Meticulous analysis of one-dimensional elastic-plastic wave evolution in sandwich bar system (part Ⅰ): transmitted and reflected waves for typical loading waves

The reflected and transmitted waves in split Hopkinson pressure bar (SHPB) tests provide crucial information for obtaining the stress-strain relationship of materials. Accurately analyzing the formation process and influencing mechanisms of the reflected and incident waves is a key prerequisite for precise experimental design and accurate data processing. In this paper, the propagation and evolution of one-dimensional elastic-plastic waves in the loading stages of the SHPB test are presented particularly for a sandwich bar system consisting of the incident wave, specimen, and transmitted bar. Based on the theory of elastic-plastic incremental waves and numerical simulation calculations, the propagation of elastic-plastic waves in the specimen, the transmission and reflection of elastic-plastic waves at the two interfaces, and the interaction of the resulting series of transmitted and reflected waves are quantitatively investigated. The research findings are as follows. Firstly, although the design principle of the SHPB apparatus is based on linear elastic wave theory, the elastic-plastic waves, especially the stress waves, have a major influence on the transmission and reflection at the elastic-plastic interface, while the transmission and propagation of purely elastic waves have a relatively minor effect. Secondly, when the loading interval of the incident wave has a certain width, the multiple transmission and reflection of elastic waves at the two interfaces in bar 2 attenuate the reflected wave while further strengthening the transmitted wave. This attenuation causes the peak of the reflected wave for the half-sine wave to occur earlier than at 0.5 nondimensional time. Thirdly, in contrary to the preliminary laws of elastic wave transmission and reflection at interfaces in traditional SHPB analysis, variations in the Young’s modulus and density of the specimen material have little effect on the waveform and peak intensity of the transmitted wave, regardless of whether the incident wave is rectangular, trapezoidal, or half-sine. This investigationprovides a scientific basis for the refined design of SHPB experiments and precise analysis of data.