Influence law of compound admixture on the mechanical properties of filling slurry before and after curing
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摘要: 为了提高煤矿充填浆体固化前后的性能，利用硫酸钠和聚羧酸减水剂复掺制备成复合外加剂，通过宏观实验探究其对充填浆体固化前后工作性能和力学性能的影响，并结合微观实验分析其影响机制。实验表明，0.5wt%硫酸钠与0.2wt%聚羧酸减水剂复掺的充填浆体，其水泥用量可减少2%，塌落度可增加4.1 cm，初凝时间和终凝时间可缩短20 min，减水率可提高7.7%，3天和28天单轴抗压强度最高可增加22%和42%。分析表明，硫酸钠的早强机制、聚羧酸减水剂的静电斥力作用和空间位阻作用及二者的互促作用是影响充填浆体固化前工作性能的主要原因，而针状性产物钙矾石和白色纤维状物质水化硅酸钙是影响充填浆体固化后力学性能的主要物质，二者的生成提高了充填膏体的单轴抗压强度。Abstract: In order to improve the performance of coal mine filling slurry before and after solidification, sodium sulfate and polycarboxylic acid water reducing agent were used to prepare a composite admixture, and the effect on the working performance and mechanical properties of the filling slurry before and after solidification was explored through indoor macroscopic experiments. Its influence mechanism was analyzed in combination with indoor microscopic experiments. Experiments show that the cement consumption of 0.5wt% sodium sulfate and 0.2wt% polycarboxylic acid water-reducing agent mixed filling slurry can be reduced by 2%, the slump can be increased by 4.1 cm, the initial and final setting time can be shortened by 20 min, and the water reduction rate can be increased by 7.7%, the 3rd day and 28th day uniaxial compressive strength can increase up to 22% and 42%. The analysis shows that the early strength mechanism of sodium sulfate, the electrostatic repulsion and steric hindrance of polycarboxylic acid water-reducing agent, and the mutual promotion of the two are the main reasons that affect the working performance of the filling slurry before curing. The needle-like product ettringite and the white fibrous substance calcium silicate hydrate are the main substances that affect the mechanical properties of the filling paste after solidification, and the formation of the two improves the uniaxial compressive strength of the filling paste.
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Keywords:
- filling slurry /
- compound admixture /
- ettringite /
- hydrated calcium silicate /
- influence mechanism
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碳化钨颗粒增强钢铁基(WCP/Fe)复合材料因兼顾金属基体的良好韧性与陶瓷增强颗粒的高强度、高硬度、高模量而广泛应用于机械制造、能源开发、交通运输等领域，但基体与增强颗粒间热物理性能差异过大使复合材料在激冷激热环境下服役时产生热应力，诱发界面处裂纹的萌生与扩展[1-4]。而将WC充分溶解，W在熔体中均匀扩散形成合金化复合层能有效解决该问题，故研究WC/Fe复合材料中W扩散均匀性十分必要[5-7]。
蜂窝结构因形状连续、比强度高等特性而对复合材料的综合性能产生重要影响[8-10]。Magotteaux公司发明X-win蜂窝结构ZTAP/Fe复合材料技术，制造的磨辊使用寿命提高两倍以上[11]；WU等[12]从模拟与实验角度出发，揭示预制体孔径与孔距作为蜂窝结构重要参数对复合材料力学性能的影响；SONG等[13]成功制备蜂窝结构还原氧化石墨烯增强环氧树脂(rGH/EP)复合材料，电磁屏蔽效能与导电性明显提升。但对蜂窝预制体结构与元素扩散均匀性间的关联机制仍研究较少。
本文采用真空消失模铸渗(V-EPC)工艺制备WC/Fe复合材料[14-15]，选取孔径孔距比相同孔径不同的蜂窝预制体，并将W质量分数最高与最低的预制体原孔壁与原孔心处W质量分数作为W扩散均匀性的判断条件[16-17]。表征复合层的显微组织、物相组成、元素分布，并检测预制体原孔壁与原孔心处W质量分数、硬度及复合层耐磨性，揭示其孔径对W质量分数分布的影响规律。通过求解非稳态扩散方程得解析解，对预制体孔内熔体凝固时的热物理场进行有限元模拟，并通过二次开发程序对其原孔内W质量分数分布进行数值模拟，揭示其孔径对W扩散均匀性的影响机制；提出W扩散均匀性与复合层耐磨性间的关联机制，为工程应用提供理论依据。
1. 实验材料与方法
为避免铸渗时W粉因粒径过小而大量烧损，选取铸造WC颗粒(WC/W2CP)为合金化提供W；表1为WC/Fe复合材料中预制体的成分组成，配置预制体粉末300 g，与5wt%水玻璃粘结剂均匀混合；表2为WC/Fe复合材料中预制体的结构参数，填充到预制体孔径孔距比相同孔径不同的蜂窝模具内，其轮廓为50 mm×100 mm×6 mm；采用CO2硬化与微波烧结方法，得最终预制体。
表3为WC/Fe复合材料中基体的成分组成。配置基体并采用中频感应炉熔炼20 kg。图1为WC/Fe复合材料的制备过程，采用V-EPC工艺成型，浇注温度为1 500℃，型腔负压为0.05 MPa。
表 1 WC/Fe复合材料中预制体的成分Table 1. Composition of preform in WC/Fe compositesComposition Mass fraction/wt% Size/μm WC 40 150-200 Ni60 30 60-90 FeCr55C6.0 30 150-200 表 2 WC/Fe复合材料中预制体的结构参数Table 2. Structure parameters of preform in WC/Fe compositesDiameter R/mm Distance d/mm Number n 3 6 63 6 12 16 9 18 7 表 3 WC/Fe复合材料中基体的成分Table 3. Composition of matrix in WC/Fe compositesComposition C Cr Mn Si Fe Mass fraction/wt% 1.2-1.3 18.0-20.0 0.4-0.6 1.0-1.2 Balance ![]()
图 1 WC/Fe复合材料的制备过程Figure 1. Preparation process of WC/Fe composites ((a)V-EPC (Vacuum-expendable pattern casting); (b)Honeycomb preform; (c)Transformation between preform and layer)采用尼康MA200型OM表征复合层显微组织，并统计预制体原孔壁与原孔心处平均晶粒尺寸分布。采用岛津7000S/L型XRD、牛津仪器Ultim Extreme型EDS面扫描表征复合层物相组成、元素分布。采用牛津仪器Ultim Extreme型EDS点扫描、上海光学仪器厂HX1000型显微硬度计表征复合层预制体原孔壁与原孔心处元素质量分数、硬度。采用广州试验仪器厂MS-5E型三体磨料磨损机表征复合层耐磨性，载荷为2 kg、转速为40 r/min、预磨时间为30 min、磨粒粒径为200~550 μm，并采用蔡司EVO18型SEM表征预制体原孔心处磨损形貌。采用COMSOL Multiphysics 5.4有限元模拟预制体孔内熔体凝固时的热物理场。采用MATLAB R2015b通过二次开发程序数值模拟预制体原孔内W质量分数分布。
2. 结果与分析
2.1 WC/Fe复合材料复合层的显微组织与元素分布
图2为不同预制体孔径下WC/Fe复合材料复合层的显微组织。熔体填充预制体孔洞，WC高温下分解，W由其孔壁扩散至孔心处，形成复合层。图3为不同预制体孔径下WC/Fe复合材料复合层原孔内的平均晶粒尺寸分布，随预制体孔径增加，其原孔壁处晶粒尺寸基本不变，而在其原孔心处先减小后增大。
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图 3 不同预制体孔径下WC/Fe复合材料复合层原孔内的平均晶粒尺寸分布Figure 3. Average grain size distribution into initial hole of layer in WC/Fe composites with different hole diameters of preform图4为不同预制体孔径下WC/Fe复合材料复合层原孔内的平均晶粒尺寸分布。表明复合层中均形成W2C、WC、Ni17W3、Fe3W3C、(Fe,Cr)3C。根据W-C相图，WC/W2CP中WC分解形成W2C、C，而C扩散到熔体中使(Fe,Cr)3C增多；根据Fe-W-C相图，熔体与W2C发生包晶反应形成Fe3W3C；WC、Ni60分解使W、Ni质量分数增加，形成镍钨化合物Ni17W3。
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图 2 不同预制体孔径下WC/Fe复合材料复合层的显微组织Figure 2. Microstructure of layer in WC/Fe composites with different hole diameters of preform![]()
图 4 不同预制体孔径下WC/Fe复合材料复合层的物相组成Figure 4. Phase composition of layer in WC/Fe composites with different hole diameters of preform根据Fe-Cr-C相图[18-19]，推测熔体(Cr：18.0wt%~20.0wt%，C：1.2wt%~1.3wt%)为典型亚共晶成分合金(Cr：11.0wt%~30.0wt%，C：<2.8wt%)，凝固时先析出一次奥氏体枝晶，待温度降至共晶点发生共晶转变形成共晶奥氏体与二次碳化物的混合共晶组织，而复合层为网状形貌的M3C型碳化物[7,20]。图5为不同预制体孔径下WC/Fe复合材料复合层的元素分布。Cr分布在共晶奥氏体与二次碳化物中，W、Ni弥散分布在一次奥氏体枝晶内。
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图 5 不同预制体孔径下WC/Fe复合材料复合层的元素分布Figure 5. Element distribution of layer in WC/Fe composites with different hole diameters of preform图6为不同预制体孔径下WC/Fe复合材料复合层原孔内的W质量分数分布。其原孔壁处W质量分数较高，而在其原孔心处较低。与晶粒尺寸的变化相反，随预制体孔径增加，其原孔壁处W质量分数基本不变，而在其原孔心处先增大后减小。为进一步表征W扩散均匀性，通过计算得不同预制体孔径下W扩散均匀性分别为84.1%、88.7%、86.9%，表明W扩散均匀性随其孔径增加而先增大后减小，W扩散均匀性的表达式为
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图 6 不同预制体孔径下WC/Fe复合材料复合层原孔内的W质量分数分布Figure 6. W mass fraction distribution into initial hole of layer in WC/Fe composites with different hole diameters of preformδ=1−2√3πR2C(0,tmax (1) 式中：δ为W扩散均匀性；C(0,tmax)、C(R/2,tmax)分别为预制体原孔壁、原孔心处W质量分数。
2.2 WC/Fe复合材料复合层的硬度分布与耐磨性
图7为不同预制体孔径下WC/Fe复合材料复合层原孔内的硬度分布。其原孔壁处硬度较高，而在其原孔心处较低。与W质量分数的变化相同，随预制体孔径增加，其原孔壁处硬度基本不变，而在其原孔心处先增大后减小。图8为不同预制体孔径下WC/Fe复合材料复合层原孔心处的磨损形貌。R=3 mm时其原孔心处犁沟最明显，R=9 mm时次之，R=6 mm时最不明显。图9为不同预制体孔径下WC/Fe复合材料复合层的磨损量。表明复合层耐磨性随其孔径增加而先增大后减小。
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图 7 不同预制体孔径下WC/Fe复合材料复合层原孔内的硬度分布Figure 7. Hardness distribution into initial hole of layer in WC/Fe composites with different hole diameters of preform![]()
图 8 不同预制体孔径下WC/Fe复合材料复合层原孔心处的磨损形貌Figure 8. Wear morphologies at initial hole center of layer in WC/Fe composites with different hole diameters of preform![]()
图 9 不同预制体孔径下WC/Fe复合材料复合层的磨损量Figure 9. Wear amount of layer in WC/Fe composites with different hole diameters of preform2.3 WC/Fe复合材料复合层的W扩散均匀性机制
为进一步探究影响W扩散均匀性的因素，对预制体原孔内W质量分数分布进行数值模拟。将W扩散区看作受固液界面移动驱动的半无限大物体，且扩散时间近似为预制体孔内熔体凝固时间[21-22]。下式为W扩散区边界条件的表达式：
\left\{ \begin{array}{l} C\left( {x,t} \right) = {C_{{\rm{SL}}}},x = x\left( t \right) \\ C\left( {x,t} \right) = {C_{{\rm{LS}}}},x < x\left( t \right) \end{array}\right. (2) 式中，CSL、CLS分别为固液界面固、液相侧W质量分数。根据Arrhenius方程，W质量分数分布为
\left\{ \begin{array}{l} C\left( {x,t} \right) = \dfrac{{{C_{{\rm{SL}}}}}}{{{\rm{erf}}\left( k \right) - 1}}\left( {{\rm{erf}}\left( {\dfrac{x}{{2\sqrt {Dt} }}} \right) + 1} \right) \\ D = {D_0}{\rm{exp}}\left( { - \dfrac{{{E_{\rm{A}}}}}{{{k_{\rm{B}}}T}}} \right) \end{array} \right. (3) 式中：x为W扩散距离；t为W扩散时间；T为W扩散温度；D为W扩散系数；k为常数；EA为W元素扩散激活能；kB为玻尔兹曼常数[22]。W扩散总时间为
{t_{{\rm{max}}}} = \frac{{{R^2}}}{{64{k^2}D}} (4) 通过解析解得W扩散过程同时受温度与固液界面移动影响。故先采用有限元模拟软件COMSOL Multiphysics 5.4模拟预制体孔内熔体凝固时的温度场与相场，表4为预制体孔内熔体凝固时热物理场模拟的参数设置。图10为预制体孔内熔体凝固时热物理场的有限元模拟。发现固液界面明显存在，且其左侧温度较高，熔体为液相，而其右侧温度较低，熔体为固相，即其孔壁处熔体先凝固，且固液界面移动驱动W扩散。此外，随预制体孔径增加，其孔内熔体高温区增多，使其平均温度增高，W扩散系数受W扩散温度影响，扩散温度越高扩散系数越大，其原孔内W质量分数分布曲线斜率绝对值越大；图11为不同预制体孔径下WC/Fe复合材料复合层原孔内W质量分数分布的数值模拟。再将该有限元模拟结果代入数学分析软件MATLAB R2015b的二次开发程序中进行数值模拟，最终得其原孔内W质量分数分布曲线，发现其原孔内W质量分数为W扩散距离的单调递减函数。因预制体孔径孔距比相同且W扩散区为受固液界面移动驱动的半无限大物体，故设置W初始质量分数相同。随预制体孔径增加，其原孔内W质量分数分布曲线斜率绝对值增大，故R=3 mm时其原孔心处W质量分数较R=6 mm时低，但R=6 mm时W扩散距离较R=9 mm时短，故其原孔心处W质量分数R=6 mm时最高，R=9 mm时次之，R=3 mm时最低，即该数值模拟与实验结果相符。
表 4 预制体孔内熔体凝固时热物理场模拟的参数设置Table 4. Parameters setting of thermal physical field simulation when internal matrix of preform solidifiesPhase Density/(kg·m−3) Thermal conductivity/(W·m−1·K−1) Heat capacity/(J·kg−1·K−1) Fe(s) 8 500 200 400 Fe(l) 7 800 450 550 Inlet temperature/°C Melting temperature/°C Temperature transition half width/K Surface emissivity 1 500 1 100 50 0.8 Specific heat/(J·kg−1·K−1) Solidification latent heat/(kJ·kg−1) Heat transfer coefficient/(W·m−2·K−1) 60 200 800 ![]()
图 10 不同预制体孔径下孔内熔体凝固时热物理场的有限元模拟Figure 10. Finite element simulation of thermal physical field when internal matrix solidifies with different hole diameters of preform![]()
图 11 不同预制体孔径下WC/Fe复合材料复合层原孔内W质量分数分布的数值模拟Figure 11. Numerical simulation of W mass fraction distribution in initial hole in WC/Fe composites with different hole diameters of preform预制体孔径较大时，其孔内熔体较多，温度也较高。一方面扩散时间较长，有利于W扩散；另一方面扩散距离较长，不利于W扩散均匀，使预制体原孔心处W质量分数降低。同理，预制体孔径较小时，扩散距离虽短，但扩散时间较短，使W扩散不充分，其原孔心处W质量分数较低，故W扩散均匀性也较低；故预制体孔径适中时，因兼顾扩散距离与扩散时间而使W扩散均匀性最高。综上所述，W扩散过程同时受扩散距离与扩散时间的影响。
2.4 WC/Fe复合材料复合层的耐磨性与W扩散均匀性间关联机制
亚共晶Fe-Cr-C系合金中含大量低硬度、高韧性的一次奥氏体，硬度、耐磨性较低，而W弥散分布在一次奥氏体枝晶内形成M6C型碳化物Fe3W3C，细化晶粒使复合层冲击韧性未明显降低，且引入硬质相使其硬度明显提高[20,23]，一定范围内也提高其耐磨性[24]。W扩散均匀性越高，预制体原孔心处W质量分数越高，形成硬质相越多，硬度也越高，最终提高复合层耐磨性。
3. 结 论
采用真空消失模铸渗(V-EPC)工艺制备WC/Fe复合材料，选取预制体孔径孔距比相同孔径不同的蜂窝预制体，并将其原孔壁与原孔心处W质量分数作为W扩散均匀性的判断条件，得如下结论。
(1) WC高温下分解，W由预制体孔壁至孔心处扩散，形成弥散分布的硬质相Fe3W3C。
(2)预制体原孔壁与原孔心处W质量分数与硬度相差随孔径增加而先增大后减小，复合层耐磨性的变化亦然。
(3) W扩散均匀性同时受扩散距离与扩散时间的影响。预制体孔径较小时，扩散距离虽短，但扩散时间较短，不利于W扩散；预制体孔径较大时，扩散时间虽长，但扩散距离增长，仍不利于W扩散；预制体孔径适中时，因兼顾扩散距离与扩散时间，利于W扩散。
(4)耐磨性与W扩散均匀性间存在关联，W扩散均匀性越高，预制体原孔心处W质量分数越高，形成硬质相越多，硬度也越高，一定范围内复合层耐磨性也越高。
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图 1 不同浓度Na2SO4和聚羧酸减水剂(PCS)复掺下充填浆体的坍落度测试结果
Figure 1. Slump test results of filling slurry mixed with different concentrations of Na2SO4 and polycarboxylate superplasticizer (PCS)
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图 2 复合外加剂下充填浆体凝结时间测试结果
Figure 2. Test results of setting time of filling slurry under compound admixture
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图 4 减水剂PCS的化学结构示意图 (a) 和结构模型 (b)
Figure 4. Schematic diagram of water reducer PCS chemical structure (a) and structure model (b)
R1, R2, R3— —H or —CH3; a, b, c, x, y, n—Integers greater than 1
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图 5 减水剂PCS的减水机制模型
Figure 5. Water-reducing mechanism model of water-reducing agent PCS
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图 7 复合外加剂的水泥吸附量测试结果
Figure 7. Test results of cement adsorption capacity of composite admixtures
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图 8 煤矿充填膏体(CPB)的单轴抗压强度(UCS)变化
Figure 8. Uniaxial compressive strength (UCS) change of cemented paste backfill (CPB)
①, ②—Cement content is 10wt%; ③—Cement content is 8wt%
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图 9 3天时CPB的SEM图像：(a) 对照组；(b) 0.5wt%Na2SO4+0.2wt%PCS
Figure 9. SEM images of CPB at the 3rd day: (a) Control; (b) 0.5wt%Na2SO4+0.2wt%PCS
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图 11 28天时CPB的SEM图像：(a) 对照组；(b) 0.5wt%Na2SO4+0.2wt%PCS
Figure 11. SEM images of CPB at the 28th day: (a) Control; (b) 0.5wt%Na2SO4+0.2wt%PCS
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图 12 CPB的XRD图谱
Figure 12. XRD patterns of CPB
1—Ettringite (AFt); 2—Tricalcium silicate (C3S); 3—Dicalcium silicate (C2S); 4—Calcium hydroxide (CH); 5—SiO2
表 1 充填骨料化学成分(wt%)
Table 1 Chemical composition of filling aggregate (wt%)
Material SiO2 Al2O3 Fe2O3 CaO MgO K2O Others Cement 21.38 4.23 3.58 66.49 2.50 1.07 0.74 Fly ash 53.94 30.91 2.38 6.53 0.92 1.02 4.29 Coal gangue 59.10 18.90 4.30 2.36 1.41 1.89 12.03 
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表 2 充填浆体减水率测试结果
Table 2 Test results of water reduction rate of filling slurry
Group Cement/kg Fly ash/kg Coal
gangue/kgPCS/kg Na2SO4/kg Water
consumption/kgSlump/mm Water reduction
rate/%G-0 1 4 5 0 0 3.09 22 0 G-S 0 0.005 3.09 22 0 G-PCS 0.002 0 2.91 22 5.0 G-PCS-S 0.002 0.005 2.85 22 7.7 Notes: G-0—No adding Na2SO4 and PCS; G-PCS—Adding only PCS; G-S—Adding only Na2SO4; G-PCS-S—Adding PCS and Na2SO4 at the same time.
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表 3 CPB的XRD图谱结果分析
Table 3 Analysis of XRD patterns results for CPB
2θ Name Chemical formula 8.98° Ettringite Ca6(Al(OH)6)2(SO4)3·26H2O 14.86°, 42.97°, 43.27° Tricalcium silicate C3S 15.57°, 32.66° Dicalcium silicate C2S 18.04°, 34.11°, 47.12° Calcium hydroxide Ca(OH)2 21.06°, 26.73°, 36.92°, 42.89° Quartz SiO2
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