PSI - Issue 65

Akhmetkhanov R. S. et al. / Procedia Structural Integrity 65 (2024) 1–5 Akhmetkhanov R.S. / Structural Integrity Procedia 00 (2024) 000–000

3 3

Let's consider the statistical data, which are given in Table. They are presented in relative units gray scale (image of thermograms in gray scale, from black to white).

Table. Table of statistical data of thermograms at local heating.

Thermograms Without defect

Mean square deviation

Asymmetry

Excess

Peak height

Coefficient of variation, %

0.268225 0.186305

1.14735 0.444805

-0.287677 -1.65663

0.649339 0.74793

50.48

With defect

55.034

In cases of a defect in the material the temperature is higher in the heating region. The temperature difference is largely due to the presence of the defect trapping heat. It can be seen visually that the heat spots are not symmetrical. Non-symmetry of the heat spot is due to the inhomogeneity of the material and, as a consequence, the inhomogeneity of thermal conductivity of the material in different directions. This is most evident in the presence of a defect. Statistical characteristics of the thermal field - kurtosis and asymmetry - help to evaluate differences in heat spots. Thermograms in the defect region had the highest excess and asymmetry compared to the corresponding sequence. Figure 3 presents the characteristics of the thermal field in the form of different graphs, which show the features of temperature distribution in the areas without defect and in the presence of defects. To statistical data were used to evaluate the peculiarity of the thermal fields, multi-fractal spectra, Minkowski connectivity and distribution of n (number of zones) of size r (average radius) with the same level of deformation (clusters). The multi-fractal spectra are related to the type of these distributions. The Minkowski connectivity is defined by a function μ(z), which quantifies the connectivity of the of the image in terms of the values of temperature

w N N N 

,





b

where N denotes the total number of pixels. N w denotes the number of continuous sets of "white" pixels (clusters at a certain level z of coloration of the image - levels of image colorization in gray scale). Pixels that are below the threshold are called "black" pixels. N b denotes the number of continuous sets of black pixels. For the temperature field "white" pixels have a higher temperature than "black" pixels.

Fig. 3. Characteristics of thermogram in the defect-free zone: (a) multifractal spectrum; (b) Minkowski connectivity μ(z); (c) size distribution of zones r with similar temperature levels.

Multifractal spectra show the distributions of scale elements (temperatures) in the distribution of local zones of deformation levels. And Minkowski connectivity μ characterizes the homogeneity of the distribution of local zones