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A number of theoretical investigations [4-8] have been carried out in the field of fracture mechanics by considering the fractal nature of materials.
In more detail, a finer grained and comparatively ordered material (for example, SF 50 steel in comparison with SCMn 2A steel) presents a lower value of the threshold size TD (as a matter of fact, 2TD < 1TD )
Obviously, the applicability of a self-similar fractal model is confined to the so-called mesoscopic scale range of the material, defined by an upper limit, corresponding to the geometrical sizes of the cracked body, and a lower limit, related to the microstructure of the medium (e.g. aggregate size for concrete, grain size for metals) [8].
Monofractal scaling law for fatigue crack growth The well-known Paris-Erdogan law [30] describes the kinetics of the crack propagation in the intermediate range of IK∆ : m IKC N a ∆= d d , (31) where C and m are material constants, N is the number of fatigue cycles; dNda / and IK∆ are the crack propagation rate and the SIF range, respectively.

In modern analytical investigations which deal with the interaction between titanium and gaseous media, the effects of external parameters (time, temperature, pressure) and internal ones (defects, grain boundaries) are explained differently.
Additional effects upon the gaseous saturation are forced by chemical reactions which take place on the defects of the lattice, on the dislocations and on the grain boundaries.
With respect to the high-temperature interaction between titanium and gaseous media, a number of experimental data reveal that, under special conditions of rarefaction, a new phase is formed on the titanium surface simply by long isothermal exposures [9].
In a number of cases of diffusion saturation of bulky metallic objects by a gaseous impurity, the diffusion zone is appreciably smaller than the thickness of the object.

Macroscopically speaking, AVR is classified as leucocrat, with phaneritic texture of medium to coarse-grain.
SPI is classified as fine grained, non-porfiroid, with two micas but dominantly biotitic, with homogeneous grey/bluish colour [26, 28].
Chosen mesh had a total number of elements of 93,000.
The major limiting factors found in this work for the finite element model are: the computational power required for solving large models with high number of elements (93,000); the assumptions concerning stone heterogeneities (granites were assumed as homogenous and isotropic) that might limit model applicability; the assumptions regarding the use of a linear elastic model which present limitations after the initiation of non-linear behaviour of the materials involved.

Here again, the versatility of the optical characterization allows the observation scale of specimens to be changed by changing the focal length of the camera, the resolution of the images to be increased or decreased by changing the data acquisition frequency of the digital camera (number of images per seconds).
It is also possible to increase the number of image per second if the resolution is lowered.
Namely, it can strongly depend on the microstructure of the alloy substrate, in relation for instance to the crystal orientation of the grain or to the presence of a grain boundary underneath the oxide scale.

INTRODUCTION The study of the soil as a corrosive environment is necessary due to the large number of buried pipelines; their deterioration can represent a real economical and environmental problem through the years.
The X52 steel microstructure consisted of fine pearlite and ferrite with a grain size around 10–20 μ as is shown in Fig. 1.
Low carbon steels tend to have a ferrite–pearlite structure containing little pearlite in the grain boundaries mainly.
It was concluded that the number of ions present in the soil composition is a key factor for the determination of the corrosivity of the soils.

The simple shear testing of sheet metals is not yet standardised and can be implemented in a number of ways.
The number of correlated points and the standard deviation of the mean is given.
An ODF is a function which describes the volume fraction of grains with a crystallographic orientation in the range g±dg (see Eqn. 2 (a)).
Two Taylor type crystal plasticity models are currently implemented in HMS: (i) a classic full constraints Taylor model, referred to here as FC Taylor, implemented as described in [23], and (ii) an extended Taylor-type model incorporating grain interactions and morphology effects, referred to as ALAMEL and presented in [24].

The crumb grain of the loaves was assessed using a digital image analysis system (Crowley,Grau,&Arendt, 2000).
The crumb grain features chosen were number of cells.
Table 1 Effect of MBG on the bread quality parameters Control MBG Specific volume (cm3/g) 3.31±0.19a 4.07±0.23b Number of cells 430±21a 501±19b Moisture content ( % ) 38.12±0.14a 41.5±0.22b Values followed by the same letter are not significantly different (p < 0.05).

To avoid or at least limit clinical complications related to in-service failure, the stents are designed to endure high cycle fatigue (HCF) due to the high number of cycles caused by the blood pressure (4x107 cycles/year).
According to these approaches, fatigue cracks initiate in the planes of maximum shear and propagate through the grains.
Dang van's criterion Dang Van assumes that fatigue crack initiation occurs in critical stress raiser areas due to the unfavourable orientation of certain material grains with regard to the imposed loadings.
As many other approaches, Goodman considers a combination between the alternating and mean stress to state when a material fails at some given number of cycles.

This search studying an experimental fulfillment on the thermal conductivity, apparent porosity, and Diametrical Strength of porous copper-zinc manufactured by the convert to carbon since firing process and combined with the oxygen cause to CO2 gas that rises up to air and leaves the number of pores. the basic metals are Cu and Zn pure powder metals with a different ratio (10-20-30)% of natural leaves especially palm leaves which is widely found in our natures, Cu fine powder (220 µm) has purity 99.5% as a matrix material to prepared composite material with ratio 80% of material total weight, 500g, Zn fine powder added as 20% from material total weight, the Zn metallic powder has purity 99.5%.
The additives natural that is a grounded palm leaves were cut to small parts then milled by using electrical mortar to get a fine powder which have a grain size (less than 0.75 𝜇m) which result by sieving process and added on to three ratios (10%-20%-30%) of 80%Cu-20%Zn as MMC and with pure composites metals of Cu-Zn composites. mixed manual mortar then pressed at (5 ton) for 15 min by using a hydraulic pressing which called a dry pressing.
During the sintering temperature raised up to 950̊Cfor (2 hr), then (P.L) burned at 950̊C which consist (natural materials like (lignin- cellulose and hemicelluloses) materials that appear due to HPLC test that convert to carbon since firing process and combined with the oxygen cause to CO2 gas that raises up to air and leaves the number of pores.

The SMT industry's products on the number of residual tin beads are certain norms.
So we focused on the study of literature for some of tin beads resulted in a large number of factors and residual principle lie, in Ning-Cheng Lee, the study that caused large tin beads of reasons solder of SMT particle size, Opening plate design, welding pad size and welded to the impact of such factors curve [2].AIM in the literature that caused tin beads is a key element plate opening size and shape of solder of SMT printing parameters, the viscosity solder of SMT back solder of SMT welding curve and particle size and other factors all affect tin beads have a lot of factors [3].
，However, in recent years due to patent protection has expired gradually, coupled with the semi-finished products and technical advances, to meet the high-end technology development, low-cost, component performance and the overall package size of demand, Grain and in particular high I/O, high-frequency demand, Minute crystal technology have become high-end package the best choice [5][6].
Discussion This section is the application of the Taguchi method (Taguchi method) in the Minute crystal system - which is a tin slag residue quality improvement and the best design parameters, the experimental design is the use of impact surface mount technology manufacturing process to design factors, and the system under way after the residue in the passive components on the tin beads number and size as a basis for assessment (Figure 9 below), because too many beads tin residues in flux-cleaning system, is likely to be washed down to the internal chip, making the chip caused the tin-lead Bump short circuit, which will affect product quality.
Barajas, Process Control in High-Noise Environments Using a Limited Number of Measurements，School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA, 30332, 2002