Fast Fourier transform approach to strain gradient crystal plasticity: Regularization of strain localization and size effect

Amirhossein Lame Jouybari, dr. Samir El Shawish and dr. Leon Cizelj from the Reactor Engineering Division at Jožef Stefan Institute published the research article “Fast Fourier transform approach to strain gradient crystal plasticity: Regularization of strain localization and size effect” in International Journal of Plasticity, which is a highly renowned international journal in the field of plastic deformation, damage and fracture behaviour of solids.

The paper proposes a novel Strain Gradient Crystal Plasticity (SGCP) model, called the strict MicroSlip SGCP model, and investigates its Fast Fourier Transform (FFT) implementation in an in-house code to simulate strain localization and size effects of polycrystalline aggregates under external loads. The proposed model is best suited for materials with strain-softening behavior, such as neutron-irradiated metals, which can lead to the formation of strain localization bands in crystal grains and stress concentrations at grain boundaries. The FFT implementation of the model includes special numerical strategies to accelerate the resolution of equilibrium problems relying on a fixed-point algorithm. The method is demonstrated to successfully and efficiently overcome numerical instabilities associated with strain localization, providing regularized strain localization bands independent of grid resolution and controlled by a single non-local model parameter.

Figure: Simulation result of 2D polycrystalline aggregate model with 200 grains at 0.01 applied tensile strain. (a) Distribution of cumulative shear strain at grid resolution of 60 × 60 voxels per grain. Insets (b) and (c) show an enlarged region of the same quantity at two grid resolutions. Insets (d) and (e) show the corresponding von-Mises stress and rotation angle at 60 × 60 voxels per grain.