Scaling of structural parameters and mechanical properties of metals and alloys

Gordienko, Yuri; Zasimchuk, E. É.; Turchak, T.

doi:10.1016/j.physme.2007.08.002

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…Again, on the initial stage of this one-step aggregation process the probability distribution function f (n, t) does not "feel" the boundary condition f (0, t) = 0, because from the physical point of view the cluster size cannot reach the boundary immediately, but only after some time t 0,w , when the first cluster disappear due to detaching monomers. When t t 0,w all clusters have nearly the same size n ≈ n 0 , and the solution of (10) has not influenced by differences in n significantly and that is why it has approximate solution, which is close to solution of the heat equation ( 7):…”

Section: Modelmentioning

confidence: 68%

“…They correspond to the very late behavior of the simulated systems with the limited quantity of particles 10 6 , when the most part of time the ensemble of large clusters exchange by particles without total disappearance of any cluster. This means clusters do not "feel" the 0-boundary and the third problem with "infinite" boundary conditions −∞ < n < ∞ should be considered for equations (4) and (10). As a result these PDFs become more symmetric (lower skewness) and with quasi-normal peaks (lower kurtosis).…”

Section: Moment Analysismentioning

confidence: 99%

“…One of drawbacks of the simplified model is that the equations ( 4) and (10) and their solutions ( 5) and (11) give the idealized and rough representation of the aggregation kinetics. In fact, solutions ( 5) and ( 11) allows the "long-tails" of distribution, i.e.…”

Section: Modelmentioning

confidence: 99%

“…This unsatisfactory scaling is explained by the appearing difference in the cluster sizes, when the initial approximation n ≈ n 0 becomes not accurate. That is why (10) becomes influenced by differences in n significantly and that is why its approximate solution (12), which is close to solution of the heat equation ( 7) becomes more inaccurate with time, especially for tails, where difference in n is bigger. The same collapse of the scaled CDF curves to the asymptotic straight line can be seen on the plot (Fig.…”

Section: Scaling Analysismentioning

confidence: 99%

“…In fact, the fractal analysis of fractured surfaces by projective covering and box-counting method shows that the fractured surface can be depicted not only by one fractal dimension, but also by multifractal spectrum [6,7,8]. At the same time, surface roughness profiles of periodically deformed Al [9,10,11], slip line morphology in Cu [12,13], and dislocation patterns in Cu after tensile [14] also demonstrate the self-similar features on many scales. Recently, transition from homogeneous dislocation arrangement to scale-invariant structure was described by the statistical model of noise-induced transition [15].…”

Section: Introductionmentioning

confidence: 99%

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Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

Gordienko

2014

Physica A: Statistical Mechanics and its Applications

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The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo method in the Desktop Grid distributed computing environment to analyze "pile-up" and "wall" cluster distributions in different aggregation scenarios. Several aspects of aggregation kinetics (change of scaling, change of size distribution type, and appearance of scale-free size distribution) driven by "zero cluster size" boundary condition were determined by analysis of evolving cumulative distribution functions. The "pile-up" case with a minimum active surface (singularity) could imitate piling up aggregations of dislocations, and the case with a maximum active surface could imitate arrangements of dislocations in walls. The change of scaling law (for pile-ups and walls) and availability of scale-free distributions (for walls) were analytically shown and confirmed by scaling, fitting, moment, and bootstrapping analyses of simulated probability density and cumulative distribution functions. The initial "singular" symmetric distribution of pile-ups evolves by the "infinite" diffusive scaling law and later it is replaced by the other "semi-infinite" diffusive scaling law with asymmetric distribution of pile-ups. In contrast, the initial "singular" symmetric distributions of walls initially evolve by the diffusive scaling law and later it is replaced by the other ballistic (linear) scaling law with scale-free exponential distributions without distinctive peaks. The conclusion was made as to possible applications of such approach for scaling, fitting, moment, and bootstrapping analyses of distributions in simulated and experimental data.

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Section: Modelmentioning

confidence: 68%

Section: Moment Analysismentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Scaling Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

Gordienko

2014

Physica A: Statistical Mechanics and its Applications

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Relaxation Structure Formation in Deformation of Nickel

Zasimchuk

Gordienko

Markashova

et al. 2009

J. of Materi Eng and Perform

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The purpose of this study was to quantitatively investigate the relaxation structure formation in polycrystalline nickel deformed by rolling at room temperature. The relaxation structures were examined on polycrystalline nickel with a purity of 99.99% Ni, deformed by rolling. The sub-structure of nickel after rolling to 50-80% was examined by the TEM and X-ray analysis methods by line profile analysis. It was revealed the presence of three qualitatively different types of structural elements: microbands of a macroscopic length; cells of different shapes and dimensions; micrograins less than 80 nm in size. The normalized curves of distribution of cells dimensions coincide, which suggests a scale invariance of these parameters. On the other hand, addition of normalized dimensions of micrograins to statistical dependence of dimensions of the cells leads to distortion of the dependence. The mechanisms of formation of the cells and micrograins to be different: micrograins were shown are nuclei of primary recrystallization.Formation of structure in metal during and after plastic deformation may occur according to two scenarios:• relaxation structure formation (formation of cellular and polygonal structure, recrystallization), which is characterized by the kinetics that depends on the temperature, nature of a material, and deformation conditions; scaling (scale invariance) of dimensions and disorientations (Ref 1-10); • self-organization of deformed crystal, i.e. synergetic structure formation, which is characterized by the stepwise kinetics (can be described using the d-function), cooperative character of the process that simultaneously involves macro volumes of the material being analysed, and fractal morphology of different scales of structures .The purpose of this study was to quantitatively investigate the relaxation structure formation in polycrystalline nickel deformed by rolling at room temperature. The relaxation structures were classified through their statistical examination by the method of transmission electron microscopy (TEM). The special attention was given to the mechanism of formation of different types of the structures, which was studied by comparing the normalized curves of distribution of their dimensions.The relaxation structures were examined on polycrystalline nickel with a purity of 99.99% Ni, deformed by rolling. The sub-structure of nickel after rolling to 50-80% was examined by the TEM and X-ray analysis methods. The plastically deformed metal is a non-equilibrium system. This shows up, first of all, in the presence of micro and macrostresses, which can be easily determined by the X-ray method, e.g., by line profile analysis (Ref 14,15). For analysis we used two pairs of lines: (111) and (222); (200) and (400). To illustrate, Table 1 gives values of microstresses (r, MPa, 910 4 ) and dimensions of regions of coherent scattering (L, lm) for nickel deformed by rolling and tension. The line profile analysis method was used for the calculations. Figure 1 illustrates examples of profiles of X-Ray...

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Scaling effects in structural-phase self-organization at the “thin film - substrate” interface

Panin

Сергеев

et al. 2007

Physical Mesomechanics

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Scaling of structural parameters and mechanical properties of metals and alloys

Cited by 5 publications

References 9 publications

Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

Relaxation Structure Formation in Deformation of Nickel

Scaling effects in structural-phase self-organization at the “thin film - substrate” interface

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