Experimental analysis and theoretical prediction to piezoresistance sensing characteristics of multiwalled carbon nanotubes/natural rubber composite
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摘要: 为实现对隔震支座工作性能的有效监测，采用开炼法制备了多壁碳纳米管(MWCNT)/天然橡胶(NR)复合材料，研究了该复合材料在恒应变和间歇加载下的电阻-应变响应行为。结果表明： MWCNT/NR复合材料电阻-应变响应稳定性、重复性、单调性、对称性及“肩峰”效应依赖恒应变载荷；随着间歇时间的增加电阻变化幅值趋于稳定，所建立的理论模型能有效预测该幅值变化。不同脱层形式下MWCNT/NR复合材料表现出不同的压阻行为，采用Digimat和Workbench解释了其响应机制。基于MWCNT导电网络和橡胶材料黏弹性，一个能够完整表征和预测循环电阻-应变响应的数学模型被提出和验证，模型拟合结果与实验结果高度吻合，为实现MWCNT/NR复合材料的工业应用奠定理论基础。
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关键词:
- 多壁碳纳米管/天然橡胶复合材料 /
- 电阻-应变响应 /
- 恒应变 /
- 间歇载荷 /
- 理论模拟
Abstract: A multiwalled carbon nanotubes (MWCNT)/natural rubber (NR) composite was prepared by two-roll method to achieve effective monitoring for the working performance of isolation bearings. The resistance-strain response behaviors of MWCNT/NR composites under constant strain and interval loading were studied. The results show that the stability, repeatability, monotonicity, symmetry and ‘shoulder peak’ effect of the resistance-strain response are depended on the constant strain loading. The variation amplitude of resistance tends to be stable with the increase of interval time, and the change of the amplitude can effectively be predicted via the theoretical model established. The piezoresistance behaviors for MWCNT/NR composite under different delamination forms show distinct characteristic, and the response mechanism is explained by Digimat and Workbench. A mathematical model that can completely characterize and predict the dynamic resistance-strain response was established and verified based on viscoelasticity of NR and conductivity network of MWCNT. The analytical results obtained by mathematical model are in good agreement with the experimental results, which lay a theoretical foundation for the industrial application of MWCNT/NR composites. -
图 1 压敏测试系统
Figure 1. Testing system of compression sensitive
MWCNT—Multiwalled carbon nanotubes; NR—Natural rubber
图 2 多壁碳纳米管(MWCNT)/天然橡胶(NR)复合材料在不同恒应变下的电阻-应变响应(a)、最大灵敏系数(b)和机制示意图(c)
Figure 2. Resistance-strain response under different constant strain (a), maximum gauge factor (b) and mechanism diagram (c) of multiwalled carbon nanotubes (MWCNT)/natural rubber (NR) composite
R—Resistance values of composites under loading strain; R0—Initial resistance value
图 3 MWCNT/NR压缩形变及导电网络变化：(a) 位移前；(b) 位移后；(c) 导电网络位移轨迹(灰色阴影表示位移前导电网络结构；红色箭头表示位移较大的MWCNT)
Figure 3. Compressive deformation and change of conductive network of MWCNT/NR composite: (a) Without displacement; (b) After displacement; (c) Displacement trajectory of conductive network (Gray shadow represents the structure of conductive network without displacement; Red arrow represents the MWCNT with large displacement)
图 4 MWCNT/NR复合材料动态电阻-应变响应((a)~(c))和应力-时间曲线(d)
Figure 4. Dynamic resistance-strain response ((a)-(c)) and stress-time curve (d) of MWCNT/NR composites
图 5 MWCNT/NR复合材料间歇加载示意图(a)、传感响应(b)和理论模型预测结果(c)
Figure 5. Schematic diagram (a), sensing response (b) and results predicted by the theoretical model (c) of MWCNT/NR composites
RNt—Resistance value of composite at interval time t; RN0—Resistance value of the composite at the starting point of interval time
图 6 外围橡胶层(a)和上下面橡胶层(b)作用下MWCNT/NR复合材料传感特性
Figure 6. Sensing property of MWCNT/NR composite circumscribed by outer rubber (a) and upper and lower rubber layers (b)
图 7 不同脱层形式下MWCNT/NR复合材料传感行为：((a)、(a')) 恒应变0%，下脱层；(b) 恒应变10%，下脱层；(c) 恒应变20%，下脱层；(d) 恒应变20%，上下脱层；(e) 恒应变30%，上下脱层
Figure 7. Sensing behavior of MWCNT/NR composite at different delamination forms: ((a), (a')) Constant strain 0%, bottom delamination; (b) Constant strain 10%, bottom delamination; (c) Constant strain 20%, bottom delamination; (d) Constant strain 20%, top and bottom delamination; (e) Constant strain 30%, top and bottom delamination
图 8 不同脱层形式下MWCNT/NR复合材料形变及导电网络变化：((a)~(c)) 下脱层；((d)~(f)) 上下脱层(灰色阴影表示位移前导电网络结构；红色箭头表示位移较大的MWCNT)
Figure 8. Deformation and conductivity network changes of MWCNT/NR composites under different delamination forms: ((a)-(c)) Bottom delamination; ((d)-(f)) Top and bottom delamination (Gray shadow represents the structure of conductive network without displacement; Red arrow represents the MWCNT with large displacement)
图 9 下脱层MWCNT/NR复合材料不同位置的MWCNT间相对位移与加载历程曲线：(a) 试样外围；(b) 试样中部
Figure 9. Curves of relative displacement between MWCNT at different location and loading process for MWCNT/NR composite under bottom delamination: (a) Sample periphery; (b) Sample center
图 10 MWCNT/NR复合材料的理论模型与实验拟合结果及其预测曲线(a)、模型预测误差分布(b)、模型拟合参数(c)
Figure 10. Fitting result of theoretical model and experiment and its prediction curves (a), prediction error distribution (b), fitting parameters (c) of model of MWCNT/NR composite
E—Tuning parameter; εc—Yield strain; m—Parameter related to fractal structure of conductive network; $ {n}_{\epsilon }— $Exponential scale; $ \zeta —{k}_{2}{N}_{0} $, $ {k}_{2} $—Constant related to matrix properties and conductive network, $ {N}_{0} $—Number of initial conductive networks per unit volume; $ {\eta }_{1},{\eta }_{2} $and k—Constants associated with the destruction and reconstruction of the conductive network
图 11 不同恒应变下MWCNT/NR复合材料导电通路(CP) (a)和隧穿距离(TD) (b)的变化
Figure 11. Change of conductive paths (CP) (a) and tunning distance (TD) (b) of MWCNT/NR composite under different constant strain
表 1 公式(25)的拟合参数
Table 1. Fitting parameters of equation (25)
Constant strain β1 β2 β3 β4 V δV Goodness of fit 0% 0.024 1.149 10.918 −125.490 −0.114 −0.412 0.99 5% 0.106 −5.376 101.476 −456.155 −0.125 −1.689 0.99 10% 0.063 −9.600 358.092 −2333.490 −0.145 −0.868 0.99 20% 0.049 6.538 408.723 −3570.640 −0.376 −0.262 0.99 30% −0.256 50.409 72.143 −2806.220 −0.517 0.989 0.99 Notes: β1, β2, β3, β4—Parameters related to the number of conductive paths; V and δ—Constant. 
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