New formulations for the Hopkinson bar technique to extract a response of the constituent material in composite specimens

During stress wave propagation through a composite material, the wave veloc ities through the fibre and matrix are different because of the differences in the respective moduli and densities. The stresses and strains generated in the constituent material are accordingly related to the wave velocities . In a typical split Hopkinson pressure bar (SHPB) experiment, the composit e coupon is held in between the incidence and transmitter bars and a global response is obtained. While this provides a basis of comparison between va rious material systems, the information is not sufficient to predict failur e of the composite precisely. Knowledge of the individual responses of the fibres and the matrix is needed for accurate failure analysis. However, the existing SHPB formulations are not capable of extracting individual respon ses from a regular test set-up. In the current investigation, a new set of mathematical formulations has been derived from the momentum concept so tha t the individual strain and stress responses of the fibres and the matrix c an be estimated from regular SHPB tests. Coaxial cylindrical coupons have b een designed and fabricated for this purpose. Test results indicate that th ere is good correlation between the predicted and experimental data, especi ally at lower strain rates. Details of the mathematical derivations and exp erimental procedures are described in the paper.