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Intorduction So far, a great number of research activities have been devoted to modeling and predicting surface roughness for the grinding process[1].
In order to simplify the grinding kinematic analysis, the assumptions adopted in the present work for predicting the cross-sectional surface roughness are as follows: 1) the abrasive grains are conical in shape; 2) the distribution of the grain intervals is uniform, and the grain interval can be determined as [6], where is the grit number and is the structure number of the wheel; 3) the grain protrusion height is distributed with mean value and standard deviation .
Set as the depth of cut and as the minimum radius in one row, and then the limit value of the intersection of the grain with the cross-section can be expressed as (5) The parameter can be solved from Eq. (5) as (6) The range of the engaged grains through the cross-section can be determined as (7) Along each row, number the grains engaged with the cross-section as, and then the grain in row which will leave marks on the cross-section can be determined as (8) 1.2 Prediction of surface roughness.
The grain mesh size is 180, the structure number is 8, the wheel spindle speed is 4500 rpm and the table speed is 0.06 m/s.
In practice, the grain interval is random and the grain shapes are complex basic geometries, such as ellipsoid, tetrahedron, cuboids and octahedron.

The diameter of a crystal grain of AZ31B-430 is larger than that of AZ31 B-O.
The diameter of a crystal grain of AZ31B-200 is larger than that of AZ31 B-O.
The diameter of a crystal grain of AZ31B-430 is much larger than that of AZ31 B-O, and the form of a crystal grain also changes.
The number of load cycles, which generates a crack from an initial-crack tip, is shown in Table 3.
We define the number of load cycles when half crack length exceeds 10μ m as the crack generating number of load cycles.

They were comprised by nearly equiaxed grains with a mean grain size of ~2.5 μm.
The FSWed aluminum alloy are reported to be prone to abnormal grain growth [3].
The driving pressure related to the grain-boundary energy is given by [5, 11]: , (4) Where is the mean grain size.
The produced microstructure was predicted to be relatively stable against abnormal grain growth.
Acknowledgements The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.578.21.0097 (ID number RFMEFI57814X0097) is gratefully acknowledged.

The grain oriented silicon steel containing 3%Si-0.5%Cu was produced by low slab reheating temperature technique.
Material and experimental The material used in this study was Fe-3%Si-0.5%Cu grain oriented silicon steel.
The chemical composition of the precipitates was analyzed using energy dispersive X-ray analysis (EDX) Table 1.Chemical composition of studied steel C Si Mn P S Als Cu N 0.04 3.03 0.2 0.008 0.01 0.023 0.47 0.0083 Results and discussion In Fe-3%Si-0.5%Cu grain oriented silicon steel, the average grain size of the primary recrystallization matrix is about 20μm which indicate that the precipitations have effect on inhibiting grain growth (shown Figure 1).
During secondary recrystallization annealing, the precipitation of Cu2S coarsens abruptly and the number decrease suddenly, which lead to the abnormal growth of grains.
A spot of coarse cubical AlN with the size of ~200nm are formed during hot rolling which have not the effect on inhibiting the grain growth.

A greater step size would give rise to only very few data points for each retained austenite grain, since they had an average grain size of about 1 µm and this would risk erasing the grain when performing data clean-up procedures.
A third reason is found in the relationship that is observed between the number of neighbouring BCC grains a retained austenite grain has and the smallest misorientation from an ideal transformation product.
It is found that grains that have the lowest misorientation have an average number of neighbours between three and four, while grains with the highest misorientation have on average between two and three neighbours.
This finding, combined with the small orientation differences between the different orientation relationships, may lead to the conclusion that the local environment of the grain, i.e. the interaction of the grain with its neighbours, plays a decisive role in which orientation relationship prevails. 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 (a) Frequency, % Variant number Figure 3: Histogram showing the frequency of the different variants: (a) Kurdjumov-Sachs, (b) Nishiyama-Wassermann, (c) Pitsch orientation relationships.
The horizontal line shows the expected number of variants in case of no variant selection. 1 2 3 4 5 6 7 8 9 10 11 12 0 2 4 6 8 10 12 14 16 (b) Frequency, % Variant number 1 2 3 4 5 6 7 8 9 10 11 12 0 2 4 6 8 10 12 14 16 (c) Frequency, % Variant number Fig. 3 shows the distribution of the different variants for the KS, NW and Pitsch orientation relationship.

It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix. 1.
Moreover, we find out that one-grain-cube creates very high stress (~45MPa) merely around the grain at 48h while ten-grain-cube generates less stress (~15MPa).
In the meanwhile, the stress is smoothly distributed among the grains providing one micro-crack network at 48h after mixing up stage.
Hygro-mechanical stress variation at 48h after mixing up created by the number of grains: a) 2 grains b) 3 grains c) 6 grains d) 10 grains at 48h on the left and the micro-crack observation around one sand grain by SEM (A: aggregate; CP: cement paste). 5.
According to the numerical results, it has been found out that the number of inclusion influences the magnitude of hygro-mechanical stresses around the sand grains, the higher number of inclusions inducing the greater stresses.

Grain boundary element formulation.
Given a volume bounded by an external surface and containing grains, two kinds of grains can be distinguished: the boundary grains, intersecting the external boundary, and the internal grains, completely surrounded by other grains.
Let and be two adjacent grains.
The present formulation requires only meshing of the grain surfaces.
The grain size is ASTM G=12 (calculated number of grains per : [12]).

Introduction Overwhelming majority of publications on SPS (experiencing exponential growth in numbers during the last decade - see Fig.1) describe empiric trial-and-error attempts to consolidate various powder material systems 1.
The developed model pursues the purpose of outlining a concept of a combined account of various material transport mechanisms in electric-current- assisted sintering, omitting a number of factors (such as spatial current density, temperature, porosity and grain size nonuniformities, different sources of grain growth, role of surface diffusion, phase transforma- tions, possible (still debatable) plasma formation, presence of surface oxides, etc).
Constitutive Model The flux of matter J r caused by the grain boundary diffusion is determined by Nernst-Einstein equation [1] including the chemical potential gradient along the grain boundaries due to the normal stresses and the electromigration: EC Cσ σ = +J E r r r ∇∇∇∇ (1) Here E r is the component of the electric field in the tangent plane of the grain boundary, σ∇ r is the gradient of stresses normal to the grain boundary, Cσ =δgbDgb/kT, where Dgb is the coefficient of the grain boundary diffusion, δgb is the grain boundary thickness, k is the Boltzman's constant, T is the absolute temperature.
Fortunately, the theory of electromigration is quite well-developed (however, never applied in models of sintering, as mentioned before), therefore the necessary model parameters and stress-strain assess- ments are readily available for a number of materials.
The calculations have been conducted for different grain sizes: (a) G=40µm, (b) G=1µm, (c) G=100nm.

Finally, the load transfer between grains during yielding of the sample was studied.
This tensor describes differences between loadings for different grains.
During yielding, plastic deformation gradually begins for different grains leading to load transfer between groups of grains [1-3].
At the grain-scale, plastic deformation occurs due to slip on the crystallographic planes.
The dislocations are necessary for crystal glide, but if they are in an excessive number, they block each other and this leads to an increase of critical stress for the associated slip.

In such a set-up, the heat is extracted by a number of laminar water jets placed at regular intervals along the length of the run-out table [1].
The average grain sizes were measured to be 3.2, 2.8 and 2.5 m for ACC, UFC+ACC and UFC, respectively.
The increase in the density of high angle grain boundaries can lead to more effective strengthening by grain refinement because the presence of low mis-orientations between some grains may contribute to the reduced ky value in comparison to the ferrite grains with high mis-orientations [5].
Therefore, the better grain refinement strengthening can be achieved by UFC than by ACC.
By using UFC, the number of NbC (with the size of 5 nm) has been increased as compared to the cases of ACC and UFC+ACC, resulting in obvious refinement of precipitates.