Thermal reliability testing of functionally gradient materials using thermal shock method

We found a solution of an unsteady two-dimensional heat conduction equation in a functionally gradient material (FGM) which is subjected to a double t hermal shock, namely, a local heating of a specimen by a power laser beam a nd cooling of a heated surface by a water-air spray. We developed an analyt ical method whereby a coating is described as a laminated plate composed of n layers with the constant material properties within a layer. Temperature distribution in a nonhomogeneous laminated plate is obtained in a form of series using the Laplace-Hankel integral transforms. In order to extend the model of a laminated plate to describe FGM where thermal physical characte ristics are continuous functions of spatial coordinate, we considered the l imiting case of the obtained temperature distribution when the thickness of the layer i Delta(i) --> 0, and the number of layers n --> infinity. This allowed us to obtain the temperature distribution in an easy-to-use analyti cal form which can be used for determining thermal stresses in FGM. The dep endence of the temperature distribution in FGM on the operating parameters of a double thermal shock method, e.g., a duration of heating, laser beam r adius, the rate of a spray cooling, is discussed.