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Overall，the average ferrite grain sizes in the three tested rebar are fine, which have fine grained strengthened effect and are contribute to improve strength and plasticity.
Ferrite content /% Pearlite content /% Bainite content /% Ferrite grain size /um Ferrite grain grade /grade 1# 59.3 40.7 / 8.5 10.4 2# 49.1 26.8 24.1 8.6 10.6 3# 56.7 36.6 6.7 8.6 10.6 Table 3 Quantitative analysis results of microstructure and ferrite grain size for different microalloyed rebars.
According to the test results of precipitates, a large number of V(CN) and Nb (CN) precipitates with size of 5～30nm are formed and distributed on ferrite matrix, grain boundary and dislocation lines.
The cleavage fracture is composed of a large number of cleavage plane with the size being equivalent of the grain size.
Becauce when crack grow and propagate, it would go through a certain number of parallel cleavage plane with different orientation,which result in grain boundaries become obstacles to crack propagation, grain size effect crack propagation that is the cleavage plane size increases with grain size increasing and grain boundaries crossed by crack propagation is lesser, therefore, the crack easily propagate and propagation rate is also faster, which easily lead to cleavage brittleness fracture.

Each particle size of abrasive corresponds to a diameter range (dmin~dmax). dmax is diameter of the largest grain for a standard grain size (mm), and dmin is diameter of the smallest grain for a standard grain size (mm).
Table 1 Sizes of dmax, dmin, and dmean Grain size # 36 46 54 60 70 80 90 100 dmax(mm) 0.476 0.354 0.291 0.255 0.211 0.178 0.152 0.142 dmin(mm) 0.354 0.291 0.255 0.211 0.178 0.152 0.142 0.114 dmean(mm) 0.415 0.323 0.273 0.233 0.194 0.165 0.147 0.128 The number of abrasive particles per unit area (grains/mm2) in the belt can be determined as , (2) Where Sg is density of coating grain (%) and rm is the mean radius (mm).
The total number of active grains (i.e. grains contributing to cutting action) within certain time is known, then (20) Then the material removal rate can be given by (21) (a) (b) Fig.4 (a) The relationship between the contact pressure and the indentation depth for the various abrasive grain size; (b) The material removal rate predictions for the various indentation depth (zirconia corundum grits, the belt speed is 10m/s, U71Mn material).
The material removal rate is smaller for larger grain size, since the number of abrasive particles per unit area contributed to cutting action is fewer at greater grain size.
The material removal rate is greater for greater belt velocity, since the number of abrasive particles per unit time contributed to cutting action is more within certain limits.

Ultra-fine grained (UFG) microstructures having mean grain sizes less than 1mm fabricated by the SPD processes exhibit remarkable mechanical properties due to grain refinement hardening.
UFG materials also have large number of other lattice defects introduced by the SPD process.
It was found that the increase in hardness by aging process decreased with increasing the number of the ARB cycles.
In the as-ST or as-ARB specimen (Fig.2(a)), the strength increased with increasing the number of the ARB cycle while elongation decreased by the ARB.
(2) The strength of the ARB processed specimen increased with increasing the number of the ARB process while the elongation decreased by the ARB process.

Under these conditions, Ostwald ripening is the dominating mechanism of grain coarsening in the stage of high liquid fraction, in which grains continuously coarsen and the small grains gradually melt [9].
Shape factor of solid grains was calculated by applying the Eq. 1 [10]: SF= 1(1Np2/4πA)/N (1) In which A, N, and P are the area, the number of experiments and perimeter of solid particles, respectively.
Fig. 2 The effect of Ti addition on grain size.
Because of this low amount of liquid phase, it cannot soak into the grain boundries; hence, grain boundaries are not uniform and continuous.
Due to these two mechanisms, grain boundaries between adjacent grains disappear, causing larger grain with irregular shapes.

In terms of the average number of grains through the sheet thickness, r0 had 35, r10 had 12.5, and r20 had 24.
The biaxial limit strain of r0 was lower than would be expected on the basis of a simple relationship between the number of grains through the sheet thickness, as indicated by Wilson et al
Using this definition of the limit strain, the effect of the number of elements- representing grains- through the thickness and also of the degree of orientation clustering could be evaluated.
There is a clear effect of domain thickness; limit strains in both strain states increase as the number of "grains" through thickness increases.
Predicted in-plane limit strains (ε1*) as functions of number of grain through thickness, N, for CPFEM simulations with spatially uncorrelated orientations.

Brittle intergranular failure in grain aggregates.
Within that approach, the material is assumed to consist of grains bonded to one another.
The crack propagation corresponds to the transition from the state with a lower number of broken bonds (configuration with less ones) to the state with a higher number of broken bonds (configuration with more ones).
Then the decrease in elastic strain energy can be expressed as: ∆Eelastic = − C × (number of broken parallel-to-loading chains of grains) 3/2.
The basic idea is to represent each bond between two grains by a binary variable.

If the sample, of which the deformation strain is 2%, are taken to be observed, a large number of dislocations can be founded in the grain interior due to the occurred deformation(Fig. 1 (a)), and apparent dislocation networks can also be found in some regions(Fig. 1 (b)).
The trend of polygon is very obvious in the local area (Fig. 1 (e)), while in other regions, sub-grain boundaries began to dissociate, which is the start of sub-grain polymerization mechanism.
The arrow of the figure1(g) shows that after the sub-grain boundaries are completely dissociated, the sub-grain A and B that is merged, and it continues to grow up here by recrystallization.
It is shown from figure1 (h) that the dislocation density inside grains becomes high.
Acknowledgments The authors would like to acknowledge the financial support of the National Natural Science Foundation of China under granted number 50974063 and Jiangxi Provincial Education Department program under granted number GJJ09228.

XRD, FESEM and EDS results showed that a large number of fine TiB2 platelets were uniformly embedded in irregular TiC grains, a few Cr-Al metallic phases or in between those phases.
FESEM images and EDS results showed that a large number of randomly-orientated, fine TiB2 platelets (presented by the dark areas in Fig. 2) were uniformly embedded in the irregular TiC grains (presented by the grey areas in Fig. 2) and Cr metallic phases (presented by the white areas in Fig. 2), and a few inclusions of α-Al2O3 were also observed, as shown by the isolated black particles in Fig. 2.
Hence, rapid growth of TiC is the other reason for the achievement of fine-grained microstructures in current TiC-TiB2 composites.
According to the literature [9], larger is grain size of TiC grains, smaller is the critical shear stress inducing the cracking of TiC grains, so transcrystalline fracture almost takes place in the irregular coarsened TiC grains.
XRD, FESEM and EDS results showed that a large number of fine TiB2 platelets were uniformly embedded in irregular TiC grains, a few Cr-Al metallic phases or in between those phases, and a few of isolated irregular α-Al2O3 inclusions were also detected in the ceramic, whereas Cr-Al metallic phases were also concentrated at central part of the sample.

Here, the grain morphology is the dominant one.
The second zone corresponds to columnar grain zone.
It corresponds to the zone of equiaxed grains.
· White spots (islands): observed near the grain boundaries and inside the grains.
Furthermore, a small number of tertiary dendrite arms are formed.

The numbers 0~8 in the figures correspond to each other, and refers to the different deformation stages.
The numbers correspond to those in Fig. 4.
Numbers 0-4 correspond to those in Fig. 4.
� � Matrix Journal Title and Volume Number (to be inserted by the publisher) 5 473K, 10-3s-1.
Besides the matrix, two DRX grains were observed, grains A and B.