Spectral database solutions to elasto-viscoplasticity within finite elements: Application to a cobalt-based FCC superalloy

Abstract

We present a computationally efficient, multi-scale model based on crystal plasticity theory for simulations of heterogeneous plastic deformation of metallic components in commercial finite element (FE) codes. Although the model can handle a single crystal, the primary purpose with the present model is to embed a meso-scale polycrystal homogenization at a FE integration point, with the meso-scale homogenization being a Taylor-type model. The responses of single crystals are obtained using a recently developed non-iterative solver, which is based on databases of discrete Fourier transforms allowing for fast retrieval of pre-computed crystal plasticity solutions. We have shown that, when this non-iterative solver is used in place of the Newton–Raphson iterative solver, substantial wall-clock speedups can be achieved. Additionally, the implementation presented here takes the advantage of calculations of the elastic properties based on the spectral representation. To calibrate and validate the new FE elasto-viscoplastic model, we use stress-strain curves and texture data of the cobalt-based face-centered cubic superalloy Haynes 25. For this purpose, the material was deformed monotonically in compression over a wider range of strain rates and temperatures. The model is subsequently applied to simulate the macro-scale mechanical response of the material in compression and rolling. We show that the predictions of the model compare favorably with experimental measurements in terms of the mechanical response and texture evolution. Finally, the evolution of the underlying crystallographic texture in rolling predicted by the new model is compared against the corresponding predictions from the finite element visco-plastic self-consistent (FE-VPSC) model. It is observed that both implementations produce similar predictions, but the model presented here is substantially faster.