Effect of Porosity on the Stiffness of Cast Steel

Abstract

The effect of porosity on the elastic behavior of cast steel is investigated experimentally, and an approach for including porosity effects in finite element analysis (FEA) simulations is presented. Porous cast steel specimens are mechanically tested having apparent elastic moduli reduced between 17 and 61 pct. Analysis of radiographs and tomography is used to measure and reconstruct the porosity distribution in these test specimens. The porosity distribution is incorporated into FEA simulations, where elastic mechanical properties are dependent on the locally varying porosity. A relationship between elastic modulus and porosity E(ϕ) is determined by minimizing the difference between the simulations and the measurements: \( E{\text{(}}\phi {\text{)}}\;\, = \;E_{0} \;{\left( {1\, - \phi \mathord{\left/ {\vphantom {\phi {0.5}}} \right. \kern-\nulldelimiterspace} {0.5}} \right)}^{{\,2.5}} \), where E 0 is the elastic modulus of the sound material and ϕ is the porosity volume fraction. It is found that the elastic modulus decreases nonlinearly with porosity and that the steel exhibits a critical porosity level above which it loses all stiffness. This study shows that the stiffness of porous materials depends not only on the amount of porosity, but on how it is distributed and other characteristics such as pore shape and size. By modeling the effect of the porosity distribution in the simulations, the measured strain is predicted within ±10 pct agreement.