Kelvin Modes Based Cubic Plasticity and Induced Anisotropic Damage: Application to Creep of AM1 Single Crystal

Abstract

Modelling the anisotropic elasto-visco-plastic and damage behavior of FCC single crystal superalloys is a crucial issue, especially in the aircraft engines industry that widely uses such alloys for parts such as turbine blades. If micro-scale written models based on the theory of crystal plasticity and developed at the slip system level have already proved efficient in several loading cases, it is also possible to propose a novel meso-scale model based on Kelvin decomposition of  Hooke elasticity tensor which is here applied to the initial cubic symmetry of these superalloys. Three modes (and three corresponding stresses) are then highlighted and used to build a yield criterion which is extended to plasticity and then to visco-plasticity; this fully defined model is identified and validated on different loading cases. The Kelvin modes decomposition also enables the full construction of an anisotropic damage model (described by a second order tensor damage variable), from the definition of a cubic effective stress ensuring the coupling of elasto-visco-plasticity (micro- or meso-scale written) with damage, to the incremental damage law. Coupling is here detailed and carried out at 950 °C for $\langle 001\rangle , \langle 111 \rangle$ and $\langle 011 \rangle$ oriented creep (primary to tertiary) of AM1 single crystal, thus validating the proposed visco-plastic and damage models and corresponding parameters sets that are easily identified thanks to the decoupling of Kelvin modes in crystalline orientations $\langle 001 \rangle$ and $\langle 111 \rangle$.