Construction and application of the limit strain surface for evaluating the plasticity of porous bodies

Abstract

Traditional failure criteria for solid materials are not applicable to powder materials due to the presence of porosity, which acts as a sink for dislocations, alters defect accumulation kinetics, and slows structural degradation. This study presents a comprehensive analysis of the deformation behavior of cylindrical porous iron-based samples. The deformed state on the sample surface was determined using the coordinate grid method, while displacement measurements were performed with a high-precision instrumental microscope, enabling the calculation of strain rate components at each stage up to macrocrack formation. To ensure a wide variation of the stress state index and the Nadai–Lode parameter, eight loading paths were implemented, including free upsetting under different friction conditions and deformation in steel shells. The parameters η₀ and μσ were calculated considering porosity functions, ensuring an adequate representation of void effects on the stress state. Experimental data were processed using successive approximation methods to identify key model parameters. As a result, an analytical expression for the limit deformation surface was obtained, describing the failure condition of the material. A significant finding is the confirmation of the invariance of the plasticity resource of the base material with respect to initial porosity, provided the matrix composition and structure remain unchanged. This enables the obtained surface to be considered a universal characteristic of sintered iron. The developed approach provides a reliable tool for predicting defect formation and optimizing powder metallurgy processes such as pressing, calibration, and bulk forming.