Search

A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed by Gurtin (2004) through the prescription of a free energy dependent on Nye’s dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals a significant influence of the plastic shear strain and spin due to a mechanism associated with the higher-order boundary conditions allowing dislocations to exit the body. This mechanism leads to an unexpected mechanical response in terms of bending moment versus curvature, dependent on the foil length, if either viscoplasticity or isotropic hardening are included in the model. In order to study the effect of dissipative higher-order stresses, the mechanical response under non-proportional loading is also investigated. [ABSTRACT FROM AUTHOR]

A finite element model of the flexible micro-bending process based on various grain sizes of pure copper is developed. The geometrical model of grain structure is established with Voronoi tessellation, which is employed to describe the polycrystalline aggregation. A model based on dislocation density is adopted to describe the flow stress of grain interior (GI) and grain boundary (GB) quantitatively. In this paper, silicon rubber is used as the flexible punch and four annealing conditions of pure copper as the workpieces, respectively. The influence of grain structure and grain size is discussed. It is observed that as the ratio of workpiece thickness ( t ) to grain size ( d ) decreases, the forming depth increases. The inhomogeneous deformation occurs in the coarse-grained micro-parts. Furthermore, the results indicate that the surface asperity increases with grain size. The numerical simulation results agree well with the tendency of experimental results. During the micro-bending process, the phenomenon of stress concentration occurs at the grain boundary of the micro-parts. The maximum von mises stress appears at the grain boundary located at the fillet position. The maximum von mises plastic strain primarily concentrates on the junction of the grain interior and grain boundary in the fine-grained parts, while it concentrates at the surface of the grain interior in the coarse-grained parts. [ABSTRACT FROM AUTHOR]