An Implicit Cycle Scale Integrator For Accelerated Fatigue Simulations

The properties of polycrystalline materials are strongly influenced by the underlying microstructural features such as grain size, orientation, grain boundaries and crystal defects. Various methods such as Discrete Dislocation Dynamics (DDD), Crystal Plasticity Finite Element Method (CPFEM), Crystal Plasticity Fast Fourier Transform (CPFFT), etc. are used to simulate the mechanical behaviour of polycrystalline materials at the microstructural level; and numerous examples can be found in the literature which show the fidelity of these methods to capture microstructure sensitive grain-level phenomena in polycrystalline materials in a computationally efficient manner for problems with monotonic loading. However, very limited attempts can be seen for problems involving cyclic loading. This paper presents a comprehensive study using CPFEM to predict crack nucleation in polycrystalline materials under high cycle fatigue. However, due to the large number of cycles till crack nucleation, such analysis can be computationally exhaustive. So, an implicit multi-time scale method involving cyclic scale integration is used in this study. The implicit method used in this study has an advantage over other conventional techniques which assumes periodicity and can provide incorrect response due to the strong non-periodic temporal evolution of plastic variables and localization in the spatial domain. In this method, first fine scale cyclic integration is done for few number of cycles, which is then followed by coarse scale cyclic integration resulting in significant acceleration. A cubic polycrystalline domain is simulated using the method to demonstrate its accuracy and efficiency.