Tensile properties and constitutive relation of modified polyurethane concrete at different temperatures
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摘要: 钢桥面铺装材料易受温度影响而产生破坏，其中拉伸破坏最为常见。改性聚氨酯混凝土是一种新型钢桥面铺装材料，为研究温度对其拉伸性能的影响，在−10℃、0℃、15℃、40℃和60℃这5组温度环境下分别进行单轴拉伸试验研究。为保证拉伸试验成功，率先设计并制作了两种拉伸试件(哑铃形试件、经圆弧过渡的哑铃形试件)。同时设计用于匹配试件的拉伸试验新型夹具，开展两种试件的对比试验。通过拉伸试验，测得该材料在单轴受拉时的应力-应变曲线，依据该曲线计算得到各拉伸性能指标。研究结果表明：使用经圆弧过渡的哑铃形试件与新夹具的组合方案的拉伸效果更优。新型夹具可通过增设螺栓约束夹具的变形，从而有效改善加载过程中试件的局部应力集中效应。随温度的升高，改性聚氨酯混凝土的抗拉强度、拉伸弹性模量均呈减小趋势；峰值应变、断裂能密度和拉压比均呈增大趋势。提出了各拉伸性能指标的温度相关计算式。构建适用于改性聚氨酯混凝土的单轴拉伸本构关系，计算与试验结果吻合良好，为该材料未来的工程应用提供参考。Abstract: The steel bridge deck pavement materials are susceptible to damage caused by temperature, among which tensile damage is the most common. Modified polyurethane concrete is a new type of steel bridge deck pavement material. In order to study the effect of temperature on its tensile properties, uniaxial tensile experiments were carried out at −10°C, 0°C, 15°C, 40°C and 60°C. In order to ensure the success of the experiment, two kinds of experimental specimens (dumbbell-shaped specimen and dumbbell-shaped specimen with circular arc edge) were first designed. Meanwhile, a novel tensile testing fixture used to match the specimen was designed, and the experiment comparison of the two specimens was carried out. Through the uniaxial tensile experiment, the stress-strain curves were obtained and the tensile performance indexes were calculated according to the curve. The results show that using the dumbbell-shaped specimen with circular arc edge and the new tensile testing fixture has better effect. The new fixture can restrain the deformation of the fixture by adding bolts, so as to effectively reduce the stress concentration in the loading process. With the increase of temperature, the tensile strength and tensile elastic modulus of modified polyurethane concrete decrease. The peak strain, fracture energy density and tension-compression ratio all increase. The temperature related expressions of the tensile performance indexes are proposed. The uniaxial tensile constitutive relation of modified polyurethane concrete is constructed, and the calculation is in good agreement with the experimental results. The results can serve as basic references for the future engineering application of this material.
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图 1 单轴拉伸试件尺寸图
R—Radius of the arc transition zone; LS—Name of the tensile specimen
Figure 1. Size of uniaxial tensile specimen
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图 5 单轴拉伸试验装置
p1, p2, p3—Strain gauge paste position
Figure 5. Uniaxial tensile experiment device
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图 6 部分改性聚氨酯混凝土试件断裂图
Figure 6. Fracture of some specimens for modified polyurethane concrete
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图 7 部分改性聚氨酯混凝土试件断裂面图
Figure 7. Fracture cross section of some specimens for modified polyurethane concrete
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图 8 改性聚氨酯混凝土抗拉强度与温度的关系
T, T0—Test temperature and 15℃; ft, T, ft,T0—Axial tensile strength of modified polyurethane concrete at temperature T and T0; R2—Coefficient of determination; v2—Residual sum of squares
Figure 8. Relationship between tensile strength and temperature of modified polyurethane concrete
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图 9 改性聚氨酯混凝土峰值应变与温度的关系
εt, T, εt,T0—Peak strain of modified polyurethane concrete at temperature T and T0
Figure 9. Relationship between peak stress and temperature of modified polyurethane concrete
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图 10 改性聚氨酯混凝土拉伸弹性模量与温度的关系
Et, T, Et,T0—Tensile elastic modulus of modified polyurethane concrete at temperature T and T0
Figure 10. Relationship between elastic modulus and temperature of modified polyurethane concrete
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图 11 温度对改性聚氨酯混凝土轴向拉伸应力-应变曲线的影响
Figure 11. Effect of temperature on stress-strain curves of modified polyurethane concrete
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图 12 改性聚氨酯混凝土单轴拉伸本构关系模型计算值与试验值的对比
Figure 12. Comparison between calculated values of constitutive relation model and experiment values for modified polyurethane concrete
表 1 改性聚氨酯混凝土配合比
Table 1 Mix proportion of modified polyurethane concrete
Component Particle size D/mm Mass fraction/wt% Fineness modulus Apparent density
/(kg·m−3)Coarse aggregate
(4.76-9.52 mm)4.76≤D≤9.52 30 3.4 2600 Fine aggregate
(0.16-4.76 mm)0.16≤D≤0.62 17.8 2.5 2580 0.62≤D≤2.35 20 2.35≤D≤4.76 16.8 Modified polyurethane binder – 15.2 – – Catalyst – 0.2 – – 
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表 2 改性聚氨酯混凝土单轴拉伸试验方法效果对比
Table 2 Effect comparison of uniaxial tensile experiment method for modified polyurethane concrete
Number Experimental method Diagram Thickness w Specimen failure Damage feature Reference LS-1 End bond tensile
dumbbell-shaped specimen
w=75 mm 
Cracks mostly occur at the loading
end and finally destroyed[24-25] LS-2 End bond tensile
dumbbell-shaped specimen with circular arc edge
(bolts added)
w=75 mm 
Specimens are broken
in the middle without obvious
stress concentrationNew design Note: ϕ—Diameter of the steel bar.
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表 3 改性聚氨酯混凝土单轴拉伸试验结果
Table 3 Results of uniaxial tensile experiment for modified polyurethane concrete
Temperature/℃ Tensile strength/MPa Peak strain/% Elastic modulus/GPa Fracture energy density/(N·mm−2) Compressive strength/MPa[9] −10 10.28 0.0681 16.86 3.304 81.78 0 10.80 0.0690 16.16 3.929 81.83 15 9.79 0.0958 11.93 4.247 58.87 40 5.87 0.1432 6.23 5.561 39.50 60 3.95 0.4967 1.21 12.843 20.91
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表 4 不同温度下的改性聚氨酯混凝土拉压比
Table 4 Tensile-compression ratio of modified polyurethane concrete at different temperatures
Temperature/℃ Tensile
strength
/MPaCompressive
strength/MPaSplitting tensile
strength/MPaTension-compression
ratio W1/%Tension-compression
ratio W2[32]/%Relative error/% −10 10.28 86.67 8.24 11.86 9.51 19.81 0 10.80 79.62 7.93 13.56 9.96 26.55 15 9.79 71.93 7.11 13.61 9.88 27.40 40 5.87 42.97 4.77 13.66 11.1 18.74 60 3.95 26.19 2.67 15.08 10.19 32.43
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表 5 改性聚氨酯混凝土5组温度下与温度相关的上升段参数aT和bT的拟合值
Table 5 Fitting values of aT and bT of modified polyurethane concrete under five groups of temperatures
Temperature/°C aT bT −10 1.30 1.06 0 1.00 1.00 15 1.19 0.98 40 0.51 1.23 60 0.37 1.36
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目的
钢桥面铺装材料易受温度影响而产生破坏，其中拉伸破坏最为常见。改性聚氨酯混凝土是一种新型钢桥面铺装材料，具有较好的耐磨性、防水性，与钢材的黏结性较好，且具有较好的工作性。目前改性聚氨酯混凝土已应用于国内多座桥梁的桥面铺装工程中，但目前国内外没有人对改性聚氨酯混凝土的受拉本构关系进行深入研究，对其温度相关性的受拉本构关系的研究更是少之又少。本文通过进行单轴拉伸试验研究温度对其拉伸性能的影响。
方法为保证拉伸试验成功，率先设计并制作了两种拉伸试件(哑铃形试件，经圆弧过渡的哑铃形试件)。同时设计用于匹配试件的拉伸试验新型夹具，开展两种试件的对比试验。选取效果更好的拉伸试验方案后，在-10℃、0℃、15℃、40℃和60℃五组温度环境下分别进行单轴拉伸试验。通过恒温恒湿箱控制试件的温度，通过1000kN微机控电液伺服试验机(WAW-1000-G)进行试件的加载并直接读取荷载数据，通过贴片式应变采集仪(HBM MGC plus)测量应变。测得该材料在单轴受拉时的应力-应变曲线，依据该曲线计算得到各拉伸性能指标。
结果对比试验中，使用经圆弧过渡的哑铃形试件与新夹具的组合方案的拉伸效果更优。新型夹具可通过增设螺栓约束夹具的变形，从而有效改善加载过程中试件的局部应力集中效应。改性聚氨酯混凝土单轴拉伸试验中，随着荷载的不断增加，主裂缝逐渐扩展贯穿整个横截面，最终绝大多数的试件从中间部分断裂成两部分。试件主裂缝整齐，断裂面平整，无偏心受拉现象。随温度的升高，改性聚氨酯混凝土的抗拉强度、拉伸弹性模量均呈减小趋势；峰值应变、断裂能密度和拉压比均呈增大趋势。将各拉伸性能指标和温度无量纲化后通过最小二乘准则进行回归分析，提出了各拉伸性能指标的温度相关计算式。将单轴拉伸试验得到的拉伸应力-应变曲线中的应力与应变无量纲化，同时引入和两个温度相关参数，通过最小二乘准则进行回归分析，构建适用于改性聚氨酯混凝土的单轴拉伸本构关系。
结论提出了一种适用于改性聚氨酯混凝土的单轴拉伸试验方案，经试验验证效果良好，改性聚氨酯混凝土试件几乎都在中间位置被拉断。提出了改性聚氨酯混凝土各拉伸性能指标的温度相关计算式，拟合的相关系数R均大于0.95，残差平方和v均小于0.05。构建适用于改性聚氨酯混凝土的单轴拉伸本构关系，并对其中的和两个温度相关参数提出建议取值，计算结果与试验数据吻合良好。本文所得改性聚氨酯混凝土各拉伸性能指标的温度相关计算式和单轴拉伸本构关系，可为该材料未来的工程应用提供参考。
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改性聚氨酯混凝土是一种钢桥面铺装的新材料，具有较好的耐磨性、防水性，与钢材的黏结性较好，常温条件即可铺装成型，桥面铺装完毕后两小时即可通车。钢桥面铺装材料易受温度影响而产生破坏，其中拉伸破坏最为常见。作为一种新型混凝土，国内外对改性聚氨酯混凝土的拉伸性能和本构关系研究较少，对其与温度相关的本构关系研究尚处空白，阻碍该材料的进一步广泛应用。
本文自主设计和制作了拉伸试验新试件和新试验夹具，与参考相关文献制作的试件进行了对比试验，发现新试件与新夹具组合的试验方案有效改善了加载过程中试件的局部应力集中效应，效果较好。本文使用自主设计的试验方案在-10℃、0℃、15℃、40℃和60℃五组温度下分别对改性聚氨酯混凝土进行单轴拉伸试验研究，得到其单轴拉伸应力-应变曲线和各种拉伸性能指标。试验结果表明，随温度的升高，改性聚氨酯混凝土的抗拉强度、拉伸弹性模量均呈减小趋势；峰值应变、断裂能密度和拉压比均呈增大趋势。其中60℃时的抗拉强度(3.95MPa)仅为15℃条件下(9.79MPa)的40.35%，受温度影响较为明显。提出了各拉伸性能指标的温度相关计算式。构建适用于改性聚氨酯混凝土的单轴拉伸本构关系，计算与试验结果吻合良好。为该材料未来的工程应用提供参考。
单轴拉伸试验试件(a)和试验夹具(b)的尺寸图
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