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International Journal of Thermophysics

, Volume 28, Issue 1, pp 60–82 | Cite as

“Thermal Mirror” Method for Measuring Physical Properties of Multilayered Coatings

  • T. Elperin
  • G. Rudin
Article

In this study theoretical principles underlying the photothermal displacement (“thermal mirror”) method for measuring physical properties of opaque multilayered and functionally graded coatings with low thermal conductivity are analyzed. In this method, the specimen is locally heated by a power laser beam, and a two-dimensional transient temperature field is formed in a specimen. The physical basis for the photothermal displacement method is the non-stationary buckling and displacement of an irradiated surface due to a non-uniform thermal expansion. The surface is monitored by a low-power probe beam of a second laser, which is reflected from the specimen, i.e., the system operates as a convex “thermal mirror.” The photoinduced displacement varies with time, and the probe beam is reflected at a different angle depending on the slope of the displacement. The deflection angle is measured as a function of time by a position sensor, and the results of these measurements are compared with the theoretical dependence of the deflection angle on time and physical properties of a coating. This dependence was determined analytically from the solution of the two-dimensional thermal elasticity problem. It is shown that for the specimen composed of a substrate and a coating it is feasible to determine the properties of the coating, e.g., the thermal diffusivity and coefficient of linear thermal expansion provided that the analogous properties of the substrate are previously measured or otherwise known.

Keywords

laser heating multilayer coating surface displacement thermal elasticity 

Nomenclature

c

specific heat

d

substrate thickness

E0

total laser power absorbed by a specimen

F0

Fourier number

G

shear module

I0

laser beam intensity absorbed by a coating

Ji (x )

ith order Bessel function of the first kind

k

thermal diffusivity

r

radial coordinate

r0

radius of a laser beam

p, s

parameters of Hankel (p) and Laplace (s) transforms with respect to r and t, respectively

t

time

T

temperature

\({\overline{\theta}(s,p,z)}\)

Laplace–Hankel transform of temperature

u, w

radial and axial components of displacement

Vm,Vc

volume content (m: metal, c: ceramics)

z

axial coordinate

α

coefficient of linear thermal expansion

\({\Delta}\)

coating thickness

\({\varepsilon}\)

laser beam deflection angle

λ

thermal conductivity

\({\theta}\)

Hankel transform of temperature

\({\nu}\)

Poisson’s ratio

σij

thermal stress

\({\sigma_{rr}, \sigma_{\Psi\Psi}}\)

radial and tangential stresses, respectively

\({\tau_{0}}\)

duration of a laser pulse

Subscripts

 

0

substrate

i =  1,...,n

number of a layer in a coating

Superscript

 

 + , −

upper and lower surfaces of a layer in a coating, respectively

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Pearlstone Center for Aeronautical Engineering StudiesBen-Gurion University of the NegevBeer-ShevaIsrael

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