Thermal expansion

About: Thermal expansion is a research topic. Over the lifetime, 21040 publications have been published within this topic receiving 349407 citations. The topic is also known as: heat expansion.

An analytical model of rumpling in thermal barrier coatings

Abstract: Multilayer thermal barrier coatings (TBCs) deposited on superalloy turbine blades provide protection from combustion temperatures in excess of 1500 °C. One of the dominant failure modes comprises cracking from undulation growth, or rumpling, of the highly compressed oxide layer that grows between the ceramic top coat and the intermetallic bond coat. In this paper, a mechanistic model providing an analytical approximation of undulation growth is presented for realistic cyclic thermal histories. Thickening, lateral growth straining and high temperature yielding of the oxide layer are taken into account. Undulation growth in TBC systems is highly nonlinear and characterized by more than 20 material and geometric parameters, highlighting the importance of a robust yet computationally efficient model. At temperatures above 600 °C, the bond coat creeps. Thermal expansion mismatch occurs between the superalloy substrate and the oxide layer and, in some systems, the bond coat. In addition, some bond coats, such as PtNiAl, exhibit a martensitic phase transformation accompanied by nearly a 1% linear expansion, giving rise to a large effective mismatch. These two mismatches promote undulation growth. Nonlinear interaction between the stress in the bond coat induced by the constraining effect of the thick substrate and normal tractions applied at the surface of the bond coat by the compressed, undulating oxide layer produces an increment of undulation growth during each thermal cycle, before the stress decays by creep. A series of problems for systems without the ceramic top coat are used to elucidate the mechanics of undulation growth and to replicate trends observed in a series of experiments and in prior finite-element simulations. The model is employed to study for the first time the effect on undulation growth of a shift in the temperature range over which the transformation occurs, as well as the relative importance of the transformation compared to thermal expansion mismatch. The role of the top coat and other viable ways of reducing undulation growth are considered.

Limitations of the Fictive Temperature Concept

Abstract: The fictive temperature formalism, in which the structural state of the glass is characterized by the fictive temperature T, is very useful in the qualitative description of the effects of thermal treatment in the transformation range. Experimental data are presented which show, however, that such a one-parameter description has only a limited quantitative significance. When samples of a borosilicate crown, glass, annealed at various constant cooling rates, are compared with samples annealed at constant temperature, it is found that a single parameter does not specify all physical properties simultaneously and that the two types of samples differ markedly in transformation-range kinetic phenomena. Properties studied include density, refractive index, low-temperature thermal expansion, approach to equilibrium at constant temperature, and thermal expansion during heating in the transformation range.

Crystal structure and thermal expansion of La1-xSrxFeO3-δ materials

Abstract: Crystal structure and thermal properties of La 1-x Sr x FeO 3-δ (x = 0, 0.1, 0.3, 0.4, 0.5, and 0.75) have been studied by high-temperature X-ray diffraction and thermal analysis in air and nitrogen (p(O 2 ) 10 -3 atm) atmosphere. The first-order phase transition from orthorhombic-to-rhombohedral La 1-x -Sr x FeO 3-δ (x = 0, 0.1) was strongly shifted to lower temperatures with increasing Sr content. The phase-transition temperature was observed significantly lower in polycrystalline ceramics compared with fine powders. The temperature depression of the phase transition in the ceramics was qualitatively explained by stresses induced both by the anisotropic thermal expansion of LaFeO3 and the observed volume contraction of the phase transition. Rhombohedral La 1-x Sr x -FeO 3-δ (x = 0.3, 0.4, 0.5) were observed to transform to the cubic perovskite structure during heating. The second-order phase-transition temperature decreased with increasing Sr content and decreasing partial pressure of oxygen. On the basis of the present findings, a pseudobinary phase diagram of the LaFeO 3 -SrFeO 3-δ system is presented. Finally, a severely nonlinear thermal expansion was observed for the Sr-rich materials at high temperature. The high thermal expansion in this region is due to a chemical expansion resulting from a reduction of the valence state of Fe.