亚表面异质缺陷对功能梯度材料表面温度场的影响

马晓波; 王飞; 陈德珍

doi:10.7498/aps.63.194401

摘要

基于双曲型热传导方程，采用镜像法和波函数展开法，求解了含亚表面异质圆柱缺陷的半无限功能梯度材料的表面温度场，给出了功能梯度材料中热波散射的一般解. 分析了亚表面异质圆柱缺陷的几何参数（如埋藏深度）和热物理参数（如导热系数、热扩散长度、热扩散率及热弛豫时间等）对功能梯度材料表面温度场的影响. 温度波由调制的超短脉冲激光在功能梯度材料表面激发，异质圆柱缺陷表面的边界条件为导热边界. 研究结果可望为功能梯度材料的红外热波无损检测、导热反问题提供计算方法和参考数据.

关键词:

Abstract

In this paper, based on the hyperbolic equation of heat conduction, utilizing the image method and the wave function expansion method, the temperature distributions on the surface of a functionally graded material(FGM) containing a cylindrical inclusion are investigated. According to the model of thermal waves, a general solution of scattered fields of thermal waves is obtained. Effects of different physical parameters (such as the depth of buried inclusion, the thermal conductivity, the thermal diffusion length, the thermal diffusivity, and the thermal relaxation time) on the distribution of temperature are analyzed. The thermal waves are excited on the surface of the FGM by a periodically modulated laser. A cylindrical defect is taken as an inclusion under a thermal conduction condition. Results are expected to provide calculation methods and reference data for infrared thermal wave nondestructive evaluation of an FGM and the inverse problems in mathematical physics.

Keywords:

functionally graded material /
hyperbolic equation of heat conduction /
temperature distributions /
cylindrical inclusion

作者及机构信息

1.
同济大学, 机械与能源工程学院, 上海 201804

基金项目: 国家自然科学基金（批准号：51276129）和高超声速冲压发动机技术重点实验室基金（批准号：20130103007）资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, Tongji University, Shanghai 201804, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51276129), and the Open Project of the State Key Engine Laboratory of Aerospace Engineering (Grant No. 20130103007).

参考文献

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[2]	Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[3]	Akbarzadeh A H, Chen Z T 2012 Int. J. Thermophys. 33 1100
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[9]	Atefi G, Talaee M R 2011 Arch. Appl. Mech. 81 569
[10]	Mishra S C, Sahai H 2012 Int. J. Heat Mass Transfer 55 7015
[11]	Yu J G, Wu B, He C F 2010 Int. J. Eng. Sci. 48 1709
[12]	Liu X Z, Zhu Y, Zhang F, Gong X F 2013 Chin. Phys. B 22 024301
[13]	Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[14]	Zhao W T, Wu J H 2013 Acta Phys. Sin. 62 184401(in Chinese) [赵伟涛, 吴九汇 2013 物理学报 62 184401]
[15]	Ma X B, Tan H P 2006 J. Funct. Mater. 37 1507(in Chinese) [马晓波, 谈和平 2006 功能材料 37 1507]
[16]	Bakkali A, Azrar L, Aljinaidi A A 2013 J. Intell. Mater. Syst. Struct. 24 1754
[17]	Gray L J, Kaplan T, Richardson J D 2003 J. Appl. Mech.-T. ASME 70 543
[18]	Sutradhar A, Paulino G H, Gray L J 2002 Eng. Anal. Bound. Elem. 26 119
[19]	Wang Z X, Guo D R 1979 Special Functions (Beijing: Science Press) pp437-438 (in Chinese) [王竹溪, 郭敦仁 2003 特殊函数概论(北京: 科学出版社)第437–438页]
[20]	Wu Q R, Wu J Q 1996 J. Inorg. Mater. 2 343 (in Chinese) [吴清仁, 吴建青 1996 无机材料学报 2 343]
[21]	Wu Q R, Liu Z Q 2003 Thermal Physics of Inorganic functional materials (Guangzhou: South China University of Technology Press) pp108-420 (in Chinese) [吴清仁, 刘镇群 2003 无机功能材料热物理(广州: 华南理工大学出版社)第108–420页]

施引文献

[1]	Asemi K, Ashrafi H, Salehi M, Shariyat 2013 Acta Mech. 224 1849
[2]	Li Q H, Chen S S, Zeng J H 2013 Chin. Phys. B 22 120204
[3]	Akbarzadeh A H, Chen Z T 2012 Int. J. Thermophys. 33 1100
[4]	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, 张铮, 张存林 2012 物理学报 61 024202]
[5]	Wang Y Z, Song X N 2012 Acta Phys. Sin. 61 234601(in Chinese) [王颖泽, 宋新南 2012 物理学报 61 234601]
[6]	Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273
[7]	Cattaneo C 1958 Atti Sem. Mat. Fis. Univ. Modena 3 83
[8]	Terron J M, Sanchez-Lavega A, Salazar A 2001 J. Appl. Phys. 89 5696
[9]	Atefi G, Talaee M R 2011 Arch. Appl. Mech. 81 569
[10]	Mishra S C, Sahai H 2012 Int. J. Heat Mass Transfer 55 7015
[11]	Yu J G, Wu B, He C F 2010 Int. J. Eng. Sci. 48 1709
[12]	Liu X Z, Zhu Y, Zhang F, Gong X F 2013 Chin. Phys. B 22 024301
[13]	Xu H Y, Qi H T, Jiang X Y 2013 Chin. Phys. B 22 014401
[14]	Zhao W T, Wu J H 2013 Acta Phys. Sin. 62 184401(in Chinese) [赵伟涛, 吴九汇 2013 物理学报 62 184401]
[15]	Ma X B, Tan H P 2006 J. Funct. Mater. 37 1507(in Chinese) [马晓波, 谈和平 2006 功能材料 37 1507]
[16]	Bakkali A, Azrar L, Aljinaidi A A 2013 J. Intell. Mater. Syst. Struct. 24 1754
[17]	Gray L J, Kaplan T, Richardson J D 2003 J. Appl. Mech.-T. ASME 70 543
[18]	Sutradhar A, Paulino G H, Gray L J 2002 Eng. Anal. Bound. Elem. 26 119
[19]	Wang Z X, Guo D R 1979 Special Functions (Beijing: Science Press) pp437-438 (in Chinese) [王竹溪, 郭敦仁 2003 特殊函数概论(北京: 科学出版社)第437–438页]
[20]	Wu Q R, Wu J Q 1996 J. Inorg. Mater. 2 343 (in Chinese) [吴清仁, 吴建青 1996 无机材料学报 2 343]
[21]	Wu Q R, Liu Z Q 2003 Thermal Physics of Inorganic functional materials (Guangzhou: South China University of Technology Press) pp108-420 (in Chinese) [吴清仁, 刘镇群 2003 无机功能材料热物理(广州: 华南理工大学出版社)第108–420页]

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