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As this process can be repeated, the total shear can be accumulated to give an ultra-fine grained structure having a large proportion of high angle grain boundaries.
For the fabrication of ultra-fine grained wires or fibres the original form of ECAP may not be appropriate.
This also means that the number of tortuous channels leading through the discs is strongly reduced by reducing the disc grade.
Effective grain refinement associated with the new microstructure formed by dynamic recrystallization was observed as the processing temperature was apparently too low to induce further grain growth.
Under the conditions chosen for this preliminary work, significant grain refinement was achieved.

The types and number of grain boundaries after heat treatment at 1290°C, 1310°C and 1330°C were counted and the results are shown in Fig. 3.
The number of low-angle and medium-angle grain boundaries was significantly reduced and the proportion of high-angle grain boundaries increased after heat treatment at 1290°C.
Since low-angle grain boundaries and medium-angle grain boundaries are generally the boundaries between sub grains or other crystalline substructures, the more of both, the greater the number of sub grains or substructures.
This reduces the number of low-angle and medium-angle grain boundaries.
When the heat treatment temperature was increased to 1330°C, the sum of the number of low-angle grain boundaries and medium-angle grain boundaries decreased to 11.1% from 15% at 1310°C.

With the increase of cooling rate, the grain size decreases and there are a large number of microcrystals in the microstructure.
In Fig. 5(a), a large number of spherical quasicrystal phases uniformly distribute in the matrix Mg7Zn3 phase, and the average grain size is less than 0.8 mm.
In Fig. 5 (a), (b), (c), there are a large number of gray white cellular or granular grain, whose size is very small.
With the increase of cooling rate, the grain size decreases, and the number of quasicrystal increases per unit area.
They collide together and form a large number of extremely tiny grains before they all grew up.

Measurements were performed at room and at 100 °C, 200 °C and 250 °C on each grain.
These grains were subjected to the nanoindentation measurements. 9 indentations have been carried out for each grain at each temperature in array of 3x3 with spacing of 25 μm.
As one can see, indentation hardness slightly decreases with increasing temperature for grain D from room temperature up to 250 °C from 2.9 GPa to 2.3 GPa, for grain G from 2.8 GPa to 2.1 GPa and for grain C for 2.7 GPa to 2.1 GPa.
This differences between individual grains can be related to various number of active slip system in grains [7].
This can be explained with various number of active slip system in the individual grains.

A distinguishing feature of the model is that all the relevant mechanical fields are represented in terms of grain-boundary variables only, which simplifies data preparation and re-meshing and reduces the overall number of DoFs with respect to other popular techniques.
Numerical tests In this section, the cracking behavior of a polycrystalline SiC 10-grain morphology with ASTM grain size G = 12 is tested.
(a) (b) Fig. 1: a) Grain boundary mesh of a 10-grain polycrystalline morphology with ASTM grain size G = 12; b) Volume stress average as a function of the load factor for the two considered values of the ratio between the inter- and trans-granular fracture toughness.
Future work will involve morphologies with larger numbers of grains and the coupling with other polycrystalline deformation mechanisms such as crystal plasticity [10].
Mallardo, A grain boundary formulation for crystal plasticity.

The results show that the grain of the sample steel before pre-treatment (cold rolled then pre-annealed before leaving the factory) is coarser, and the microstructure of the steel plate after solution treatment has obvious refinement tendency and a large number of annealing twins are formed.
Moreover, the size of the grains is uniform.
It can be seen that the structure under water cooling conditions is very heterogeneous, part of the grain grows abnormally and undergoes secondary recrystallization (as shown in Fig. 4 (i)), the number of annealing twins is greatly reduced, also, it can be seen that the crystal grains obtained under air cooling conditions are also relatively large, and the dissolved carbide in the matrix precipitates again at the grain boundaries.
The grain increases the number of grain boundaries of the prior austenite, also, increases the number of nucleation in the subsequent cooling stage then achieves the purpose of refining the grain size; in the solution treatment at 1050 °C for 5 s, secondary recrystallization occurs, accompanied by the abnormal growth of some grains, which causes uneven grain of the structure, thus, the strength, hardness and the plasticity of the material decrease, which adversely affects the product property.
In the interval of 950 °C-1050 °C, the result shows that the number of annealing twins is significantly reduced and the carbides discontinuously precipitate along the grain boundaries, also this process is accompanied by abnormal growth of some grains, which seriously degrades the material properties.

The term ‘‘ultrafine grain size’’ is usually used for the grain size upper than 250 nm.
The number of dislocations piled up against a GB decreases as the grain size is decreased, at a fixed stress level, since this number is a function of the applied stress and of the distance to the source (The sources are assumed to be in the center of the grain, leading to positive and negative dislocation pile-ups generated by the activation of a Franck–Read source) [3].
The mean back stress associated with the loop of a dislocation accumulated at the GBs is proportional to the inverse of the grain size [22], and the net back stress from dislocations accumulated along the GBs is thus expressed by: (23) where M and n are the Taylor factor and the number of dislocations accumulated at the GBs of MC materials, respectively.
The flux of dislocations arriving at a GB per slip band can be calculated as [33-34]: (24) here, is the equivalent plastic strain, λ is the mean spacing between slip bands and is the maximum number of dislocation loops at the GB in the coarse grained metals.
The presented constitutive equation is used to predict the mechanical behavior of MC copper with the unit cell model for which a larger number of experimental data is available.

The grain refinement strengthening can be generally described by a Hall-Petch equation [9].
The grain size decreases with the increase of pass number.
Fig. 3 shows the variations of friction coefficient with pass number.
Fig. 3 Variations of friction coefficient with pass number.
The decrease of wear volume of the alloy after ECAE with pass number is mainly due to the improvement of mechanical properties caused by grain refinement.

EBSD analysis revealed that absence of B induces fine ferrite grain size and many high angle grain boundaries. 1.
The grain identification angle is 5°.
As the amount of B increases, the number of high angle grain boundary (misorientation angle >15 o ) decreases.
It seems that the fine grain size and a large number of high angle grain boundary in steel B0 are attributed to large volume fraction of dynamic recrystallization.
In addition, the absence of B led to decrement of ferrite grain size and increase of high angle grain boudnaries in hot-rolled high strength IF steels.

Fig. 2 Transfer of the larger angle grain boundary with grain growing up.
As shown in Fig. 2, grain boundary migration is achieved by the stepwise reduction of the lattice orientation difference in the grains.
As a result, the number of grain boundaries decreases, the grain boundary surface energy decreases, So that the organization in a more stable thermodynamic state.
In this case, the coarser fibrous structure will be due to the disappearance of grain boundaries within the region and into the strip grain, the original strip grain is likely due to the same reason to become larger size equiaxed grains, Which to a certain extent, eliminating the previous stage due to ruminal extrusion deformation caused by the grain.
The recrystallization process of the surface metal has a periodic characteristic of recovery, recrystallization and grain growth The violent vibration at the time of firing of the gun resulted in a large increase in the number of nuclei and accelerated the formation of recrystallized tissue, which was one of the important reasons for limiting the grain size.