The “Open” Hopkinson Pressure Bar: Towards Addressing Force Equilibrium in Specimens with Non-uniform Deformation
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Split Hopkinson Pressure Bar
Bar (unit)
Stress wave
A theoretical relation is formulated by which the impulsive force generated at a contact part can be estimated, when an aluminum bar whose end is a truncated cone collides axially, perpendicularly against a plane wall at a comparatively low speed. In the formulation, the effect of the stress wave propagation is taken account. By comparing experimental results in which aluminum bars whose ends are of a variety of shape of truncated cones, collided against a devised sensing plate, with calculated results, the effectiveness of the theoretical relation for estimating the impulsive force which varies complexly with the shape of the contact end, impact velocity and length of the bar is confirmed.
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Stress wave
Axial symmetry
Contact force
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The impact force is measured usually by the method of Hopkinson Pressure Bar. However, the measurable time range of this method is restricted by the length of the bar. The author suggests a usefull measuring method based on the theory of propagation of longitudinal elastic stress wave. In this method, the external force, ranging from quasi-static to impact, at the end of a cylindrical bar can be estimated by measuring stresses at two suitable points on it. Also the length of the measuring bar can be shorter than in another methods.
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Split Hopkinson Pressure Bar
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The progress in experimental determination of mechanical behavior of energetic materials(EMs) at high strain rate based on Split Hopkinson Pressure Bar (SHPB) technique is reviewed.Due to the low Young′s modulus,density and wave resistance of EMs,there are some difficulties,such as stress equilibrium and mismatch of wave resistance when SHPB is employed to measure the mechanical properties of EMs.It has been proved by many researchers that to achieve accurate and reliable experimental results,conventional SHPB is no longer applicable.New techniques such as pulse shaper,piezoelectricity crystals can be added to SHPB experiments to solve the problems of stress equilibrium and mismatch of wave resistance,etc.The SHPB technique can also been used to provide experimental results for establishment of material constitutive equation and research on failure pattern or damage evolution.In the end,several future topics are proposed with 44 references.
Split Hopkinson Pressure Bar
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Stress wave
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Split Hopkinson Pressure Bar
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Split Hopkinson Pressure Bar
Stress wave
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Split Hopkinson Pressure Bar (SHPB) has become a frequently used technique for measuring uni-axial compressive stress-strain relationship of various engineering materials under high strain rates. The pulse shape generated in the incident bar is sensitive to the length of the striker bar. In this paper, a finite element simulation of a Split Hopkinson Pressure Bar is performed to estimate the effect of varying length of striker bar on the stress-strain relationship of a material. A series of striker bars with different lengths, from 200mm to 350mm, are employed to obtain the stress-strain response of AL6061-T6 in both simulation and experiment. A comparison is made between the experimental and the computed stress-strain curves. Finally the influence of variation of striker bar length on the sample's stress-strain response is presented.
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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.
Split Hopkinson Pressure Bar
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Dispersion relation
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Split Hopkinson Pressure Bar
Stress wave
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Transmission coefficient
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Bar (unit)
Split Hopkinson Pressure Bar
Stress wave
Strain gauge
Collation
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The true value of impact force, in high speed deformation test of metals, is commonly measured by the Hopkinson-bar method. But, a drawback to this method is the restriction of measurable time because of the length of the bar. One of the authors suggested construction a measuring theory for impact force acting on a bar with uniform cross sectional area, based on the theory of the propagation of longitudinal elastic stress waves. From the stresses detected at two points on the bar, two stress waves travelling in opposite directions along the bar axis are separated, and the impact force is estimated, without the restriction of the measuring time. This paper presents a new theory for measuring the impact force which acts on a bar having two different diameters. The results of the experiments clearly confirm the validity and usefulness of this theory.
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Split Hopkinson Pressure Bar
Impact
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