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Analysis shows that GSS creep in geological and glacial materials can be accounted for in terms of four “universal”, mesoscopic scale constants of average values, γ0= 0.197, γB = 0.415 J.m-2, N = 8.9 and a = 0.166, where γ0 is the average shear strain associated with a basic boundary sliding event at the level of the atomistics, γB is the specific grain boundary energy (assumed to be isotropic),N is the number of boundaries that align to form a mesoscopic boundary glide plane and “a” is a constant that obeys the condition 0grain shape and size distribution in the material.
It is emphasized that in geological and glacial materials the grain size varies from extremely coarse to fine grain sizes.
The number and distribution of such free volume sites at a boundary will depend on its misorientation.
When the grain shape is irregular and there is a grain size distribution, “a” obeys the condition 0 < a <0.50 [8].
N (0number of boundaries that align to form a plane interface . γB (0<γB<1.5 Jm-2) is the specific grain boundary energy (assumed to be isotropic).

The phase field variable varies smoothly across the interface from fi = 1 in the ith grain to fi = 0 in other grains.
The time evolution equations for the phase-field and carbon concentration variable, C, are given by the following equations: (1) (2) Here, n is the number of phase fields at an arbitrary point.
According to a study of the ferrite nucleation during the austenite-to-ferrite transformation during continuous cooling reported by Umemoto et al. [7], the number of ferrite grains nucleated on a unit area of the austenite grain boundary in a unit of time is calculated by the following equation: (6) where Dg is the diffusion coefficient of a carbon atom in the austenite phase.
In Fig. 2(a), the translucent gray region indicates the austenite grain boundary and the colored regions represent the ferrite grains.
Figure 3 Size distribution of ferrite grains.

It may be noted that the formation of a large number of low angle boundaries is attributed to the multidirectional deformation processing which promotes rapid formation of intersecting sub-boundaries compared to uniaxial compressive deformation [7,8].
Although some sub grains and ferrite grains elongated in the rolling direction have been retained, a large number of equiaxed ultrafine ferrite grains in the submicron range surrounded by high angle grain boundaries were observed.
However, among the grain boundaries with misorientation angles of 1.50 or higher, high angle grain boundaries of 150 or more and low angle grain boundaries with relatively large misorientation of each account for approximately 35% of total grain boundary length.
(I). work hardened grains; (II). mixed grains consisting of work hardened grains and dynamically recrystallized (DRX) grains and (III).
DRX grains.

The combination of diffraction and extinction information aids the grain indexing operation, in which pairs of diffraction and extinction images are assigned to grain sets. 3D grain shapes are determined by algebraic reconstruction from the limited number of extinction projections, while crystallographic orientation is found from the diffraction geometry.
To extract all the information contained in such an image, a number of data processing steps are required.
A number of criteria are used to achieve this.
By exploiting both extinction and diffraction spots during the data analysis the grain indexing algorithm is simplified, allowing large numbers of grains to be successfully treated.
In future, it is hoped that improvements can be made to the algorithm to allow samples with even larger numbers of grains (>1000) to be mapped, and to accommodate samples with greater levels of mosaicity than can be handled at present.

A linear relationship between the area fraction of DRX and the number fraction of Σ3 boundaries was observed during hot deformation.
It is observed that like Σ3 boundaries, a linear relationship is exists between area fraction of DRX grains and number fraction of Σ9 boundaries.
For example, the number fraction of S3 boundaries increases from 0.45 in the SA condition to 0.58 in the specimen shown in Fig. 2, while the number fraction of S9 and S27 boundaries increases from 0.029 and 0.008, respectively, in SA condition to 0.078 and 0.041, respectively, in the same specimen.
These large numbers of S3-S3-S9 and S3-S9-S27 triple junctions, in turn, fragments the connectivity of random HABs in the GBE microstructure.
A linear relationship between the area fraction of DRX grains and the number fraction of Σ3 boundaries is observed during hot deformation.

Two different shapes of the grains are introduced in the RVEs of CP-FEM in order to study the effect of the grain morphology.
The grains in each RVE are given different texture and grain shape.
For each texture, 400 orientations are numerically generated using a Gaussian distribution function [4] with a small value of the orientation spread around the ideal component, and mixed with 400 random orientations generated using a random number generator.
It was assumed that this number of grains is enough to predict accurately the stress states at yielding for each texture [4,5].
FC-Taylor model versus CP-FEM with one element per grain, CP-FEM with one element per grain versus eight elements per grain, and CP-FEM with one element per grain versus elongated grains.

In this case grain 2 Title of Publication (to be inserted by the publisher) coarsening by grain growth may dominate over grain refinement by dynamic recrystallization.
Fo39 Fo40 Fo41 Fo42 Fo43 Fo44 HIP4 HIP5 Deformation (D) or HIPped-only (H) D D D D D H H H Initial sample length 16 16 16 5.3 16 16 5 5 Initial sample diameter 8 8 8 8 8 8 11 11 HIP-duration [hrs] 3 24 9 14 15 17 9 40 Deformation-duration [hrs] 17.8 18.8 17.9 30.2 35.4 - - - 4.80 9.30 1.13 5.23 10.80 Strain rate [10-6 s -1 ] 5.07 5.01 5.12 5.85 1.26 - - - 17.3 31.3 9.9 41.1 83.0 Flow stress average [MPa] 33.1 32.0 24.8 32.3 31.6 - - - Final: Axial shortening strain [%] 28.0 27.9 27.1 45.6 28.4 - - - Mean grain size [µm] 1.4 1.2 1.1 1.5 1.3 0.8 0.6 0.7 Standard error 0.06 0.05 0.04 0.08 0.05 0.02 0.01 0.01 Average Feret90/0 ratio 1.1 1.1 1.1 1.1 1.0 1.1 1.1 1.1 Number of grains analysed 203 280 347 180 274 772 1207 1005 Journal Title and Volume Number (to be inserted by the publisher) 3 0 10 20 30 40 50 60 70 80 0 10 20 30 strain [%] stress [MPa] Fo39 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25
Quantitative grain size analysis.
The low n-value, the weak LPO and the lack of any change in average feret90/0 ratio of the grains are observations that point to a GSS, possibly grain boundary sliding (GBS) dominated, Journal Title and Volume Number (to be inserted by the publisher) 5 Fig. 4 Average grain size-time plot of HIPedonly and deformed samples; error-bars show standard error of the average value.
The model of Ashby and Verall [12] involves grain switching during GBS, which increases the probability of high-sided grains coming into contact with low-sided grains, therefore stimulating grain growth.

After ARB processing an ultrafine-grained microstructure is obtained.
The stacking order with increasing number of ARB cycles N can be seen in Table 1.
Structure of AA6014/AA5754 laminates with increasing number of ARB cycles N.
The evolution of the grain structure with increasing number of ARB cycles is shown in Figure 3.
The grains of the AA5754 layers are finer than the grains in AA6014.

To this purpose a model is presented in which the grain size that appears in the Hall-Petch relation is substituted by an effective grain size that is dependent of the grain-shape morphology and the crystal orientation.
With the approximation of the grain shape as an ellipsoid, the grain size parameter Dθ was defined as the equivalent diameter of an ellipse which is the result of the intersection of the ellipsoid grain with the slip plane (cf.
The equivalent grain size for this slip plane and this grain ellipsoid is D0 ≈1.8 µm.
A spread of 15° from the ideal crystal orientation was allowed in order to include a representative number of grains in the statistics (cf.
Such a material is also very likely to produce a non-equi-axed grain shape, which also contributes to the grain shape anisotropy.

This can be explained by the formation of the necklace structure with small grains along the upper grain boundary of the elongated grain [see Fig. 2 (a)] that facilitates an easy grain boundary sliding (GBS).
The largest sliding takes place along the upper grain boundary of the elongated grain with the second largest - along the lower grain boundary of the same grain.
Considerable grain growth takes place in the stagnant zones and in contrast to this the formation of a number of small grains (necklace structure [20]) can be seen along the upper grain boundary of the elongated grain.
Elongated grain disappears at early stages of deformation being split into three grains, firstly, by low-angle grain boundaries that later transform into large-angle ones.
Small grains are mostly found along high-angle grain boundaries of larger grains.