亚表面缺陷对功能梯度条形板表面温度场的影响
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摘要
与半无限体结构相比,条形板要考虑其上下边界对热波的多重散射,因此引入复变函数,基于非傅立叶导热定律,采用镜像法和波函数展开法,求解了含亚表面圆柱缺陷的功能梯度条形板的表面温度场,给出了功能梯度条形板中热波散射的解析解。热波由调制的超短脉冲激光在功能梯度条形板表面激发,亚表面圆柱缺陷表面的边界条件为绝热边界,条形板上下表面的边界条件等于环境温度。分析了亚表面圆柱缺陷的几何参数和热物理参数对功能梯度条形板表面温度场的影响,并重点讨论了功能梯度条形板非均匀参数对条形板表面温度的影响。研究结果可望为功能梯度条形板的红外热波无损检测提供计算方法和参考数据。
Compared with the semi-infinite structure,the slab should consider the multiple scattering of thermal waves about the upper and lower bounds.In this paper,based on the non-Fourier heat conduction equation,the temperature distributions at the surface of functionally graded slab containing a cylindrical defect are investigat〗ed by using image method and wave function expansion method.According to the model of thermal wave,a general solution of scattered fields of thermal waves is obtained.The thermal waves are excited on the surface of functionally graded slab by periodically modulated laser.The cylindrical defect is taken as a cavity under thermal insulation condition.The boundary condition of the surface is adiabatic.Boundary conditions of the upper and lower of the functionally graded slab are equal to the environment temperature.The amplitude of the changes in temperature at the frontal surface in the cylindrical defect due to different physical and geometrical parameters is analyzed and presented graphically using the analytical method,and the impact of non-uniform parameters of functionally graded slab on surface temperature is focused on.The results of this paper are expected to provide calculation methods and references data for infrared thermal wave evaluation of functionally graded slab.
Compared with the semi-infinite structure,the slab should consider the multiple scattering of thermal waves about the upper and lower bounds.In this paper,based on the non-Fourier heat conduction equation,the temperature distributions at the surface of functionally graded slab containing a cylindrical defect are investigat〗ed by using image method and wave function expansion method.According to the model of thermal wave,a general solution of scattered fields of thermal waves is obtained.The thermal waves are excited on the surface of functionally graded slab by periodically modulated laser.The cylindrical defect is taken as a cavity under thermal insulation condition.The boundary condition of the surface is adiabatic.Boundary conditions of the upper and lower of the functionally graded slab are equal to the environment temperature.The amplitude of the changes in temperature at the frontal surface in the cylindrical defect due to different physical and geometrical parameters is analyzed and presented graphically using the analytical method,and the impact of non-uniform parameters of functionally graded slab on surface temperature is focused on.The results of this paper are expected to provide calculation methods and references data for infrared thermal wave evaluation of functionally graded slab.
引文
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[2]Asghari M,Rahaeifard M,Kahrobaiyan M H,et al.The modified couple stress functionally graded Timoshenko beam formulation[J].Materials&Design,2011,32(3):1435-1443.
[3]Li Jiawei,Chen Jimao.NDT manual[M].Beijing:China Machine Press,2002:12-50.李家伟,陈积懋.无损检测手册[M].北京:机械工业出版社,2002:12-50.
[4]Ma Xiaobo,Hu Chao,Tan Heping.Thermal wave multiple scattering by subsurface cylinders[J].Acta Optica Sinica,2005,25(12):1707-1711.马晓波,胡超,谈和平.亚表面圆柱体对热波的多重散射问题[J].光学学报,2005,25(12):1707-1711.
[5]Vandenrijt J F,Thizy C,Alexeenko I,et al.Mobile speckle interferometer in the long-wave infrared for aeronautical nondestructive testing in field conditions[J].Optical Engineering,2013,52(10):101903.
[6]Ghali V S,Mulaveesala R,Takei M.Frequency-modulated thermal wave imaging for non-destructive testing of carbon fiber-reinforced plastic materials[J].Measurement Science and Technology,2011,22(10):104018.
[7]Alexeenko I,Vandenrijt J F,Pedrini G,et al.Nondestructive testing by using long-wave infrared interferometric techniques with CO2 lasers and microbolometer arrays[J].Applied Optics,2013,52(1):A56-A67.
[8]Ma X B,Wang F,Chen D Z.Temperature distributions at the surface of functionally graded materials containing a cylindrical defect[J].Journal of Applied Physics,2014,115(20):203505.
[9]Wang Fei,Ma Xiaobo,Li Zhiyong.Multiple scattering of thermal waves by subsurface cylinders in functionally graded materials[J].Journal of Functional Materials,2014,45(15):15089-15092.王飞,马晓波,李志永.功能梯度材料中亚表面圆柱缺陷的热波散射问题研究[J].功能材料,2014,45(15):15089-15092.
[10]Ma Xiaobo,Tan Heping.Multiple scattering of thermal waves by subsurface spheroids in functionally graded materials[J].Journal of Functional Materials,2006,37(9):1507-1509.马晓波,谈和平.功能梯度材料亚表面缺陷的热波多重散射问题[J].功能材料,2006,37(9):1507-1509.
[11]Ma Xiaobo,Tan Heping.Thermal wave scattering from subsurface cylinders in the semi-infinite slab[J].Journal of Harbin Institute of Technology,2007,39(9):1453-1458.马晓波,谈和平.含缺陷半无限条形体中热波多重散射与温度分布[J].哈尔滨工业大学学报,2007,39(9):1453-1458.
[12]Bakkali A,Azrar L,Aljinaidi A A.Micromechanical modeling of magnetoelectroelastic composite materials with multicoated inclusions and functionally graded interphases[J].Journal of Intelligent Material Systems and Structures,2013,24(14):1754-1769.