Determination of the Coefficient of Thermal Expansion in a Non-Linear Elastic Rod of Two Concentric Layers

Abstract

The present theoretical paper treats the problem of determination of the coefficient of thermal expansion of a rod with two concentric longitudinal layers. The layers exhibit non-linear elastic behaviour. Besides, the layers have different thickness. The rod is exposed to temperature influence. The coefficient of thermal expansion of the rod is derived by analysing the thermal strains in the two layers. Since the layers are connected, the strains in the layers are equal (this fact is used to work out an equation for determining the coefficient of thermal expansion of the rod). The case when the two layers are continuously inhomogeneous along the rod length is also considered. In this case the material properties of the layers vary continuously in longitudinal direction. Here again the layers have non-linear elastic mechanical behaviour. Analysis of the distribution of strains along the length of the rod is carried-out when deriving the coefficient of thermal expansion of the rod. A comparison with the coefficient of thermal expansion of a rod having linear-elastic mechanical behaviour is performed for check-up of the solutions obtained in the present paper.

Keywords

• Concentric layers
• Rod
• Circular section
• Coefficient of thermal expansion

References

1. Dolgov, N. (2005). Determination of stresses in a two-layer coating. Strength of Materials, 37, 422-431.
2. Hoa, S.V., Gay, D., & Tsai, S W. (2003). Composite materials (1st ed.). Boca Raton: CRC Press.
3. Kaul, A. B. (2014). Two-dimensional layered materials: Structure, properties, and prospects for device applications, Journal of Material Research, 29, 348-361.