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The RVEs were generated as follows: at first, M grains are distributed in the system; where M grains are assumed to be non-overlapping spheres with a radius between 2.5 - 7.5μm.
martensite grain inclusion particle =micro void X　 Y　 Z　 Figure 2.
Further, the perfectly-equal configuration of M grains and I particles were utilized in both the Msoft and Mhard samples.
Furthermore, the number of I particles found on the fracture surface decreases with the increasing value of KM.
However, in this study, M grains are assumed to be non-overlapping spheres for simplicity.

When machined, the metal sticks to the tips of abrasive grains; thus, abrasive tool wear byproducts are transferred to the machined surface [7].
The actual grain grinding depth and the length of the arc of tool-and-material contact were reduced.
This reduces the intensity of metal sticking to abrasive wheel grains, with less metal being transferred to the machined surface (Fig. 1c).
At higher operating speeds, the number of grain tips passing along a section of the machined surface in a given time is increased.
Adhesion results in the titanium alloy being stuck to grain tips, then transferred by cohesion to the machined surface in a next wheel rotation.

Introduction Centrifugal casting has become increasingly effective for producing a great number of special castings, such as tubes, rolls and graded materials [1-3].
The quick solidification of the thin film makes the grain refined.
Consequently, it is beneficial to change the initial temperature of the mold and control rotation speed to gain refined grain [9].
Higher rotation speed is better for the formation of refined grain in real centrifugal casting
Program number: 2009ZX04014-081 References [1] H.G.Fu, Q.

Some researches shown that nanostructural composite ceramics prepared not only by a large number of nano particles, but also a small number of those can lead to obvious effects[6-8].
Zirconium oxide(Yixing zirconium industry co., LTD, 99.9%), Y2O3(Yixing Xinwei Licheng rare earth co., LTD, 99.6%), nano-Al2O3 (Nanjing Xiaoke nanostructured ceramic technology development co., LTD,99.99%, grain size -30nm).
The stability of tetragonal phase is mainly related to doping ion radius, oxygen vacancy concentration and grain size.
The uniform porosity of Al2O3-ZrO2 green body is reduced but the grain size distribution, bulk density and flexural strength increase after being sintered.

The grain shapes were uniform and the average grain size was about 1 µm.
On the contrary, the samples dopped with CPP additives showed poor densified bodies with large numbers of 0.5-1.2 µm intergranular pores in the matrix, and the average grain size was maintained at about 1 µm.
Factors tending to increase degradation rate include the increase in porosity and the increase in number of crystal imperfections [8-10], and the porosity plays a dominant role in degradation of ceramics [10].

Recently, ECAP processes at elevated temperatures have been applied to improve the formability of magnesium alloys through grain refinement.
Significant grain refinement has been demonstrated in a variety of magnesium alloys [3-5].
The theoretical analysis of Iwahashi et al.[6] states that for 2 Title of Publication (to be inserted by the publisher) sufficiently large billets and assuming idealized frictionless conditions, the material undergoes deformation by shear as shown in Eq. (1). ) 2 1 2 1 (eccos) 2 1 2 1 cot(2 ΨΨΨΨ++++ΦΦΦΦ ΨΨΨΨ++++ΨΨΨΨ++++ΦΦΦΦ====γγγγ (1) The effective deformation per pass according to the von Mises criterion is given by Eq. (2), where N is the number of passages through the dies. 3 Nγγγγ ====εεεε (2) The application of Eq. (1), and (2) with the die angle (Φ =135o and Ψ =45o ) of the present study represents theoretical equivalent plastic strain value of 0.577 Experimental procedure The experiments were conducted using a magnesium alloy cast (AZ31).
The initial number of nodal points and elements were 2320 and 1595 (7×4×57), respectively.
In; Zhu YT et al., editors, Ultrafine grained materials II.

During SPD at room temperature the grain size of Al-based alloys decreases dramatically.
The high-pressure torsion (HPT) is one of the SPD methods with the possibility of producing bulk materials with uniform ultra-fine grain structure [1].
Physical simulation was carried out in the following mode – temperature T = 350 °C, rotation speed v = 700 rotation per minute, number of rotation n = 1.
It can be seen that the grid with the same number of elements (32,000 pieces) in the model used in this work is the main part of the grid nodes in the working part of the samples, while in the full-scale model the main part of the grid nodes is in the “grippers”; • more accurate calculations.
Prangnell, The simulation of nugget zone grain structures in high strength Al-alloy friction stir welds by high strain torsion testing, Friction Stir Welding Proceedings, (2003)

The size and shape of iron oxide grains depends slightly on the potential of passivation.
As the number of cycles increases, the anodic currents of oxidation peaks decreases.
The size distribution of grains is narrow, with average diameter of 50 nm.
Other authors [21,29] have also observed the formation of nanosize oxide grain formation as a result of rapid nucleation and growth processes during electrochemical passivation.
The size and shape of iron oxide grains depends slightly on the potential of passivation.

A large number of -5um spinel particles (MgAl2O4) were synthesized at 1600~ 1700℃, which could absorb FeO, MnO and other impurities in slag to form composite spinel phase.
The spinel phase exited as small grains below 5 micrometers and massed together, and did not assume obvious octahedral structure (see Figure 9 and Figure 10).
Table 4 Chemical composition of the residue brick Distance from the hot face MgO Al2O3 SiO2 CaO Fe2O3 MnO 0mm 5.06 71.89 0.39 21.31 1.34 --- 10mm 4.89 72.03 0.56 21.07 1.45 --- 20mm 7.06 64.88 5.79 20.65 0.89 0.74 30mm 4.57 62.95 11.10 19.61 1.00 0.76 40mm 5.15 65.12 13.38 16.01 0.34 --- penetraion layer reaction layer CA2 C12A7 CA Fig.3 Sample of 40mm thickness (20×) Fig.4 Reaction layer (100×) Al2O3 CA6 CA2 Al2O3 Al2O3 Matrix Fig.5 Boundary of reaction layer Fig.6 Penetration layer(20×) and penetration layer(80×) Matrix CA6 Al2O3 CA6 C2AS MA Fig.7 Penetration layer(100×) Fig.8 Matrix of penetration layer(100×) Fig.9 Tiny synthetical spinel(3000×) Fig.10 A large number of activated spinel massed(4000×) Wear mechanism analysis.
Usually, the primary components of the slag such as CaO, Al2O3, SiO2 and MgO, gradually penetrated into the block along pores, air gaps and grain boundary and eroded through chemical reaction.
According to the phenomenon that corundum aggregate of the reaction layer was completely eroded, the reaction process must be enduring and complete so that it could actually postpone erosion process of molten slag, and indeed improved the resistance of samples to slag corrosion; at the same time synthetic phase was a mineral phase of high melting point ,its activity was very high because of tiny grain size,as shown in Figure 10, so it was very easy to dissolve the impurities in the slag such as FeO, MnO, playing the role in penetration resistance[3].

Such structural changes in the material change the size of grain cells, the angle of misorientation between them, the thickness of the interface, the density of dislocations [6].
High density of grain-boundary dislocations and lattice defects form long-range elastic stress fields, which cause significant distortions of the crystal lattice [6-8AIP].
A significant drawback of annealing effects on nanocrystal structures is the undesirable increase in grain sizes.
Ultrasonic field, affecting dislocations, causes a number of phenomena: self-organization of dislocation ensembles, transverse sliding, increase of tight vacancies, drift movement of dislocation walls, dislocation reactions, for example, rupture of dipole, etc.
Nazarov, Nonequilibrium grain boundaries in bulk nanostructured metals and their recovery under the influence of heating and cyclic deformation.