A NON-SCHMID CRYSTAL PLASTICITY FINITE ELEMENT APPROACH TO MULTI-SCALE MODELING OF NICKEL-BASED SUPERALLOYS

This paper develops non-Schmid crystal plasticity constitutive models at two length scales, and bridges them in a multi-scale framework. The constitutive models address thermomechanical behavior of Nickel-based superalloys for a large temperature range, viz. 300K to 1223K, and include orientation dependencies and tension-compression asymmetry. The orientation dependencies result in tension-compression asymmetry for almost all orientations on the standard unit triangle. However simulations show different trends for the stronger direction (tension or compression) in terms of yield stress and hardening. The multi-scale framework includes two sub-grain and homogenized grain scales. For the sub-grain scale, a size-dependent, dislocation density-based FEM model of the representative volume element (RVE) with explicit depiction of the $\gamma \text{-}{\gamma }^{\text{'}}$ morphology is developed as a building block for homogenization. For the next scale, an activation energy based crystal plasticity (AE-CP) model is developed for single crystal Ni-based superalloys. The homogenized AE-CP model develops functional forms of constitutive parameters in terms of characteristics of the subgrain $\gamma \text{-}{\gamma }^{\text{'}}$ microstructural morphology including ${\gamma }^{\text{'}}$ shape, volume fraction and $\gamma$ channel-width in the sub-grain microstructure. This homogenized model can significantly expedite crystal plasticity FE simulations due to the parametrized representation, while retaining accuracy.