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As a standard approach, for simplicity, in the following discussion on polycrystals (with n grains, where n is a number which is big enough to represent a non-textured polycrystal), we shall assume that all yield stress to be normalized by the yield stress of uni-axial tension, unless it does not exist.
In the first scheme, the start of phase transformation depends only on one grain that produces the maximum K.
Any interaction among grains is ignored.
In the second scheme, the interaction among grains is counted by a simple average over all grains.
Since it is the driving forces of all grains that are averaged, this scheme is different from many traditional methods, such as Voigt approximation, Reuss approximation, and Taylor’s method [5].

The grain sizes of natural freezing snow-ice are quite consistent and the average size is 4 mm.
There are some minute air bubbles that are uniformly distributed within the grain boundary ( less than 1 mm in diameter ).
It included that the microscopic crystals “grain of node stress”( the binding force between the particles ) damaged and internal stress changed.
The snow-ice clearing’s difficulty depends on its internal structure, each particle binding form and grain knot (as show in Fig. 5).
Its regularity is weak, and it is difficult to determine the snow grain’s size and shape; the size, shape and number of the intergranular organization and the link between organizations and organizations such as internal organizational structure.

In unlined rock tunnels the resistance coefficient is independent of the Reynolds number because of the large relative roughness value usually obtained.
Thus the Von Karman-Prandtl equation for fully rough flow based on the Nikuradse sand grain data should be applicable.
This equation in terms of Darcy`s f, pipe diameter Dm, and equivalent san grain diameter K is (1) A measure of over break k in unlined tunnels can be expressed as (2) Where Dm and Dn are the equivalent diameters based on the area Am and An as shown in Fig. 2.
The relative roughness of the tunnel also can be expressed as (3) The k dimension is approximately twice the mean over break thickness and, therefore , is a parameter similar to the Nikuradse sand grain diameter Ks.

In general, the grain size decreases with increasing layer number.
With increasing layer number, the Bragg diffraction peaks become broadened.
It is suggested that the residual stress together with the small grain size should be responsible for the broadening of the Bragg diffraction peaks.
Fig.6 shows the relationship between the layer number and adhesion strength of the coatings.
Fig. 6 The critical load as a function of the layer number.

The number of layers may be as many as 14 continuous layers [1].
This only means the seeding methods does not give much effect to the growth and grain size of the diamond films.
Figure 2(d) shows the NCD grains on the surface of the NCD layer.
The cross section data is presented from sample CC with 2.5μm x 2.5μm scan area, equivalent to about 50,000 x magnification of diamond grains with clear boundaries.
This can be explained that there are smaller grains within a particle that is not detected by the AFM.

This approach builds on a recent project to correlate the phenomenon of roping in AA 6xxx alloy sheet for car body applications to the occurrence of band-like clusters of grains with similar crystallographic orientation.
For the streakiness on the 37 µm foil a number of maps were acquired to cover a much larger area of 18.0×1.3 mm².
The texture differences between the three samples were small, independent of thickness and processing, and are possibly mainly caused by insufficient grain statistics of the EBSD-derived orientation data.
This is at variance to the roping simulations in AA 6xxx series autobody sheet [8], where it was concluded that roping can be attributed to a grain-to-grain variation in the through-thickness strain rate d33.
This is at variance to the roping simulations in AA 6xxx series autobody sheet [8], where the occurrence of roping was assigned to a grain-to-grain variation in the through-thickness strain rate d33.

The grain growth was hardly observed in the weld region and the heat-affected zone.
Their good engineering performance has led to an increasing number of applications, mainly in corrosive environments such as sour gas pipelines and chemical reaction vessels.
The grain growth was hardly observed in the weld region and the heat-affected zone.
These micro fine grain and white elongated band are austenite.
The grain growth was hardly observed in the weld region and the heat-affected zone.

The number and the diameter size of pit on the sample surface increase with applied stress increasing.
It can be seen that average diameter of the grain is tiny and no more than 10 um.
The grain outspread along the rolled direction, mainly composed of acicular ferrite and multilateral ferrite.
It can be seen that corrosion on the sample surface is uniform distribution pitting, with the stress increases, pitting number and size increase gradually.
The number and the diameter size of pit increase with applied stress increasing.

Supposing that is ratio of number of fibers in the feeding web whose length is between and to the total amount of fibers in different lengths (namely frequency), the number of fibers from bundles is in the length of.
Therefore, the total number of fibers is from feeding place to .If fibers from the bundles are in the same length, each fiber in above equation also has equal length.
Fig.3 Fiber Number Distribution in Front Drafting Area In Fig.3, total number of fibers through section we require, subtracting the amount of slow fiber held by back roller and then deducting the number of fast fiber that is held by front roller after drawing, is the quantity of floating fiberthat is fed into back-roller at X section.
Thus, the integral of fast fiber number fromto is: (4) Substituting Eq. 2, Eq. 3 and Eq. 4 in Eq. 1, it is obtained: (5) Eq. 5 represents fiber accumulative length frequency in the range of fiber length at X section divided by the number of heads per length.
Table 2 Experimental Data for New and Old Drafting Form at Different Speeds Three-over-three Three-over-five Speed( nips /min) 250 300 350 400 250 300 350 400 Evenness CV (%) 3.4 3.14 3.07 2.78 3.2 3.4 3.53 3.82 Nep (grain /g) 25 24 22 20 22 24 25 28 Impurity (grain /g) 18 18 19 18 19 17 19 18 Table 3 Experimental Data to 31mm Long Fibers in Old and New Drafting Form Combed silver eveness CV (%) Combed cotton nep (grain/g) 1 2 3 1 2 3 Three-over-three pressure bar 2.77 2.84 2.78 18 19 18 Three-over-five 3.55 3.45 3.52 24 23 25 As indicated in Table 2 and Table 3, we find that, the technical qualification of three-over-five drafting form is better than that of three-over-three at low speed of 300 nip/min.

Furthermore, due to a higher strength of fine-grained materials, the mechanically induced grain refinement positively contributes to the wear resistance as well [5].
id Process Rotational velocity n [min-1] Feed f [mm] Rolling force FTL [kN] Number of passes np [-] Tool freq.
This included a realization of surface roughness, hardness, residual stress and grain size measurements.
Furthermore, a grain refinement of the material structure below the submicrometer-grained surface layer is clearly seen for deep rolled specimen DR2 and vibrorolled specimen VR2.
Shaw, Bulk materials with a nanostructured surface and coarse-grained interior, in: M.