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The results of proposed unified model enable a computational prediction of a probable number of loading cycles that a wheel-rail system can sustain before development of the initial crack in the rail, as well as the number of loading cycles required for a crack to propagate from initial to critical length, when the final fatigue failure (squat) can be expected to occur.
The methods for fatigue analysis are most frequently based on Coffin-Manson relation between deformations, stresses and number of loading cycles and are usually modified to fit the nature of the stress cycle, e.g. repeated or reversed stress cycle [4].
The number of loading cycles required for fatigue crack to appear, can be determined with the strain-life method ε-N, where the relationship between the specific deformation increment ∆ε and the number of loading cycles N is fully characterized with the following equation [4]: ( ) ( ) , 2 2 c f bfp a NN E E ε'+ σ' = ε∆ + σ = ε∆ (1) where σf' is the fatigue strength coefficient, b the strength exponent, εf' the fatigue ductility coefficient and c the fatigue ductility exponent.
The strain-life method ε-N is not an ideal model for fatigue damage initiation analysis at the micro structural level since the micro-crack initiation in crystal grains and dislocation theory are not taken into account.
However, it has been established that fatigue damage initiation can be represented by transition of a certain number of loading cycles before the first actual fatigue damage occurs in the assumed initial homogenous state of material [4].

The Al2O3 film was an amorphous structure, smooth surface with a nanoscale grain size.
The CIGS films grown on Mo/Al2O3/SLG substrate showed flat round grains as shown in Fig. 2(c), whereas the CIGS films grown with Na incorporation on Mo/Al2O3/SLG revealed relatively sharp grains as shown in Fig. 2(d).
The increase of (112) texture leaded to the increase of sharp grains that looked like the triangle shape.
And the increase of (220)(204) texture leaded to the increase of flat grains as seen from surface morphology.
We could see that the Ga-graded CIGS film had the lower thickness according to the number of interference fringes.

Selection of Coating Materials The coatings applied onto the substrate surface must meet a number of requirements.
Hardness Hardness HV 1 0 1200 1600 2000 2400 Rotational Speed Ratio NL 0,5 2,0 0,5 2,0 Hardness HV 0.1 0 1200 1600 2000 2400 Measuring Systems Leitz Miniload II (HV 1) Fischerscope H100 (HV 0.1) Pre-Treatment Face Lapping Lapping Grains F1200 Substrate Material Al2O3 Si3N4 HV 1 HV 0.1 Hardness Hardness HV 1 Hardness HV 1 0 1200 1600 2000 2400 Rotational Speed Ratio NL 0,5 2,0 0,5 2,0 Hardness HV 0.1 0 1200 1600 2000 2400 Measuring Systems Leitz Miniload II (HV 1) Fischerscope H100 (HV 0.1) Pre-Treatment Face Lapping Lapping Grains F1200 Substrate Material Al2O3 Si3N4 Substrate Material Substrate Material Al2O3 Si3N4 HV 1 HV 0.1 Fig. 2: Hardness HV 0.1 and HV 1 of substrates Al2O3 and Si3N4 Moreover, the micro hardness of the thin coatings was measured.
Residual Stress / Scratch Test Rotational Speed Ratio NL 0,5 2,0 0,5 2,0 Critical Load LC2 80 N 40 20 0 Lapping Grain F1200 Lapping Grain F280 Measuring Systems Huber 4-Circle Diffractometer Nikon Revetester Pre-Treatment Face Lapping Rotational Speed Ratio NL = 2,0 0,0 0,5 1,0 1,5 2,0 2,5 -1500 -1400 -1300 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 II Informationstiefe ?
Al2O3 + ZrN 0,0 0,5 10 1,5 2,0 2,5 Residual Stress Residual Stress -300 -1500 -1300 -1100 -900 -700 MPa 02 , 5 1,51,00,5 µm Subsurface MPa - 400 - 200 0 200 400 600 02 , 5 1,51,00,5 µm Subsurface 1000 Rotational Speed Ratio NL = 2,0 Si3N4 + ZrN Substrate Material Al2O3 Si3N4 Residual Stress / Scratch Test Rotational Speed Ratio NL 0,5 2,0 0,5 2,0 Critical Load LC2 80 N 40 20 0 Lapping Grain F1200 Lapping Grain F280 Measuring Systems Huber 4-Circle Diffractometer Nikon Revetester Pre-Treatment Face Lapping Rotational Speed Ratio NL = 2,0 0,0 0,5 1,0 1,5 2,0 2,5 -1500 -1400 -1300 -1200 -1100 -1000 -900 -800 -700 -600 -500 -400 -300 -200 II Informationstiefe ?

Three hypotheses are necessary to derive an universal probability function of failure for brittle materials (F=1 - exp[-Nc,s] where Nc,s is the mean number of critical defects in the specimen): (i) the density of defects has to be low enough so that interaction between flaws can be neglected, (ii) the material will fail when the weakest defect fails, and (iii) one can define a density of critical defects ρ.
Only surface defects (i.e. large grains, Fig. 4) were found as failure origins.
a b c d Fig. 4: a) A/AZ fracture surface presenting a fracture mirror and "waves" perpendicular to the interface in the fourth layer, arrow indicates fracture origin, b) abnormal large grains found in the laminates, c) large grains in A laminate acting like a notch, d) grain size comparison in A and AZ.
Through fractography, the presence of abnormally large grains (up to ~25 µm depth), which were responsible for failure, was revealed in both investigated materials (Fig. 4a, b and c).
This behaviour can be justified by the fact that the A/AZ as well as the A-laminate fractured due to a similar defect population, namely, large alumina grains at the tensile surface of the bend specimens.

The Vickers hardness of AZ91 alloys is also shown for comparison (these values were converted from the Brinell hardness numbers given in Ref. 7).
Mg grain growth is considered to be inhibited with increasing Al2O3 particle content during hot pressing.
The discs were electrolytically etched and the Mg grain sizes were measured.
Mg grain growth is considered to be independent of the Al2O3 particle size and the Al2O3 content because all the discs have similar grain sizes (5-8 μm).
Therefore, inhibition of Mg grain growth with increasing Al2O3 particle density is considered to have a very small effect.

When the sintering temperature is higher than 1100°C, the grain of CaZr4(PO4)6 ceramics grows abnormally, and microcracks are produced in the interior, which leads to the decrease of the strength.
As can be seen from fig. a, the internal structure of the material is loose and there is a large number of pores.
As can be seen from fig. c, there is an apparent abnormal grain growth inside the ceramic.
We can see that with the increase of sintering temperature of CaZr4(PO4)6 ceramic grain diameter increases, gas hole increases and porosity increases.
Because the high temperature will lead to excessive grain growth, may even lead to two times recrystallization, grain boundary grows over the bubbles, bubbles can not be ruled out, air holes increase gradually and grow up, reduce the density of samples.

Firstly, preparing the workpiece and polishing it with sandpaper from the numbers 80, 220, 360, 600, 800, 1000, 1200, and 1500 grit.
The HAZ contains three distinct regions: the coarse grain region, the grain-refining region, and the partial grain-refining region [10].
The grain size remains consistent in both the Heat Affected Zone (HAZ) region and the Unaffected Zone region.
There is no significant difference in grain size.
The weld metal region's microstructure is fine and indicates a high cooling rate benefit to prevent re-precipitation, including grain growth [12].

Hosseini et al. [8] researched the most relevant criteria when evaluating the risk of sigma phase formation in DSS, such as the peak temperature, the accumulated time in the critical temperature range and the number of thermal cycles.
The shape of austenite in Fig.2a was allotriomorphic and it precipitated from the ferrite grain boundary.
In Fig.2d, the austenite began to precipitate from the ferrite grain interior and turned into coarser block.
When t8/5 was lower than 20 s, the austenite was allotriomorphic shape and precipitated from ferrite grain boundary, as shown in Fig.3a and b.
When the cooling time became longer, austenite was coarse-blocky shape and the precipitation began to expand to the ferrite grains.

On the other hand, the fine-grained structure produced by other SPD techniques improved the corrosion resistance of metallic materials [13].
With the polishing after the SMAT, all the dimples at the surface of the Mg alloy could be removed; leaving the material surface with only a few numbers of shallow scratches, as indicated in Fig. 3 (c).
Zhang, Sliding wear-induced microstructure evolution of nanocrystalline and coarse-grained AZ91D Mg alloy, Wear 266 (2009) 666-670
Estrin, Corrosion of pure Mg as a function of grain size and processing route, Adv.
Davies, Grain character influences on corrosion of ECAPed pure magnesium, Corros.

With increasing cycle number, the cell exhibits a well cycle performance with more than 95% coulombic efficiency and the maintenance of 61% of its discharge capacity after 50 cycles.
The grain dimensions are estimated to be below 50 nm in thickness and about 0.5-1 μm in edge.
After annealed treatment at 650ºC, the flake structure of HT sample is cracked and wrecked, which is characterized by an overlapping fragmental structure with a grain size of about 100-200nm.
The low coulombic efficiency 37% observed in the first cycle improves with increasing cycle number and reach 94% after 50 cycles.