Enhanced Strain Gradient Crystal Plasticity theory: Evolution of the length scale during deformation

An Enhanced Strain Gradient Crystal Plasticity (Enhanced-SGCP) theory, based on the quadratic energy contribution of the Nye tensor, is developed within a thermodynamically consistent framework to accurately capture shear band formation in terms of slip and kink bands within the microstructure. The higher-order modulus in the theory is intrinsically linked to the evolving microstructural properties during applied loading, introducing a physical length scale that governs shear band formation and evolution. It is demonstrated that the Classical-SGCP model (a Gurtin-type nonlocal theory) leads to an increasing width of localization bands, which eventually disappear, resulting in homogeneous deformation within the microstructure. This effect arises from the excessive annihilation of geometrically necessary dislocations, which suppresses localization and may lead to physically meaningless results in the formation of shear bands. To address this issue, the proposed Enhanced-SGCP theory effectively preserves the shear band width and maintains localization throughout the loading process by reducing the higher-order modulus associated with the sweeping away of hardening defects and local softening mechanism. Furthermore, the theory establishes a direct link between lattice curvature in kink bands and the Nye tensor, demonstrating that the kink bands transform into slip bands. Consequently, the Enhanced-SGCP theory breaks the equivalence between slip and kink bands, providing a more accurate physical representation of strain localization mechanisms in irradiated materials.

To computationally solve the governing balance equations, a fixed-point algorithm based on the fast Fourier Transform (FFT) method is developed. To validate the algorithm, an analytical solution for the Enhanced-SGCP theory is derived. High-resolution single-crystal simulations confirm that the kink bands transition into regularized slip bands through different physical length scales within the proposed Enhanced-SGCP framework. Furthermore, high-resolution simulations are performed on two-dimensional and three-dimensional polycrystalline aggregates, considering different length scales and various higher-order interface conditions at the grain boundaries. The results reveal that the strain gradient effects during applied loading are saturated and stabilized by the Enhanced-SGCP theory, ensuring sustained localization.

These findings highlight the capability of the proposed Enhanced-SGCP theory and the developed FFT-algorithm to provide a robust and physically consistent framework for modeling strain localization in crystalline materials. The proposed model offers significant improvements over classical approaches, particularly in preserving localization phenomena and accurately describing the interplay between slip and kink bands.