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Критерии оценки усталостных свойств металла сварных швов..pdf

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ɍȾɄ 621.791
ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ
E.A. Krivonosova
ɉɟɪɦɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ
Perm National Research Polytechnic University
ɄɊɂɌȿɊɂɂ ɈɐȿɇɄɂ ɍɋɌȺɅɈɋɌɇɕɏ ɋȼɈɃɋɌȼ
ɆȿɌȺɅɅȺ ɋȼȺɊɇɕɏ ɒȼɈȼ
CRITERIANES OF MEASURING OF FATIGUE
PROPERTY OF WELDING METAL
ɉɪɢɜɟɞɟɧ ɚɧɚɥɢɡ ɤɪɢɬɟɪɢɟɜ ɨɰɟɧɤɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɡɜɢɬɢɸ ɭɫɬɚɥɨɫɬɧɵɯ ɬɪɟɳɢɧ ɜ ɧɢɡɤɨɭɝɥɟɪɨɞɢɫɬɵɯ, ɫɪɟɞɧɟ- ɢ ɜɵɫɨɤɨɥɟɝɢɪɨɜɚɧɧɵɯ ɫɜɚɪɧɵɯ ɲɜɚɯ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɦɟɬɚɥɥ ɫɜɚɪɧɵɯ ɲɜɨɜ, ɭɫɬɚɥɨɫɬɶ, ɬɪɟɳɢɧɵ, ɤɨɷɮɮɢɰɢɟɧɬ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ, ɤɪɢɬɟɪɢɣ ɨɰɟɧɤɢ.
The analysis methods of fatigue crack resistant of welding metal of low carbon steel, middle- and
high-ligature steel is considered.
Keywords: methods analysis of fatigue property, welding metal, crack resistant, stress intensity
range, criterianes of measuring.
ɉɪɨɛɥɟɦɚ ɩɨɜɵɲɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɭɫɬɚɥɨɫɬɢ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ
ɨɫɬɚɟɬɫɹ ɚɤɬɭɚɥɶɧɨɣ ɧɟɫɦɨɬɪɹ ɧɚ ɡɧɚɱɢɬɟɥɶɧɵɟ ɭɫɢɥɢɹ ɢɧɠɟɧɟɪɧɨɣ ɧɚɭɤɢ
ɢ ɩɪɚɤɬɢɤɢ ɜ ɞɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ɉɪɢ ɢɫɩɵɬɚɧɢɢ ɭɫɬɚɥɨɫɬɧɵɯ ɫɜɨɣɫɬɜ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ ɧɟɢɡɛɟɠɧɨ ɜɨɡɧɢɤɚɟɬ ɩɪɨɛɥɟɦɚ ɦɚɥɵɯ ɪɚɡɦɟɪɨɜ ɨɛɪɚɡɰɚ,
ɤ ɤɨɬɨɪɵɦ ɧɟ ɜɫɟɝɞɚ ɦɨɠɧɨ ɤɨɪɪɟɤɬɧɨ ɩɪɢɦɟɧɢɬɶ ɬɪɚɞɢɰɢɨɧɧɵɟ ɦɟɬɨɞɵ ɢɡɦɟɪɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ ɫɜɨɣɫɬɜ, ɩɪɢɦɟɧɹɟɦɵɟ ɞɥɹ ɨɛɪɚɡɰɨɜ ɫɬɚɧɞɚɪɬɧɵɯ ɪɚɡɦɟɪɨɜ. Ɉɩɢɫɚɬɶ ɩɪɨɰɟɫɫ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ (ɡɚɪɨɠɞɟɧɢɟ ɢ ɪɚɡɜɢɬɢɟ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ) ɫ ɟɞɢɧɵɯ ɩɨɡɢɰɢɣ ɩɨɤɚ ɟɳɟ
ɧɟ ɭɞɚɟɬɫɹ. ɉɪɢ ɚɧɚɥɢɡɟ ɫɬɚɞɢɢ ɡɚɪɨɠɞɟɧɢɹ ɬɪɟɳɢɧɵ ɨɬ ɤɨɧɰɟɧɬɪɚɬɨɪɚ
ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɸɬ ɬɪɚɞɢɰɢɨɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨɛ ɭɫɬɚɥɨɫɬɢ ɩɪɢ ɰɢɤɥɢɱɟɫɤɨɦ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ, ɬɨɝɞɚ ɤɚɤ ɚɧɚɥɢɡ ɫɬɚɞɢɢ ɪɨɫɬɚ ɬɪɟɳɢɧɵ ɜɵɩɨɥɧɹɸɬ
ɫ ɩɨɦɨɳɶɸ ɦɟɯɚɧɢɤɢ ɪɚɡɪɭɲɟɧɢɹ [1].
ɂɫɫɥɟɞɨɜɚɧɢɹ ɜ ɨɛɥɚɫɬɢ ɦɟɯɚɧɢɤɢ ɪɚɡɪɭɲɟɧɢɹ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɩɪɢ ɩɟɪɟɦɟɧɧɵɯ ɧɚɝɪɭɠɟɧɢɹɯ ɩɨɡɜɨɥɢɥɢ ɭɫɬɚɧɨɜɢɬɶ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ
dl
ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ ɩɪɢ ɢɡɝɢɛɟ v
ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɪɚɡɦɚɯɚ ɤɨɷɮdN
88 ɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɄI. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ, ɢɡɜɟɫɬɧɚɹ ɤɚɤ
ɤɢɧɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ (ɪɢɫ. 1), ɛɵɥɚ ɩɪɢɧɹɬɚ ɡɚ
ɨɫɧɨɜɭ. Ⱦɢɚɝɪɚɦɦɚ ɢɦɟɟɬ ɬɪɢ ɯɚɪɚɤɬɟɪɧɵɯ ɭɱɚɫɬɤɚ. ɇɚ ɭɱɚɫɬɤɟ 1 ɩɪɢ ɡɧɚɱɟɧɢɹɯ ɄI, ɦɟɧɶɲɢɯ ɩɨɪɨɝɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɫɬɪɚɝɢɜɚɧɢɹ ɬɪɟɳɢɧɵ Ʉth, ɬɪɟɳɢɧɚ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɪɚɫɬɟɬ. Ɂɧɚɱɟɧɢɟ Ʉth ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ɤɚɤ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɄI, ɩɪɢ ɤɨɬɨɪɨɦ ɫɤɨɪɨɫɬɶ ɪɨɫɬɚ ɭɫɬɚɥɨɫɬɧɨɣ
ɬɪɟɳɢɧɵ ɧɟ ɩɪɟɜɵɲɚɟɬ 3˜10–10 ɦ/ɰɢɤɥ ɧɚ ɩɪɨɬɹɠɟɧɢɢ 106 ɰɢɤɥɨɜ.
Ɋɢɫ. 1. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ
ɍɫɥɨɜɧɨ ɩɪɢɧɢɦɚɸɬ, ɱɬɨ ɩɪɢ ɄI = Ʉth ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɟɯɨɞ ɨɬ ɩɟɪɜɨɣ ɫɬɚɞɢɢ ɪɚɡɜɢɬɢɹ ɪɚɡɪɭɲɟɧɢɹ ɤɨ ɜɬɨɪɨɣ, ɩɪɢɱɟɦ ɫɤɨɪɨɫɬɶ ɪɨɫɬɚ ɬɪɟɳɢɧɵ ɫɤɚɱɤɨɦ
ɜɨɡɪɚɫɬɚɟɬ ɨɬ ɧɭɥɹ ɞɨ 5˜10–8 ɦ/ɰɢɤɥ. ɍɱɚɫɬɨɤ 2 ɤɢɧɟɬɢɱɟɫɤɨɣ ɞɢɚɝɪɚɦɦɵ ɪɚɡɪɭɲɟɧɢɹ ɦɨɠɟɬ ɫɨɫɬɚɜɥɹɬɶ ɡɧɚɱɢɬɟɥɶɧɭɸ ɱɚɫɬɶ ɪɟɫɭɪɫɚ ɤɨɧɫɬɪɭɤɰɢɢ. ɋɤɨɪɨɫɬɶ ɪɨɫɬɚ ɬɪɟɳɢɧɵ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɨɞɱɢɧɹɟɬɫɹ ɭɪɚɜɧɟɧɢɸ ɉɷɪɢɫɚ:
dl
dN
C ˜ Ʉ Im ,
ɝɞɟ C ɢ m – ɩɚɪɚɦɟɬɪɵ ɦɚɬɟɪɢɚɥɚ, ɨɩɪɟɞɟɥɹɟɦɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ.
Ɂɚɜɢɫɢɦɨɫɬɶ ɷɬɨɣ ɫɤɨɪɨɫɬɢ ɨɬ ɄI ɫɬɟɩɟɧɧɚɹ (ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɯ ɤɨɨɪɞɢɧɚɬɚɯ ɜɵɝɥɹɞɢɬ ɤɚɤ ɧɚɤɥɨɧɧɵɣ ɨɬɪɟɡɨɤ ɩɪɹɦɨɣ).
ɋɪɟɞɧɢɣ ɭɱɚɫɬɨɤ ɤɢɧɟɬɢɱɟɫɤɨɣ ɞɢɚɝɪɚɦɦɵ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ,
ɢɫɫɥɟɞɨɜɚɧɢɟɦ ɤɨɬɨɪɨɝɨ, ɤɚɤ ɧɚɢɛɨɥɟɟ ɜɚɠɧɨɝɨ ɫ ɩɪɢɤɥɚɞɧɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ,
ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɪɨɫɬɚ
ɬɪɟɳɢɧɵ ɨɤɨɥɨ 10–8 ɦ/ɰɢɤɥ.
ɍɱɚɫɬɨɤ 3 ɤɢɧɟɬɢɱɟɫɤɨɣ ɞɢɚɝɪɚɦɦɵ – ɭɱɚɫɬɨɤ ɭɫɤɨɪɟɧɧɨɝɨ ɪɨɫɬɚ ɬɪɟɳɢɧɵ (dl dN ! 10–6 ɦ/ɰɢɤɥ), ɩɪɟɞɲɟɫɬɜɭɸɳɢɣ ɩɟɪɟɯɨɞɭ ɤ ɫɤɚɱɤɨɨɛɪɚɡɧɨɦɭ
89
ɩɪɨɞɜɢɠɟɧɢɸ ɩɪɢ ɩɪɟɞɟɥɟ ɰɢɤɥɢɱɟɫɤɨɣ ɬɪɟɳɢɧɨɫɬɨɣɤɨɫɬɢ, ɛɥɢɡɤɨɦɭ ɩɨ ɡɧɚɱɟɧɢɸ ɤ ɜɹɡɤɨɫɬɢ ɪɚɡɪɭɲɟɧɢɹ ɄIɋ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɜɵɱɢɫɥɹɥɢ ɩɨ ɫɩɪɚɜɨɱɧɵɦ
ɞɚɧɧɵɦ ɞɥɹ ɩɥɨɫɤɢɯ ɨɛɪɚɡɰɨɜ ɫ ɨɫɬɪɵɦ ɤɨɧɰɟɧɬɪɚɬɨɪɨɦ [2]:
ɄI
6M
SlY (D), D l W ,
tW 2
ɝɞɟ M – ɢɡɝɢɛɚɸɳɢɣ ɦɨɦɟɧɬ; t, W, l – ɪɚɡɦɟɪɵ ɨɛɪɚɡɰɚ; Y(D) – ɬɚɪɢɪɨɜɨɱɧɵɣ
ɤɨɷɮɮɢɰɢɟɧɬ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ
Y (D) 1,122 1, 4D 7,33D 2 13,08D3 14D 4 .
Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ ɭɱɢɬɵɜɚɥɢ ɝɪɚɧɢɰɵ ɩɪɢɦɟɧɢɦɨɫɬɢ ɮɨɪɦɭɥɵ ɞɥɹ ɤɨɷɮl
d 0,6.
ɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ: D
W
Ɇɟɬɨɞɢɤɚ ɦɚɥɨɨɛɪɚɡɰɨɜɵɯ ɢɫɩɵɬɚɧɢɣ ɧɚ ɭɫɬɚɥɨɫɬɧɵɣ ɢɡɝɢɛ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ. ɂɫɩɵɬɚɧɢɹ ɩɪɨɜɨɞɢɥɢ ɧɚ ɨɛɪɚɡɰɚɯ ɦɟɬɚɥɥɚ ɫɜɚɪɧɨɝɨ
ɲɜɚ ɭɝɥɟɪɨɞɢɫɬɵɯ [2–5], ɚ ɬɚɤɠɟ ɫɪɟɞɧɟ- [6, 7] ɢ ɜɵɫɨɤɨɥɟɝɢɪɨɜɚɧɧɵɯ ɫɬɚɥɟɣ [8–13]. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɫɜɚɪɧɵɟ ɲɜɵ ɜɵɩɨɥɧɹɥɢɫɶ ɷɥɟɤɬɪɨɞɚɦɢ ɬɢɩɚ
ɗ46 ɜ ɤɚɧɚɜɤɭ ɧɚ ɩɨɥɨɫɚɯ ɫɬɚɥɢ ɋɬ. 3 ɬɨɥɳɢɧɨɣ 6 ɦɦ ɡɚ ɨɞɢɧ ɩɪɨɯɨɞ. ɉɪɢ
ɬɚɤɢɯ ɭɫɥɨɜɢɹɯ ɫɜɚɪɤɢ ɫɭɳɟɫɬɜɨɜɚɥɢ ɨɩɪɟɞɟɥɟɧɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ ɩɨ ɪɚɡɦɟɪɚɦ ɨɛɪɚɡɰɚ. Ⱦɥɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢɡ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ ɢɡɝɨɬɚɜɥɢɜɚɥɢ ɨɛɪɚɡɰɵ ɒɚɪɩɢ (ȽɈɋɌ 9454–78, ɬɢɩ 14). ȼɢɞ ɤɨɧɰɟɧɬɪɚɬɨɪɚ V-ɨɛɪɚɡɧɵɣ,
ɞɥɢɧɚ L = 55 ɦɦ, ɲɢɪɢɧɚ t = 2,5r0,05 ɦɦ, ɜɵɫɨɬɚ W = 8r0,01 ɦɦ. ɇɚɞɪɟɡ
ɨɪɢɟɧɬɢɪɨɜɚɥɢ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɬɪɟɳɢɧɚ ɩɪɨɲɥɚ ɱɟɪɟɡ ɲɨɜ ɩɚɪɚɥɥɟɥɶɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫɜɚɪɤɢ (ɪɢɫ. 2).
V
V
G
t
l
W
L
ɚ
ɛ
Ɋɢɫ. 2. Ɉɛɪɚɡɰɵ ɞɥɹ ɭɫɬɚɥɨɫɬɧɵɯ ɢɫɩɵɬɚɧɢɣ (ɚ, ɲɬɪɢɯɨɜɤɨɣ ɭɤɚɡɚɧɨ
ɪɚɫɩɨɥɨɠɟɧɢɟ ɡɨɧɵ ɫɜɚɪɧɨɝɨ ɲɜɚ) ɢ ɫɯɟɦɚ ɧɚɝɪɭɠɟɧɢɹ ɨɛɪɚɡɰɚ (ɛ)
90 Ⱦɥɹ ɢɫɩɵɬɚɧɢɣ ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ ɫɩɟɰɢɚɥɶɧɚɹ ɭɫɬɚɧɨɜɤɚ ɢɫɩɵɬɚɧɢɹ ɧɚ ɭɫɬɚɥɨɫɬɧɵɣ ɢɡɝɢɛ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɫɢɥɨɜɨɝɨ ɛɥɨɤɚ, ɧɚ ɛɚɡɟ ɦɨɞɟɪɧɢɡɢɪɨɜɚɧɧɨɣ ɦɚɲɢɧɵ ɞɥɹ ɭɫɬɚɥɨɫɬɧɵɯ ɢɫɩɵɬɚɧɢɣ, ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɪɨɫɬɨɦ
ɬɪɟɳɢɧɵ, ɫɢɫɬɟɦɵ ɤɨɧɬɪɨɥɹ ɱɢɫɥɚ ɨɛɨɪɨɬɨɜ, ɚ ɬɚɤɠɟ ɬɚɪɢɪɨɜɨɱɧɨɝɨ ɩɪɢɫɩɨɫɨɛɥɟɧɢɹ. ȼɨɨɛɳɟ, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɪɨɝɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɞɨɫɬɚɬɨɱɧɨ ɢɫɩɵɬɚɬɶ ɨɞɢɧ ɨɛɪɚɡɟɰ, ɜɵɪɚɳɢɜɚɹ ɬɪɟɳɢɧɵ ɪɚɡɧɵɯ ɞɥɢɧ
ɢ ɞɨɛɢɜɚɹɫɶ ɢɯ ɬɨɪɦɨɠɟɧɢɹ. Ɉɞɧɚɤɨ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨɝɨ 95%-ɧɨɝɨ
ɭɪɨɜɧɹ ɧɚɞɟɠɧɨɫɬɢ, ɩɪɢɧɹɬɨɝɨ ɜ ɬɟɯɧɢɱɟɫɤɢɯ ɪɚɫɱɟɬɚɯ, ɢɫɩɵɬɚɧɢɹ ɩɨɜɬɨɪɹɥɢ ɧɚ
3–4 ɨɛɪɚɡɰɚɯ ɦɟɬɚɥɥɚ ɲɜɚ ɞɥɹ ɤɚɠɞɨɝɨ ɫɨɫɬɚɜɚ ɷɥɟɤɬɪɨɞɧɨɝɨ ɩɨɤɪɵɬɢɹ, ɚ ɪɟɡɭɥɶɬɚɬɵ ɫɬɚɬɢɫɬɢɱɟɫɤɢ ɨɛɪɚɛɚɬɵɜɚɥɢɫɶ.
ɉɟɪɢɨɞɢɱɟɫɤɢ ɩɨ ɦɟɪɟ ɪɨɫɬɚ ɬɪɟɳɢɧɵ ɩɪɨɜɨɞɢɥɚɫɶ ɬɚɪɢɪɨɜɤɚ ɧɚɝɪɭɡɤɢ
ɧɚ ɨɛɪɚɡɟɰ ɩɨ ɜɟɥɢɱɢɧɟ ɩɪɨɝɢɛɚ ', ɡɚɞɚɜɚɟɦɨɝɨ ɦɚɲɢɧɨɣ, ɞɥɹ ɤɚɠɞɨɣ ɞɥɢɧɵ
ɬɪɟɳɢɧɵ.
Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ. ȼ ɯɨɞɟ ɢɫɩɵɬɚɧɢɣ ɮɢɤɫɢɪɨɜɚɥɢ ɤɪɢɜɵɟ
ɪɨɫɬɚ ɞɥɢɧɵ ɬɪɟɳɢɧɵ l ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ ɰɢɤɥɨɜ ɧɚɝɪɭɠɟɧɢɹ N. ȼɢɞ
ɤɪɢɜɵɯ ɪɨɫɬɚ ɬɪɟɳɢɧɵ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɫɜɚɪɧɵɯ ɲɜɨɜ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 3.
Ɋɢɫ. 3. Ɂɚɜɢɫɢɦɨɫɬɶ ɞɥɢɧɵ ɭɫɬɚɥɨɫɬɧɨɣ ɬɪɟɳɢɧɵ L ɨɬ ɱɢɫɥɚ ɰɢɤɥɨɜ
ɭɫɬɚɥɨɫɬɧɵɯ ɢɫɩɵɬɚɧɢɣ N ɞɥɹ ɦɟɬɚɥɥɚ ɲɜɚ ɷɥɟɤɬɪɨɞɨɜ: 1 ɢ 3 – ɷɥɟɤɬɪɨɞ 1808
(' = 1 ɢ 1,5 ɦɦ); 2 ɢ 4 – ɷɥɟɤɬɪɨɞ 1809 (' = 1 ɢ 1,5 ɦɦ)
Ⱦɥɹ ɦɟɬɚɥɥɚ ɲɜɚ ɜɫɟɯ ɫɨɫɬɚɜɨɜ ɯɚɪɚɤɬɟɪɧɨ ɞɨɫɬɚɬɨɱɧɨ ɩɥɚɜɧɨɟ ɧɚɪɚɫɬɚɧɢɟ ɞɥɢɧɵ ɬɪɟɳɢɧɵ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɱɢɫɥɚ ɰɢɤɥɨɜ ɧɚɝɪɭɠɟɧɢɹ ɛɟɡ ɩɟɪɟɝɢɛɨɜ
ɞɨ ɞɥɢɧɵ ɩɪɢɦɟɪɧɨ l = 5…6 ɦɦ. ɉɪɢ ɷɬɨɦ ɩɪɟɞɟɥɟ ɧɚ ɤɪɢɜɵɯ ɩɨɹɜɥɹɟɬɫɹ ɩɟɪɟɝɢɛ, ɫɜɹɡɚɧɧɵɣ ɫ ɢɡɦɟɧɟɧɢɟɦ ɫɯɟɦɵ ɢɡɝɢɛɚ. ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɪɚɛɨɱɟɝɨ ɫɟɱɟɧɢɹ ɨɛɪɚɡɰɚ ɫɯɟɦɚ ɢɡɝɢɛɚ, ɜɵɩɨɥɧɹɸɳɚɹɫɹ ɜ ɧɚɱɚɥɟ ɢɫɩɵɬɚɧɢɹ, ɧɚɪɭɲɚɟɬ
91
ɫɹ, ɞɟɮɨɪɦɢɪɨɜɚɧɢɟ ɫɬɚɧɨɜɢɬɫɹ ɜɨɡɦɨɠɧɵɦ ɜ ɧɟɫɤɨɥɶɤɢɯ ɧɚɩɪɚɜɥɟɧɢɹɯ
ɢ ɷɮɮɟɤɬ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɫɬɢ ɞɟɮɨɪɦɚɰɢɢ ɢɫɱɟɡɚɟɬ, ɧɚ ɤɪɢɜɵɯ l = f(N) ɧɚɛɥɸɞɚɟɬɫɹ ɡɚɦɟɞɥɟɧɢɟ ɪɨɫɬɚ ɞɥɢɧɵ ɬɪɟɳɢɧɵ.
Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɢɧɚ ɬɪɟɳɢɧɵ l = 5…6 ɦɦ ɹɜɥɹɟɬɫɹ ɩɪɟɞɟɥɨɦ ɩɪɢɦɟɧɢɦɨɫɬɢ ɮɨɪɦɭɥɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɬɚɪɢɪɨɜɨɱɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ 8 ɜ ɭɪɚɜɧɟɧɢɢ
ɉɷɪɢɫɚ. Ⱦɥɹ ɫɨɯɪɚɧɟɧɢɹ ɤɨɪɪɟɤɬɧɨɫɬɢ ɩɨɫɥɟɞɭɸɳɟɝɨ ɚɧɚɥɢɡɚ ɯɚɪɚɤɬɟɪɚ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɨɝɪɚɧɢɱɢɜɚɥɢɫɶ ɨɛɥɚɫɬɶɸ ɧɚɱɚɥɶɧɵɯ ɢ ɫɪɟɞɧɢɯ ɞɥɢɧ
ɬɪɟɳɢɧ.
ɗɬɚɩɭ ɡɚɪɨɠɞɟɧɢɹ ɬɪɟɳɢɧɵ ɩɪɟɞɲɟɫɬɜɭɟɬ ɢɧɤɭɛɚɰɢɨɧɧɵɣ ɩɟɪɢɨɞ, ɢɡɦɟɧɹɸɳɢɣɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɨɫɬɚɜɚ ɲɜɚ, ɫɬɪɭɤɬɭɪɵ ɢ ɜɟɥɢɱɢɧɵ ɢɡɝɢɛɚɸɳɟɝɨ ɦɨɦɟɧɬɚ. Ⱦɥɹ ɩɪɨɝɢɛɚ ' = 1 ɦɦ ɢɧɤɭɛɚɰɢɨɧɧɵɣ ɩɟɪɢɨɞ ɫɨɫɬɚɜɥɹɟɬ
(2…3)˜105 ɰɢɤɥɨɜ ɞɥɹ ɲɜɨɜ ɫ ɝɪɭɛɨɣ ɫɬɪɭɤɬɭɪɨɣ ɢ (7…8)˜105 ɰɢɤɥɨɜ ɞɥɹ ɦɟɥɤɨɡɟɪɧɢɫɬɵɯ ɲɜɨɜ. ɗɬɢ ɬɪɟɳɢɧɵ ɡɚɪɨɠɞɚɸɬɫɹ ɬɟɦ ɪɚɧɶɲɟ, ɱɟɦ ɜɵɲɟ ɭɪɨɜɟɧɶ ɰɢɤɥɢɱɟɫɤɢɯ ɧɚɩɪɹɠɟɧɢɣ ɢ «ɝɪɭɛɟɟ» ɫɬɪɭɤɬɭɪɚ ɦɟɬɚɥɥɚ ɲɜɚ. ɉɨɞɨɛɧɭɸ
ɡɚɜɢɫɢɦɨɫɬɶ ɢɧɤɭɛɚɰɢɨɧɧɨɝɨ ɩɟɪɢɨɞɚ ɡɚɪɨɠɞɟɧɢɹ ɬɪɟɳɢɧɵ ɨɬ ɭɪɨɜɧɹ ɧɚɩɪɹɠɟɧɢɣ ɧɚɛɥɸɞɚɥɢ ɜ ɪɚɛɨɬɟ [8]. Ⱥɧɚɥɨɝɢɱɧɵɟ ɧɚɛɥɸɞɟɧɢɹ ɛɵɥɢ ɫɞɟɥɚɧɵ
ɜ ɞɪɭɝɢɯ ɪɚɛɨɬɚɯ ɞɥɹ ɧɢɡɤɨɥɟɝɢɪɨɜɚɧɧɵɯ ɫɬɚɥɟɣ: ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɡɜɢɬɢɸ
ɭɫɬɚɥɨɫɬɧɵɯ ɬɪɟɳɢɧ ɢ ɛɨɥɟɟ ɜɵɫɨɤɢɟ ɡɧɚɱɟɧɢɹ Ʉth ɯɚɪɚɤɬɟɪɧɵ ɞɥɹ ɫɬɚɥɟɣ
ɫ ɝɪɭɛɨɣ ɫɬɪɭɤɬɭɪɨɣ (ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɧɟ ɧɚ ɫɜɚɪɧɵɯ ɲɜɚɯ).
Ʉɢɧɟɬɢɱɟɫɤɢɟ ɞɢɚɝɪɚɦɦɵ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ
ɲɜɨɜ ɛɵɥɢ ɩɨɫɬɪɨɟɧɵ ɞɥɹ ɫɪɟɞɧɟɝɨ ɢɧɬɟɪɜɚɥɚ ɪɚɡɪɭɲɟɧɢɹ, ɤɚɤ ɧɚɢɛɨɥɟɟ
ɜɚɠɧɨɝɨ ɫ ɩɪɢɤɥɚɞɧɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ.
Ⱦɥɹ ɨɛɪɚɛɨɬɤɢ ɤɢɧɟɬɢɱɟɫɤɢɯ ɞɢɚɝɪɚɦɦ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɫɜɚɪɧɵɯ ɲɜɨɜ ɢɫɩɨɥɶɡɨɜɚɥɢ ɞɜɚ ɜɚɪɢɚɧɬɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ:
dl
C ˜ Ʉ mI ,
– ɩɨ ɭɪɚɜɧɟɧɢɸ ɉɷɪɢɫɚ
dN
dl
– ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ
A ˜ exp a ˜ Ʉ I , ɝɞɟ ɋ, Ⱥ, m
dN
ɢ a – ɩɚɪɚɦɟɬɪɵ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɦɚɬɟɪɢɚɥɚ ɢ ɮɨɪɦɵ ɨɛɪɚɡɰɚ.
Ɋɟɡɭɥɶɬɚɬɵ ɜɵɪɚɜɧɢɜɚɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ ɭɝɥɟɪɨɞɢɫɬɵɯ ɫɬɚɥɟɣ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 4, ɧɚ ɤɨɬɨɪɨɦ ɫɨɜɦɟɳɟɧɵ ɞɜɚ ɜɚɪɢɚɧɬɚ ɜɵɪɚɜɧɢɜɚɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɪɚɜɧɟɧɢɹ ɬɨɱɧɨɫɬɢ ɩɪɢɛɥɢɠɟɧɢɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢ ɤɪɢɜɵɦɢ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ
ɧɚɢɛɨɥɶɲɟɣ ɬɨɱɧɨɫɬɶɸ ɨɛɥɚɞɚɟɬ ɩɪɢɛɥɢɠɟɧɢɟ ɩɨ ɭɪɚɜɧɟɧɢɸ ɉɷɪɢɫɚ. Ɍɚɤɢɦ
ɨɛɪɚɡɨɦ, ɛɵɥɨ ɪɟɲɟɧɨ ɨɝɪɚɧɢɱɢɬɶɫɹ ɩɟɪɜɵɦ ɜɚɪɢɚɧɬɨɦ ɜɵɪɚɜɧɢɜɚɧɢɹ. ɇɚ
ɪɢɫ. 5 ɩɪɢɜɟɞɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɬɪɟɳɢɧɵ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɜ ɥɨɝɚɪɢɮɦɢɱɟɫɤɨɦ ɦɚɫɲɬɚɛɟ.
ɂɧɬɟɪɟɫɧɵɦ ɹɜɥɹɟɬɫɹ ɬɨɬ ɮɚɤɬ, ɱɬɨ ɤɢɧɟɬɢɱɟɫɤɢɟ ɞɢɚɝɪɚɦɦɵ ɪɚɡɪɭɲɟɧɢɹ ɦɟɬɚɥɥɚ ɲɜɚ ɷɥɟɤɬɪɨɞɚ 1808 ɯɨɪɨɲɨ ɫɨɜɩɚɞɚɸɬ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ, ɩɨɥɭɱɟɧ92 ɧɵɦɢ ɜ ɪɚɛɨɬɚɯ ȿɤɨɛɨɪɢ ɞɥɹ ɤɪɢɜɵɯ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ
ɬɪɟɳɢɧ ɜ ɦɚɥɨɭɝɥɟɪɨɞɢɫɬɨɣ ɫɬɚɥɢ, ɩɨɫɬɪɨɟɧɧɵɦɢ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɡɜɢɬɢɹ
ɦɢɤɪɨ- ɢ ɦɚɤɪɨɬɪɟɳɢɧ. ɉɨɤɚɡɚɬɟɥɶ ɭɪɚɜɧɟɧɢɹ ɉɷɪɢɫɚ ɜ ɨɩɵɬɚɯ ȿɤɨɛɨɪɢ
m = 3, ɜ ɧɚɲɢɯ ɨɩɵɬɚɯ – 2,1–2,6. ȼɨɨɛɳɟ, ɩɨɤɚɡɚɬɟɥɶ ɭɪɚɜɧɟɧɢɹ ɉɷɪɢɫɚ ɞɥɹ
ɦɚɬɟɪɢɚɥɨɜ ɷɬɨɝɨ ɤɥɚɫɫɚ ɦɨɠɟɬ ɢɡɦɟɧɹɬɶɫɹ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 2 ɞɨ 7.
Ɋɢɫ. 4. ȼɵɪɚɜɧɢɜɚɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ ɭɫɬɚɥɨɫɬɧɵɯ ɢɫɩɵɬɚɧɢɣ
dl
C ˜ Ʉ mI ,
ɞɥɹ ɦɟɬɚɥɥɚ ɲɜɚ ɷɥɟɤɬɪɨɞɚ 1808: 1 – ɩɨ ɭɪɚɜɧɟɧɢɸ ɉɷɪɢɫɚ
dN
ɋ = 4,14˜10–12; m = 2,26; 2 – ɩɨ ɷɤɫɩɨɧɟɧɬɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ
dl
A ˜ exp a ˜ Ʉ I , A =10–9 a 0,115; + – ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɬɨɱɤɢ
dN
Ɋɢɫ. 5. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɬɪɟɳɢɧɵ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɣ ɞɥɹ ɦɟɬɚɥɥɚ ɲɜɚ ɷɥɟɤɬɪɨɞɨɜ ɬɢɩɚ ɗ46:
1 – ɈɄ46, m = 2,4; 2 – ɗɥ. 1808, m = 2,26
93
ȼ ɩɪɨɰɟɫɫɟ ɢɫɩɵɬɚɧɢɣ ɧɚ ɦɟɬɚɥɥɟ ɲɜɚ ɧɟɤɨɬɨɪɵɯ ɷɥɟɤɬɪɨɞɨɜ ɧɚɛɥɸɞɚɥɫɹ ɷɮɮɟɤɬ ɩɨɹɜɥɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɪɟɳɢɧ, ɪɚɡɜɢɜɚɸɳɢɯɫɹ ɩɨ ɥɢɧɢɢ
ɫɩɥɚɜɥɟɧɢɹ. Ⱥɧɚɥɨɝɢɱɧɵɟ ɷɮɮɟɤɬɵ, ɜ ɱɚɫɬɧɨɫɬɢ ɜɥɢɹɧɢɟ ɫɨɡɞɚɸɳɢɯ ɤɨɧɰɟɧɬɪɚɰɢɸ ɧɚɩɪɹɠɟɧɢɣ ɞɟɮɟɤɬɨɜ, ɬɚɤɢɯ ɤɚɤ ɩɨɞɪɟɡɵ, ɩɨɜɟɪɯɧɨɫɬɧɵɟ ɩɨɪɵ, ɧɟɩɪɚɜɢɥɶɧɚɹ ɮɨɪɦɚ ɲɜɚ, ɦɟɥɤɢɟ ɬɪɟɳɢɧɵ, ɧɟ ɜɵɹɜɥɟɧɧɵɟ ɩɪɢ ɤɨɧɬɪɨɥɟ ɧɟɪɚɡɪɭɲɚɸɳɢɦɢ ɫɩɨɫɨɛɚɦɢ, ɨɬɦɟɱɟɧɵ ɜ ɪɚɛɨɬɟ [1].
ɋɤɚɡɵɜɚɸɬɫɹ ɢ ɜɧɭɬɪɟɧɧɢɟ ɞɟɮɟɤɬɵ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ. ɇɚ ɪɢɫ. 6 ɩɪɟɞɫɬɚɜɥɟɧɚ ɫɢɬɭɚɰɢɹ ɩɨɹɜɥɟɧɢɹ ɢ ɪɚɡɜɢɬɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɪɟɳɢɧ ɨɬ ɧɟɦɟɬɚɥɥɢɱɟɫɤɢɯ ɜɤɥɸɱɟɧɢɣ ɢ ɦɚɤɪɨɞɟɮɟɤɬɨɜ ɜɛɥɢɡɢ
ɤɪɚɹ ɭɫɬɚɥɨɫɬɧɨɝɨ ɢɡɥɨɦɚ.
Ɋɢɫ. 6. Ɍɪɟɳɢɧɚ ɨɬ ɜɧɭɬɪɟɧɧɟɝɨ ɦɚɤɪɨɞɟɮɟɤɬɚ
ɜ ɦɟɬɚɥɥɟ ɲɜɚ ɧɢɡɤɨɭɝɥɟɪɨɞɢɫɬɨɣ ɫɬɚɥɢ. ×20
ɋɞɟɥɚɟɦ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ:
1. ɉɪɢ ɢɫɩɵɬɚɧɢɢ ɭɫɬɚɥɨɫɬɧɵɯ ɫɜɨɣɫɬɜ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ ɧɟɢɡɛɟɠɧɨ ɜɨɡɧɢɤɚɟɬ ɩɪɨɛɥɟɦɚ ɦɚɥɵɯ ɪɚɡɦɟɪɨɜ ɨɛɪɚɡɰɚ, ɤ ɤɨɬɨɪɨɦɭ ɧɟ ɜɫɟɝɞɚ ɦɨɠɧɨ
ɤɨɪɪɟɤɬɧɨ ɩɪɢɦɟɧɢɬɶ ɬɪɚɞɢɰɢɨɧɧɵɟ ɦɟɬɨɞɵ ɢɡɦɟɪɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ ɫɜɨɣɫɬɜ,
ɩɪɢɦɟɧɹɟɦɵɟ ɞɥɹ ɨɛɪɚɡɰɨɜ ɫɬɚɧɞɚɪɬɧɵɯ ɪɚɡɦɟɪɨɜ.
2. ɉɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ ɢɫɩɵɬɚɧɢɣ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɛɪɚɡɰɨɜ ɦɚɥɵɯ
ɪɚɡɦɟɪɨɜ ɧɚ ɭɫɬɚɥɨɫɬɧɵɣ ɢɡɝɢɛ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ, ɩɨɡɜɨɥɹɸɳɚɹ ɤɨɪɪɟɤɬɧɨ ɨɰɟɧɢɬɶ ɯɚɪɚɤɬɟɪ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɜ ɨɛɥɚɫɬɢ ɧɚɱɚɥɶɧɵɯ
ɢ ɫɪɟɞɧɢɯ ɞɥɢɧ ɬɪɟɳɢɧ.
3. ɍɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɞɥɹ ɤɪɢɜɵɯ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɭɫɬɚɥɨɫɬɧɵɯ
ɬɪɟɳɢɧ ɜ ɦɟɬɚɥɥɟ ɫɜɚɪɧɨɝɨ ɲɜɚ ɧɢɡɤɨɭɝɥɟɪɨɞɢɫɬɨɣ ɫɬɚɥɢ, ɩɨɫɬɪɨɟɧɧɵɦɢ ɩɨ
ɪɟɡɭɥɶɬɚɬɚɦ ɪɚɡɜɢɬɢɹ ɦɢɤɪɨ- ɢ ɦɚɤɪɨɬɪɟɳɢɧ, ɩɨɤɚɡɚɬɟɥɶ ɭɪɚɜɧɟɧɢɹ ɉɷɪɢɫɚ
ɪɚɜɟɧ 2,1–2,6. ȼɨɨɛɳɟ, ɩɨɤɚɡɚɬɟɥɶ ɭɪɚɜɧɟɧɢɹ ɉɷɪɢɫɚ ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ ɷɬɨɝɨ
ɤɥɚɫɫɚ ɦɨɠɟɬ ɢɡɦɟɧɹɬɶɫɹ ɜ ɩɪɟɞɟɥɚɯ ɨɬ 2 ɞɨ 7.
94 ɋɩɢɫɨɤ ɥɢɬɟɪɚɬɭɪɵ
1. Radai D. Design and analysis of Fatique Resistant Welding Structures. –
Abington Publisning, 1990. – 380 p.
2. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., əɡɨɜɫɤɢɯ ȼ.Ɇ., ȼɚɫɫɟɪɦɚɧ ɇ.ɇ. ɋɬɪɭɤɬɭɪɧɵɟ ɚɫɩɟɤɬɵ ɭɫɬɚɥɨɫɬɧɨɝɨ ɪɚɡɪɭɲɟɧɢɹ ɦɟɬɚɥɥɚ ɫɜɚɪɧɵɯ ɲɜɨɜ // Ɍɹɠɟɥɨɟ ɦɚɲɢɧɨɫɬɪɟɧɢɟ. – 2005. – ʋ 9. – ɋ. 20–23.
3. ɋɬɪɭɤɬɭɪɧɵɟ ɮɚɤɬɨɪɵ ɯɥɚɞɨɫɬɨɣɤɨɫɬɢ ɫɜɚɪɧɵɯ ɲɜɨɜ / ȼ.Ɇ. əɡɨɜɫɤɢɯ, ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ, ȼ.ɂ. ɒɭɦɹɤɨɜ, ɂ.ɘ. Ʌɟɬɹɝɢɧ, ɇ.ȼ. ȼɵɥɟɠɧɟɜɚ //
ɋɜɚɪɨɱɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɨ. – 2002. – ʋ 1. – ɋ. 12–14.
4. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., əɡɨɜɫɤɢɯ ȼ.Ɇ., ȼɵɥɟɠɧɟɜɚ ɇ.ȼ. ȼɥɢɹɧɢɟ ɧɟɦɟɬɚɥɥɢɱɟɫɤɢɯ ɜɤɥɸɱɟɧɢɣ ɧɚ ɪɚɡɜɢɬɢɟ ɞɟɮɨɪɦɚɰɢɢ ɫɜɚɪɧɵɯ ɲɜɨɜ // Ɍɹɠɟɥɨɟ ɦɚɲɢɧɨɫɬɪɨɟɧɢɟ. – 2003. – ʋ 12. – ɋ. 36–39.
5. Ɉɩɬɢɦɢɡɚɰɢɹ ɫɨɫɬɚɜɚ ɷɥɟɤɬɪɨɞɧɨɝɨ ɩɨɤɪɵɬɢɹ ɫ ɫɢɥɢɤɨɦɚɪɝɚɧɰɟɦ
ɜ ɤɚɱɟɫɬɜɟ ɪɚɫɤɢɫɥɢɬɟɥɹ / ȼ.Ɇ. əɡɨɜɫɤɢɯ, ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ, ȼ.ɂ. ɒɭɦɹɤɨɜ,
ɂ.ɘ. Ʌɟɬɹɝɢɧ // ɋɜɚɪɤɚ ɜ ɋɢɛɢɪɢ. – 2005. – ʋ 2. – ɋ. 46–48.
6. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., Ɋɭɞɚɤɨɜɚ Ɉ.Ⱥ. ȼɥɢɹɧɢɟ ɫɬɪɭɤɬɭɪɵ ɨɬɞɟɥɶɧɵɯ ɫɥɨɟɜ ɫɜɚɪɧɵɯ ɲɜɨɜ ɫɬɚɥɢ 10Ƚ2ɎȻɘ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɭɫɬɚɥɨɫɬɧɨɦɭ ɪɚɡɪɭɲɟɧɢɸ // ɋɜɚɪɨɱɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɨ. – 2012. – ʋ 11. – ɋ. 6–9.
7. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., Ɋɭɞɚɤɨɜɚ Ɉ.Ⱥ. Ɉɩɪɟɞɟɥɟɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɭɫɬɚɥɨɫɬɢ ɦɧɨɝɨɫɥɨɣɧɵɯ ɫɜɚɪɧɵɯ ɲɜɨɜ ɫɬɚɥɢ 10Ƚ2ɎȻɘ // ȼɟɫɬɧɢɤ
ɉɟɪɦ. ɧɚɰ. ɢɫɫɥɟɞ. ɩɨɥɢɬɟɯɧ. ɭɧ-ɬɚ. Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, ɦɚɬɟɪɢɚɥɨɜɟɞɟɧɢɟ. –
2012. – Ɍ. 14, ʋ 2. – ɋ. 29–36.
8. ȼɥɢɹɧɢɟ ɪɟɠɢɦɚ ɫɜɚɪɤɢ ɧɚ ɫɬɪɭɤɬɭɪɭ ɢ ɫɜɨɣɫɬɜɚ ɡɨɧɵ ɬɟɪɦɢɱɟɫɤɨɝɨ
ɜɥɢɹɧɢɹ ɫɬɚɥɟɣ ɫ ɤɚɪɛɨɧɢɬɪɢɞɧɵɦ ɭɩɪɨɱɧɟɧɢɟɦ / ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ,
ȼ.Ɇ. əɡɨɜɫɤɢɯ, Ɉ.Ⱥ. Ɋɭɞɚɤɨɜɚ, Ƚ.ȼ. ȼɫɬɨɜɫɤɢɣ // Ɍɹɠɟɥɨɟ ɦɚɲɢɧɨɫɬɪɨɟɧɢɟ. –
2009. – ʋ 7. – ɋ. 23–27.
9. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., ɋɚɥɨɦɚɬɨɜɚ ȿ.ɋ., Ɋɭɞɚɤɨɜɚ Ɉ.Ⱥ. ȼɥɢɹɧɢɟ ɫɨɫɬɚɜɚ
ɷɥɟɤɬɪɨɞɧɨɝɨ ɩɨɤɪɵɬɢɹ ɧɚ ɩɪɨɰɟɫɫɵ ɫɬɪɭɤɬɭɪɨɨɛɪɚɡɨɜɚɧɢɹ ɜ ɫɜɚɪɧɵɯ ɲɜɚɯ
ɜɵɫɨɤɨɥɟɝɢɪɨɜɚɧɧɵɯ ɫɬɚɥɟɣ // ȼɟɫɬɧɢɤ ɉɟɪɦ. ɝɨɫ. ɬɟɯɧ. ɭɧ-ɬɚ. Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, ɦɚɬɟɪɢɚɥɨɜɟɞɟɧɢɟ. – 2010. – Ɍ. 12, ʋ 1. – ɋ. 103–108.
10. Ɋɚɡɪɚɛɨɬɤɚ ɦɟɬɨɞɢɤɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɤɨɪɪɨɡɢɨɧɧɨɣ ɭɫɬɚɥɨɫɬɢ ɫɜɚɪɧɵɯ
ɫɨɟɞɢɧɟɧɢɣ ɦɚɝɢɫɬɪɚɥɶɧɵɯ ɝɚɡɨɧɟɮɬɟɩɪɨɜɨɞɨɜ / Ɉ.Ⱥ. Ɋɭɞɚɤɨɜɚ, ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ, ȿ.ɋ. Ɂɚɯɚɪɨɜɚ, Ɇ.ɏ. Ⱥɪɢɩɨɜ // ȼɟɫɬɧɢɤ ɉɟɪɦ. ɝɨɫ. ɬɟɯɧ. ɭɧ-ɬɚ. Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, ɦɚɬɟɪɢɚɥɨɜɟɞɟɧɢɟ. – 2010. – Ɍ. 12, ʋ 2. – ɋ. 58–64.
11. ɋɬɪɭɤɬɭɪɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɞɟɮɨɪɦɢɪɨɜɚɧɢɹ ɫɜɚɪɧɵɯ ɲɜɨɜ ɜɵɫɨɤɨɥɟɝɢɪɨɜɚɧɧɵɯ ɫɬɚɥɟɣ / ȿ.Ⱥ. Ʉɪɢɜɨɧɨɫɨɜɚ, Ɉ.Ⱥ. Ɋɭɞɚɤɨɜɚ, ȿ.ɋ. ɋɚɥɨɦɚɬɨɜɚ,
Ⱥ.ɂ. Ƚɨɪɱɚɤɨɜ // ɋɜɚɪɤɚ ɢ ɞɢɚɝɧɨɫɬɢɤɚ. – 2011. – ʋ 3. – ɋ. 14–17.
12. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ., ɋɢɧɤɢɧɚ ȿ.Ⱥ., Ƚɨɪɱɚɤɨɜ Ⱥ.ɂ. ȼɥɢɹɧɢɟ ɬɢɩɚ ɩɨɤɪɵɬɢɹ ɷɥɟɤɬɪɨɞɨɜ ɧɚ ɤɨɪɪɨɡɢɨɧɧɭɸ ɫɬɨɣɤɨɫɬɶ ɦɟɬɚɥɥɚ ɲɜɚ ɫɬɚɥɢ
08ɏ18ɇ10Ɍ // ɋɜɚɪɨɱɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɨ. – 2012. – ʋ 4. – ɋ. 38–41.
95
13. Ʉɪɢɜɨɧɨɫɨɜɚ ȿ.Ⱥ. Ɉɰɟɧɤɚ ɪɚɡɦɟɪɨɜ ɡɨɧɵ ɩɨɜɵɲɟɧɧɨɣ ɩɥɚɫɬɢɱɟɫɤɨɣ
ɞɟɮɨɪɦɚɰɢɢ ɩɪɢ ɭɫɬɚɥɨɫɬɧɨɦ ɪɚɡɪɭɲɟɧɢɢ ɦɟɬɚɥɥɚ ɫɜɚɪɧɨɝɨ ɲɜɚ // ȼɟɫɬɧɢɤ
ɉɟɪɦ. ɧɚɰ. ɢɫɫɥɟɞ. ɩɨɥɢɬɟɯɧ. ɭɧ-ɬɚ. Ɇɚɲɢɧɨɫɬɪɨɟɧɢɟ, ɦɚɬɟɪɢɚɥɨɜɟɞɟɧɢɟ. –
2012. – Ɍ. 14, ʋ 2. – ɋ. 71–76.
ɉɨɥɭɱɟɧɨ 15.02.2013
Ʉɪɢɜɨɧɨɫɨɜɚ ȿɤɚɬɟɪɢɧɚ Ⱥɥɟɤɫɚɧɞɪɨɜɧɚ – ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ,
ɩɪɨɮɟɫɫɨɪ, ɉɟɪɦɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ
ɭɧɢɜɟɪɫɢɬɟɬ (614990 ɉɟɪɦɶ, Ʉɨɦɫɨɦɨɥɶɫɤɢɣ ɩɪ., 29, e-mail: katerinakkkkk@mail.ru).
Krivonosova Ekaterina Aleksandrovna – Doctor of Tecnical Sciences, Professor, Perm National Research Polytechnic University (614990, Perm, Komsomolsky av., 29, e-mail: katerinakkkkk@mail.ru).
96 
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