Temperature change generated longitudinal fracture of inhomogeneous bars with fixed supports

Continuously inhomogeneous structural materials are characterised by smooth change of their properties in a solid. The most typical examples in this relation are the functionally graded materials that have a quickly growing use in a variety of structural applications in up-to-date engineering. In many cases different continuously inhomogeneous structural members are subjected to temperature change that may have significant influence on structural integrity. This paper aims to clarify how the longitudinal fracture of continuously inhomogeneous bars with fixed supports is affected by temperature change. In particular, we consider a bar with circular cross-section. The bar has two portions with different radius. Besides, the bar hosts a longitudinal crack representing a circular cylindrical surface. Due to the fact that the bar is statically indeterminate structure (both supports of the bar are fixed), the temperature change to which the bar is subjected induces stresses that have influence on longitudinal fracture. The problem of strain energy release rate (SERR) in the bar is solved. An approach from the literature is used for checking. Since the bar has nonlinear elastic behaviour under temperature change, the complementary strain energy is used for deriving SERR. A variety of graphs revealing the influence of temperature change and other bar model parameters on SERR are presented.