Papers on Theory of (Split) Hopkinson Bar
One-Dimensional Theory
[1] Evolution of Specimen Strain Rate in Split Hopkinson Bar Test. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(13), 4667–4687, 2019.
Open-Access Publication: https://doi.org/10.1177/0954406218813386
[Paper Commentary]
This paper reveals the physical origin of the varying nature of the specimen strain rate in the SHB test, which is fundamental for exploiting the SHB as a tool to investigate the high-strain-rate behavior (properties) of materials. It is highly worthwhile for researchers to read at least the introduction of the paper, which will reward them knowledge on what were unknown (unsolved) thus far in the SHB technology and what are solved in the current paper for (1) understanding the physical origin of the varying nature of the specimen strain rate, (2) verifying the SHB test result, (3) predicting the specimen strain rate before the SHB test, (4) predicting the maximum specimen strain, (5) achieving a pseudo-constant strain rate, and (6) predicting the operatability of the SHB instrument (which is: Eq (10) >0).
[2] One-Dimensional Analyses of Striker Impact on Bar with Different General Impedance. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234 (2), 589–608, 2020.
Publisher’s site: https://doi.org/10.1177/0954406219877210
Accepted paper: Here
[Paper Commentary]
This paper analyzes the physics/mechanics of bar impact using the formulated one dimensional equations here based on (1) momentum conservation, (2) energy conservation, and (3) Newton’s second law. It explains the nature of the wave profile in the striker and bar depending on the relative general impedance. The formulated one-dimensional equations and predicted wave profiles are verified using numerical analysis (explicit finite element analysis).
Dispersion Correction & SHB Calibration
[3] Pochhammer–Chree Equation Solver for Dispersion Correction of Elastic Waves in a (Split) Hopkinson Bar. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(1), 80–87, 2022.
Open-Access Publication: https://doi.org/10.1177/0954406220980509
Up-to-date revised solver at: Zenodo (Pochhammer–Chree Equation Solver forDispersion Correction of Elastic Waves in a (Split) Hopkinson Bar - A Revised
Version. ResearchGate, 2022)
[Paper Commentary]
This paper provides the open-source program and algorithm for solving the Pochhammer-Chree equation (PCE) up to n = 20, normalized sound speed (C) of 500, and normalized frequency (F) of 25, in the Poisson’s range from 0.05 to 0.48 at intervals of 0.001. It first transforms the Bankroft version of the PCE in terms of the normalized sound speed and normalized frequency, followed by the iterative search of the solution by employing the methods of linear interpolation, extrapolation, and bisection. The solution is accurate down to nineth decimal place.
[4] Sound Speed and Poisson’s Ratio Calibration of (Split) Hopkinson Bar via Iterative Dispersion Correction of Elastic Wave. ASME Journal of Applied Mechanics, 89(6), 061007, 2022.
Open-Access Publication: https://doi.org/10.1115/1.4054107
Open-Access Manual: https://www.mdpi.com/2306-5729/7/5/55 (Manual for Calibrating Sound Speed and Poisson’s Ratio of (Split) Hopkinson Bar via
Dispersion Correction Using Excel and Matlab Templates. Data, 7(5), 55, 2022)
Open-Access Templates: https://doi.org/10.5281/zenodo.7678056 (Templates for Calibrating Sound Speed and Poisson’s Ratio of (Split) Hopkinson Bar via
Dispersion Correction of Elastic Wave. Zenodo, 2022).
[Paper Commentary]
The first contribution of this paper is that it provides the method and tool (open-source program) for calibrating the sound speed and Poisson’s ratio of the bar in very high precision (down to several decimal places). It resorts to the iterative dispersion of the elastic wave in time domain.
The second contribution of this paper is that it, for the first time, accurately carried out dispersion correction using the PCE solver instead of using the approximate PCE solution in previous studies on dispersion correction. One can suitably use the provided tool (open-source freeware) to carry out dispersion correction of their own elastic wave profile.
The final, but probably the most important, contribution is that it, for the first time, experimentally verified the combimed theory of Pochhammer-Chree and Fourier on a quantitative base; the combined theory was used first time by Davies.
[5] Calibration of Bar Properties, Measured Strain, and Impact Velocity in Bar Impact Test. Mechanics of Advanced Materials and Structures, Online First, 2023.
Open-Access Publication: https://doi.org/10.1080/15376494.2023.2224797
Open-Access Manual: https://doi.org/10.3390/data8030054 (Manual of GUI Program Governing ABAQUS Simulations of Bar Impact Test for Calibrating Bar
Properties, Measured Strain, and Impact Velocity. Data, 8(3), 54, 2023)
Open-Access Templates: https://doi.org/10.5281/zenodo.7652652 (GUI Program Governing ABAQUS Simulations of Bar Impact Test for Calibrating Bar
Properties, Measured Strain, and Impact Velocity, Zenodo 2023)
[Paper Commentary]
This paper provides the method and tool (GUI program) for calibrating the bar elastic modulus and Poisson’s ratio in the bar-impact test by employing the separately measured bar density. It simultaneously calibrates the measured bar strain with reference to the impact velocity.
The contribution of this paper is that it proves via explicit finite element that the sound speed obtained in the above paper (paper [4]) can be used to obtain the elastic modulus of the bar by employing the measured bar density and 1D relationship: E=(density) x (sound speed)^2.
As the rsult of applying the presented calibration methodology, this paper discloses that the sound speed and elastic modulus values of the bar introduced to the author’s lab under the premise of the maraging steel C350 specification are different from the literature values by as high as 17.6% and 8.5%, respectively. Whatever is the reason for such a discrepancy, the observed notable discrepancy indicates the necessity of bar property calibration. As far as the bar is utilized within its elastic limit, the necessity of re-calibrations of the bar properties is not high but it is advisable to calibrate the bar properties at least once after installation using reliable methods such as the ones presented here.
Fundamentals of (Split) Hopkinson Bar
[6] Understanding the Anomalously Long Duration Time of the Transmitted Pulse from a Soft Specimen in a Kolsky Bar Experiment. International Journal of Precision Engineering and Manufacturing, 17, 203–208 (2016).
Accepted paper: Here
[7] Design Guidelines for the Striker and Transfer Flange of a Split Hopkinson Tension Bar and the Origin of Spurious Waves. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(1), 137–151, 2020.
Open-Access Publication: https://doi.org/10.1177/0954406219869984
Accepted paper: Here
[8] Stress Transfer Mechanism of Flange in Split Hopkinson Tension Bar. Applied Sciences 10(21), 7601, 2020.
Open-Access Publication: http://https://doi.org/10.3390/app10217601
[9] Minimum Required Distance of Strain Gauge from Specimen for Measuring Transmitted Signal in Split Hopkinson Pressure Bar Test.MATEC Web of Conferences 308, 04005, 2020.
Open-Access Publication: Here
[10] A Numerical Verification of the Reliability of a Split Hopkinson Pressure Bar with a Total Bar Length of 3 m and a Diameter of 1 Inch. Applied Mechanics and Materials (Volumes 799–800) 681–684, 2015.
Quick paper delivery upon request via ResearchGate
[11] Numerical Investigation into the Stress Wave Transmitting Characteristics of Threads in the Split Hopkinson Tensile Bar Test. International Journal of Impact Engineering, 109 (11), 253–263, 2017.
Quick paper delivery upon request via ResearchGate
Related Papers: Friction Compensation
[12] Numerical Verification of the Schroeder-Webster Surface Types and Friction Compensation Models for a Metallic Specimen in Axisymmetric Compression Test. ASME Journal of Tribology, 141(10), 101401, 2019.
Accepted paper: Here
[13] Determination of the Flow Stress–Strain Curve of Aluminum Alloy and Tantalum Using the Compressive Load–Displacement Curve of a Hat-Type Specimen. ASME Journal of Applied Mechanics, 86(3), 031012 (2019).
Quick paper delivery upon request via ResearchGate
[14] A Design of a Phenomenological Friction-Compensation Model via Numerical Experiment for The Compressive Flow Stress–Strain Curve of Copper (in Korean), Korean J. Computational Design Engineering, 2019.
Open-Access Publication: Here
Related Papers: Constitutive Model
[15] Flow Stress Description Characteristics of Some Constitutive Models at Wide Strain Rates and Temperatures. Technologies, 10(2), 52, 2022.
Open-Access Publication: https://doi.org/10.3390/technologies10020052
[16] A Phenomenological Constitutive Model to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes. ASME Journal of Engineering Materials and Technology, 132, 021009, 2010. https://doi.org/10.1115/1.4000225
[17] Comparison of Plasticity Models for Tantalum and a Modification of the PTW Model for Wide Ranges of Strain, Strain Rate, and Temperature. International Journal of Impact Engineering 36(5), 746–753, 2009.
Quick paper delivery upon request via ResearchGate