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地应用于建筑、医学、航空航天等各个领域中，然而其损伤监测一直是国内外专家和学者关注的难点问题之一。本文将形状记忆合金(SMA)埋入到复合材料中，考虑了界面层的应变传递作用，利用SMA的电阻传感特性建立了基于应变传递的SMA复合材料塑性损伤监测模型，实现复合材料塑性损伤应变的实时监测。基于该监测模型讨论了不同材料参数条件对SMA和复合材料间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条件下损伤监测行为。研究结果表明：减小界面层厚度、增加界面层剪切模量及增加SMA的埋入长度均增加界面平均应变传递率，SMA电阻变化和复合材料塑性损伤应变呈分段线性关系。本文可为SMA复合材料损伤监测的进一步优化设计和应用提供理论基础。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.
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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
r—Radial direction
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 dx微元段SMA复合材料应力分布
Figure 3. Stress distribution of dx microelement SMA composite
$ {\sigma _{\rm{m}}} $—Composite axial stress; $ {\sigma _{\rm{i}}} $—Interface layer axial stress; $ {\sigma _{\rm{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 马氏体体积分数与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埋置长度与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 界面层厚度与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 界面层剪切模量与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}} $<马氏体相变结束温度($ {{{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}} $< ends temperature of martensitic transformation ($ {{{M}}_{\rm{f}}} $)
图 9 奥氏体相变开始温度($ {{{A}}_{\rm{s}}} $)<$ {{T}} $<奥氏体相变结束温度($ {{{A}}_{\rm{f}}} $)时SMA电阻相对变化和应变的关系
Figure 9. Relationship between SMA resistance relative change and strain at starts temperature of austenite trasformation ($ {{{A}}_{\rm{s}}} $)<$ {{T}} $<ends temperature of austenite trasformation ($ {{{A}}_{\rm{f}}} $)
图 10 $ {{T}} $>$ {{{A}}_{\rm{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 $ {{T}} $>$ {{{A}}_{\rm{f}}} $
图 11 $ {{{M}}_{\rm{f}}} $<$ {{T}} $<马氏体相变开始温度($ {{{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}} $< starts temperature of martensitic transformation ($ {{{M}}_{\rm{s}}} $)
表 1 SMA纤维材料参数
Table 1. SMA fiber material parameters
$ {{{E}}_{\rm{A}}} $/MPa $ {{{E}}_{\rm{M}}} $/MPa $ {{{M}}_{\rm{f}}} $/℃ $ {{{M}}_{\rm{s}}} $/℃ $ {{{A}}_{\rm{s}}} $/℃ $ {{{A}}_{\rm{f}}} $/℃ $ \theta $/(MPa·℃−1) 67×103 26.3×103 9 18.4 34.5 49 0.55 $ \sigma _{\rm{s}}^{{\rm{cr}}} $/MPa $ \sigma _{\rm{f}}^{{\rm{cr}}} $/MPa $ {{{C}}_{\rm{M}}} $/(MPa·℃−1) $ {{{C}}_{\rm{A}}} $/(MPa·℃−1) $ {\varepsilon _{\rm{L}}} $ $ {{v}} $ $ {{{r}}_{\rm{f}}} $/m 100 170 8 13.8 0.067 0.33 0.001 $ {{{C}}_{{\rm{M1}}}} $/(Ω·m·℃−1) $ {{{C}}_{{\rm{M2}}}} $/(Ω·m) $ {{{C}}_{{\rm{A1}}}} $/(Ω·m·℃−1) $ {{{C}}_{{\rm{A2}}}} $/(Ω·m) $ {{{L}}_{\rm{f}}} $/m 7×10−10 0.87×10−6 8×10−10 0.72×10−6 0.1 Notes: $ {{{E}}_{\rm{A}}} $ and $ {{{E}}_{\rm{M}}} $—Elastic modulus of SMA austenite and martensite; $ {{{M}}_{\rm{s}}} $ and $ {{{M}}_{\rm{f}}} $—Starts and ends temperature of martensitic transformation; $ {{{A}}_{\rm{s}}} $ and $ {{{A}}_{\rm{f}}} $—Starts and ends temperature of austenite transformation; $ \theta $—Thermal elastic modulus of SMA; $ \sigma _{\rm{s}}^{{\rm{cr}}} $ and $ \sigma _{\rm{f}}^{{\rm{cr}}} $—SMA reorientation starts and ends critical stress; $ {{{C}}_{\rm{M}}} $ and $ {{{C}}_{\rm{A}}} $—Stress influence coefficient of martensite and austenite; $ {\varepsilon _{\rm{L}}} $—Maximum residual strain of SMA; $ {{v}} $—Poisson's ratio of SMA; $ {{{C}}_{{\rm{M1}}}} $, $ {{{C}}_{{\rm{M2}}}} $, $ {{{C}}_{{\rm{A1}}}} $ and $ {{{C}}_{{\rm{A2}}}} $—Material parameters related to resistivity; $ {{{r}}_{\rm{f}}} $—Fiber radius of SMA; $ {{{L}}_{\rm{f}}} $—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}}_{\rm{m}}} $/m $ {\varepsilon _{{\rm{mt}}}} $ $ {{{G}}_{\rm{i}}} $/GPa $ {{{r}}_{\rm{i}}} $/m $ {{{E}}_{\rm{i}}} $/GPa 0.1 0.0125 1.3 0.002 2.3 Notes: $ {{{L}}_{\rm{m}}} $—Axial length of composite; $ {\varepsilon _{{\rm{mt}}}} $—Maximum elastic strain of composite; $ {{{G}}_{\rm{i}}} $—Shear modulus of epoxy resin; $ {{{r}}_{\rm{i}}} $—Radius of epoxy resin; $ {{{E}}_{\rm{i}}} $—Elastic modulus of epoxy resin.
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