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Szekeres [8] referred to these abnormally large prior austenite grains, larger than 1 mm, as "blown-grains" and contended that the existence of abnormally large prior austenite grains is the key factor and mandatory prerequisite for transverse cracking [8,9].
In the limit of powder diffraction when the gage volume contains an infinite number of randomly oriented crystallites, full Debye-Scherrer rings are recorded.
Preliminary neutron diffraction studies confirmed that large delta-ferrite grains transform to large austenite grains.
Large austenite grains seem to originate from large delta-ferrite grains.
Delta grains are typically greater than a millimeter in diameter and very large austenite grains are likely to develop from the large delta-ferrite grains in the thin solidifying shell close to the meniscus although the surface grains that initially form on solidification may be small.

Martensite nucleation events may take place in a number of grains leading to a certain number of clusters or spreads.The fill-in and the spread are illustrated in Fig. 1.
This quantity is important because is a measure of spread event that is independent of impingement.The number of grains in a spherical cluster containing tetrakaidecahedral grains the number of grains located within the cluster, γS, γS = 243π 1024 (λEG λγ )3 (2) where λγ is the mean intercept length of the parent austenite grains.
There are a high number of clusters with a small number os grains.
At the end of the simulation the number of grains per cluster is recorded.
Fig. 5 shows the mean number of grains per cluster as a function transformation probability.

In particular the α grain size could be over-estimated.
It can be also noticed that by increasing the temperature, the number of α grains decreases for the same surface analyzed and so a grain growth occurs.
It appears that the β fraction around 60%, can induce modifications of the nature and number of interfaces/boundaries (α/α and/or β/α and/or β/β) and so to probably interfere with the grain boundary sliding mechanism as well as with the accommodation mechanisms.
However none assumption can be made on the evolution of the β texture because the number of grains analyzed is insufficient and so the statistics is not good enough.
In particular the high hardening could be due to the grain growth but also to the decrease of the “α/thin-β/α” interfaces number.

that the accommodation process, i.e., the dislocation glide inside the grains, becomes more difficult with decreasing grain size in the nanometer grain size range, even though the grain boundary sliding as the major process becomes facilitated.
Thus, the reverse grain size dependence of superplastic elongation has been confirmed in the nanometer grain size range.
It should be noted that virtually no dislocation can be observed in the grains of the as-quenched specimen, while an appreciable number of dislocations are observed both in the α and β-phase grains of the aged specimen.
The m values of ultrafine-grained and normally fine-grained specimens were 0.38 and 0.48, respectively, which were chose to the theoretical values for the viscous dislocation glide inside the grain, 0.33, and the grain boundary sliding, 0.5.
The dislocation glide inside grain, the accommodation process, will rate-control the whole process in the ultrafine-grained specimen, while the grain boundary sliding, the main process, will be the rate-controlling in the normally fine-grained specimen.

Traces of crystallographic sliding appear inside some grains.
With an increase in the number of impacting pulses, accumulation of damage is observed.
The energy and the number of impacting laser pulses were changed.
Grain boundaries appeared.
Grain boundaries and traces of crystallographic sliding within grains were observed.

The variation of the strength with the pass number was explained by the texture and grain size.
Fig. 3 shows the variations of the average grain size, yield stress(YS), tensile strength(UTS), uniform elongation and total elongation as a function of pass number in ECAP process.
In Fig. 3, the grain size decreases continuously as the pass number increases.
The grain size after 8 passes is 3.6µm.
The yield stresses of 6 and 8 passed materials are also lower than that of 1 passed material. 0 1 2 3 4 5 6 7 8 9 0 10 20 30 40 50 60 0 50 100 150 200 250 300 Grain Size (µm), Elongation (%) Pass Number Grain Size Uniform elongation Total elongation Yield Stress Ultimate Stress Stress (MPa) Fig. 3 Grain size and mechanical properties of the ECAPed AZ31 Mg Alloy as a function of pass number in ECAP process.

However, perhaps the most important characteristic of the grain structure is the grain intensity λ (the more common notation in metallographic praxis is �V), namely the mean number of grains per unit volume or, equivalently, its reciprocal value - the mean grain volume Ev.
However, even this structure is not encountered in real polycrystals the grains of which grains are approximate irregular polyhedrons with number of faces about 14 and more; typically only three grains meet along a common edge and four grains meet in a common vertex.
The intercept intensity λ" (the mean number of grain chords or intercepts per unit length of the test lines) as estimated by profile count is then λ" = (s/4)λ.
In sections of normal tessellation is the mean number of vertices per profile 6 and in every vertex meet three profiles, so that the number of vertices PA can be estimated by 2�A.
For example, without changing appreciably the grain shape and volume and the mean number of grains per unit volume, the boundaries become wavy in such a way that their total area is doubled.

In practice, non-neighboring grains in the initial microstructure (separated by a certain number of grains) can be grouped to form global LS (GLS) functions.
This approach allows to use a small number of functions Np compared to the total number of grains constituting the microstructure Ng and thus limits the numerical cost.
The number of possible values for the energy jump ej − ei is then rather limited because Np << Ng.
We are currently interested in an improvement of this formalism which would both enables to use a small number of LS functions and to define an independent stored energy for each grain in the same time.
It is obvious that the complexity of such a brutal algorithm is linear (i.e. in O(e)), where e is the number of elements contained in the collection.

The numbers in the figure represent the maximum pole intensities
After this processing, each sample, taking A-1 for example, became into three ones as denoted by A-1-1, A-1-5 and A-1-10 (A-1 series) in which the last number represents the holding time (taking minute as unit) of annealing at 270 o C after cold rolling.
The fraction of grain boundaries with different character was determined on the basis of length fraction with the error less than 1.0%.
This is confirmed by the microstructure of early stage of recrstallization as shown in figure 4b in which lot of ∑3 boundaries appear size only around 10 microns, some grains with the same orientation but tend to grow larger by its boundary migration during annealing after cold rolling must be distributed evenly and the space between any two of this kind of grains is very short, it creates the possibility for the coalescence of the SBs clusters.
The initial microstructure which is at the end of primary recrystallization with fine grain size, a fair quantity of annealing twins and a random orientation can definitely result in a final grain boundary character distribution (GBCD) mainly composed of special boundaries (SBs) implying the GBCD has been optimized in satisfaction.

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