Modeling of the process of hot isostatic pressing of single crystals of nickel-based superalloy, taking into account plastic flow and vacancy diffusion

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A complex model of pore annihilation during hot isostatic pressing (HIP), which takes into account the simultaneous action of the mechanisms of material plastic flow and diffusive pore dissolution due to the emission of vacancies by the pore surface, has been proposed. The obtained mathematical equations are applied to analyze the kinetics of pore annihilation in single crystals of the nickel-based superalloy CMSX-4 during HIP used for this alloy in industry. It follows from the analysis that both mechanisms (plastic flow and vacancy diffusion) make comparable contributions to the reduction of pore volume under these conditions. As the HIP pressure increases, the contribution of plastic flow increases, while the contribution of vacancy diffusion decreases. Large pores shrink in volume mainly due to the mechanism of plastic flow, however, at the final stage of pore closure, the mechanism of vacancy diffusion is more active. To ensure reliable pore healing by the vacancy mechanism, HIP should be carried out at a moderate argon pressure in the HIP plant.

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Sobre autores

А. Epishin

Merzhanov Institute of Structural Macrokinetics and Materials Science of the RAS

Email: a.epishin2021@gmail.com
Rússia, Chernogolovka

D. Lisovenko

Ishlinsky Institute for Problems in Mechanics of the RAS

Autor responsável pela correspondência
Email: lisovenk@ipmnet.ru
Rússia, Moscow

Bibliografia

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2. Fig. 1. Model for describing the kinetics of pore annihilation during HIP – thick-walled isotropic sphere with a central pore under the action of external HIP pressure pe and pore surface tension gM.

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3. Fig. 2. Dots – dependence of the minimum creep rate of CMSX-4 alloy single crystals of different crystallographic orientations on the applied stress [16]. Solid and dashed lines – approximation of dots for orientation [001], respectively, with sB ≠ 0 and sB = 0. Dash-dotted line – assumed dependence for low-symmetry orientations [011] and [123].

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4. Fig. 3. Finding the optimal value of the degree n by maximizing the determination coefficient r 2 = f (n).

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5. Fig. 4. Kinetics of pore diameter reduction assuming different HIP mechanisms. Plastic flow (P), vacancy diffusion (D) and P+D together under external pressure pe are respectively the blue, green and dashed red curves. The solid red curve is plastic flow with diffusion under the total pressure Sp = pe + pL (Laplace pressure).

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6. Fig. 5. Kinetics of HIP under conditions of the combined action of plastic flow mechanisms with diffusion under the total pressure Sp = pe + pL. (a) Change in the total and partial pore compression rates. (b) Total change in pore volume (in %) and contributions to it from plastic deformation and diffusion.

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7. Fig. 6. Dependence of the annihilation time of pores of different initial diameters Dp,0 on the HIP pressure.

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8. Fig. 7. Contributions (in %) of plastic deformation mechanisms (solid curves) and diffusion (dashed curves) to the volume compression of pores of different initial diameters Dp,0 at different HIP pressures.

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9. Fig. 8. Experimental facts indicating the pore annihilation mechanisms operating in nickel-based heat-resistant alloys during HIP. (a, b) CMSX-4 alloy after 0.5 h HIP at a temperature of 1288 °C and a pressure of 103 MPa. (a) – Slip bands near the pore surface. TEM [12]. (b) – γ′-phase shell around the pore and faceting of its surface. SEM [21]. (c) – Formation of a ring-shaped raft structure of the γ′-phase around a pore in the ZhS6U-VI alloy during HIP at a temperature of 1210 °C (below the γ′-solvus) and a pressure of 150 MPa. SEM [22].

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