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On-line Access: 2014-05-04

Received: 2014-02-13

Revision Accepted: 2014-03-27

Crosschecked: 2014-04-22

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Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.5 P.323-330


Measurement of thermal expansion at low temperatures using the strain gage method

Author(s):  Ke Tang, Long Sha, Yi-jian Li, Tao Jin, Shu-juan Liu

Affiliation(s):  . Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   ktang@zju.edu.cn

Key Words:  Thermal expansion, Linear contraction, Strain gage method, Cryogenic temperature

Ke Tang, Long Sha, Yi-jian Li, Tao Jin, Shu-juan Liu. Measurement of thermal expansion at low temperatures using the strain gage method[J]. Journal of Zhejiang University Science A, 2014, 15(5): 323-330.

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%A Ke Tang
%A Long Sha
%A Yi-jian Li
%A Tao Jin
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T1 - Measurement of thermal expansion at low temperatures using the strain gage method
A1 - Ke Tang
A1 - Long Sha
A1 - Yi-jian Li
A1 - Tao Jin
A1 - Shu-juan Liu
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VL - 15
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A1400051

Accurate thermal expansion data of material at low temperatures are important in material selection and structural design for a cryogenic system. In this study, an experimental setup with a proportional-integral-derivative (PID) temperature control system was developed to measure the thermal expansion of solid materials at low temperatures (77–293 K), using the strain gage method. To avoid the impact of the varied sensitivity coefficient of the strain gage with the temperature to ensure an accurate measurement, we corrected the sensitivity coefficient in the temperature range of 77–293 K, by comparing the measured thermal expansion data for 304 stainless steel with the source data from the National Institute of Standards and Technology, USA. With the corrected sensitivity coefficient of the strain gage, the measured linear contractions of oxygen-free copper become quite consistent with the NIST data (with a relative deviation of 2.37%) for the cooling-down process from 293 K to 80 K.


创新要点:完成了卡玛合金箔应变片在77-293 K低温温区敏感系数的修正,保证了基于应变片技术的低温条件材料热膨胀特征参数测量的精度;所研制装置合理的热设计和等速率式温度控制模式使得材料热膨胀特征参数在77-293 K温区的测量可在14小时内快速完成。
研究方法:针对77-293 K温区,基于应变片测量方法,研制了采用比例-积分-微分(PID)温控系统的固体材料热膨胀特征参数测量装置(见图2和3)。通过将304不锈钢的测量数据与美国国家标准与技术研究院(NIST)公布数据进行比较,完成了卡玛合金箔应变片在77-293 K低温温区的敏感系数修正(见图7和8)。采用修正后的敏感系数进行无氧铜线性收缩率测量,并与NIST公布数据比较(见图9和表2),验证了该装置在77-293 K低温温区的测量精度。
重要结论:获得了77-293 K低温温区卡玛合金箔应变片敏感系数的修正结果;基于修正敏感系数的应变片法测量装置,采用0.3 K/min的等速率式温度控制模式,可实现77-293 K低温温区固体材料热膨胀特征参数的精确、快速测量。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] ASTM E228-2006, . Standard Test Method for Linear Thermal Expansion of Solid Materials with a Push-rod Dilatometer. American Society for Testing Materials, :

[2] Clark, A.F., 1968. Low temperature thermal expansion of some metallic alloys. Cryogenics, 8(5):282-289. 

[3] Corruccini, R.J., Gniewek, J.J., 1961. Thermal Expansion of Technical Solids at Low Temperatures: A Compilation from the Literature, US Department of Commerce, National Bureau of Standards,:

[4] Deng, D.Q., Xu, L., 2003. Measurements of thermal expansion coefficient of phenolic foam at low temperatures. Cryogenics, 43(8):465-468. 

[5] Hannah, R.L., Reed, S.E., 1992.  Strain Gage Users Handbook. Elsevier Science Publishers Ltd.,London :

[6] James, J.D., Spittle, J.A., Brown, S.G.R., 2001. A review of measurement techniques for the thermal expansion coefficient of metals and alloys at elevated temperatures. Measurement Science and Technology, 12(3):R1

[7] Kaufman, A., 1963. Investigation of strain gages for use at cryogenic temperatures. Experimental Mechanics, 3(8):177-183. 

[8] Poore, M.W., Kesterson, K.F., 1978. Measuring the thermal expansion of solids with strain gages. Journal of Testing Evaluation, 6(2):98-102. 

[9] Scalea, F.L., 1998. Compensation of thermal output of strain gages on orthotropic materials: case of one compensating gage for multiple active ones. Experimental Techniques, 22(6):30-33. 

[10] Tezvergil, A., Lassila, L.V.J., Vallittu, P.K., 2003. The effect of fiber orientation on the thermal expansion coefficients of fiber-reinforced composites. Dental Materials, 19(6):471-477. 

[11] Valentich, J., 1985. Thermal expansion of solids from −261 °C to 173 °C using strain gauges. Cryogenics, 25(2):63-67. 

[12] Walsh, R.P., Reed, R.P., 1994. Thermal expansion measurements of resins (4 K–300 K).  Advances in Cryogenic Engineering Materials. Springer,USA :1145-1151. 

[13] Yamaura, Y., 1991. Measurement of strain and displacement in cryogenic environment with strain gauges. Cryogenics, (in Japanese),26(6):448-455. 

[14] Yasmin, A., Daniel, I.M., 2004. Mechanical and thermal properties of graphite platelet/epoxy composites. Polymer, 45(24):8211-8219. 

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