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Grain strengthening, solid solution strengthening and precipitation strengthening are the main three strengthening mechanisms for cast alloys and the contribution of precipitation strengthening to this kind alloy is uppermost.
For sand mold casting process, a continuous Gaussian nucleation distribution dn/d(ΔT), is used to describe the grain density evolution.
It can be seen that the number density of precipitates increases rapidly during the under aged stage until the number density reaches a maximum.
The following is the coarsening process and the dissolution of precipitates occurs, decreasing the number density to maintain the growth of other particles whose radius rp>r*.
In addition, from Fig.3(a), we can observe that the maximum number of precipitates under 1450C is much higher than that at 1600C.

More generally, the proposed computational framework can be considered as an ideal tool for the study of many deformation-diffusion coupled phenomena in hydrogen-storage-related applications including, but not limited to, hydrogen embrittlement, grain boundary diffusion, and various cyclic behaviors.
In this area of research, a number of challenging problems are characterized by the strong coupling of-possibly plastic-lattice deformation and the kinetics of hydrogen atoms.
Acknowledgements We gratefully acknowledge the support of the Ministerio de Econom´ıa y Competitividad of Spain (DPI2012-32508) and the Department of Energy (DoE) National Nuclear Security Administration (NNSA) under Award Number DE-FC52-08NA28613.

All alloys having single martensite phase at room temperature showed martensitic transformation at elevated temperature as well as a linear change of the characteristic martensitic transformation temperatures (As, Af, Ms and Mf) with the number of valence electron to atom ratio (e/a).
The c/a ratio showed an increase as the e/a ratio was increased (where e/a ratio is the ratio of the total number of valence electrons and the total number of atoms).
The increased crystallographic disorder results in decreased grain size in polycrystalline materials.
TC value show a tendency to shift to lower temperatures with the reduction in grain size Similar results have been reported in rapidly solidified Nd-Fe-B samples [19].

In this context, directionally solidified (DS) as well as single crystal (SX) nickel superalloys were developed for achieving an improved fatigue resistance and a significantly increased creep rupture strength by eliminating grain boundaries [1].
This has led to local stress and local strain approaches based on the Basquin equation and the Coffin Manson equation [4] and . ( 1 ) Thereby, the symbol Ni denotes the number of load cycles related to a suitable end-of-life criterion.
The relation ∆σ => Ni then forms a surface of equal number of cycles-to-failure.
Obviously, for the uniaxial load ∆σd in either of the characteristic directions both, the general multiaxial approach of Eq ( 3 ) and the uniaxial formulation ( 2 ) have to predict the same number of cycles-to-failure, i.e. , where ∆σd denotes the stress tensor components produced by ∆σd.
After iteration for the Hill parameters, the number of cycles-to-failure is determined by where the Hill function is defined according to Eq ( 4 ).

It has been documented that ECP can be used to improve the properties of the metallic materials, including refining grain size, improving chemistry homogeneity and eliminating defect.
Compare with the XRD spectra of hypoeutectic Fe-C alloys without ECP, the number of cementite peak decrease, the intensity of ferrite peak increase and generate graphite peak after ECP treatment.
This phenomenon can produce a large number of free carbon atoms.
And graphite nucleation near the dislocation pile-up doesn’t need the diffusion of substituted atom to vacate space and decrease the driving force of phase transformation of graphite, so the increasing number of dislocation pile-up which around cementite is benefit to graphite nucleation.
When the temperature below the eutectoid temperature, austenite area becomes carbon-depleted region because of large numbers of graphite formation.

It is generally acknowledged that the main stress brought by wire ropes bending-over-sheaves is tensile stress, bending stress and extrusion stress. 1) Tensile stress The tensile stress of wire rope can be calculated approximately is expressed as (1) Where is the axial load of rope, is the number of wires, is the diameter of wires and is the lay angle of the strand in rope. 2) Bending stress The researchers such as Ridge [8] from University of Reading have done research about the measuring and theoretical calculating of bending stress of wire ropes, the formula for calculating bending stress of wire is given by (2) Where is the initial radius of curvature, is the radius when on the sheave and is the elastic modulus of wires.
Formula for calculating extrusion stress of the contact point between wire and the groove is expressed as (5) Where , is the elastic modulus of groove, is the number of outer wires and is the curvature of contact point. 3.
The effective bearing area of the wire cross-section is reduced due to wear and deformation, and the local stress becomes larger, micro cracks appear on the grains of wire surface.
With the increase of number of bending, cracks continue to expand, the effective bearing area of wire cross-section is becoming smaller while the local stress is becoming larger, once the remaining wire cross section is no longer able to carry the load, the wire will break.
With increasing of number of bending, the damage will have a great influence on fatigue failure. 5.

In the presence of hundreds or thousands of features, it is common that a large number of features are not informative because they are either irrelevant or redundant with respect to the target concept [2].
Theoretically, the optimal feature selection requires an exponentially large search space (O(2m), where m is the number of features) [1].
As the category information of rare classes is not adequate, only the most common 10 categories are used in our experiments, which are Earn, Acq, Money-fx, Grain, Crude, Trade, Interest, Wheat, Ship and Corn.
We preprocess the data in a formal way: all numbers and stopwords are removed, words are converted into lowercase, word stemming is performed using the Porter stemmer, some noisy words are removed.
The parameter of selected feature number has great influence on the performance comparison.

To prevent the occurrence of seizure, a large number of investigations on the effect of processing conditions on the seizure of titanium were carried out [7, 8, 9].
Table 1 Multi-stage deep drawing conditions of pure titanium blank Stage number 1 2 3 4 5 6 7 8 9 10 Fold pressure / kN 10 0 0 0 0 0 0 0 0 0 Dies / mm Materials Cold tool steel (JIS-SKD11) Hole distance 39 37 35 33 31 29 27 25 23 21 R radius 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 Corner radius 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 Punch / mm Materials Cold tool steel (SKD11), Carbon steel (JIS-S50C) Distance 38 36 34 32 30 28 26 24 22 20 R radius 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 Corner radius 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 Drawing ratio 2.56 1.05 1.06 1.06 1.06 1.09 1.07 1.08 1.09 1.10 Lubricants Molybdenum disulfide Clearance / mm 0.5 - 0.7 0.5 - 0.7 0.5 - 0.7 0.5 - 0.7 0.7 - 0.9 0.9 0.9 0.9 0.9 0.9 Figure 1 Schematic illustration of square cup deep drawing process of titanium blank Table 2 Mechanical properties of pure titanium JIS-grade2 Oxidation treatment Tensile axis to R.D. / o Proof strength / MPa Fracture elongation
The variations of the surface roughness with the stage number for the titanium cups are shown in Fig. 4.
(a) 1st stage (b) 2nd stage (c) 3rd stage Figure 2 Appearances of the drawn cups of pure titanium sheets treated by oxide coating (a) corner at 1st (b) corner at 2nd (c) corner at 3rd Figure 3 The surfaces of the drawn cups Figure 4 Relationship between surface roughness and stage number (a) 1st stage (b) 2nd stage Position relation Figure 5 Distributions of wall thickness strain of the drawn cups by multi-stage deep drawing (a) No heated (b) Heated at 3rd stage Figure 6 Appearances of the drawn cups at 3rd stage after heating at 2nd stage Figure 7 Appearances of the drawn cups with intermediate annealing (a) 1st, 2nd, 3rd, 4th (b) 5th, 6th, 7th, 8th, 9th, 10th Figure 8 Distributions of wall thickness
Kim, Annealing effects on the corrosion resistance of ultrafine-grained pure titanium, Corrosion Science, 89 (2014), 331-337

Laser welding has proven to be a superior process as it provides low average heat input, resulting in a narrow heat-affected zone (HAZ), less segregation of alloys leading to higher corrosion resistance, and less time at annealing temperatures compared to arc and plasma welding to effect diffusion and homogenization of the grain structures.
Unlike in case of fatigue loading of pressure vessels, where the loading is with high range of pressure changes from zero to maximum, i.e. with load asymmetry R = 0, and the number of cycles during the service life is limited, in pipelines the loading is of a high-cycle character with higher load asymmetry given by numerous pressure fluctuations from the mean pressure.
High-cycle fatigue (HCF) resistance was expressed as S-N curves of mostly ten specimens including endurance limit, which was evaluated on the basis of target number of cycles 10 million.
If the specimen did not fail till this target number of cycles, the stress amplitude was considered as the endurance limit provided that another tested specimen loaded with stress amplitude further reduced by 5 – 10 % did not fail either.
The section headings Number of indentation Fig. 7: HV 5 hardness course through laser weld Course of hardness HV 5 from base metal through HAZ and weld metal is documented in Fig. 7.

This difference can be conveniently written as the Hamming distance in the configuration space, , where and are the two spin configurations of the system which subject to the same thermal noise and the same set of random number, N is the number of the total spins on the lattice studied.In theory of codes, the Hamming distance between two strings of bits is the number of different bits.
It can also be a grain film[1].
The NWs form a triangular array with dimension ( is the number of NWs or hexagonal-close packed patterns along the horizontal direction) with lattice constant S [20].