The effect of temperature dependent elastic anisotropy on residual stresses and ratcheting in transpiration cooled Nickel gas turbine blades

Abstract

The conditions required for the ratcheting of a structure due to thermal and load cycling are typically calculated assuming a constant Young's modulus throughout the cycle. We show that this type of incremental collapse occurs at lower cyclic loads when the variation in Young's modulus with temperature is taken into account. This is because the increase of Young's modulus upon unloading from the high temperature operation state to the room temperature shutdown state enhances the residual stress field $\rho$, and therefore the cyclic variation of stresses. In this respect, we find that Koiter's kinematic shakedown theorem still works as if the material has a room temperature yield stress that decreases as $\rho$ increases. This more broadly implies that conventional shakedown and low cycle fatigue analysis methods which have relied upon the fictitious elastic stress cannot be deemed credible for high temperature problems, since any location of a structure experiences an enhanced cyclic stress variation compatible with the enhancement of $\rho$ with Young's modulus. Our practical example is a double plate unit of a transpiration cooled single crystal Nickel gas turbine blade, whereby the two-fold increase of Young's modulus upon cooldown from $1100°C$ to $20°C$ leads to compressive ratcheting at over 30% lower temperature differences than previously predicted. Our work informs the design of clean energy, transport and defence assets suffering severe thermal loads, including fusion/fission reactors, re-useable rockets, cryogenic hydrogen and transpiration cooling systems.