Identification of the crushing behavior of brittle foam: From indentation to oedometric tests

Compaction of the core of plasterboard is one of the limiting phenomena for its mechanical performance. This mechanism is studied herein in an indentation test. A cylinder made of foamed gypsum is indented in situ in an X-ray lab tomograph with a sphere of millimeter radius. The reported experiments show that foamed plaster displays a sharp transition between an undamaged state (with linear elastic behavior) and a compacted state with collapsed porosity under the indenter. Tomographic acquisitions of the sample under load associated with a global version of Digital Volume Correlation allow displacement fields to be measured at different load levels. However, because of the heterogeneous nature of the indentation test, a fine spatial resolution of the displacement fields is required to measure the strains at the crushing limit. A dedicated procedure exploiting computed displacement fields within the digital volume correlation procedure is utilized. It allows for the quantification of stress fields that are post-processed to identify the crushing criterion. It is shown that this analysis is very consistent with more macroscopic oedometric tests. Last, predictions of a Mohr-Coulomb model are compared with macroscopic and microscopic data. It is shown that despite the fact that this model reproduces very well the load-displacement response of the indentation test, a poorer prediction of the experimental crushed zone is observed. In particular, the transition between compacted plaster and its pristine state is not captured by the model, which predicts a very progressive transition rather than an abrupt one. The same conclusions are drawn for a crushable foam model when compared with experimental evidence of an in situ oedometric test.