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Thirteen coarse grains are observed in the Cu portion and are numbered 1-13. 2.2.
Inverse pole figure map showing the orientation of individual grains, and definition of numbers of individual grains.
Fig.6 shows the relation between the displacement amplitude at the specimen end Δδ1/2 and the number of cycles N.
Fig. 6 Relationship between the net displacement amplitude of cantilever and number of cycles in fatigue experiment.
Acknowledgement This work was supported by JSPS KAKENHI Grant Numbers 21226005, 24686018 and 25000012.

The grain structure of the alloy is anisotropic grains, the average transverse size of which is 2.3 μm.
The average grain size of the formed phases was 25 nm.
In the fine-grained VT6 alloy, the density of boundaries is determined mainly by the transverse grain size.
Fig. 2 For a more thorough analysis of the effect of corrosion processes, a number of studies of the corrosion resistance of titanium alloy VT6 in a microcrystalline state have been carried out before and after ion implantation with aluminum ions in an acidic medium.
For a more thorough analysis of the effect of corrosion processes, a number of studies of the corrosion resistance of titanium alloy VT6 in a microcrystalline state have been carried out before and after ion implantation with aluminum ions in an acidic medium.

The size of the lamellae does not change significantly with the increasing number of cycles in AA8006 specimens.
Moreover, in contrast to the AA8006 specimens, lND shows a clear decreasing tendency with the increasing number of cycles.
initial, LM lND (ARB processed, TEM) Alloy lRD lND 2 cycles 3cycles 4 cycles 7 cycles AA8006 19 14 - 0,36 0,36 0,33 AA5754 13 9 0,26 0,21 0,09 - AA8011 - 9 - - - 0.17 Grain subdivision by low-angle boundaries (LAGB) and a progressive conversion of LAGB into high-angle grain boundaries occurs with increasing number of cycles in all alloys (Figs. 6a,b).
Thus, the process of grain subdivision and grain refinement is the most intensive in AA5754 alloy.
On the contrary, the alloys AA8011 and AA5754 exhibit a steady increase in hardness with increasing number of ARB cycles.

There are a number of factors to be allowed for in order to improve the predictions: (a) a realistic polyhedral shape of interacting grains and their respective spatial coordination; (b) relative rotation of neighboring differently oriented crystals due to their difference in strain rate; (c) dependence of each crystal slip pattern on the plastic strain distribution among its immediate neghbors.
On the polycrystal surface, where constitutive grains have a less number of neighbors, a kind of periodical conditions is employed: a lacking number of neighbors (with their crystal orientations) are reproduced by appropriate grains from an opposite side of the aggregate.
Here, the strain rate imposed on the grain interface by its neighborhood is expressed as ∑= − Σ − = 14 1i i 1ki Cn 1k S S 1 D D , ∑ = Σ = 14 1i iSS , (3) where Si is the area of grain face number i.
Iterations can be interrupted at any number of active slip systems, in particular k<5, and at respective residual ||∆||.
Some inaccuracy of the prediction may also be ascribed to idealization of such factors as actual shapes of considered grains and the numbers of their next neighbors.

As can be seen from Figure 2A, the original microstructure of Ni30 superalloy is uniform, showing an equiaxial distribution, a small amount of particulate matter is distributed at grain boundaries and inside grains, and there are white bulk microstructure produced during casting on the surface of the microstructure, and a large number of plat-like annealed twin microstructure.
When the solution temperature is 1180℃, a large number of annealing twins appear throughout or along the grain boundary.
In the process of solution treatment, new phase nucleation produces a large number of layer faults, and then a large number of twins are formed [10].
Influence of solution temperature on grain size With the increase of solution temperature, the grain size of the alloy increases, the number of grain boundaries per unit area decreases, and the total interfacial energy decreases.
At the same time, a large number of γ 'precipitates are precipitated in the aging process, the fraction of γ' phase increases, and the alloy precipitation strengthening increases, which also avoids the abnormal grain growth at high temperature.

With the increasing of annealing temperature, semi-solid primary α-Mg grain boundary become obscure gradually, grain growth is indistinct and β-Mg17Al12 phase is precipitated from the inner α-Mg grain.
Fig.2 shows that the grain of primary-Mg grain is round and the boundary is distinct, the Fig.6 shows that the roundness of primary-Mg grain had greatly changed and the boundary of some grain is obscure.
Contrast Fig.2 with Fig.3-6, it was found that the biggest change happen in the number and shape of the aberrated eutectic around primary-Mg grain, as the temperature increase, the number of -Mg phase in eutectic structure increases, and their continuous state become half-continuous and then blocky.
In a word, as the temperature rises, the growth of primary -Mg grain is obscure, but the boundary become obscure gradually; The α-Mg grain number and size increases continuously in the eutectic structure, and becomes blocky, separates gradually from β-Mg17Al12 phase, approaching the equilibrium solidification structure(-Mg in primary +-Mg eutectic structure and β- Mg17Al12 at the grain boundary), β-Mg17Al12 phase precipitates from the inner α-Mg grain; β-Mg17Al12 phase in the eutectic structure increase continuously and mesh together, distributing on the boundary of -Mg grain.
The reason is that though there are a large number of α-Mg grains in the eutectic structure, they are smaller than those in the primary α-Mg and their boundary are bigger, and β phase also exists in the eutectic structure, all these make the hardness of liquid region higher than the α-Mg phase, but as the temperature increases, α-Mg grain in the liquid region grows up, and also the β-Mg17Al12 phase, but the α-Mg grain grows up in a lager scale, then the hardness decreases, when the temperature exceeds 400℃, β-Mg17Al12 precipitates from the inner α-Mg grain, this makes the β-Mg17Al12 grow in a lager scale, and cause strengthening process, so the hardness increases.

The thickness of each layer was almost 10% of the average grain size and the number of sections varied from 8 to 12 depending on the steel.
In order to calculate the grain boundary pole, an algorithm was used to connect the related grain boundaries of two adjacent sections.
This method was used to connect the grain boundaries of two adjacent sections and to calculate the average grain boundary pole throughout a grain boundary.
For each pair of orientations, it is assumed that a spherical grain with cube orientation is inside a grain with different orientation, so that there is a uniform distribution of grain boundary poles.
Depending on the neighboring grain, magnetic free poles with different magnitude of density will appear at grain boundaries.

Minimization of heat-affected zone size in welded ultra-fine grained steel under cooling by liquid nitrogen during laser welding Hideki Hamatani 1, a, Yasunobu Miyazaki1, b, Tadayuki Otani1, c and Shigeru Ohkita1, d Environmental Conscious Ultra-Fine-Grained Steel Consortium of JRCM (The Japan Research and Development Center of Metals) 1 Welding and Joining research center, Nippon Steel Corporation, Futtsu, Chiba, 293-8511, Japan a hamatani@re.nsc.co.jp Keywords: Laser welding, YAG, ultra-fine grained steel, heat-affected zone, softening, and liquid nitrogen Abstract Ultra-fine grained steel (UFGS) with an average grain size of less than 1µm has been developed and is expected to demonstrate superior properties.
The employed UFGS consists of Ferrite and Martensite with a grain size of around 1µm.
For this experiment, the occurrence of porosity was expressed as the number of blowholes/pits to a bead length of 100mm.
The Ferrite grain size at the softest position was almost the same with that at base metal, and microstructures of re-crystallized grain and non re-crystallized grain at both positions were, also, the same.
In the case of CO2 laser welding, when the laser had to pass through a liquid nitrogen layer, larges numbers of pit or blowhole were produced.

Austenite grain size does not exceed ASTM number 6.
Austenite grain is refined with increasing bismuth content.
Austenite grain size in lead and bismuth steels is the same.
Presence of bismuth refines the austenite grain of the forged steel even if aluminum content is critical and cannot provide grain size of ASTM number 6 (Table 6).
Austenite grain size is not greater than ASTM number 6.

Grain growth modeling confirms the effect of particle alignment on the grain morphology and shows significant control of the particle distribution nature and the initial grain size on the grain anisotropy.
Oxide particles were found within the grains and along the grain boundaries.
Journal Title and Volume Number (to be inserted by the publisher) 3 0 5 10 15 20 25 30 350,1 1 10 100 1000 10000 Annealing time at 1000°C (min) 10% 16% Fig. 2.
For the correlated distribution, particles were aligned in an arbitrary direction identified as the extrusion direction (Fig.4) using the following relationships )N(randomx = (3a) N/dpL ; )L(randomy = = (3b) where N is the total number of sites through one direction, x and y are site coordinates, dp is the distance between particle sites in the extrusion direction and L is the line number which was fixed in the present case to be 10.
Figure 6 depicts the effect of the initial grain size on the mean aspect ratio of the grains after grain growth.