A model of diffusion annihilation of gas-filled spherical pores during hot isostatic pressing

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Abstract

A diffusion model of dissolution of gas-filled spherical pores in a solid during hot isostatic pressing (HIP) is proposed. It is assumed that the pore surface emits vacancies when a solid is loaded with external pressure, as a result of which the pores shrink in size. Two specific cases are considered: pores with a constant amount of insoluble gas and pores with a gas diffusively dissolving in the material surrounding the pore. In the first case, the increasing internal pressure of the gas in the pore first slows down the process of pore contraction and finally stops it completely when the internal pressure of the gas in the pore becomes equal to the sum of the externally applied HIP pressure and the Laplace pressure due to the pore surface tension. In the second case, the internal gas pressure in the pore decreases rapidly due to the dissolution of the gas in the material surrounding the pore and therefore pore contraction does not stop. When the pore reaches a sub-micron size, the pore contraction is quickly accelerated due to the increasing Laplace pressure and finally the pore annihilates.

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About the authors

A. I. Epishin

Merzhanov Institute of Structural Macrokinetics and Materials Science of the RAS

Author for correspondence.
Email: a.epishin2021@gmail.com
Russian Federation, Chernogolovka

D. S. Lisovenko

Ishlinsky Institute for Problems in Mechanics of the RAS

Email: lisovenk@ipmnet.ru
Russian Federation, Moscow

M. I. Alymov

Merzhanov Institute of Structural Macrokinetics and Materials Science of the RAS

Email: a.epishin2021@gmail.com
Russian Federation, Chernogolovka

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2. Fig. 1. Vacancy model of dissolution of gas-filled pores in Influenza: a subgranular pore of radius Rs with a central spherical pore of radius Rp, bounded by a small-angle boundary of the IUG (LAB), consisting of edge dislocations. The gypsum pressure pe acts on the subgranule, the gas in the pore is under pressure pi. Vacancies and gas atoms diffuse from the pair to the MUG. (a) Vacuum time. (b) A pore containing gas.

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3. Fig. 2. Change in the dimeter of the Dp (a) pore and the pressure inside the pi (b) pore during the gypsum process (T = 1288 °C, pe = 103 MPa) at different initial gas pressure inside the pi,0 pore in a nickel alloy. The initial pore diameter is 10 microns. The colored solid lines represent the numerical solution of the differential equation (2.16), the black dashed lines represent the analytical solution of (2.25) and (2.27). (c) The dependence of the limiting diameter Dp,min of the pore on pi,0.

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4. 3. Temperature dependence of solubility of O in solid Ni. The Seybolt data was obtained by digitizing the graph in Fig. 6 from [33].

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5. 4. Kinetics of the evolution of vacuum pores and pores with nickel-soluble gases (N and O) in the Gypsum process at a temperature of T = 1288 °C and an external pressure of pe = 103 MPa. The calculation takes into account the dissolution of gas (oxygen, nitrogen) in the metal surrounding the pore. (a) The change in gas pressure in the pores. (b) Changing the pore size. The initial pore diameter is 10 microns, and the initial gas pressure in gas–filled pores is 7.5 MPa.

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