Influence of the Size of Gas-Filled Pores and Gas Pressure in the Pores on the Bulk Modulus of the Material

Abstract—Currently, there is no direct method for measuring the gas pressure inside closed pores. The application of various indirect methods for determining gas pressure within сlosed pores allows for the assumption that this pressure can reach thousands of atmospheres. This work derives an equation for the bulk modulus of porous material as a function of pore pressure. The expression for the bulk modulus with solid inclusion has been taken as a basis. The study focuses on materials with porosity of 0.1 or less where all pores are closed. To establish the influence of gas pressure within the pores on the elastic moduli of the material, a relationship is introduced between the bulk moduli of the material at maximum pore pressure and in the absence of gas pressure. It is shown that the maximum pressure in porous materials varies in the range of 100–1000 MPa depending on the pore radius. It is established that the values of the bulk moduli in the absence of gas pressure within the pores and at maximum gas pressure differ by less than 1%. It is also found that increasing porosity from 0.01 to 0.1 leads to an increase in the ratio of the bulk moduli. Measuring the elastic moduli of porous bodies could be of interest in terms of measuring gas pressure in closed pores.