Unique existence of this effect. In the present

Unique mechanical properties of nanocrystalline metals have
attracted considerable interest over the past two decades. A vast majority of
nanocrystalline metals exhibit ultra-high strengths or hardness, but lower
tensile elongation and fracture toughness, which severely limit their
application in many fields.There are many different technologies to
produce them. However, whichever is their production technology, the vast
majority of them undergo grain coarsening. Grain coarsening is a thermodynamics
driven process. Due to the monotonic reduction of the Gibbs free energy versus the grain
size, nanocrystalline materials exhibit a significant mechanical behavior but the
aforementioned mechanical improvement is prone to thermodynamic
instability at elevated temperatures.
The most promising production technique is the High Energy Ball Milling
(HEBM) in which the grain sizes are found to
decrease with milling time down to a constant value which appears to scale with
the melting temperature of the given element. This implies a balance between
defect creation and recovery during deformation.
Although the problems of contamination
from milling process (by attritors or absence
of inert gas environment) and  powder consolidation without coarsening need
to be solved, mechanical attrition could provide the possibility of production
of nanocrystalline materials in notable quantities. The driving force behind this
production effort is the synthesis of materials with
strengths approaching the theoretical value by reducing the grain size based on
the Hall–Petch relationship which is related to the material microstructure. Generally, it is observed
that the rate of strength increases by decreasing the mean grain size below 100
nm and the strength decreases by decreasing the grain size below about 20–10 nm
mean grain size; such a behavior has been commonly indicated as inverse
Hall-Petch breakdown, implying a transition in the deformation modes of metals
by decreasing the grain size from nanocrystalline range down to very low
levels. Though researchers have expressed the
existence of the negative Hall Petch effect, there is a lack of information to
validate the existence of this effect.

In the present paper, a
numerical modeling is performed to calculate the modulus of elasticity of
nanocrystalline material. Their microstructure and the basic mechanical material
properties (such as density, Young’s Modulus, Poisson ratio) have been
extracted from open literature.

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of nanocrystalline materials SEM/TEM images from several publications revealed
that nanocrystalline materials consist of randomly polyhedral shaped grains. In order to represent the
realistic microstructure of nanocrystalline materials into Representative Volume
Element (RVE), the microstructure geometry has been developed using Voronoi
tessellation algorithm. In each RVE, detailed three-dimensional modeling of the
grain and grain boundaries as randomly-shaped sub-volumes is performed (Figure 1), ?he previously
stated technique has been utilized in arranging to produce the
microstructure of nanocrystalline materials. The Voronoi algorithm has been used for
the creation of random grain volume fractions by generating periodic geometries
based on the technique of Christoffersen 1. The procedure for the generation
of periodic discretization of the granulates (grains) for application with the
finite element method is described in detail. The developed procedure is
applied to pure nanocrystalline copper at volume fractions of 80% and 90%
taking also into account the parameter of grain size.

The RVE geometrical model is
meshed using tetrahedral finite elements (Figure 2), proper material laws at
each sub-volume are assigned and the RVE is loaded under representative loading
conditions. Thus, the basic mechanical properties of the material ( for
instance  Young’s Modulus of Elasticity)
can be numerically predicted without the need to perform an extensive
mechanical test campaign. For validation purposes, a limited number of
experiments is necessary. The developed methodology will provide the means to
design the essential nanocrystalline material microstructure based on the
required material properties.


The results of finite-element modeling of nanocrystalline
materials’ realistic microstructure for the evaluation of Young’s Modulus, taking
into consideration the volume fraction of grains and their grain boundaries, are reported. The aforementioned computational results have been
compared with the most commonly used analytical expressions of Mori-Tanaka and
Rule of Mixtures for the evaluation of the mechanical behavior of composite
materials. The above comparison gave a clear evidence that the computational
results are in compliance with the analytical expressions without any notable divergence.

?he computational model
presented, will be extended for the evaluation of the Yield Strength taking
into account the parameter of grain size and grain boundary thickness. In a
future work, the aforementioned model will be able to simulate the
representative deformation mechanisms which are taking place in the nanoscale,
as for example the grain boundary sliding.