Topics: Anisotropic thermoelasticity, thermoelastic boundary value problems with cylindrical symmetry 1. Turbine blades are made from single crystal nickel superalloys. A nickel superalloy single crystal has cubic symmetry and has the following elastic constants: C11 = 246.5 GPa, c12 = 147.3 GPa, and c44 = 127.4 GPa. The thermal expansion coefficient is 14 10-6/C in all directions (isotropic thermal expansion). Suppose a small rectangular-shaped sample of initial height ho = 10 mm, where the lattice is aligned with the sample frame (e1, e2, e3), is placed between two large, relatively rigid, Invar platens as shown in Fig. 1, which constrain the height of the sample, but allow it to expand freely in the and 3 directions. Invar is used because it has a very low thermal expansion coefficient. Now suppose the sample is heated from 25C to 125C, and at the same time, the space between the Invar platens is reduced by 5 m (5 10-3 mm), thus, reducing the sample height by this amount. What is the resulting stress and strain state assuming the material remains elastic? Neglect any friction between the sample and platens. ho= 10 mm e Figure 1: Nickel single crystal sample between rigid Invar platens.