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Split Hopkinson pressure bar

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Project Report on

STRESS WAVE PROPAGATION IN SPLIT HOPKINSON PRESSURE BAR TEST

Submitted by: ABHISHEK SARASWAT 2009CE10271 Under the Guidance of: DR. TANUSREE CHAKRABORTY DR. VASANT MATSAGARIn partial fulfillment of the requirements of the degree of Bachelor of Technology to the Department of Civil Engineering, Indian Institute of Technology DelhiNov 2012

CERTIFICATEI do certify that this report explains the work carried out by me in the courses CED411 Project-Part 1, under the overall supervision of Dr. Tanusree Chakraborty and Dr. Vasant Matsagar. The contents of the report including text, figures, tables, computer programs, etc. have not been reproduced from other sources such as books, journals, reports, manuals, websites, etc. Wherever limited reproduction from another source had been made the source had been duly acknowledged at that point and also listed in the References.

ABHISHEK SARASWAT Date: 19th Nov, 2012

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CERTIFICATE

This is to certify that the report submitted by Mr. Abhishek Saraswat describes the work carried out by him in the courses CED-411 Project Part 1, under my overall supervision.

Dr Tanusree Chakraborty Supervisor

Dr. Vasant Matasagar Co-Supervisor

Date: 19th Nov, 2012

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ACKNOWLEDGEMENTI would like to express my sincere thanks & gratitude to Dr. Abhishek Saraswat for his continuous and unfailing support, guidance and help, which have been invaluable during the course of this project. His knowledge, insight and constant motivation at each step of the project has been instrumental in its completion.

Abhishek Saraswat

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ABSTRACTThe split Hopkinson bar test is the most commonly used method for determining material properties at high rates of strain. The theory governing the specifics of Hopkinson bar testing has been around for decades. It has only been the last decade or so, however, that significant data processing advancements have been made. It is the intent of this thesis to offer the insight of its author towards new advancements.

The split Hopkinson bar apparatus consists of two long slender bars that sandwich a short cylindrical specimen between them. By striking the end of a bar, a compressive stress wave is generated that immediately begins to traverse towards the specimen. Upon arrival at the specimen, the wave partially reflects back towards the impact end. The remainder of the wave transmits through the specimen and into the second bar, causing irreversible plastic deformation in the specimen. It is shown that the reflected and transmitted waves are proportional to the specimens strain rate and stress, respectively. Specimen strain can be determined by integrating the strain rate. By monitoring the strains in the two bars, specimen stress-strain properties can be calculated.

Several factors influence the accuracy of the results, including longitudinal wave dispersion, impedance mismatch of the bars with the specimens, and transducer properties, among others. A particular area of advancement is a new technique to determine the bars dispersive nature, and hence reducing the distorting effect .

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TABLE OF CONTENTSPAGE CERTIFICATES..i ACKNOWLEDGMENT.iii ABSTRACT.iv TABLE OF CONTENTS ....v LIST OF FIGURES vi CHAPTER 1: OVERVIEW OF SPLIT HOPKINSON BAR 1.1 Introduction.......2 1.2 Fundamentals of Hopkinson Bar Testing.. ...2 1.3 Complications With Testing And Data Processing....5 1.4 Areas Of Advancement......6 1.5 Topics Covered in Thesis ......7 CHAPTER 2: BACKGROUND AND LITERATURE REVIEW8 2.1 Introduction ...8 2.2 The Hopkinson Bar A Chronological Development...8 2.3 The Split Hopkinson Pressure Bar Additional Information...12 CHAPTER 3: SPLIT HOPKINSON BAR THEORY ...14 3.1 Introduction15 3.2 Axial Vibration of Bars......15 3.3 Longitudinal Wave Propagation In Bars......18 3.4 Specimen Stress..19 CHAPTER 4: CONCLUSIONS AND FUTURE WORK ..25 REFERENCES ...26

CHAPTER 1 OVERVIEW OF SPLIT HOPKINSON BAR TEST

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1.1

INTRODUCTION

The design of structures is based almost solely on tabulated material data, usually in the form of a stress-strain diagram. Optimal designs require accurate and complete tables for materials tested under a variety of conditions. The majority of available tabulated material properties were gathered by deforming the specimen very slowly. According to Shigley & Mitchell [1], the average strain rate used in obtaining the stress-strain diagram is about 0.001 in-s/in or less. It has been known for years that materials are stronger at higher rates of strain, such as caused by an impact. The behavior of structures to impacts has been of interest to many engineers for purposes of design as well as developing constitutive models of the materials tested.

The split Hopkinson bar apparatus has quickly become the most widely used device to test materials at high strain rates. Though integral to the research presented in this thesis, the purpose of this thesis is not to test materials at high strain rates. Rather it is to introduce improvements to the current testing techniques and data processing currently employed in split Hopkinson bar testing.

Over the past two years, the Naval Surface Warfare Center Dahlgren Division along with Virginia Tech has been building up a program for split Hopkinson bar testing. The facility is now equipped to perform compression tests on a wide range of materials while employing the latest in data acquisition and data processing techniques. The author would not be at all surprised to see NSWCDDs Hopkinson bar program become a leader in high strain rate testing.

1.2

FUNDAMENTALS OF HOPKINSON BAR TESTING

The split Hopkinson bar test is the most commonly used method for determining material properties at high rates of strain. Significant advancements implemented from the areas of testing techniques, numerical methods, and signal processing have2

improved the accuracy and repeatability of high strain rate testing. Constant strain rate tests can be performed at strain rates approaching 10 4 s-1 relatively easily.

In the split Hopkinson bar test, a short cylindrical specimen is sandwiched between two long elastic bars, as shown in figure 1.1. The bars are generally made of a high strength maraging steel with diameters less than 0.75 and a length near five feet.

Specimen Striker Bar Input Bar Output Bar

Strain gage A

Strain gage B

Figure 1.1 Schematic of Split Hopkinson bar Apparatus Ballpark specimen dimensions are diameter and length. The ends of the

pressure bars and specimen are machined flat to enforce prescribed boundary conditions. Typically a projectile (striker bar) is fired into the end of the input bar generating a compressive stress pulse. Immediately following impact, this pulse

travels along the bar towards the input bar-specimen interface at which the pulse is partially reflected into the input bar and partially transmitted through the specimen and into the output bar. The reflected pulse is reflected as a wave in tension, whereas the transmitted pulse remains in compression. The strain histories in the two pressure bars are recorded by strain gages A and B.

So long as the pressures in the bars remain under their elastic limits, specimen stress, strain, and strain rate may be calculated from the recorded strain histories. Under certain deformation conditions, qualified later, only two important strain pulses need be identified. These are the reflected pulse and the pulse transmitted through the

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specimen. Kolsky [2] developed the following relation for calculating the specimen stress.o s (t ) = E A A T (t )

(1.1)

where E is the output pressure bars elastic modulus, Ao is the output bars cross sectional area, A is the samples cross sectional area, and T(t) is the transmitted strain history. Specimen strain rate may be calculated from d s ( t ) 2C = o R (t ) dt L

(1.2)

where R(t) is the reflected input bar strain history, L is the specimen length prior to impact, and Co is the infinite wavelength wave velocity in the input pressure bar, calculated from elementary vibrations as

Co =

E

(1.3)

where E and are the bars elastic modulus and density, respectively. Equation 1.2 can be integrated in time to yield the specimens strain, given by Equation 1.4.t

s (t ) =

2Co R (t )dt L 0

(1.4)

Though these equations have been around since the late 40s, it has only been in the last decade or so that significant data processing advancements have been possible, mainly due to high-speed computers. FFT analysis and other numerical procedures can be completed quickly on a PC based machine.

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1.3

COMPLICATIONS WITH TESTING AND DATA PROCESSING

As discussed in the previous section, the pulses of concern are the time dependent transmitted and reflected pulses. For a homogeneously deforming sample, the

amplitudes of these pulses are proportional to specimen strain rate and stress, respectively. Recall that specimen strain is simply calculated by integrating the strain rate. Though generating stress-time and strain-time diagrams is quite easy, they are not very useful. Therefore these time dependent pulses must somehow be combined to generate a dynamic stress-strain diagram, quite familiar to the engineer. One may suggest simply aligning the first temporal point of each diagram, second point, and so on. This is exactly correct, but determining the first point of each pulse is not a simple or precise task. Since the impact events are on the order of a few hundred

microseconds, alignment of the stress and strain pulses becomes difficult. To the authors knowledge other investigat