PSI - Issue 20

Vinokurov G.G. et al. / Procedia Structural Integrity 20 (2019) 265–269 Vinokurov G.G., Popov O.N. / Structural Integrity Procedia 00 (2019) 000 – 000

267

3

Table 1. Statistical approaches for the description of formation and wear of a macrostructure of powder coatings and materials

Number

Direction of a research

Mathematical formalism

The received results

1

Formation of a macrostructure of powder coatings when dusting on smooth and rough substrates Wear of a macrostructure of powder coatings and materials at a sliding friction. Correlation of density in a macrostructure of powder coatings and materials Formation of a macrostructure of powder materials at unilateral pressing Wear of a macrostructure of powder coatings and materials at a sliding friction Assessment of a resource of powder coatings at frictional wear Wear of a macrostructure of powder coatings and materials at a sliding friction Formation of a layered macrostructure of powder coatings

Continuous Markov processes, Fokkera-Planck's equation without drift Continuous Markov processes, Fokkera-Planck's equation with drift composed. Computer modeling by Monte Carlo method Statistical modeling by Monte Carlo method Polynomial and binomial distributions. Moivre-Laplace's theorem. Computer modeling with statistical scales of linear wear of particles. Statistical modeling according to the theory of percolation. Uniform simple and infinite Markov chains

Distribution and average values of density (porosity) of powder coatings depending on a condition of a substrate Linear wear, distributions of coordinates and characteristic of cross profiles (roughness, mean square deviation, etc.) Distribution, autocorrelated function of local density, coefficients of correlation of density of layers Distribution, correlation of density of layers, coordination numbers of particles of powder material Linear wear, distributions of coordinates and characteristic of cross profiles (roughness, mean square deviation, basic curves, correlation functions, etc.) Threshold of percolation of linear wear. Areas of the predicted resource of a powder coating. Linear wear, distributions of coordinates and characteristic of cross profiles (roughness, mean square deviation, etc.) Distribution and average values of porosity of powder coatings depending on a condition of a substrate (smooth, rough)

2

3

4

5

6

7

8

Uniform simple Markov chains

Statistical modeling of the formation and wear of the macrostructure makes it possible to investigate various characteristics of wear-resistant powder coatings and materials: porosity and density distributions as on Fig. 1, a) and b), coordinate distribution and cross-sectional characteristics, linear wear, as on Fig. 2, a) and b), estimate the predicted resource coatings with sliding friction (see Fig. 3).

П, %

10

a

b

F( П, n)

8

6

4

2

0

П ,%

0,00

0,20

0,40

0,60

0,80

1,00

n/1 00

х, mm

xx

Fig. 1. Distributions of average porosity: (a) Experimental (points) and settlement (curve) against thickness of the gas-thermal coating which is raised dust on a smooth substrate; (b) by layers of a macrostructure at a coating on smooth substrate at p=0.01; matrix 101× 101.