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where grain boundary movement typically appears in simulations of grain boundary migration and static/dynamic recrystallization.
The first one - called the majority rule -, defined in the previous work [2], is simply taking the Moore neighbourhood, eight nearest and second nearest neighbours and counting the total number of neighbours belonging to another grain of a given cell.
If the number exceeds some predefined value a reorientation of given cell is performed.
The outer shape is the initial circular grain whereas inner shapes represents snapshots of the shrinking grain.
Islands of the shrinking grain immersed in the surrounding grain are produced as well.

The lamellar grain fragments within a given region are most commonly comprised of only a limited number of texture components, either arranged alternately (e.g.
Considerable grain growth was first required before the lamellar grains spheroidised.
A number of investigations have predicted an increase in the density of LAGBs during grain coarsening when a strong texture is present in the starting material [14-16].
Following cryogenic PSC the deformation structures were dominated by bands of a limited number of texture components (Fig. 4a).
Because of the limited number of texture components in the deformed state, during annealing, lamellar grains with a growth advantage will expand sideways and eventually encounter a grain of a similar orientation, forming a new LAGB by orientation impingent.

This paper analyzed the microstructure evolution and grain-refining mechanism in producing ultra-fine grained steel sheet by heavy rolling of lath martensite.
The initial austenite grain size was about 200μm.
During phase transformation, an austenite grain will divide into four martensite packets with the same habit plane; a martensite packet is composed of three martensite blocks with different K-S orientation; each martensite block contains two variants with specific K-S relationship; each variants formed by a number of laths.
The average size of new equiaxed grains was 22.4nm.
Fig. 4 Effect of annealing temperature on hardness and grain size Curve 1-hardness; Curve 2¬-grain size Conclusions Heavy cold-rolling of lath martensite is a simple method to produce ultra-fine grained steels without severe plastic deformation.

According to Ma et al., we characterize the misorientation field corresponding to an arbitrary distribution for grain boundary in system (2) where θij is the misorientation angle between grain i and grain j with orientationsηi and ηj.
The parameter K is a variable dependent on grain boundary energy., The grid sizeA time step for integration is.36 orientation The 36 number of field variables was chosen. 　
However inhomogeneous grain boundary migration rate affect grain boundary structure.
The at the later stage computed microstructure becomes heterogeneous which consists of large grains and small grains.
In in homogenous systems grain size distributions in simulated grain structures were binodal distributions.

Such effects can be eliminated by means of a grain size distribution including two distinguished peaks at the coarse-grain and Nano/ultra-fine grain regions.
In order to obtain the minimum number of regions containing all potential cracks, the number of regions was increased.
The modeling process was initiated with four sections and their number was increased till no more new cracks could be observed in each section.
As it is observed in Fig. 4 and Fig. 5, the obtained results from the elastic-plastic-fracture analysis using XFEM contains a number of dents that could be due to the occurrence of main cracks.
Generally, one can conclude that in fixed volume fractions, the more the number of coarse grains, the more appropriate results may be obtained.

The fracture of studying materials were characterized as the ductile fracture due to the existence of a large number of dimples.
The grains of the material before ECAP were heterogeneous and had grain size from 50 to 200 μm.
Simultaneously elongation decreases with higher number of ECAP passes at RT and 200°C.
The number of dimples increased with the increasing testing temperature.
The fracture of ECAP-ed AZ61 alloys were characterized as the ductile fracture due to the existence of a large number of dimples.

With further deformation the number and the misorientation of the deformation bands increase, finally leading to the subdivision of original grains by these bands and then the development of fine grains with an average size of about 6 µm at ε=12.
The initial structure consisted of essentially equaxed grains with average grain sizes of ∼300 µm.
Further deformation in strain interval from ε=2 to 8 leads to an increasing number of DBs and formation of new fine grains in the regions with high density of DBs (Fig. 1c).
The number of DBs and their intersections increase with further deformation to high strains.
The number and average misorientation angle of these boundaries increase with deformation, finally leading to development of a new fine-grained structure.

Effect of grain refinement on cold formability behavior on medium C-Boron steel Ilaria Salvatori1, a, Claudio Guarnaschelli1, b and Tommaso Coppola1, c 1Centro Sviluppo Materiali SpA, Via di Castel Romano 100, 00128, Roma, Italy ai.salvatori@c-s-m.it , bc.guarnaschelli@c-s-m.it, ct.coppola@c-s-m.it Keywords: Ultrafine Grain Steel (UFG), ferrite grain refinement, cold formability, plastic damage.
Calibration of the model was carried out by analyzing the ultrafine grained steel, produced in pilot mill whose grain size was about 2-3 mm and the conventional steel industrially produced (grain size about 12 mm).
The screw head is formed through a number of steps including a) Step 1: extrusion in die; b) Step 2: first heading; c) Step 3: second heading; d) Step 4: flange and key hole forming.
The conventionally rolled material grain size was around 12 mm.
Actually, it has been found that for a significant number of pieces the real cause of rejection was not due to forging bursts, but to surface defects which were pre-existing on the wire rod.

The experimental results show that the copper billets with refined grains have higher strength than those with coarse grains prepared by annealing treatments.
Experimental Setup Grain Refinement.
Without the reduction of the initial billet cross-section, the process can be repeated a number of times and the billet is rotated by different routs between consecutive passes in order to obtain uniform strain.
This phenomenon is particularly clear in the case with the coarse grains (annealed copper) at 25 ºC.
An inhomogeneous deformation occurs in the case with coarse grains as illustrated in Fig. 5(a).

Especially, the effect of heat temperature on the original austenite grain size was more obvious, such as the austenite grains grew up quickly with the increase of heating temperature, and the original austenite grain diameter was 37.8 μm when the temperature reached 1050 ℃.
There are a few martensite packets in a original austenite grain, and martensite packet comprise of a number of lath with the same dimensions and roughly parallel space orientation.
Fig. 4 Relationship between micro-grain Fig. 5 Relationship between the austenitic size numbers and heating temperature grain size and heating temperature Conclusions After heated to 950 ℃ and soaked for 2, 5, 10 and 15 min respectively was quenched by die, the yield strength of the hot forming steel WHT1300HF presented earlier decrease and later increase trend with the extension of holding time, while the tensile strength was first reduced and then maintained at more than 1400 MPa.
The influence of the heating temperature on the original austenite grain size is remarkable.
The austenitic grains grew up quickly with the increase of heating temperature.