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of grains” means the number of grains where in GB, NGB, or IG-position is the indent located.
“Number of skipped grains in matrix” means the number of in-matrix-lying grains without indent.
“Maximum number of indent in 1 grain” means the maximum number of indents located in one grain, the indent lies inside the grain.
Number of measured grains increases with increasing distance between indents for the same number of indents, however the number of skipped grains increases and therefore measurement efficiency is decreasing.
Number of inside-grain indents depends on microstructure.

The literature reports a considerable number of research works that deal with grain coarsening problem in FSS welds.
The grain size is measured by IMAGEJ software.
It is observed the presence of large columnar ferrite grains.
It’s observed that the addition of Aluminum (Al) or Titanium (Ti) reducing the grains size and increase the equiaxed grains fraction with varying degrees.
The fracture surface morphology of sample treated by powder mixture (Al+Ti) addition displayed ductile morphology which is characterized by larger number of dimples and pores.

As a result we get a large number of tiny grains.
Because the grain boundary atoms are arranged in disorder, and there are a large number of defects such as dislocations, empty.
Besides on both sides of the grain size of a grain boundary to different, so it will hinder dislocation from one grain to another grain movement.
The number of toughening nest became fewer, and its morphology is smaller.
Toughening nest increase in the number with smaller in size, uniform in morphology, no particles.

The material was considered as a composite of grain interior phase and grain boundary (GB) phase.
As soon as strain surpasses threshold value corresponding to ultimate strength, grains within shear band begin to rotate and dislocations in grain interior begin to slip, which leads to shape changes for grains, especially like elongation.
The following assumptions are made with shear band deformation mechanism stated above: (1) grains are spherical before unchanged, and grains’ sizes are identical; (2) grains with different orientations are randomly distributed; (3) rotational velocities for grains are same and synchronous; (4) rotational angle of grain is proportional to strain in the softening stage.
(3) where and are the number of softening grains with orientations parallel with shear band and the total number of grains in the aggregate, respectively; is the strain in softening stage, is the strain corresponding to ultimate strength and is the failure strain.
(7) FEM simulation for shear band The generated microstructure consists of 160 grains and the average grain size is 62 nm.

These results show microstructure one of the sample for sample number 3 which exceed the highest average overall length A that become more globular with higher average grain size after the feedstock billets were re-heated to semisolid range temperature.
Table 3 shows average grain size measurements for microstructure of sample number 3 consists of area, perimeter, circularity, diameter and aspect ratio.
Table 3: Average grain size measurements for microstructure of sample number 3 before and after injection test.
At this time, grain spheroidization and coarsening were started when liquid phase at grains boundaries.
As the initial microstructure of feedstock billets in sample number 3 were surrounded by higher secondary phase content, it catalysed the formation of smaller α–Al solid grains.

The ECAP of the alloy results in the formation of ultrafine grained structure with a grain size of 0.8-3.5 µm independent of pressing routes and regimes.
However, at lower deformation temperatures, the plasticity and deformability of the alloy noticeably decrease because of a limited number of the effective systems of deformation.
Results and discussion The microstructure of the pressed and annealed Mg-Al-Zn alloy bar (before ECAP) is characterized by a substantial variation of grain size, from rather coarse (exceeding 15 µm) to fine grains (2.5 - 4 µm).
The ECA pressing by the regimes given in Table 1 resulted in the formation of ultrafine grained (UFG) structure with a grain size ranging between 0.8 and 3.5 µm.
The grain size in the magnesium alloy does not virtually depend on the ECAP regime and route.

Finally, the hardness values are reasonably homogenous along the disc diameter as the number of turns increases to 5 and 10 turns.
There are some reports on the grain refinement during HPT processing of Al-5% Mg [9] and Al-1% Mg [10].
The grain structures in the HPT-processed Al-0.1% Mg were also examined by EBSD using a JSM6500F SEM.
Fig. 3(a) shows the disc centre area has coarse grain structures but with higher number fractions of low-angle boundaries introduced by HPT shear deformation.
Langdon, Principles of equal-channel angular pressing as a processing tool for grain refinement, Prog.

Abstract.Within the general context of solid-state sintering process, this work presents a numerical modelling approach, at the grain scale, of ceramic grain packing consolidation.
This grain boundary surface tension condition can be written as follows: [σn]gb = γgbκn (21) over the grain boundary Γgb, and has to be added to the mechanical problem (12)-(14).
One of the difficulty of simulating grain boundary diffusion is that we have to consider one level-set function per grain.
As in [6], the simulations presented in this work have been performed by using a mesh adaptation strategy aiming to obtain accurate results while keeping a ``reasonable'' number of mesh elements.
The mesh adaptation strategy used allows to perform simulations while keeping a ``reasonable'' number of nodes and elements and is specially useful when dealing with 3D simulations as the number of mesh element is dramatically increased compared with a 2D simulation.

The coarse-grained alumina specimen, TM7, was selected for additional testing, in the hope of analysing the effect of incident wave shaper with regards to strength results.
Influence of grain size on the dynamic response behavior of alumina.
SHPB stress-strain curves for alumina ceramics with different grain sizes It is well known that microstructural inhomogeneities caused during material preparation (e.g. inclusions, grain boundary impurities, secondary phases, porosity, etc.) are the main cause of cracking and can lead to material fracture.
As the applied load increases rapidly, the inertial effect of accelerated crack expansion prevents the initial stage of material fracture from occurring, and microcracks are generated in large numbers but do not converge, the material remains integral at this point and therefore ceramic materials exhibit a high compression strength under high strain loading.
The fine grain alumina ceramic SH3 exhibited a high dynamic compressive strength of 3.80±0.25 GPa, as compared to the SHPB experiments conducted on the alumina ceramic materials.

Relevant data are available in a relatively large number on Al-Mg-Sc/Zr alloys with a Mg content ranging from 1 up to 6 mass % [8-12].
By increasing the number of passes, the sub-boundary misalignment increased, as confirmed by the increased spreading of the spots of the SAD patterns.
Grain structure of the materials investigated after 4 ECAP passes.
This effect is confirmed here by the shift of the above mentioned peaks toward lower temperatures by increasing the number of ECAP passes of the samples
Ultrafine grained materials.