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为了测试碳/碳复合材料的热扩散系数，本文提出了非线性拟合用于透射式脉冲红外检测的数据处理方法.非线性拟合通过循环迭代的方法持续调整拟合参数，让理论值不断逼近实验值，直至获得最佳结果.传统的透射式脉冲红外成像技术利用半高时间法测试材料的热扩散系数，但通常会受到采集时间不足和信噪比差的限制.本文提出的非线性拟合方法可以有效消除或减弱这两种影响.在使用该方法之前，首先选用常见的304不锈钢评估了该方法的测量精度及拟合长度对测试结果的影响.结果显示304不锈钢的测量精度达到0.3%，且当拟合长度不小于半高时间法采集时间的1/5时，拟合长度对非线性拟合结果影响很小.随后使用该拟合方法测试了不同厚度的碳/碳复合材料试件，并通过热扩散系数测量结果分析了试件之间的热参数差异性和材料自身的均匀性.In order to measure diffusivity of carbon/carbon composite,a nonlinear fitting method for data processing of transmission pulsed infrared thermography is proposed.It is a kind of method of comparing the experimental data with the theoretical values under a fitting parameter and obtaining the optimal result by an iteration method.Traditional half rise time method calculates the diffusivity through searching the half maximum temperature rise time,which is very difficult when a long capture time is required or a big temperature rise is needed.Unlike the traditional half rise time method,the nonlinear data fitting method can effectively eliminate the capture time restriction and weaken the badsignal-to-noise ratio effects.Before applying this method to carbon/carbon composite examination,a common stainless steel 304 specimen that has reliable diffusivity indicated in the literature,is employed to evaluate the measurement accuracy and confirm the effect of fitting length on the fitting results.The examination results illustrate that the measurement accuracy of stainless steel 304 is as high as 0.3%,and the influence is very small if the fitting data length keeps no less than 1/5 that of half rise time method (t1/2).Specifically,the fitting result changes less than 1% when the fitting length varies from 1 to 4 times of t1/2.With this evaluation result,the nonlinear fitting method is further applied to testing 6 carbon/carbon composite specimens from both sides of each specimen.Furthermore,the diffusivity differences among the specimens and the uniformities of the materials are analyzed through the thermal diffusivity results gained from the examination.The results demonstrate that average diffusivity values of both sides are similar,but the diffusivities among the specimens are different greatly.Of the diffusivities of specimens,the diffusivity value 5.125 is the smallest,while the diffusivity value 6.915 is the biggest.The gap between them is nearly 30% of their mean value. Some nonuniformity areas are also examined from the diffusivity images of carbon/carbon composite samples.So we can obtain not only diffusivity values but also uniformity information of the carbon/carbon composite from this nonlinear fitting transmission thermography examination.
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Keywords:
- nonlinear data fitting /
- transmission pulsed thermography /
- carbon/carbon composites /
- diffusivity measurement
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[5] Lipaev A A 2012 Meas. Tech. 54 1264
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[19] Song X L, An J R 2008 Xinbian Zhongwai Jinshu Cailiao Shouce (Beijing:Chemical Industry Press) p1029(in Chinese)[宋小龙, 安继儒2008新编中外金属材料手册(北京:化学工业出版社)第1029页]
[20] Kothandaraman C P, Subramanyan S 2013 Heat and Mass Transfer Data Book (London:New Academic Science) contd. 6
[21] Sun J G 2006 J. Heat Trans. 128 329
[22] Yi F J, Liang J, Meng S H, Du S Y 2012 J. Aeronaut. Mater. 22 16(in Chinese)[易法军, 梁军, 孟松鹤, 杜善义2012航空材料学报 22 16]
[23] Mao S S, Cheng Y M, Pu X L 2011 Probability Theory and Mathematical Statistics (Beijing:Higher Education Press) p305(in Chinese)[茆诗松, 程依明, 濮晓龙2011概率论与数理统计教程(第2版)(北京:高等教育出版社)第305页]
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[1] Windhorst T, Blount G 1997 Mater. Design 18 11
[2] Li H J, Luo R Y, Yang Z 1997 J. Mater. Eng. 8 8(in Chinese)[李贺军, 罗瑞盈, 杨峥1997材料工程 8 8]
[3] ASTM E1225-042004 Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique (West Conshohocken:ASTM International) pp1-8
[4] Tan J C, Tsipas S A, Golosnoy I O, Curran J A, Paul S, Clyne T W 2006 Surf. Coat. Technol. 201 1414
[5] Lipaev A A 2012 Meas. Tech. 54 1264
[6] Nagao Y, Yamada T, Yoshida A, Kagata K 2015 Int. J. Thermophys. 36 709
[7] Batty W J, Ocallaghan P W, Probert S D 1984 Appl. Energy 16 83
[8] Parker W J, Jenkins R J, Butler C P, Abbott G L 1961 J. Appl. Phys. 32 1679
[9] ASTM E1461-072007 Standard Test Method for Thermal Diffusivity by the Flash Method (West Conshohocken:ASTM International) pp1-11
[10] Min S, Blumm J, Lindemann A 2007 Thermochim. Acta 455 46
[11] Tao N, Zeng Z, Feng L C, Zhang C L 2012 Acta Phys. Sin. 61 174212(in Chinese)[陶宁, 曾智, 冯立春, 张存林2012 61 174212]
[12] Sun J G, Tao N 2016 AIP Conf. Proc. 1706 100004
[13] Zeng Z, Tao N, Feng L C, Zhang C L 2013 Acta Phys. Sin. 62 138701(in Chinese)[曾智, 陶宁, 冯立春, 张存林2013 62 138701]
[14] Chen D P, Zeng Z, Zhang C L, Jin X Y, Zhang Z 2012 Acta Phys. Sin. 61 094207(in Chinese)[陈大鹏, 曾智, 张存林, 金学元, 张峥2012 61 094207]
[15] Chen D P, Xing C F, Zhang Z, Zhang C L 2012 Acta Phys. Sin. 61 024202(in Chinese)[陈大鹏, 邢春飞, 张峥, 张存林2012 61 024202]
[16] Sun J G 2007 Int. J. Appl. Ceram. Technol. 4 75
[17] Xie Z, Li J P, Chen Z 2010 Nonlinear Optimization Theory and Methods (Beijing:Higher Education Press) pp168-186(in Chinese)[谢政, 李建平, 陈挚2010非线性最优化理论与方法(北京:高等教育出版社)第168–186页]
[18] Kelley C T 1999 Iterative Methods for Optimization (Philadelphia:Society for Industrial and Applied Mathematics) pp13-35
[19] Song X L, An J R 2008 Xinbian Zhongwai Jinshu Cailiao Shouce (Beijing:Chemical Industry Press) p1029(in Chinese)[宋小龙, 安继儒2008新编中外金属材料手册(北京:化学工业出版社)第1029页]
[20] Kothandaraman C P, Subramanyan S 2013 Heat and Mass Transfer Data Book (London:New Academic Science) contd. 6
[21] Sun J G 2006 J. Heat Trans. 128 329
[22] Yi F J, Liang J, Meng S H, Du S Y 2012 J. Aeronaut. Mater. 22 16(in Chinese)[易法军, 梁军, 孟松鹤, 杜善义2012航空材料学报 22 16]
[23] Mao S S, Cheng Y M, Pu X L 2011 Probability Theory and Mathematical Statistics (Beijing:Higher Education Press) p305(in Chinese)[茆诗松, 程依明, 濮晓龙2011概率论与数理统计教程(第2版)(北京:高等教育出版社)第305页]
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