Programación y Configuración del receptor de US y conexión USB

6.1. Grain boundary state and creep of

bulk nanoscale metals

Many useful properties of metallic polycrystals, in particular strength and plasticity, are affected sig-

nificantly by their structural features, especially grain boundary state [226-228], both the structural state and extent of GBs (grain size) being of importance [229,230]. Submicrocrystalline and nanostructured metallic materials produced by severe plastic de- formation are characterized by significant extent of GBs and by non-equilibrium (high energy) GB state relative to the respective coarse-grain counterparts, which may be due to long-range elastic stress fields arising on the GBs [10,231,232]. The above metals are noted for high diffusivities of their GBs, which exceed by several orders the respective values for their coarse-grain counterparts [11,233,234,235]. However, the effect of GB diffusivity on plastic defor- mation development and structural evolution regu- larities during annealing, especially at elevated tem- peratures and simultaneously applied loading (e.g. during creep), has been studied insufficiently. Few theoretical investigations (if any) are concerned with relating the diffusion features and diffusion-controlled processes in submicrocrystalline materials to their GB state. Another step in this direction may be the development of computational methods for defining static and dynamic characteristics of GBs in these materials. In particular, a method of computer-aided GB simulation technique is proposed. This enables one to relate the specific surface energy and stresses arising on the GBs in submicrocrystalline and nanostructured metals to the excess volume of GBs and to define diffusivities over the GBs. The effect of GB state on the creep features in submicrocrystalline metals has been investigated experimentally. The results obtained are presented herein.

Energy, stresses and diffusion on the GBs in submicrocrystalline and nanostructured metals. The grain boundary is a planar defect of the crystal- line structure. The equilibrium atomic bond lengths in the GB core are different from those of the ideal crystal lattice. However, only partial relaxation of the GB atomic structure is allowed due to the con- straints imposed by the neighboring grains. There- fore, even if all of the atoms are in positions corre- sponding with the minimal free energy, stresses would arise in the system containing GBs. The ex- cess stresses associated with the GBs are de- scribed by the components of the 2D tensor of stresses τ_αβ on the interface (e.g. GB) [236]:

τ_αβ = σ_αβ −σ_αβ

−∞ ∞

z

(6.1)

where the co-ordinate axis z is chosen along the normal to the GB; σαβ(z) are the volume stress ten- sor components dependent on the co-ordinate z;

σαβ

0

are the stresses concentrated in a grain far away from the GB core where the GB effect is negligible. The following equation relates the GB stresses to the specific surface energy of the GB (γ) taken per unit of GB area [236]: τ γδ ∂γ ∂ε αβ αβ αβ = + , _(6.2)

where δαβ denotes the Kronecker delta function; the partial derivatives are taken with respect to the strain tensor components εαβ in the GB plane. Eq. (6.2) relates explicitly the GB stress components, i.e. the GB tension characterized by the specific sur- face energy (γ) of the GB and the second term re- lated to the variation in γ during the deformation. Due to GB formation, the available energy would in- crease: hence γ would always be positive in sign. No constraints are imposed, however, on the sign of the derivative ∂ε_αβ/∂ε_αβ and of the GB stresses. The quan- tity τ=Σταα/2 (analog of pressure P=Σσii/3 for the 3D tensor of elastic stresses σ_ii) is a scalar charac- teristic of the GB stresses. In the presence of ten- sile stresses with the GB area tending to reduce elastically the stress τ would be positive in sign, while in the presence of compressive stresses with the GB area tending to increase elastically the stress t would be negative in sign.

On the other hand, the GB stresses, while be- ing a macroscopic quantity, are induced by the atomic structural features and interatomic forces in the GB core. Therefore, the GB stresses can be related to the atomic structural features of the GB using the excess GB volume δV, i.e. rigid-body dis- placement of grains along the normal to the GB plane, as a generalized characteristic of the GB on an atomic scale level:

δV V V

A GB B

=

a

f

where À is the GB area; VB is the perfect crystal volume; VGB is the volume of bicrystal having the same number of atoms.

The theoretical dependencies of δ and ∑ on ex- cess volume δV are obtained using the calculated values of the respective quantities as representa- tive sample of high-angle symmetrical tilt GB in model copper bicrystals. We used the well-known model of bicrystal with rigid atom layers in direc- tions normal to the GB, which bound the simulation

cell, and periodic boundary conditions in the GB plane [237]. The calculations were performed by the molecular statics method at 0K and the embedded- atom method (EAM) potential is used to describe the atomic interactions in Cu [238,239]. In the EAM framework the configuration energy E for a system of atoms can be given as the sum of contributions Ei of atoms i by the following relation

E Ei F R i i i ij ij j i =

∑

∑RST

∑

UVW

b g