Energy for Specimen Deformation in a Split Hopkinson Pressure Bar Experiment

摘要

The split Hopkinson pressure bar (SHPB) has been widely used to obtain stress-strain curves for engineering materials at high strain rates, since it was originally developed by Kolsky [1]. As an efficient device for characterizing dynamic material behavior, the SHPB has been extensively discussed by Nicholas [2], Follansbee [3], Nemat-Nasser et al. [4], Ramesh and Narsimhan [5], Gray [6], Gray and Blumenthal [7], and Chen, et al. [8] This technique has mostly been used to study the dynamic plastic flow stress of metals at strain rates between 10~(2)-10~(4) s~(-1). For the convenience of fitting constants in rate-dependent material models, it is also desired that SHPB experiments are conducted at constant strain rates. In an ideal SHPB experiment, the specimen should be in dynamic stress equilibrium such that one-dimensional stress-wave analysis may be used to reduce experimiental data. In a one-dimensional stress-wave analysis for a SHPB, the conservations of mass and momentum yield the particle velocities and stress histories at both ends of specimen such that the strain and stress in specimen can be calculated from the signals recorded by the strain gages on the incident and transmission bars. Recently, in addition to the dynamic stress-strain behavior, the absorbed energy in a deformed specimen has become a desired quantity to determine. However, the conservation of energy in a SHPB experiment was not used in the calculation of stress and strain data. Energy analysis in a SHPB experiment has not been explicitly documented. In this study, we analyzed the energy consumed in the deformation of a perfectly plastic specimen under dynamic equilibrium in a SHPB experiment. This analysis provides another point of view to understand the Hopkinson bar experiment in terms of energy in a more physical way. When an incident stress wave propagates in the bar, the mechanical energy of the wave takes the forms of the strain energy through bar deformation and the kinetic energy through bar motion. When the wave arrives at the perfectly plastic specimen, the energy to deform the specimen comes equally from the strain and the kinetic energies associated with the incident wave. In the next sections, we provide the detailed analysis of the energy transformation and balance. The results serve as an approach to calculate the energy absorption during specimen deformation in a SHPB experiment, as well as providing a better understanding of the SHPB from a new angle.