Prediction of the distribution of grain sizes in 03Kh18TBch steel
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PREDICTION OF THE DISTRIBUTION OF GRAIN SIZES IN 03Kh18TBch STEEL V. Yu. Ol’shanets’kyi1 and I. Yu. Kysil’ova2
UDC 669.15-194.57
By using the stochastic approach, we evaluate the technological plasticity of 03Kh18TBch corrosionresistant steel according to the distribution of grain sizes in this steel after two modes of heat treatment. Keywords: grain size, probability density, corrosion-resistant steels.
Formulation of the Problem Grain size is one of the parameters used for the evaluation of the technological plasticity of complexly alloyed steels. It is known that the grain size numbers of 4–6 are optimal for drop forging. However, it is important to know not only the mean grain size but also the distribution of grain sizes. To solve this problem, we use the stochastic approach. The distributions of grains and microparticles in the metals were studied (depending on the procedure of heat treatment) fairly thoroughly [1, 2]. However, the stochastic approach based on the use of differential distribution functions of the mechanical characteristics was never used. In what follows, we construct differential distribution functions of grain diameters for the 03Kh18TBch corrosion-resistant steel by using the stochastic approach.
Main Material of Investigation The differential functions of the laws of normal distribution for the yield strength of alloyed steels were obtained in [3, 4] in the form of the Gaussian density
f (τ) =
⎡ 1 ⎛ τ − τ ⎞2 ⎤ 1 exp ⎢ − ⎜ i ⎟ ⎥, Sτ 2π ⎢⎣ 2 ⎝ Sτ ⎠ ⎥⎦
(1)
where τ i and τ are the characteristics of yield of the material and Sτ is the mean square deviation. The parameters of distribution τ and Sτ for two special modes of treatment of steel are presented in Table 1. The law of distribution of the grain diameters D in ferrite was established by the method of transformation of random quantities [5]. Then we use the Hall–Petch relation relating the yield strength of the material τ to the grain diameter D [6]: 1 2
National Technical University, Zaporizhzhya, Ukraine. Zaporizhzhya National University, Zaporizhzhya, Ukraine; e-mail: [email protected] (corresponding author).
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 48, No. 3, pp. 99–102, May–June, 2012. Original article submitted April 5, 2011. 1068-820X/12/4803–0369
© 2012
Springer Science+Business Media New York
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V. YU. OL’SHANETS’KYI
τ = τ0 +
AND
I. YU. KYSIL’OVA
K , D
(2)
where τ 0 and K are coefficients that can be found (for the standard ferritic steel) by using the experimental results [5]
τ (250) = 238 МРа,
τ (2) = 475 МРа,
τ (500) = 110 МРа.
(3)
By the method of transformation of random quantities, we determine the required differential function:
ϕ(D) = f [ τ(D) ]
dτ . dD
(4)
By using Eqs. (1) and (2) and relation (4) we obtain the distribution of grain diameters in the form of the Weibull-type law
K f (D) = Sτ 8π
⎡ 1 ⎛ D −1/2 − (τ − τ )/K ⎞ 2 ⎤ 0 exp ⎢ − ⎜ ⎟ ⎥. 3 /K S 2 ⎢ ⎝ ⎠ ⎥ τ D ⎣ ⎦ 1
(5)
This result coincides with the result obtained in [7, 8], where the distributions of dis
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