Study On The Yield And Failure Behaviors Of Metal Foam Under Multi-axial Loading Based On Meso-structure Models

Metallic foams offer excellent performance in terms of light weight,specific stiffness and the efficient absorption of energy.They hold particular promise for market penetration in applications,such as aviation and space,transportation,shock and energy absorbers,etc.In practical applications,metallic foams are usually subjected to multiaxial loadings and occurs yield and failure behaviors.Hence,correct characterizations of both the yield surface and the failure surface of foams are essential and meaningful.However,owing to both the lack of abundant experimental data on metal foams under triaxial loadings especially for tensile triaxial loadings,and the scatter of experimental data,characterization of the yield surface of metallic foam is controversial.Moreover,failure behaviors of foams under tensile triaxial loadings have not been reported.In this paper,we explored a numerical method to study the yield and failure properties of closed-cell metallic foam under triaxial loadings using three-dimensional(3D)Voronoi mesostructures.Three normal stresses(including tension and compression)were proportionally applied on the cubic Voronoi foam to conduct numerical simulation experiments.The properties of yield surfaces,normalized yield surfaces,failure surfaces and normalized failure surfaces which were all affected by parameters such as relative density,shape irregularity of mesostructure and the thickness distribution of the cell-wall were analyzed and discussed in detail.The main studying contents of this paper are as followings:(1)The finite-element model of foams based on Voronoi mesostructure was established and verified.The mechanical properties of matrix were calibrated based on uniaxial experiments of closed-cell aluminum foam.We also explored the effects of several nondimensional parameters on the accuracy and efficiency of the nonlinear finite-element simulation of metallic foams based on three-dimensional(3D)Voronoi mesostructures,and three optimized nondimensional parameters were recommended.The recommended parameters constitute a good reference for numerical simulation of metallic foams in predicting mechanical behaviors.(2)The nondimensional plastic dissipation yield criterion is recommended,which not only covers the effects of all triaxial loadings but also is compatible with those in unidirectional loading(0.2% plastic strain).This criterion is more reasonable than that of the von Mises equivalent stress or the mean stress to determine the initial yield state of foams under complex loadings.(3)The properties of yield surface of metallic foam were analyzed based on numerical simulation experimental data under triaxial proportional loadings.Owing to the asymmetry of yield surface in tensile and compressive state,the yield surfaces should be normalized by compressive and tensile uniaxial yield stresses,respectively,which leads to the conclusion that normalized yield surfaces are almost independent of relative density.The properties of both yield surfaces and normalized yield surfaces affected by parameters such as relative density,shape irregularity and thickness distribution of the cell-wall were discussed in detail.(4)The properties of failure surface of metallic foam were analyzed.We proposed the peak stress failure criterion to determine the failure state of foams under triaxial loadings.The properties of failure surface in the plane of von Mises equivalent stress and mean stress affected by parameters such as relative density,shape irregularity and thickness distribution of the cellwall were analyzed and discussed in detail.In addition,effects of stress triaxiality on the equivalent plastic strain in failure state were discussed.