Evolution of specimen strain rate in split Hopkinson bar test

Abstract

The specimen strain rate in the split Hopkinson bar (SHB) test has been formulated based on a one-dimensional assumption. The strain rate is found to be controlled by the stress and strain of the deforming specimen, geometry (the length and diameter) of specimen, impedance of bar, and impact velocity. The specimen strain rate evolves as a result of the competition between the rate-increasing and rate-decreasing factors. Unless the two factors are balanced, the specimen strain rate generally varies (decreases or increases) with strain (specimen deformation), which is the physical origin of the varying nature of the specimen strain rate in the SHB test. According to the formulated strain rate equation, the curves of stress–strain and strain rate–strain are mutually correlated. Based on the correlation of these curves, the strain rate equation is verified through a numerical simulation and experiment. The formulated equation can be used as a tool for verifying the measured strain rate–strain curve simultaneously with the measured stress–strain curve. A practical method for predicting the specimen strain rate before carrying out the SHB test has also been presented. The method simultaneously solves the formulated strain rate equation and a reasonably estimated constitutive equation of specimen to generate the anticipated curves of strain rate–strain and stress–strain in the SHB test. An Excel® program to solve the two equations is provided. The strain rate equation also indicates that the increase in specimen stress during deformation (e.g., work hardening) plays a role in decreasing the slope of the strain rate–strain curve in the plastic regime. However, according to the strain rate equation, the slope of the strain rate–strain curve in the plastic deformation regime can be tailored by controlling the specimen diameter. Two practical methods for determining the specimen diameter to achieve a nearly constant strain rate are presented.

Minimum Required Distance of Strain Gauge from Specimen for Measuring Transmitted Signal in Split Hopkinson Pressure Bar Test

“…The extracted signals in the numerical simulation were processed through a one-dimensional analysis [7][8][9][10][11]:…”

“…To verify whether the strain signals extracted from a given axial position allows the reliable determination of the stress-strain and strain rate-strain curves, the strain rate equation in Ref. [10] was employed:…”

“…(5)) using the Excel program available in Ref. [10]. Curves S* and R* are the stress-strain and strain rate-strain curves predicted based the theory of specimen strain rate in the SHB 10 and the constitutive equation.…”

“…Stress-strain curves measured under the uniaxial stress condition at a wide range of strain rates are required for the calibration of a strain-rate-dependent constitutive equation. Pseudo-onedimensional impact systems such as the split Hopkinson bar (SHB) [7][8][9][10][11] and the direct impact bar (DIB) [12][13][14][15][16] are widely used for measuring the uniaxial stressstrain curves of various materials at strain rates of approximately 10 2 -10 4 s -1 and over 10 4 s -1 , respectively.…”

“…According to a recent study [10], the diameter of oxygenfree high thermal conductivity copper specimen needs to be far less than the bar diameter to obtain the stress-strain curve in the SHB test under a constant strain rate. Figure 1.…”