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 servohydraulic 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 stressstrain 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 threedimensional 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. Stressstrain curves obtained under multi-axial loading at different strain rates were used to develop and validate the elasticviscoplastic constitutive model. Excellent agreement was shown between model predictions and experimental results.