Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading : statistical analysis and size effect
Résumé
An extensive experimental programme and detailed mechanical analysis were performed to test and model the statistical response of metallic foams under complex loading conditions. Tensile tests were performed on more than 80 specimens of closed-cell aluminium foams with four different specimen sizes. These test results show a large scatter and a significant size effect especially on standard deviation. The average fracture stress and, more significantly, the corresponding scatter decrease for increasing volume sizes. An attempt is made to use the Weibull statistical analysis to interpret these variations. A Weibull modulus close to 8 is found. Compression tests were also carried out. Both mean fracture stress in tension and mean peak stress in compression and the corresponding dispersions are correctly described by a single set of Weibull parameters. The statistical model is extended to multi-axial loading conditions by introducing an effective stress measure involving both the deviatoric part of the stress tensor and its trace. One additional parameter is identified using the average shear yield stress obtained from pure shear tests and torsion tests on solid bars. It is shown that the model is able to predict the dispersion found for the shear strength. Two types of combined tension/compression–torsion loading conditions were then tested experimentally. The non-proportional loading path consists of a tension test followed by torsion, keeping the axial stress constant. In the proportional loading path, shear and axial stress follow a straight line in the stress space. The corresponding surface of average yield/fracture stress is found to be symmetric. The experimental results are in good agreement with the predictions of the statistical model. The model predicts a bell-shaped surface for the first loading path and a quasi-elliptic one for the proportional one. The scatter found in the description of this surface is also accounted for accurately by the model. A brief discussion of an extension of Beremin's micromechanical model to the statistical failure of brittle foams is presented.