分别为5 cSt矿物油(5/2.76)、10 cSt二甲基硅油(10/2.01)、10 cSt矿物油(10/2.87)、100 cSt二甲基硅油(100/2.1)和蓖麻油(680 cSt/3.74×10⁻²N·m⁻¹)。在图6(a)中，随着界面润滑剂黏度增大，五种不同SLIPS上液滴速度分别为976、785、598、539、17 μm·s⁻¹。由此可以很明显看出，润滑剂黏度与液滴的运动速度成相反变化趋势，结果与F_H理论公式相吻合，润滑剂黏度越大，液滴滑动阻力F_H越大。此外，在图6(b)对润滑油的表面张力与液滴滑动速度的定量分析中，并未发现明显规律。基于以上动力学分析，可以通过选择润滑剂种类来决定液体传输性能，在这种需要液滴快速精准运输的场景下宜选择黏度较小的润滑油，但由于矿物油稳定性比起硅油较差，在此次研究中选择10 cSt二甲基硅油对粗糙基底进行润滑处理。

图 6 润滑剂黏度 (a) 和表面张力 (b) 对液滴运动的影响(含量为5wt%Fe₃O₄的SLIPS)

Figure 6. Influence of lubricant’s viscosity (a) and surface tension (b) on droplet’s motion (5wt%Fe₃O₄-doped SLIPS)

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2.4 利用智能SLIPS操控不同种类液滴

要实现全方面的智能液滴运动操控，除了能够控制水滴外，外界刺激响应界面还应能实现不同类型液滴动态操控，这对于实现在芯片实验室、微流控反应器、远程液体输送等领域的广泛应用是很有必要的^[5,31,43]。利用SLIPS操控液滴的前提条件是目标液滴与基底表面润滑剂不相溶，在满足此前提基础上，选择乙醇、乙二醇、丙三醇、水和NaCl溶液，来展示光热响应SLIPS操纵各种液滴的能力。如图7所示，随着五种目标液滴的表面张力逐渐增大(2.28×10⁻²、4.84×10⁻²、6.33×10⁻²、7.27×10⁻²、8.66×10⁻² N·m⁻¹)，θ_A和θ_R都逐渐增大，可以改变液滴特征长度即润湿面积，其相应的滑动速度分别测定为205、667、500、785和662 μm·s⁻¹。由此可见，各种类型液滴的滑动速度与其表面张力不成线性关系，但与表面张力相关这点毋庸置疑。通过利用单侧近红外刺激实现不同类型液滴的智能精准输送，足以证明此界面可在多环境下展现其不受时空间限制的潜在优势。

图 7 在5wt%Fe₃O₄的SLIPS上受近红外驱使的五种液滴随着表面张力不断增大的平均滑动速度变化

Figure 7. Corresponding variations of NIR-actuating droplet’s average sliding velocity with the increasing of five droplet’s surface tension on 5wt%Fe₃O₄-doped SLIPS

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3. 结论

(1) 利用飞秒激光正交线扫描技术，快速制备了一种掺杂Fe₃O₄纳米颗粒的光热响应润滑剂注入型光滑多孔表面(SLIPS)。利用温度梯度导致的液滴两端润湿梯度和内部马兰格尼流，通过简单加载/撤离单侧近红外光刺激，可选择性控制掺杂Fe₃O₄纳米颗粒SLIPS表面的液滴滑动/钉扎状态。通过调整近红外光触发位置，也可操控其表面各种类型液滴趋向任意方向滑动。

(2) 基于液滴运动过程中流体动力学模型，定量分析SLIPS表面Fe₃O₄含量、润滑剂流变参数及液滴类型对液滴滑动速度和响应时间的影响，以实现SLIPS表面液滴操控性能优化。

(3) 光响应操控界面的液滴动力学定量分析，为仿猪笼草光响应润滑表面设计及在微芯片技术、微流控技术、生物医学检测等相关领域的进一步应用提供了帮助。

图 1 不同长径比的钢纤维

Figure 1. Steel fibers with different aspect ratios

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图 2 试验装置示意图

Figure 2. Diagram of test device

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图 3 UHPFRC轴拉应力-应变曲线

Figure 3. Uniaxial tensile stress-strain curves of UHPFRC

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图 4 UHPFRC轴压应力-应变曲线

Figure 4. Uniaxial compressive stress-strain curves of UHPFRC

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图 5 UHPFRC轴拉本构曲线^{[13-14, 47, 71-82]}

A—Undetermined coefficient

Figure 5. Uniaxial tension constitutive curves of UHPFRC^{[13-14, 47, 71-82]}

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图 6 经验模型的判定系数R²

Figure 6. Determination coefficient R² of empirical model

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图 7 UHPFRC轴拉本构方程控制系数η与纤维增强因子K关系

Figure 7. Relationship between control coefficient η of uniaxial tension constitutive equation and fiber reinforcement factor K of UHPFRC

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图 8 UHPFRC抗拉本构模型与试验数据对比

Figure 8. Comparison between tensile constitutive model and test data of UHPFRC

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图 9 UHPFRC轴压本构方程控制系数与纤维增强因子关系^{[26, 35, 50, 84-95]}

Figure 9. Relationship between control coefficient of uniaxial compression constitutive equation and fiber reinforcement factor of UHPFRC^{[26, 35, 50, 84-95]}

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图 10 UHPFRC抗压本构模型与试验数据对比

Figure 10. Comparison between compressive constitutive model and test data of UHPFRC

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表 1 超高性能纤维增强混凝土(UHPFRC)配合比(质量比)

Table 1 Mix proportion of ultra-high performance fiber reinforced concrete (UHPFRC)(Mass ratio)

Aggregate				Binding material		Superplasticizer
0.212-0.428 mm	0.428-0.850 mm	0.850-1.700 mm	0.038 mm	Cement	Silica fume	Superplasticizer
0.14	0.41	0.53	0.09	1	0.3	0.025

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表 2 A组和B组试验方案

Table 2 Test scheme of group A and group B

Test group	Specimen	Steel fiber volume fraction/vol%	Steel fiber aspect ratio	Test group	Specimen	Steel fiber volume fraction/vol%	Steel fiber aspect ratio
A	C-S0313-1.0vol%	1.0	43	B	T-S0313-3.0vol%	3.0	43
	C-S0313-2.0vol%	2.0	43		T-S0213-0.5vol%	0.5	65
	C-S0313-3.0vol%	3.0	43		T-S0213-1.0vol%	1.0	65
	C-S0213-1.0vol%	1.0	65		T-S0213-1.5vol%	1.5	65
	C-S0213-2.0vol%	2.0	65		T-S0213-2.0vol%	2.0	65
	C-S0213-3.0vol%	3.0	65		T-S0213-2.5vol%	2.5	65
	C-S0220-1.0vol%	1.0	100		T-S0213-3.0vol%	3.0	65
	C-S0220-2.0vol%	2.0	100		T-S0220-0.5vol%	0.5	100
	C-S0220-3.0vol%	3.0	100		T-S0220-1.0vol%	1.0	100
B	T-S0313-0.5vol%	0.5	43		T-S0220-1.5vol%	1.5	100
	T-S0313-1.0vol%	1.0	43		T-S0220-2.0vol%	2.0	100
	T-S0313-1.5vol%	1.5	43		T-S0220-2.5vol%	2.5	100
	T-S0313-2.0vol%	2.0	43		T-S0220-3.0vol%	3.0	100
	T-S0313-2.5vol%	2.5	43
Notes: C—Uniaxial compression test; T—Uniaxial tension test; S0313—Diameter of steel fiber is 0.30 mm and the length is 13 mm; S0213—Diameter of steel fiber is 0.20 mm and the length is 13 mm; S0220—Diameter of steel fiber is 0.20 mm and the length is 20 mm.

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A值( $A = {E_0}/{E_{\text{c}}}$ )的取值范围

Value range of A ( $A = {E_0}/{E_{\text{c}}}$ )

Function form	Ref.	A value range
Tertiary polynomial	[19]	1.5<A<3
Quartic polynomial	[24]	1.33<A<2.67
Quintic polynomial	[26-27]	1<A<1.67
Sextic polynomial	[22]	1<A<1.5
Rational fraction	[34]	1<A
Notes: E₀—Initial modulus of elasticity; E_c—Secant modulus.

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长摘要

目的
超高性能纤维增强混凝土(UHPFRC)的单轴本构关系是认识其材料特性和非线性结构设计的基础。学者们围绕UHPFRC本构关系已开展了大量研究，但研究结果呈现出方法各异、形式多样、结果各有优劣、适用场景各不相同的特点。本文旨在揭示钢纤维对单轴本构关系的影响，提出包含钢纤维参数的UHPFRC轴拉和轴压本构方程式，为非线性结构设计和数值模拟提供本构方程式。
方法
本文系统梳理了国内外UHPFRC轴拉和轴压本构关系相关研究，按照本构方程函数模型确定方法对其进行归纳分析，对比分析了各本构函数模型的推荐函数和适用场景。随后针对现有本构函数的不足，对掺入3种长径比、6种体积率钢纤维的UHPFRC开展了轴拉和轴压试验，并分析纤维对本构关系的影响。
结果
UHPFRC本构经验模型函数形式简单，适用于设计计算，但缺乏力学原理支撑，其可靠性高度依赖于样本数量。经验模型函数构建的关键在于上升段和下降段函数形式的选择，轴拉模型上下两段多采用有理分式；轴压上升段早期较多采用多项式，近年来有理分式的应用逐渐增多，而下降段为有理分式。本文通过试验数据的对比分析，认为轴拉、轴压本构方程都采用有理分式时，拟合效果更优，随后综合试验与文献数据建立了单轴本构关系经验模型方程式。此外，UHPFRC本构损伤模型符合损伤原理，更吻合试验应力-应变曲线特征，有利于认识材料本质特征。损伤模型建立的关键在于损伤因子的构建和损伤演化函数的确定，以真实应力构建损伤因子，假定其符合Weibull分布，可得到较为吻合的本构方程式。通过试验数据分析钢纤维参数对UHPFRC单轴本构损伤模型的影响，发现损伤模型控制系数与纤维增强因子显著相关，综合试验与文献数据建立了考虑纤维参数影响的UHPFRC本构损伤模型方程式。UHPFRC本构简化模型易于计算和简化分析，适用于简化计算与数值模拟，其构建核心在于线型选择。轴拉本构简化模型多采用三折线模型以充分体现其假性应变硬化特征，轴压本构多采用双折线模型以简化计算。
结论
UHPFRC经验模型适用于结构设计计算，轴拉和轴压本构方程均宜采用有理分式形式；简化模型适用于简化受力分析和数值模拟，其中轴拉宜采用三折线模型，轴压宜采用双折线模型；损伤模型中的损伤演化函数多采用Weibull分布。研究表明，钢纤维增强因子与损伤模型的控制系数存在较强相关性，基于试验数据，通过数值分析得到钢纤维参数与本构方程控制系数间的关系式，进而提出包含钢纤维变量的轴拉和轴压损伤本构方程；并收集文献数据进行验证和修正，结果表明本文提出的本构关系式与试验数据吻合良好。