The work presented here provided a generalized structure for modelling polycrystals from micro- to nano-size range. The polycrystal structure was defined in terms of the grain core, the grain boundary and the triple junction regions with their corresponding volume fractions. Depending upon the size of the crystal from micro to nano, different types of analyses were used for the respective different regions of the polycrystal. The analyses encompass local and non-local continuum or crystal plasticity. Depending upon the physics of the region dislocation-based inelastic deformation and/or slip/separation was used to characterize the behaviour of the material. The analyses incorporate interfacial energy with grain boundary sliding and grain boundary separation. Certain state variables were appropriately decomposed into energetic and dissipative components to accurately describe the size effects. This new formulation did not only provide the internal interface energies but also introduces two additional internal state variables for the internal surfaces (contact surfaces). One of these new state variables measures tangential sliding between the grain boundaries and the other measures the respective separation. Additional entropy production was introduced due to the internal subsurface and contacting surface. A multilevel Mori–Tanaka averaging scheme was introduced in order to obtain the effective properties of the heterogeneous crystalline structure and to predict the inelastic response of a nanocrystalline material. The inverse Hall–Petch effect was also demonstrated. The formulation presented here was more general, and it was not limited to either polycrystalline- or nanocrystalline-structured materials. However, for more elaborate solution of problems, a finite element approach needs to be developed.

Modeling of Strengthening and Softening in Inelastic Nanocrystalline Materials with Reference to the Triple Junction and Grain Boundaries Using Strain Gradient Plasticity. G.Z.Voyiadjis, B.Deliktas: Acta Mechanica, 2010, 213[1-2], 3-26