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Journal Title and Volume Number (to be inserted by the publisher) texture developed in conventional rolling and thermal processes of aluminum alloy sheets, in which the <111>//ND component is lacking.
It is noted that most grain boundaries are of high angle.
When pulled in TD, the Goss oriented grains are much harder than the cube oriented grains, and hence retains a higher surface level than the cube oriented grains.
Journal Title and Volume Number (to be inserted by the publisher) [9] H.
Ultrafine Grained Materials III., ed.

Essentially, there are two basic methods which can be applied for promoting formation of a dominant equiaxed grain zone with finer grain size in solidification structure of steel castings: melt stirring during solidification or introduction of a larger number of solid particles to the melt prior to solidification.
The applied stirring induced multiple fluid flows of liquid metal inside the melt, breaking dendrites during the course of their growth and creating a larger number of heterogeneous nucleation sites – broken dendrites for enhancing formation of equiaxed grains, thus, leading to final more uniform solidification structure with an enlarged equiaxed grain zone.
As-cast structure of 42CrMo4 steel exhibited a large number of micro-pores evenly distributed over entire volume of the specimen which is dominated by a columnar zone consisting of columnar grains of larger sizes (Fig.3a).
The area fraction is a ratio of points falling into the zone of interest to the total number of grid points.
In the case of determining the area fraction of the occurred porosity, the 225-point test grid was placed randomly over 10 fields of dimension 4000×4000 µm in the solidification structure; and the area fraction of the occurred porosity is a ratio of the average number of points falling into the pores and the total number of the grid points.

Metals with Grain Interactions Atish K.
A high degree of interaction between adjacent grains can be accommodated inside the bulk of the grain.
However, the increase in average number of active slip systems would lead to different end textures.
The average number of slip systems active per grain is lower than the above interacting case.
Thus it can be argued that the general observation of S-texture in high SFE metals [2] comes directly as a result of grain interaction and the individual grains attain a state of deformation where slip is carried out in an excess number of slip systems even though it is energetically less favorable.

Ultrafine-grained metals whose grain size is less than 1 mm have attracted interest as high-strength materials.
However, measurement of the yield surface of ultrafine-grained metals requires considerable labor.
The material parameters in Eq. 16 cannot be determined in unique because the number of results for the detailed yield surface is too large to solve simultaneous equations.
In the genetic algorithm calculation, the number of individuals is 20, and the rates of crossover, averaging, mutation, and copy are 14:3:1:1.
The unit-cell model is composed of 35 grains whose mean grain size is 954 nm.

Secondly, after interrupting the electro-hydraulic servo testing machine applied a specified cycle number, the crushed rock sample was taken out the box and the grain size distribution of the sample after vibration was measured by sieving of the crushed rock sample.
After vibration, the grain size distribution curves of the crushed rock sample corresponding to a cycle number of vibrating load, i.e. 20000 cycles, are indicated in Fig. 3.
In order to compare conveniently the grain size variation, the initial grain size distribution curves are also shown in Fig. 3.
The test curves of grain size change in the coarsely crushed rock layers with three main grain sizes of 16−40, 25−50 and 50−80 mm before vibration are presented.
This tendency to degradation of the grain sizes in the coarsely crushed rock samples after a 20000 cycles vibrating load is stronger with increasing of the initial grain size.

Considering non-oriented electrical steel has a general tendency toward thinner and coarser-grained, there are few numbers of grains in both the thickness and blanking clearance sections.
Xu et al. [6] reported that as for thinner and coarser-grained sheet, the blanked edge morphology has a strong integrated relationship with clearance and grain size.
Therefore, with the reduction of grain number across thickness and clearance sections, grain size effect becomes more significant.
It suggested that for coarse grain sheets, the grain size becomes an important factor in blanking process which is often ignored in macro blanking process.
It indicates that the traditional indicator (c/t) is no longer suitable for blanking thin sheets when the number of grains in thickness is countable.

According to the empirical Eq.7, the initial node number of the hidden layer is 6.
Then make use of the successive steps of growth to determine the node number of optimum implication layer as eleven.
Eq.6 ； Eq.7 ; In Eq.7, l refers to the number of hidden nodes; m refers to the number of input nodes; n refers to the number of output nodes; a refers to constant between 1 to 10.
Research on Coarse Grain Soil Maximum Dry Density Test[J].
Fractal Graphic of Coarse-Grained Soil Category[J] .

Based on stereology, the reciprocal of grain size is proportional to grain boundary area.
Even if the s phase is precipitated at the fcc grain boundaries, some precipitates are left inside the fcc grains after the grain boundary motion.
In general, diffusion rate along grain boundary is higher than that in grain interior.
(3) The average grain size is known to be inversely proportional to the total grain boundary area.
Acknowledgement This work was supported by Grant-in-Aid for Scientific Research (B) (JSPS KAKENHI Grant Number 20H02464) in Japan.

After these pioneering works the subject of superplastic UFG alloys became quite popular and the progress in this trend was successfully demonstrated in a number of recent reviews [8,9].
The fatigue tests of blades were performed on a special vibration testing machine VEDS – 400A at room temperature and symmetric loading cycle R= -1, the number of cycles 2x107, frequency f=500 Hz [15].
Smaller Zn grains with sizes between ~50 and ~150 nm were located at the triple junctions of the aluminum grains.
Although there is some grain growth during superplastic deformation, the grain size remained less than 100 nm (Fig. 4a).
Langdon, Twenty-five years of ultrafine-grained materials: Achieving exceptional properties through grain refinement, Acta Mater. 61 (2013) 7035-7059

A number of attempts have been made to study the austenite grain growth in the presence of second-phase particles.
Grain growth modeling.
Therefore, the net driving force ΔP for grain growth is governed by the sum of all driving and retarding forces acting upon the grain boundary motion.
The driving force for grain growth is given as a pressure per unit area of grain boundary and it can be expressed according to Smith and Zener (1948) [5] as (3) where kd is the driving force parameter, γg the grain boundary energy, and D the grain size.
Non-isothermal grain growth in metals and alloys.