Damage monitoring model of shape memory alloy composites based on strain transfer
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摘要:
复合材料由于其优异的性能已被广泛应用在各个领域，然而其损伤监测一直是国内外学者亟待解决的难点之一。近些年来有学者提出将形状记忆合金 (Shape Memory Alloy，SMA) 作为传感器，实现对基体材料健康情况的实时监测。本文将SMA埋入复合材料，应用SMA电阻传感特性和复合材料应变传递关系，建立了基于应变传递的SMA复合材料损伤监测模型。基于该模型，分析了马氏体体积分数、界面层厚度和SMA埋入长度等材料参数对SMA和复合材料平均应变传递率的影响，并讨论了SMA在不同初始状态和温度下的损伤监测行为。 马氏体体积分数和平均应变传递率的关系 $ {{\text{A}}_s} $ <$ T $ <$ {{\text{A}}_f} $ 时SMA电阻相对变化和应变的关系Abstract: Composite materials have been widely used in architecture, medicine, aerospace and other fields because of their excellent properties, however, the damage monitoring of composite materials has always been one of the difficult problems concerned by experts and scholars at home and abroad. In this paper, shape memory alloy (SMA) was embedded in the composite, and the strain transfer effect of the interface layer was considered. Using the resistance sensing characteristics of SMA, a plastic damage monitoring model of SMA composite based on strain transfer was established, which realizes the real-time monitoring of plastic damage strain of composite materials. Based on the monitoring model, the effects of different material parameters on the average strain transfer rate between SMA and composite were discussed, and the damage monitoring behaviors of SMA under different initial states and temperature conditions were discussed. The results show that decreasing the thickness of the interface layer, increasing the shear modulus of the interface layer and increasing the embedded length of SMA all increase the average strain transfer rate of the interface. The change of SMA resistance and the plastic damage strain of the composite are piecewise linear. This study can provide a theoretical basis for further optimization design and application of SMA composite damage monitoring.-
Key words:
- shape memory alloy /
- damage monitoring /
- strain transfer /
- interface /
- composite materials
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图 1 形状记忆合金(SMA)复合材料板示意图
Figure 1. Schematic diagram of shape memory alloys (SMA) composite material plate
图 2 三相分析模型(a)、纵剖图(b)、横剖图
Figure 2. Three phase analysis model (a), transverse sections (b), longitudinal sections
2L–Length;$ {{{r}}_{\rm{f}}} $–SMA fiber radius;$ {{{r}}_{\rm{i}}} $–Interface layer radius
图 3
$ d{\text{x}} $ 微元段SMA复合材料应力分布Figure 3. Stress distribution of
$ d{\text{x}} $ microelement SMA composite$ {\sigma _m} $–Composite axial stress; $ {\sigma _i} $–Interface layer axial stress; $ {\sigma _f} $–SMA fiber axial stress;$ {\tau _{{\text{im}}}} $–Shear stress between interface layer and composite;$ {\tau _{{\text{fi}}}} $–Shear stress between SMA fiber and interface layer
图 4 马氏体体积分数和SMA纤维和碳纳米纤维(CNFs)/环氧树脂复合材料之间的平均应变传递率的关系
Figure 4. Relationship between martensite volume fraction and average strain transmissibility between SMA fiber and carbon nanofibers (CNFs)/epoxy resin composites
图 5 SMA埋置长度和SMA纤维和CNFs/环氧树脂复合材料之间的平均应变传递率的关系
Figure 5. Relationship between embedded length of SMA and average strain transmissibility between SMA fiber and CNFs/epoxy resin composites
图 6 界面层厚度和SMA纤维和CNFs/环氧树脂复合材料之间的平均应变传递率的关系
Figure 6. Relationship between thickness of interface layer and average strain transmissibility between SMA fiber and CNFs/epoxy resin composites
图 7 界面层剪切模量和SMA纤维和CNFs/环氧树脂复合材料之间的应变传递率的关系
Figure 7. Relationship between shear modulus of interface layer and strain transmissibility between SMA fiber and CNFs/epoxy resin composites
图 8
$ {{T}} $ <$ {{{M}}_{\rm{f}}} $ 时SMA电阻相对变化和应变的关系Figure 8. Relationship between SMA resistance relative change and strain at
$ {{T}} $ <$ {{{M}}_{\rm{f}}} $ 
图 9
$ {{{A}}_{\rm{s}}} $ <$ {{T}} $ <$ {{{A}}_{\rm{f}}} $ 时SMA电阻相对变化和应变的关系Figure 9. Relationship between SMA resistance relative change and strain at
$ {{{A}}_{\rm{s}}} $ <$ {{T}} $ <$ {{{A}}_{\rm{f}}} $ 
图 10
$ {\text{T}} $ >$ {{\text{A}}_f} $ 时SMA电阻相对变化和应变的关系Figure 10. Relationship between SMA resistance relative change and strain at
$ {\text{T}} $ >$ {{\text{A}}_f} $ 
图 11
$ {{{M}}_{\rm{f}}} $ <$ {{T}} $ <$ {{{M}}_{\rm{s}}} $ 时SMA电阻相对变化和应变的关系Figure 11. Relationship between SMA resistance relative change and strain at
$ {{{M}}_{\rm{f}}} $ <$ {{T}} $ <$ {{{M}}_{\rm{s}}} $ 表 1 SMA纤维材料参数
Table 1. SMA fiber material parameters
$ {{{E}}_A} $/MPa $ {{{E}}_M} $/MPa $ {{{M}}_f} $/℃ $ {{{M}}_s} $/℃ $ {{{A}}_s} $/℃ $ {{{A}}_f} $/℃ $ \theta $/(MPa·℃−1) 67×103 26.3×103 9 18.4 34.5 49 0.55 $ \sigma _s^{cr} $/MPA $ \sigma _f^{cr} $/MPa $ {{{C}}_M} $/(MPa·℃−1) $ {{{C}}_A} $/ (MPa·℃−1) $ {\varepsilon _L} $ $ {{v}} $ $ {{{r}}_f} $/m 100 170 8 13.8 0.067 0.33 0.001 $ {{{C}}_{M1}} $/ (Ω·m·℃−1) $ {{{C}}_{M2}} $/ (Ω·m) $ {{{C}}_{A1}} $/ (Ω·m·℃−1) $ {{{C}}_{A2}} $/ (Ω·m) $ {{{L}}_f} $/m 7×10−10 0.87×10−6 8×10−10 0.72×10−6 0.1 Notes: $ {{{E}}_A} $ and $ {{{E}}_M} $ are elastic modulus of SMA austenite and martensite; $ {{{M}}_s} $ and $ {{{M}}_f} $ are starts and ends temperature of martensitic transformation; $ {{{A}}_s} $ and $ {{{A}}_f} $ are starts and ends temperature of austenite transformation; $ \theta $ are thermal elastic modulus of SMA; $ \sigma _s^{cr} $ and $ \sigma _f^{cr} $ are SMA reorientation starts and ends critical stress; $ {{{C}}_M} $ and $ {{{C}}_A} $ are stress influence coefficient of martensite and austenite; $ {\varepsilon _L} $ are maximum residual strain of SMA; $ {{v}} $ are poisson’s ratio of SMA; $ {{{C}}_{M1}} $,$ {{{C}}_{M2}} $,$ {{{C}}_{A1}} $ and $ {{{C}}_{A2}} $ are material parameters related to resistivity; $ {{{r}}_f} $ are fiber radius of SMA; $ {{{L}}_f} $ are axial length of SMA fiber. 
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表 2 碳纳米纤维/环氧树脂基复合材料和环氧树脂材料参数[21]
Table 2. Carbon nanofibers/epoxy composites and epoxy resin material parameters[21]
$ {{{L}}_m} $/m $ {\varepsilon _{mt}} $ $ {{{G}}_i} $/GPa $ {{{r}}_i} $/m $ {{{E}}_i} $/GPa 0.1 0.0125 1.3 0.002 2.3 Notes: $ {{{L}}_m} $are axial length of composite; $ {\varepsilon _{mt}} $ are maximum elastic strain of composite; $ {{{G}}_i} $ are shear modulus of epoxy resin; $ {{{r}}_i} $ are radius of epoxy resin; $ {{{E}}_i} $ are elastic modulus of epoxy resin.
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