15. Characterization and Modeling of Polymeric Foam Under Multi-Axial Static and Dynamic Loading

A polymeric foam commonly used in composite sandwich structures was characterized under multi-axial loading at strain rates varying from quasi-static to dynamic. Tests were conducted under uniaxial compression, tension, pure shear and combinations of normal and shear stresses. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson pressure bar (Kolsky bar) system made of polycarbonate bars having an impedance compatible to that of the foam material. The typical compressive stress-strain behavior of the polymeric foam exhibits a linear elastic region up to a yield point, a nonlinear elastic-plastic region up to an initial peak or “critical stress” corresponding to collapse initiation of the cells, followed by strain softening up to a local minimum (plateau or saddle point stress) and finally, a strain hardening region up to densification of the foam. The characteristic stresses of the stress-strain behavior vary linearly with the logarithm of strain rate. A general three-dimensional elastic-viscoplastic model, formulated in strain space, was proposed. The model expresses the multi-axial state of stress in terms of an effective stress, incorporates strain rate effects and includes the large deformation region. Stress-strain curves obtained under multi-axial loading at different strain rates were used to develop and validate the elastic-viscoplastic constitutive model. Excellent agreement was shown between model predictions and experimental results.