Predicting the yield strength of a 3D printed porous material from its internal geometry

Abstract

The design of any manufactured material requires the knowledge of its limit of elasticity, called yield strength. Whilst laboratory experiments are currently necessary to do so, this study is part of initiatives which aim at deriving the strength value from simple and fast numerical simulations. The seminal work of Gurson (1977) on a simplified pore structure, a single spherical pore, provided the first theoretical relationship between a material's strength and its porosity, showing that the presence of pore space is responsible for lowering the yield strength. The complexity of new structures requires however to take explicitly into account the internal geometry, usually using direct numerical simulations. This can be particularly challenging since the yield strength of a structure is actually reached after some of its parts have already entered the plastic regime. Therefore, the mere computation of the structure's yield strength currently necessitates the modelling of the exact plastic behaviour of the skeleton's material. In this contribution, we propose to simplify the numerical modelling necessary to predict the yield strength of a porous material, by postulating that yielding is mostly controlled by the geometry of the internal structure. We show that the influence of that internal geometry on the yield can effectively be retrieved from a finite element computation implementing a simple elasto-plastic model to represent the solid phase of the porous material. We showcase the predictive power of this new method against an experimental testing, initially benchmarked for 3D-printed samples with either a unique spherical void or a grid infill, before demonstrating its applicability on a complex 3D-printed real rock microstructure, reconstructed from segmented micro-Computerised Tomography scans.