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This program, with high speed and simple algorithm for random tessellation has the ability to change the level of statistical parameters such as number, mean, variance of the area of the grain.
In a random tessellation, the number of cells, the number of their segments and their shapes are all random.
This program, with high speed running and simple algorithm for random tessellation has the ability to change the level of statistical parameters such as number, mean, variance of the grains area.
Number of alpha phase grain (brighter phase in actual picture) and beta phase grain (dark phase in the actual picture), the percentage of alpha phase and the distribution area of alpha phase are the image processing component outputs.
(b) Processed image of microstructure In Fig. 4 total number of grain are 122 and area fraction of alpha phase is 0.4.

With the change of the average grain size, d, in the 1nm…1cm interval the grain structure, the grain boundary structure and defect structure of grain volumes are changed.
In some intervals of grain sizes, the grains remain dislocation-free.
The grain consists of (1) the grain body, (2) grain boundary, (3) triple junction and (4) quadrupole node.
Grain boundary migration and grain growth occur during plastic deformation of ultra-fine grained FCC metals [15].
Deformation at the yield stress and in the interval ε = 0…5% is provided by grain boundary gliding and emission of small dislocation groups (number of dislocations n does not exceed 5) in the largest grains with cells and fragments (see Fig.6b, the darkened area).

There are two types of grains; 1) large grains (LG) with an average size of 1.4 microns and 2) the small grains (FG) with an average size of 0.5 mm.
It is also known that the number of present particles, their size, distribution pattern and interparticle distance, as well as the irregularity degree of the matrix lattice and precipitation have an effect on the material dispersion strengthening [2].
Type 1 grains are sized within 0.1-0.5 µm (let us denote them as small grains, SG).
Type 2 grains are sized within 0.5-4.0 µm (let us denote them as large grains, LG).
The total number of Ti3Al and TiAl3 phases in the I-region is 3% of the volume of material and in the II region - 10%.

The Study of the Electrochemical Graining Process in NaBO2- H3BO3 Solution and Grain Appearance on the Surface of Aluminum Alloy Jun Q.Liu 1, a, Xiao H.
The mainly process of electrochemical graining on 6063 aluminum alloy included graining at alternating current, anodizing and chemical coloring.
To quantitatively assess the process effect of graining, four score indexes were self-established, which were grain density (grain numbers/sample width), grain width, grain depth and grained color: (1) Grain density (ρ): the best range was 6cm-1≤ρ≤10cm -1, the second, 4cm-1≤ρ≤5cm-1 and 11cm-1≤ρ≤13cm-1; (2) Grain width (w): the best range was w≥280µm, the second, 200µm≤w<280µm; (3) Grain depth: enough depth was the best; (4) Grained color: the best was silvery white after treated, the second was gray.
According to the above process parameters the grained effects were as follows: grain width was 280µm, grain density was between 8cm-1and 10cm-1, grain depth was remarkable, and color of all grained samples was silvery white.
Observation of the Grained Morphology.

The material is described on a grain scale as a set of � (variable) spherical grains.
The model includes: (i) a grain boundary migration equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a dislocation-density evolution equation, such as the Yoshie-Laasraoui-Jonas or Kocks-Mecking relationship, involving strain hardening and dynamic recovery, and (iii) an equation governing the total number of grains in the system due to the nucleation of new grains.
Description of Grain Properties When deterministic evolution equations (i.e., with no stochastic terms) are used, all grains of a given age τ have undergone identical evolution and therefore have the same diameter D and dislocation density .ρ Hence, all properties of the grains in the model are one-parameter distributions, and each grain is characterized by its age .τ The following functions can then be introduced: - the number of grains of age ,τ ( ),� tτ (number per unit volume and age time); - the plastic strain within the grain ( ) ( ),d , t tt u uτετ ε−= ∫ & in which the strain rateε& is assumed to be the same for each grain (per the classical Taylor isostrain crystal-plasticity assumption); - the strain hardening of the grain as represented by its dislocation density ( ),tρτ (length per unit volume); - the grain diameter ( ),.D tτ A number of constraints connect the various functions; e.g., the overall volume is constant at all times, i.e., ( ) ( ) 3 06
t t � t D tτ τ τ π ∀ = ∫ (1) Evolution of Grain-Property Distributions Several mechanisms contribute to the evolution of grain-property distributions: (i) Grain boundary migration.
ucleation of new grains.

In this fully recrystallized region the average grain size of the cube grains (dcube) is ≈ 20µm, compared to an average size d ≈ 10µm for all grains.
A significant number of twin boundaries, as shown by the thicker lines in the misorientation map of Fig. 1b, are also seen in the fully recrystallized samples.
Each simulation was carried out 10 times, using the same experimental starting microstructure in each case, but using different seed values for the random number generator.
For each grain the mean orientation was determined, and then assigned to each site within the grain.
Figure 5: Increase in cube volume fraction as a function of grain size increase during grain growth.

It is assumed that the pinning force must overcome the driving force for grain growth to prevent the abnormal grain growth.
(3) The number of precipitate particles is few.
Austenite grain structures were evaluated with an optical microscope to determine grain coarsening temperatures.
Grain coarsening behavior.
Grain coarsening behavior.

Silicon carbide with diffierent granularity and three grain composition was used as raw material.
Table 1 Silicon carbide grain composition in the experiment Number 1.0-0.5mm (wt%) 0.5-0.1mm (wt%) ＜45μm (wt%) ＜5μm (wt%) 1 45 15 20 20 2 50 17 20 13 3 54 13 20 13 Sample Preparation.
Doped with 6% (in mass, similarly hereinafter) additive (PVA, 2% concentration) into the mixed material, after 6 hours, the mixture was molded to 56 mm×10 mm×10 mm specimens at pressure of 100 MPa by a hydraulic press (NYL-300), finally the specimens were sintered 1400 °C, 1450 °C and 1500 °C for 3h, were respectively coded as A, B and C, such as A-1, B-1 and C-1 (taking grain composition Number 1 in Table 1 for instance).
Results and Discussion Effects of grain composition on properties of silicon carbide material.
Sample A-2 has good densification, it has the best grain composition.

This addition suppresses the variation in the ZnO grain size without reducing the grain size.
The varistor voltage increases with increasing number of ZnO grain boundaries between the electrodes.
Thus, to fabricate varistors with low breakdown voltages, it is necessary to reduce the number of ZnO grain boundaries between the electrodes.
Adding only Ba or Ti to Bi-based ZnO varistors promotes grain growth enabling large ZnO grains to be obtained [2].
The resistances to electrical degradation were markedly improved for the sample to which no Ba had been added and for the sample to which approximately 0.01 mol% Sb had been added with increasing number of ZnO particles with c-axes perpendicular to the pressured surface (the diffraction peak intensities for the (002) plane increased) [4].

The white areas are the smallest grains, filtered out because considered to be more likely γ' precipitates than γ grains.
The average grain size is 10µm and the GOS is very low in most of the grains.
The initial grain size was in the range of the limiting grain size that can be calculated based on the Zener model [5].
In this case, abnormal grain growth is due to grains having enough difference in stored energy with the neighbourhood, thus triggering strain induced grain boundary migration across secondary phase particles.
According to Pande's model [6], the number of twins per grain is increasing with the distance over which grain boundaries have moved (i.e. grain size), and with the grain boundary velocity, which itself is usually decreasing when increasing grain size.