Analytical proof of the scaling laws applicability for additive manufacturing

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It is shown that the problem of describing the technology of additive laser deposition can be considered within the framework of a self-similar thermal conductivity equation. It is shown that, under certain conditions, the depth of substrate penetration is well described by a self-similar solution. Based on the obtained self-similar solution, a two-parameter dependence of the penetration depth on the Peclet number (the ratio of the scanning speed to the rate of temperature change in the material) and dimensionless enthalpy (the ratio of the specific energy absorbed by the material and the energy required for melting) was obtained. It is shown that the obtained analytical dependence describes the experimental data quite accurately.

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V. Fomin

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

编辑信件的主要联系方式.
Email: fomin@itam.nsc.ru

Academician of the RAS

俄罗斯联邦, Novosibirsk

A. Golyshev

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

Email: alexgol@itam.nsc.ru
俄罗斯联邦, Novosibirsk

A. Medvedev

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

Email: medvedev@itam.nsc.ru
俄罗斯联邦, Novosibirsk

A. Malikov

Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences

Email: smalik707@yandex.ru
俄罗斯联邦, Novosibirsk

参考

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2. Fig. 1. Scheme (a) and photographs of cross-sections of individual tracks during laser cladding of a powder mixture of VT-6 + 10% by weight SiC: thermal conductivity mode ( , ) (b); “dagger” penetration mode ( , ) (c).

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3. Fig. 2. Dimensionless half-width of penetration w/2D depending on dimensionless enthalpy B. Comparison of experimental results (circles) with calculations (line) using formula (10) for n = 0.35, k = 1.

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4. Fig. 3. Dimensionless half-width of penetration w/2D depending on the Peclet number Pe. Comparison of experimental results (circles) with calculations (line) using formula (10) at n = 0.35, k = 1.

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5. Fig. 4. Dimensionless penetration depth h/D depending on the Peclet number Pe. Comparison of experimental results (circles) with calculations (line) using formula (10) at n = 0.35, k = 1. The following regions are highlighted: I – zone of “dagger” penetration, II – zone of thermal conductivity.

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