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.