Maximum Gas Pressure in Pores

An analytical expression for estimating the maximum gas pressure within a closed pore is derived. The Lamé solution for the stress–strain state of the material around a spherical pore in an infinite medium is used as the basis. Pores at the sintering temperature of nickel and iron powders are considered as an example. It is assumed that gases in the pores are not dissolved in the matrix of the base material. The formula calculating the maximum pressure within a pore includes the theory of maximum distortion energy and the Laplace pressure, which also contributes to the stress–strain state of the material. An isothermal case without external pressure is described. The dependence of the maximum pore pressure on the pore radius is shown. The parameters of the material at temperatures close to their sintering point are used in the calculations. The maximum allowable gas pressure within closed pores is demonstrated to depend on the pore size. The maximum allowable gas pressure within a closed pore can reach high values up to some thousands of atmospheres as the pore size is reduced.