Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework

• DOI: 10.1016/j.ijplas.2024.104013
• Publication Date: 2024-05-23T23:59:52Z
• Authors: Eralp Demir; Alvaro Martinez-P...; Chris Hardie; Edmund Tarleton
• Keywords: Crystal Plasticity

Strain gradients have been cast in the form of geometrically-necessary dislocations (GND) to relate length-scale dependence strength and determine potential sites for failure initiation. The literature contains various different incompatibility measures, main ones being: total (∇×Fp), rate large displacements (∇×γ̇anaFp), slip gradient (∇γ̇a). Here these approaches are compared rigorously first time. Obtaining GND densities when using is a rank-deficit linear problem, solved by singular value decomposition (SVD) known as Least Squares Minimization (L2 method). Alternative methods find such Karush-Kuhn–Tucker (KKT) optimization also investigated. Both L2 KKT method predict unrealistic on inactive systems leading excessive strain hardening; even single crystal case. Therefore, restriction GNDs active threshold based found be essential. This proposed reveals relatively consistent results cases including: simple shear, uniaxial tension, four-point bending. In addition, small numerical differences leads discrepancies flow stress due error accumulation, strain-gradient-free hence density increment (2×102 m−2) used all models avoid formation artificial densities. Finally, applied evolution grain inside polycrystal aggregate having complex state. forms, that use curl plastic deformation gradient, with system giving lowest errors suggest them most reliable measures.