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Every time step starts with the initialization of the plastic multiplier ∆spl, k=0=0 and the history variables (internal variables), as there are the number of stopped dislocations nn+1, k=0=nn, the geometrical internal length scale Ln+1, k=0=Ln, the twin volume fraction Fn+1, k=0=Fn and the dislocation density ρn+1, k=0=ρn.
Herein, b denotes the burgers vector, k the forest hardening parameter, n0 the threshold number of stopped dislocation, whereas the variable n describes the flux of dislocations which have arrived at a twin or a grain boundary.
The extension from a scalar (see [3]) to a tensorial quantity (see [4]) allows to incorporate the directional nature of the number of dislocations stored at an obstacle.
Further, the tensorial formulation of n is directly related to the back-stress tensor X as described in eq.(7). λ stands for the mean space between slip bands, F0 for the maximum twin volume fraction, β is a fitting coefficient, εinit the critical strain, when twinning begins, d the grain size, e the twin mean thickness, M the Taylor factor, μ the shear modulus and α a fitting material constant.
Scott, Effect of grain and twin boundaries on the hardening mechanisms of twinning-induced plasticity steels, Scripta Materialia 58 (2008), 484–48

The results of the investigation of the temperature dependencies of thin films ionic conductivity (�) showed that the dependence �(T) is caused by the temperature dependence of oxygen vacancy mobility, while the number of charge carriers remains constant with temperature.
The structure of the grains of YSZ belongs to cubic symmetry.
The mobility is related to the diffusion coefficient D� via the Nernst-Einstein relation: Dv = µkT/zq = kT�/Nz 2q 2. (6) From experimental values of both the ionic conductivity � and relaxation frequency �R it is possible to calculate the number of oxygen vacancies taking part in the charge transport.
That gives evidence that the dependence �(T) of YSZ thin films is caused by the temperature dependence of oxygen vacancy mobility, while the number of charge carriers remains constant with temperature.
Investigation of the X-ray diffraction patterns showed that thin films are mixed-phase materials but the grains of YSZ belong to cubic symmetry.

For hardness testing, the average Brinell Hardness Number (BHN) readings were determined by taking two readings at different position on the specimens using a Brinell hardness tester.
During ageing, some of alloy’s compounds precipitate out of solution and end up at the grain boundaries to increase strength by interfering with the slip-planes.
The decreased of hardness with soaking times might be interrelated with the grain growth tendency.
Nucleation occurs at a relatively high temperature (often just below the solubility limit) so that the kinetic barrier of surface energy can be more easily overcame and the maximum number of precipitate particles can be formed [9].
In general, the fatigue strength decreases as the number of cycles increases.

High cost of pure CNT’s and graphene is a direct reason for numbers of studies, also conducted in this article, on the synthesis of copper and other forms of carbon.
Carbon material Grain size Iodine number Bulk density Carbon content mm [mg/g] g/cm3 wt. % Activated carbon CWZ-14 0 - 0.12 750 0.29 – 0.38 92 Cu-CNT’s wire Control system Mixing system Carbon supply device Secondary cooling system Inert gas Pulling unit Primary cooling system (Crystallizer + cooling unit) Graphite crucible Fig. 1.
Direct comparison of macrostructures for CuOFE and Cu-C (1) reveal differences in the shape and size of grains and also in their angle of inclination (for both casts the same casting speed and almost the same set of other casting parameters were used).
With the same cooling parameters less heat is being removed from solidifying composite, which is the direct reason for bigger and more longitudinally oriented grains.
Increase of pulling step from 3 to 6mm does not inflict the macrostructure of obtained casts, which is unusual in comparison to the results obtained for pure copper materials (with the increase of casting speed average size of grain decreases and angle of inclination increases).

The web points are set at the special characterized points of the structure see Fig.2 and Fig.3 in order to represent the dynamic behavior of the elements, it arranged in a equal distance from horizontal to vertical direction crossed its shape, and numbered 1,2,…We now use a loom plate wall as an example to describe how the web points are arranged.
Table 2 Testing stresses on the lid of the plate (Pa) Test points 1 2 3 4 5 6 7 Stresses before vibration -98.6 -98.6 -98.6 -221.9 -197.2 -98.6 -295.8 Stresses after vibration -147.9 -49.3 -78.9 -123.3 -73.9 0 0 3.2 Application in vibrating solidification A fine grain and well-distributed crystal by vibration solidification van be got.
The fine grain crystal compared with the static solidification shown in Fig.8 (a) and Fig.8 (b).
The well-distributed fine grain in the cross section of an element can be demonstrated by the properties of the element possessed.
The natural mode frequencies of the cast element are the results of the curve drafts by a number of web points after mode calculation.

Introduction The crystallographic axes of grains have different orientations in general.
The main problem with growth, supported by the Cartesian grid is, that despite the specified grain orientation, growth can consistently be calculated only along the principal grid axes.
The solution relates the nondimensional supersaturations for each alloying element , to the corresponding growth Peclet number by the following equation [1] , (6) where is a tip radius.
(12) Solution procedure The above equations are solved iteratively for a certain number of time steps or until complete solidification has been reached.
The function together with Peclet number and tip radius Eq. 8 can be set for each species .

Fig. 4 Replicas showing the propagation process of crack 1 Fig. 5 shows the crack length as a function of number of cycles.
Most of the researches accounted this phenomenon to the interaction between crack tip and grain boundary.
Thus, the crack tip had to penetrate through considerable differently oriented grains.
Once the crack tip reached the grain boundaries, the driving force of crack growth would reduce and the crack exhibited a dormant state consequently.
Rong Jiang would like to thank Nanjing University of Aeronautics and Astronautics (reference number: 1002-YAH18002) for financial support.

The potentiodynamic polarization was measured at a scan rate of 1 mV/s by CHI660C.The samples were immersed in 3.5%NaCl solution, then the numbered sample was taken out one by one, respectively, after immersing different time.
The Al-5Zn-0.03In alloy is mainly consisted of α-Al matrix with precipitates on grain boundaries in Fig. 3a.
For Al-5Zn-0.03Ga alloy, after 30 min immersion, some very small white particles and pits in grain can be seen.
In Fig. 4b the EDX analysis of Al-5Zn-0.03Ga alloy confirms that the grain boundaries contain Al and Zn elements.
In Fig. 4c the EDX analysis of the corroded Al-5Zn-0.03Ga indicates that the grain with very small white particles contain Al, Zn and Ga elements.

There are some dislocation groups too. 2) With the increase of deformation degree, the quantity of parallel wide short stripes increase, the dislocation configuration is still mainly straight stripes, and the crystal grains are refined. 3) At 18.83% deformation degree, wide short stripes are plentiful and the crystal grains are refined obviously. 4) With the further increase of deformation, quantity of parallel wide short stripes increase continuously, lattice distort seriously, the crystal grains are refined more obviously. 5) At 29.63% deformation degree, quantity of parallel wide short stripes increases not so much, the crystal grains are further refined.
With the increase of deformation, a large number of deformation twins appear.

The measurements were performed with an accuracy up to 0.01 mm with numbers of loading cycles N recorded.
Fig. 4 Temperature changes at time on the specimen surface along the propagation line The steel structure shown in Fig. 5 is characterized by band arrangement of ferrite (light) and pearlite (dark) of reduced size of grains, typical for materials after hot working.
The mean size of a ferrite grain varied in the range 10-20 µm, in the case of pearlite it was 4-11 µm.
In P265GH steel we can see transcrystalline cracks in grains of ferrite and pearlite in the axial section of the specimen.
We can also notice short cracks coming from the main crack and running along the grain boundaries.