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Therefore, some hypotheses are needed to simplify the complexity of real cases: (i) after welding cycle, the component is not characterized by homogeneous material: base metal, heat affected zone, melted metal have different micro structures, different grain size and hardness values which results in different yield limits, micro inclusions and irregularities; (ii) the slope of the weld contour near the toe is highly variable but generally supposed constant; (iii) rapid cooling after welding pass may produce residual stresses, very high, up to the yield limit in the weld area, with a hardly predictable variability; (iv) stresses at notch root are calculated by means of fatigue notch factor kf using empirical expressions mainly depending from fillet radius ρ, which is highly variable along the cord and strongly affected by welder skills.
The εa strain parameter correlated to the number of cycles to failure N allows building the εa-N curves, which are fatigue strength curves in terms of strain amplitude.
From these curves, obtained for welded joints which differ in geometry and load ratio R, it is possible to determine the limit value of the strain amplitude εA corresponding to the usual life of N=2 .106 cycles (for steel) or for any other number of cycles.

The fibers should be dispersed uniformly in the structure, as well as dispersed grains of the coarse fraction of aggregate in plain concrete.
For randomly dispersed fibers it is only a very small number of the fibers that is parallel with the principal stress, or within a small angular deviation.
The progressive extracting and an increase of the number of thin cracks give toughness to the SFRC.

DE clays have been widely used in drink water filtration as natural insecticide, grain protectant and immobilization of contaminants [11-14].This is attributed to the surface charge and natural pore size to the removal of cationic contaminants [15].
As the number of particles increases, the surface charge of all particles is greater, and therefore, these exhibit a strong interaction with the ion exchange capacity provided by the interstitial spaces of the DE.
Greater number Ag0 particles generate more surface charges, and therefore the interaction with the exchangeable cations available from the diatom is higher.

Fig. 3 Joint shear force of orthogonal factor index chart Orthogonal test result analysis is shown in Tab. 4, including Km (m = 1 ~ 3) for A, B and C factors of the mth of the corresponding level joint tensile strength average, the range R for K1, K2, K3,the number of 3 maximum and minimum difference, the greater the range, the factors that influence the joint tensile strength is larger.By three factors of the range all level analysis shows ,pin length has the biggest influence on the tensile share strength of welding joint, following the shouldr friction time and lastly the rotation speed.
Results of orthogonal experiment Test Number Experiment Scheme Factor A Factor B Factor C Joint Tensile Strength / KN 1 A1B1C1 1 1 1 1.20 2 A1B2C2 1 2 2 1.64 3 A1B3C3 1 3 3 1.75 4 A2B1C2 2 1 2 2.13 5 A2B2C3 2 2 3 2.46 6 A2B3C1 2 3 1 1.04 7 A3B1C3 3 1 3 1.86 8 A3B2C1 3 2 1 1.95 9 A3B3C2 3 3 2 1.51 Table 4．Analysis results of the orthogonal experiment Factor A B C K1 4.59 5.19 4.19 K2 5.63 6.05 5.28 K3 5.32 4.30 6.07 R 0.347 0.584 0.626 Weld area microstructure analysis When process parameter is optimized to be A2B2C3 (n=1000R/min, t=4s, l=3.5mm), the Macro morphology of cross-section of FSSW joint stir area is shown in Fig. 4.a.
It is due to the friction and extrusion effect of the shaft shoulder makes the grain in magnesium plate heat affected zone refine, as shown in Fig. 5.b ,which makes hardness and brittleness increase, and result in the reducing of ductility.

The particle size and the crystalline structure of the product samples were detected by means of X-ray analysis with a BD-86 diffractometer(Japan) and Mastersizer 2000 Laser grain-size analysis meter(England).
The main reason is that the number of the TiO2 surface hydroxyl restricts the photocatalytic activity[11].
This is mainly because charge layer thickness on the surface of the TiO2 decrease along with the increase in the number of lanthanum-doped.

Due to the preservation of anisotropy and less infection of grain boundary, single crystal samples can give more intrinsic and detailed properties compared with polycrystal ones.
Table 1: Conditions used to prepare a series polycrystalline and single crystal samples of La1.85Sr0.15CuO4 Sample number.
(From sample a to sample f, sample number is referred to Table 1) 20 30 40 50 60 70 80 20 30 40 50 60 70 80 (101) (103) (110) (105) (114) (200) (116) (213) (206) (217) (208) (a) (215) (213) (202) (200) (310) (110) (220) (b) (200) (220) (220) (220) (110) Intensity (a.u

Potassium sodium niobate (K0.5Na0.5NbO3 : KNN) has been regarded as a promising lead-free piezoelectric material, because of its high Curie temperature and excellent piezoelectric properties. 1-3 However, ceramics and films of KNN suffer from a high leakage current due to lattice defects probably originating from the evaporation of K with high volatility. 4,5 Leakage current properties are closely related not only to defect structure in grains but also to the microstructure of samples.
In the crystals annealed in air, a certain number of VO •• are likely to exist, probably originating from K vacancies formed during high-temperature crystal growth.
Further oxidation by the high-PO2 (35 MPa) annealing indeed decreased the number of VO •• , as expressed by VO •• + 1/2 O2 → OO* + 2 h •

The reason for the change was that the number of double bond in unit volume of marble / UP resin mixture was reduced and the cross linking among the double bonds hindering by marble powder get more difficult, which cause the reduction of total quantity of heat in unit volume of marble / UP resin mixture.
The mechanism is that the adsorption of the weak polar ester moieties in the link of polyester resin on polar particle surface of marble powder with mean grain size of 2-6μm to disperse and immerse the particles of marble powder.
However, if marble powder was excessively used, the number of weak polar ester moieties adsorbing onto polar particle surface of marble powder will be reduced, as a result, marble powder can’t be well dispersed and maybe aggregate together.

In Fig. 1 (b) we plot the evolution of the fraction of martensitic phase Φm= Nm/N (with Nm the number of particles in the martensitic phase and N the total number of particles).
In all the snapshots, colored segments indicate the elongated side of each deformed triangle, and help to distinguish between grains of different orientation.

0.77427 0.77597 0.77713 0.77778 3, 0.00099 0.02393 0.04570 0.07212 0.08575 0.09420 0.10011 0.10344 4, 0.75090 0.74356 0.71415 0.64889 0.60019 0.56381 0.53520 0.51766 5, 1.50364 1.60825 1.78091 2.18075 2.61495 3.17131 4.12462 6.17586 (b) Point Field 5.00 1.00 0.50 0.20 0.10 0.05 0.02 0.005 1, 1.50790 1.54484 1.56186 1.57732 1.58408 1.58796 1.59053 1.59193 2, 0.75545 0.78777 0.80448 0.82041 0.82757 0.83175 0.83454 0.83607 3, 0.00469 0.06833 0.11536 0.16825 0.19487 0.21128 0.22269 0.22910 4, 0.75511 0.76410 0.74416 0.68542 0.63200 0.58725 0.54918 0.52450 5, 1.51825 1.75030 1.97663 2.40741 2.86765 3.46415 4.49417 6.72041 6, 1.50379 1.62136 1.82655 2.30236 2.80030 3.42218 4.47198 6.71204 7, 0.75023 0.73047 0.70435 0.67061 0.65308 0.64221 0.63465 0.63037 8, -0.00104 -0.01149 -0.01740 -0.02297 -0.02545 -0.02692 -0.02791 -0.02846 9, 0.75058 0.75321 0.75435 0.75537 0.75582 0.75608 0.75626 0.75636 10, 1.50069 1.50311 1.50409 1.50495 1.50533 1.50555 1.50570 1.50579 The number
In the case when and for example, terms are sufficient for a 7-digit accuracy at points with and only terms are needed for a 4-digit accuracy, with the accuracy increasing from to (see Fig. 1) for the same number of terms.
Vorobev, Giant enhancement of electric field between two close metallic grains due to plasmonic resonance, Optics Letters. 35 (2010), 640-642