COMPLIANCE CALIBRATION AND SMALL STRAIN MEASUREMENT FOR THE COMPRESSION SPLIT HOPKINSON PRESSURE BAR

摘要

A critical review by the authors [1] has identified several fundamental questions associated with the split Hopkinson pressure bar (SHPB) experimental technique, the validity of the assumptions of its classic 1-D theory, and the limits of its application. Several important issues have been considered in the present study. In the fundamental assumptions of classic 1-D Hopkinson bar theory, the stress wave propagation in the bars is assumed to be one-dimensional, which is not true in the vicinity of the bar-specimen interfaces. The physical presence of material discontinuity at the incident bar-specimen (IB-S) and specimen-transmitter bar (S-TB) interfaces produces wave reflections and wave scattering, which in turn induces the higher order vibration modes. The net effect is that small strain measurement using the Hopkinson bar experiment becomes challenging. A compliance calibration methodology for SHPB has been proposed to minimize these errors which provided better accuracy in the small strain regime. Stress equilibrium is assumed at the IB-S and S-TB interfaces in the classic 1-D theory, and thus the stress wave propagation effect in the specimen is neglected. Since this assumption is not true in the first few reverberations in the specimen, it has been known that the data in this time window should be used with care. Lack of stress equilibrium is also cited as a reason for inaccurate elastic strain measurements in SHPB testing. It has been identified that the compliance of SHPB is the root cause for inaccuracy in small strain measurement. Since the stress wave equilibrium in the specimen is a function of the material properties of the specimen, this issue is resolved by considering stress wave propagation in the specimen and denoting the Hopkinson bar data as 'time-averaged non-equilibrium dynamic behavior of material.' The new analysis provides a strain correction factor, which in conjunction with compliance calibration technique provides the correct elastic modulus of an equal diameter specimen. An experimental methodology is developed for the determination of rate dependent elastic modulus of materials.