Isotropy and anisotropy of macroscopic components

Single crystals are usually mechanically anisotropic as we saw in the preceding sections. In a polycrystalline material, the grains are frequently oriented randomly, and the mechanically anisotropic effects are evened out macroscop-ically. The material is thus approximately isotropic. 

However, there are some cases where a macroscopic component can be anisotropic  

Gas turbine blades (figure 2.13(a)) are facing extreme conditions They have to withstand large mechanical loads due to centrifugal forces at high temperature. To at least partly protect the material from the extreme gas temperatures of 1200 C or more, the blades are cooled from the inside with air of about SOO C. If the wall of the turbine blade has a thickness of about 2 mm and is exposed to the process gas with a temperature of 1200 C, its surface temperature will be about Tout = 1000°C, whereas on the inside it is only Tin = bOO C (figure 2.13(b)). Due to thermal expansion, the material would expand on the outside, but is partly constrained by the cooler inside wall. Thus, large compressive thermal stresses form on the outside and tensile stresses on the inside. In the middle of the wall, there will be a neutral axis at about T = 

800 C where thermal stresses vanish. The thermal stress 7th at any point x can be calculated approximately by 

Here T x) is the local temperature. The thermal stress is thus proportional to the coefficient of thermal expansion a and to Young s modulus E. If we can reduce Young s modulus in the direction of the thermal stresses, the stresses are reduced, thus either increasing the stress tolerance or allowing to raise the temperature and thus the efficiency of the turbine. In this context, it is irrelevant that the elastic deformations due to centrifugal loads increase when E is reduced, for they are small enough not to compromise the component in any case. 

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