Modeling of the Plastic Deformation of Polycrystalline Materials in Micro and Nano Level Using Finite Element Method

Abstract

Recent experiments on polycrystalline materials show that nanocrystalline materials have a strong dependency to the strain rate and grain size in contrast to the microcrystalline materials. In this study, mechanical properties of polycrystalline materials in micro and nanolevel were studied and a unified notation for them was presented. To completely understand the rate-dependent stress-strain behavior and size-dependency of polycrystalline materials, a dislocation density based model was presented that can predict the experimentally observed stress-strain relations for these materials. In nanocrystalline materials, crystalline and grain-boundary were considered as two separate phases. The mechanical properties of the crystalline phase were modeled using viscoplastic constitutive equations, which take dislocation density evolution and diffusion creep into account, while an elasto-viscoplastic model based on diffusion mechanism was used for the grain boundary phase. For microcrystalline materials, the surface-to-volume ratio of the grain boundaries is low enough to ignore its contribution to the plastic deformation. Therefore, the grain boundary phase was not considered in microcrystalline materials and the mechanical properties of the crystalline phase were modeled using an appropriate dislocation density based constitutive equation. Finally, the constitutive equations for polycrystalline materials were implemented into a finite-element code and the results obtained from the proposed constitutive equations were compared with the experimental data for polycrystalline copper and good agreement was observed.

Application of the grain boundary formulation and image processing-based algorithm in micro-mechanical analysis of piezoelectric ceramic

“…Let consider Equations (15) and (16): the cohesive traction can be calculated via differentiation of the potential equation and by using the effective opening displacement. The normal and sliding amount of traction in local coordinates can be shown ast…”

“…In order to predict the fracture behaviour in a composite, different cohesive law models or friction phenomena can be used [15][16][17][18][19][20][21][22][23][24][25]: via cohesive law models, it is possible to predict both intergranular and transgranular crack initiations. In other words, a cohesive law is suitable in order to model interfaces between materials with different mechanical properties.…”

“…In other words, a cohesive law is suitable in order to model interfaces between materials with different mechanical properties. Depending on the possibilities to predict fracture and crack initiation, there are two different kinds of cohesive law models, the potential-based law [16][17][18] and the linear law [19][20][21][22].…”