Dissertation for the Degree of Doctor of Philosophy in Engineering Science with Specialization in Solid Mechanics presented at Uppsala University in 2002

Widehammar, S. 2002. A Method for Dispersive Split Hopkinson Pressure Bar Analysis Applied to High Strain Rate Testing of Spruce Wood. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 772. 41 pp. Uppsala. ISBN 91-554-5461-5. The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique. Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed. Tests on spruce wood specimens were carried out at a high strain rate (about 10 3 s −1 )u sing the adapted SHPB technique, and for comparison at low (8 × 10 −3 s −1 ) and medium (17 s −1 ) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.