A-19995 GE ILAAL ELECYTRICCCOZA CIN4C INAT1 ON AIRCRAFT ENGINE BU--ETC F/0 11/6MATERIAL CmAACTEI IIITO0. PART A- MECMANZCAL PROPERTIES OF TWO-ETC113MAY 82 S A EMERY F33615-7?-C-5221

UCASSIFIED tuuR-Ta-7q-g9A AFVAL-T1S.SZ-1O42-VOL-1 NL

*,alumu oil.11-I'.*MENNENflflflflK

APWAL-TR-82-2042

Volume I

MATERIAL CHARACTERIZATION, PART A MECHANICAL PROPERTIES OFTWO METALS AT SEVERAL STRAIN RATES

O S. A. EMERY

University of Dayton Research InstituteDayton, Ohio 45469

May 1982

Interim Report for period I October 1977 - 30 November 1979

Approved for public release; distribution unlimited.

Q.L AERO PROPULSION LAOATR -ETCAIR FORCE WRIGHT AERONAUTICAL LABORATOES A OCT 7 1982AIR FORCE SYSTEM COMMAND

Lpj WRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433

82 1A

82 10 07 0 03"

N&IXCE

When Government drawings, specifications, or other data are used for anypurpooe" other than in connection with a definitely related Government procure-mnnt operation, the United States Governm Lnt thereby incurs no responsibilitynor any obligation whatsoever; and the fact that the government may have formu-lated, furnished, or in any way supplied the said drawings, specifications, orother data, is not to be regarded b y i,pZication or otherwise as in any mannerlicensing the holder or any other percn or corporation, or conveying any rightsor permission to manufacture, uce, or sell any patented invention that may inany way be related thereto.

This report has been reviewed by the Office of Public Affairs (ASD/PA) andis reZeasable to the NationaZ Technical Information Service (NTIS). At 1T47S, itwill be available to the general public, including foreign nations.

This technical report has been reviewed and is approved for pubZicatio, .

SANDRA K. DRAKE ISAK J."GERSHONProject Engineer Technical Area Manager,

Propulsion Mechanical Design

FOR THE COMANDER

J. NI PMAN, MAJ, USAFDeputy Director, Turbine Engine Division

"Zf your address has changed, if You wish to be removed from our mailing list,or if the addressee in no longer rployed by your organization, please notifyA WPAPB 011 45433 to Welp us maintain a ourcnt mailing list."

Copies of this report should not be returnd 10Zsco return in required by ocurityoosidcrations, oontractual obtigationn, or notioe on a opccifio doawnent.

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READ INSTRUCTIONSREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

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AFWAL-TR-82-2042 Vol I 3-4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

MATERIAL CHARACTERIZATION, PART A Technical ReprtMECHANICAL PROPERTIES OF TWO METALS AT IOctober 1977 )ONovernber 979SEVERAL STRAIN RATES 6. PERFORMING ORG. REPORT NUMBER

UDR-TR-79-987. AUTHOR(&) S. CONTRACT OR GRANT NUMBER(&)

S. A. Emery 200-4BA-I4K47844

9. PERFORMING ORGANIZATION NAME AND ADDRESS I0. PROGRAM ELEMENT. PROJECT. TASKAREA & WORK UNIT NUMBERS

University of Dayton Research Institute

300 College Park Ave. 62203F, 3066, 12, 33Dayton, Ohio 45469

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

General Electric Company May 1982Evendale Plant - Aircraft Engine Group 13. NUMBER OF PAGES

Evendale, OH 45215 6714. MONITORING AGENCY NAME & ADDRESS(It different from Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified15I. DECL ASSI FICATION/ DOWNGRADING

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IS. SUPPLEMENTARY NOTES 4

I. KEY WORDS (Continue on reverse side it neceesary and Identfy by block number)

Stainless steel, titanium, foreign object damage, mechanicalproperties, low strain rate, intermediate strain rates, anddynamic strain rates.

20. AISTRACT (Continue on reverse side If neceeeary and Identify by block number)- This report describes mechanical property data collected in

support of a fan blade analysis model. The development of theblade model is part of a foreign object damage (FOD) study ofjet engine fan blades. Use of the properties in the model allowsone to evaluate potential fan blade materials. Part A of thisreport contains a discussion of the mechanical property testsconducted on two metallic materials: 410 stainless steel and8A1-lMo-lv titanium.L These two materials were selected because

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of-hteir use in the J-79 blade and the F-101 blade respective-ly.-3 Part B of the report contains a discussion of mechanicalproperty tests conducted on the two composite components ofa hybrid composite blade: boron/2024 aluminum and stainlesssteel wire mesh. These two composites are used in the hybridcomposite APSI blade.

Static, quasi-static and dynamic tensile tests were con-ducted on the metallic materials because (1) studies indicatethat metallic mechanical properties exhibit strain rate depen-dence and (2) tests conducted on full scale blade_, show thatvarious locations on the fan blades load at different rates.The mechanical properties mecsured include Young's Modulus(when obtainable), Poisson's ratio (when obtainable), theyield strength, the ultimate strength, and the ultimatestrain. The density of the materials was also measured

UNCLASSIFIED8 SSCUftITY CLASSIICATION OF THI2 PA@IEfWo ba n te

FOREWORD

This repor- describes a contractual work effort conducted

for the General Electric Company, Aircraft Engine Group under

Purchase Order No. 200-FBA-14K-47844 which is a subcontract

of F33615-77-C-5221.

This report covers work conducted during the period of

October 1977 to November 1979 and is part of Task IV-A.

The GE Program Manager was Mr. Joe McKenzie and the

Principal Investigator was Mr. Al Storace. The work reported

herein was performed under the direction of Susan A. Emery,

Experimental and Applied Mechanics Division, University of

Dayton Research Institute.

Technical support was provided by Mr. E. C. Klein. Program

management for the University was provided by Mr. Robert Bertke.

This report covers work conducted for project 3066, task 12,

entitled Foreign Object Impact Design Criteria. The contract

was sponsored by the Aero Propulsion Laboratory, Air Force Systems

Command, Wright-Patterson AFB, Ohio 45433 under the direction of

Sandra K. Drake (AFWAL/POTA), Project Engineer.

~Gpk

iii

.'T

TABLE OF CONTENTS

SECTION PAGE

I INTRODUCTION 1

II EXPERIMENTAL PROCEDURES 3

2.1 LOW AND INTERMEDIATE STRAIN RATE TESTS 3

2.1.1 Test Specimen and SpecimenInstrumentation 4

2.1.2 Test Procedures and Test System 4

2.1.2.1 Test System 4

2.1.2.2 Test Procedure 7

2.2 HIGH STRAIN RATE TESTS 7

2.2.1 Experimental Apparatus 7

2.2.2 Instrumen'..ation 9

2.2.3 Test Procedures and Mechanisms 11

III ANALYSIS 15

3.1 LOW AND INTERMEDIATE STRAIN RATE TESTS 15

3.2 HIGH STRAIN RATE TESTS 17

IV RESULTS AND DISCUSSION 19

REFERENCES 27

APPENDIX A: LOW AND INTERMEDIATE STRAIN RATECURVES AND DIGITAL DATA 28

APPENDIX B: HIGH STRAIN RATE CURVES ANDDIGITAL DATA 57

Iv

LIST OF ILLUSTRATIONS

FIGURE PAGE

I Specimen for Low and Intermediate StrainRate Tests. 5

2 Location of Measurement Instrumentation on theLow and Intermediate Strain Rate Specimens. 6

3 Schematic of Apparatus and Instrumentationfor High Strain Rate Tests. 8

4 Specimen for High Strain Rate Tests. 10

5 Typical Oscilloscope Traces. 12

6 Lagrangian Displacement - Time Plot for HighStrain Rate Tests. 13

7 Young's Modulus VS. Strain Rate. 23

8 Yield Stress VS. Strain Rate. 24

9 Ultimate Stress VS. Strain Rate. 25

10 Ultimate Strain VS. Strain Rate. 26

vi.

LIST OF TABLES

TABLE PAGE

1 STRAIN RATES OF METALLIC MATERIAL CHARACTERIZA-TION TESTS 3

2 MECHANICAL PROPERTIES OBTAINED FOR 8A1-lMo-IVTITANIUM 20

3 MECHANICAL PROPERTIES OBTAINED FOR 410 STAIN-LESS STEEL 21

4 DENSITY 22

vil

I _ i

I I I

SECTION I

INTRODUCTION

The material characterization tests discussed in this report

are part of a foreign object damage (FOD) study of jet engine fan

blades. The tests constitute a portion of the gross structural

damage subtask of that study. The FOD study is designed to pro-

vide two resources necessary for the successful development of

FOD resistant fan blades: (1) an analysis capability for pre-

dicting jet engine response to FOD impacts and (2) an under-standing of the mechanisms of FOD failures. The fan blade

analytical model uses inputs such as mechanical property data

(of the material under consideration) and impact loads (repre-

sentative of ice balls, ice spears, or small birds) to

predict the fan blade response to the foreign object damage

impacts. The model allows considerable evaluation of the blade

design and material prior to the manufacturinc and testing of

a full stage of blades. This eliminates many costly experiments

that have been necessary in the past.

The material characterization tests provide mechanical

properties for use in the blade model discussed above. The

materials tested include two metals, 410 stainless steel and

8A-lMo-lV titanium (used in the J-79 blade and F-101 blade,

respectively) and two composites, boron/2024 aluminum and

stainless steel wire mesh (used in the hybrid composite APSI

blade). Part A of this report contains the description of the

material chracterization tests on the metals. Part B contains

the discussion of the material chracterization tests on the

composite materials.

The mechanical properties of metals usually exhibit some

strain rate dependence.(1,2,3) In addition, experiments have

shown that the FOD impacts load various sections of the blades

at different rates. For these reasons, tensile tests were3

conducted on the metals at strain rates ranging from 10 to i1

about 10 3strain/second. The quasi-static and intermediate rate

tests (10- to 1 strain/second), conducted with an MTS closed-

loop hydraulic system, provide the following elastic and plastic

region parameters: Young's modulus, Poisson's ratio (in the

elastic region), 0.2 percent offset yield stress, ultimate stress,

and ultimate strain. The dynamic tests (500 to 700 strain/second),

conducted on a split-Hopkinson bar apparatus, provide only the

plastic region parameters: yield stress, ultimate stress, and

ultimate strain. The mechanical properties are summarized in

this report as plots of the various parameters versus strain

rate.

2

SECTION II

EXPERIMENTAL PROCEDURES

Tensile tests conducted at the strain rates shown in

Table 1 provide the desired mechanical property data. This

range of rates encompasses the range of strain rates measured

at select locations on the full scale blade tests, 12-370 strain/

second. (The full scale blade tests were conducted as part of

the gross structural damage subtask IV-A but reported with similar

tests in the Task VI report.) The quasi-static and intermediate

rate tests (10- to 1 strain/second) were run on an MTS electrchydraulic closed-loop testing machine. They require different

specimens and procedures than do the dynamic tests, which were

run on the split-Hopkinson bar apparatus. Consequently, the

two types of tests are described separately below.

TABLE 1

STRAIN RATES OF METALLIC MATERIALCHARACTERI ZATION TESTS

Material I Strain Rates (strain/second)

18A1-lMo-lV Titanium 10, 101 1, 500

403 Stainless Steel 10-, 10l, 1, 700

2.1 LOW AND INTERMEDIATE STRAIN RATE TESTS

The information obtained from the low and intermediate

strain rate tests include two elastic parameters, Young' s

modulus and Poisson's ratio, and three plastic parameters, the

yield stress, the ultimate stress, and the ultimate strain. The

following paragraphs describe the specimens used and how they

were instrumented and tested. The full true stress-true straincurves appear in Appendix A.

3

2.1.1 Test Specimen and Specimen Instrumentation

The specimens were made from bar stock which had

been worked the same amount as the finished blades. The speci-

men is illustrated in Figure 1. Its dimensions were per ASTM

standard E8-69 4~ )Three specimens of each material were tested

at each rate with one exception. Only one specimen of the

titanium was tested at 1 strain/second.

Figure 2 shows the location of measurement instru-

mentation placed on the specimens. The extensometer supplied

information for obtaining the entire stress-strain from test

start to speci.men failure. The high resistance foil strain gage

placed in the longitudinal direction (the same direction as

the applied load) provided high resolution measurements for

the parameters in the elastic region and at yield. The strain

gage in the transverse direction (to the applied load) supplied

measurements for the calculation of Poisson's ratio. The trans-

verse strain gages were applied to only one specimen of each

material at each strain rate. The data reduction equations

appear in the analysis section of this report.

2.1.2 Test Procedures and Test System

The following paragraphs contain a ;',rief descrcip-

tion of the test system and test procedures used for the low

and intermediate strain rate tests.

2.1.2.1 Test System

The low and intermediate strain rate

tests were conducted using the University's MTS electrohydraulic

closed-loop testing system. This closed-loop ttst machine can

be programmed in load, strain, or displacement control. The

machine can produce displacement rates that range from less than

0.05 in/min. to 400 in/min. The signal conditioner used with

the strain gage was a Honeywell 218 Bridge Amplifier. Included

in the test system is an X-Y recorder and a multichannel

transient recorder. An additional two pen X-Y recorder was

used for these tests.

4

1.00 inches

4 inches0.250 + 0.005

inchesdiameter

0.1875 R

Figure 1. Specimen for Low and Intermediate Strain

Rate Tests.

5

IlL i O W

-- ,,. o . L , _ _ W - _ . - - . . . . . .. .• -

Specimen instrumentedFoil for axial strain andStrain I Extensometer displacementGage measurement

Specimen instrumented! for axial strain and

Foil Extensometer displacement measure-Strain ments and transverseGage JujI strain measurements

Figure 2. Location of Measurement Instrumentation on the Lowand Intermediate Strain Rate Specimens.

6

2.1.2.2 Test Procedure

After tightening the strain gaged

specimen in the grips, the extensometer was attached and adjusted

to give the proper output voltage for the desired gage length.

With the test machine in the load control mode a linear ramp

function loaded the specimen to failure. Load and displacement

were recorded directly on the qystem X-Y recorder for the lowest

strain rate tests (10- strain/second). Load and strain were

recorded directly on the additional X-Y recorder. For the

higher strain rate tests (10-1 and 1 strain/second) the three

parameters, load, strain, and displacement were recorded on

three channels of the transient recorder for playback at slower

speeds into the X-Y recorder.

2.2 HIGH STRAIN RATE TESTS

Mechanical properties obtained from the high strain rate

tests include the following three plastic parameters: the yield

stress, the ultimate stress, and the ultimate strain. Plastic

region true stress-true strain curves were also acquired fromthe tests. (Elastic properties cannot be obtained from these

tests because the pressure waves in the Hopkinson bar are not

considered to be in equilibrium in the elastic region). The

method (and apparatus) used is the same as that used in a study

of the high strain rate tensile mechanical properties study of

beryllium.~5 The subsequent paragraphs provide a detailed

description of the experimental apparatus, the instrumentation,

and the test procedures and mechanisms. The analysis section

of this report contains the brief explanation of the data

reduction process. The results appear in Appendix B.

2.2.1 Experimental Apparatus

A schematic of the split Hopkinson bar apparatus

and the associated instrumentation appears in Figure 3. Three

parts of the apparatus are of major interest: two Hopkinson

pressure bars (bar No. 1 and bar No. 2) and the striker bar.

7

z4J

4 0'

(I4)

4r 4.LE

0~ 4-4

z 0U0

4)

CC)

zz

c2

4c 4-4

II1

Bar No. 1 must be twice the length of bar No. 2 and the striker

bar must be shorter than bar No. 2. For these experiments the

bars are 0.06, 0.15, and 0.30 m lengths of 12.7 mm diameter

AISI 4130 steel. They are mounted and aligned on a rigid base.

Detail "A" of Figure 3 shows an enlargement of a

longitudinal section of the apparatus at the location of the

specimen. To prepare for the test, the threaded tensile speci-

ment, shown in Figure 4, is screwed partially into the pressure

bars. Then a split shoulder is placed over the specimen, and

the specimen is screwed in until the shoulder is snug against

the pressure bars. The shoulder has the same outer diameter

as the pressure bars (12.7 mm) and it has an inner diameter of

6.4 mm, just large enough to clear the specimen. The shoulder

is made of the same material as the pressure bars, AISA 4130

steel. The ratio of the cross-sectional area of the shoulder

to that of the pressure bar is 3:4, while the ratio of the area

of the shoulder to the net cross-sectional area of the specimen

is 12:1.

2.2.2 Instrumentation

The recording circuitry consists primarily of

strain gages, two oscilloscopes, and a counter. See Figure 3.

The recording system is triggered when the striker bar impacts

bar No. 1. A brief review of the major parts of the recording

system follows.

Bars No. 1 and 2 are instrumented with high resis-

tance foil strain gages. The gages on eacn bar are placed

equidistant from the specimen so that the reflected and trans-

mitted wave signals are time coincident. They are far enough

from the specimen that no spurious reflections interfere with

the pulses being recorded. Gages are placed diametrically

opposite each other on the pressure bars to cancel bending.

The two oscilloscopes record data. One, a dual

beam Tektronix type 565 oscilloscope, records the complete

9

.. . . . . e

1/4-2 UHC0. 125 10.010 R1/4 - 0 UNC O NOT UNDERCUT

D-0-15tDODIA.

1.1512 1.000 DIA

NOTE: ALL DIMENSIONS IN INCHES

THREADED TENSION HOPKINSON BAR SPECIMEN

Figure 4. Specimen for High Strain Rate Tests.

10

strain time history of the test. One beam records the incident

pulse as it passes the first gage. The second beam is used in

chopped mode to record both the transmitted pulse (which is

proportional to load) and the reflected pulse (which is propor-

tional to strain rate). Figure 5(a) shows a photo of typical

traces.

The second oscilloscope, an X-Y Tektronix, records

a load-deflection curve. The reflected pulse (from gage No. 2)

passes through an electronic integrator and is fed into the X

axis of the scope. The signal is proportional to the displacement

of the specimen. The signal from gage No. 1, proportional to

the load in the specimen, is fed to the Y axis. Figure 5(b)

shows the load-deflection trace.

2.2.3 Test Procedures and Mechanisms

The experiment begins when the striker bar is

accelerated so that it impacts bar No. 1. The compression pulse

generated travels down bar No. 1 to the specimen-shoulder junc-

tion. The pulse passes almost exclusively through the shoulder

because of (1) the large area ratio of shoulder to specimen

mentioned above and (2) the loose fit of the threaded joints

(specimen and pressure bars). The portion of the pulse that

passes through the specimen is below the elastic limit of the

material. Then the compressive pulse travels through bar No.

2 to the free end, where it reflects as a tensile pulse. When

this reflected pulse reaches the specimen, part of it is trans-

mitted through the specimen and part is reflected back into bar

No. 2 (because the shoulder doesn't carry the tensile pulse).

The incident, transmitted and reflected pulses are recorded

and analyzed for the required information.

Figure 6 shows a Lagrangian x-t plot which illus-

trates the path of the pressure pulse during the test. The

amplitude of the incident pressure pulse, generated by the

striker bar impacting bar No. 1 is dependent on the striker bar

velocity. Its length is twice the longitudinal elastic wave

E.

Er

E

a Specimen: Ti-3

Vert: 465 lb/div.

fforiz:0.00155 in/div.

b

Figure 5. Typical Oscilloscope Traces.

12

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z200

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cc4)w/Y..

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(33S 2-01) 3v111

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transit time in the striker bar. The plot shows that the com-

pressive pulse passes through the entire apparatus and is

reflected from the free end of bar No. 2 as a tensile pulse,

E:i . The plot also illustrates the tensile pulse splitting

when it reaches the specimen-shoulder junction and part of it,

EV being transmitted through the specimen while part, Enr is

reflected back into bar No. 2.

14

SECTION III

ANALYS IS

This section outlines the data reduction techniques and

equations used to obtain the desired true stress-true strain

curves and specific elastic and plastic parameters. All of

the test data began as analog load-displacement curves that

were then analyzed by various computer routines particular to

the test type (low and intermediate, or high strain rate).

The results appear in the appendices in analog and digital form.

3.1 LOW AND INTERMEDIATE STRAIN RATE TESTS

The low and intermediate strain rate tests resulted in

(1) load-displacement curves from the extensometer and (2) load-

strain curves from the strain gages. Converting the displacement

measurement to true strain is relatively simple. Using u as

displacement and k as the initial gage length, one obtains the

following:

E u (engineering strain) (1)

0

E= ln (I + cE (true strain) (2)

where In is the natural logarithm.

pThe extensometer gage length, k was 1 inch for thesetests. Consequently, the digitized displacement value could

4. be used directly in calculations as engineering strain.

The strain gage data was also simple to reduce. A correc-

tion factor was applied to the strain reading to account for

the nonlinearity of the bridge circuit. The incremental error,

n, is added to the indicated, C, to obtain the actual strain,

c, causing the resistance change in the gage. For this case,

a single active gage in a quarter-bridge arrangement, the

15

correction is

F()2 xl 1- 6(3

2 -F (9) x 1

where F is the gage factor. Equation 2 is then used to obtain

true strain.

Obtaining true stress values for the low and intermediate

strain rate tests is more complicated. True stress, 0T' is

proportional to engineering stress, a." by the ratio of the

initial area, A 0 , to the current area, A. In the elastic region,

where one has small strains, the ratio of areas can be expressed

in terms of the longitudinal engineering strain so that

a Cy E(1 + E:E (elastic regionT 1 + E U1- 2v) true stress) (4)

In the plastic region one assumes the material is incompressible,

consequently the volume remains constant. Based on this assump-

tion the true stress in the plastic region becomes

UT = a ( E) (plastic region (51+E l 2v) true stress)

where U E is the engineering strain evaluated at the yield point

of the material.

Three elastic region parameters were calculated from the

strain gage data. Young's modulus is the slope of the linear

part of the curve. Poisson's ratio, v, was obtained for one

test per material per strain rate with the following relationship:

V +C transverse/ longitudinal

16

7S 7"-=7

The shear modulus, G, was calculated with the equation

G = 2 (1 E+ v)

The values of these mechanical properties appear in the results

section. An additional parameter, the yield stress, was obtained

from these curves. It was evaluated using the 0.2 percent (strain)

offset method because neither of the metals exhibits a definite

yield point. The load-displacement curves were analyzed using

Equations 2,4, and 5 to produce the full true stress-time strain

curves. The ultimate strain was taken as the final strain value

of the curve. However, the ultimate stress was calculated

using the final load divided by the final reduced area of the

specimens because Equation 5 is not accurate (complete) for

large amounts of plasticity.

These curves were all digitized on the University of

Dayton's Tektronix 4014-1 computer graphics terminal and

associated digitizing board.

3.2 HIGH STRAIN RATE TESTS

The polaroid photographs of the load-deflection traces

obtained from the high strain rate tests were digitized using

a Hewlett Packard 9800 series calculator and digitizer (located

at the AFML) to produce true stress-engineering strain curves.

Those curves were then digitized on the Tektronix 4 014-1 com-

puter graphics terminal and digitizing board (located at the

University) to produce true stress-true strain curves. A brief

review of the analysis in the two data reduction programs

follows. Details of the theory of the measurements appear in

documents by U. S. Lidom and by Lindholm and L. M.

Yeakley.(7 )

The average stress in the specimen is:

as E (A/As) Ct (6)

17j

where E and A are the elastic modulus and cross-sectional area

of the pressure bars, A sis the cross-gectional area of the

specimen and c is the transmitted wave. Using the assumption

of no volume change after first yield, Equation (6) is modified

to:

GT E(A/A ) F_ 1+ (7)

for true stress.

Engineering strain was obtained from the deflection values

using the following relationship:

E =0.265 6 -0.5 (1l-exp-056

where c represents strain in percent and 6 represents the deflec-

tion in mils between the grips.(5 This equation results from

least-squares fitting many deflection-strain plots from several

different materials. It is particular to the specimen size used,

not to a material.

The yield stress was determined as the point on the stress-

strain curve at which the increase in applied load essentially

ceased. The ultimate stress and ultimate strain were selected

as the final point on the stress-strain curve. Reasons for

this selection procedure appear in the results and discussion

section.

18

-V

SECTION IV

RESULTS AND DISCUSSION

The mechanical properties acquired from the various strain

rate tests on 8A1-lMo-lV titanium and 410 stainless steel appear

in Tables 2 and 3, respectively. Table 4 shows the measured

density of each material. Figures 7 through 10 are plots of the

mechanical properties versus strain rate. The points lacking

standard deviation marks either represent one data point or they

represent averaged data having a standard deviation smaller

than the data symbol. The true stress-true strain curves for

the low and intermediate tests (Appendix A) have two parts to

the curve in the plastic region. The solid line represents the

test data analyzed with the pla'stic region equations given in

the analysis section. Obviously these are not complete for

large strains. The dotted line joins the ultimate stress

(calculated with the final load and reduced cross-sectional

area)-ultirnate strain point to the test curve.

Studying Figures 7 through 10, one concludes that all of

the tensile mechanical properties determined by these tests

vary with strain rat,: with the exception of the elastic modulus

of titanium. Perhaps additional testing of the stainless steel

would reveal that its elastic modulus also does not vary with

strain rate. It is important to consider the coxmments in the

following paragraphs when using the curves shown as data for

calculations.

A very small specimen must be used for high strain rate

tests to satisfy assumptions made in the Hopkinson bar theory

equations. This presents problems in obtaining accurate data

* from the tests, particularly in the elastic region. one problem

is that achievable machining tolerances on the specimen in

* relation to load surface alignment make it difficult to resolve

small strains accurately. Secondly, an assumption made in

developing the Hopkinson bar equations is that many stress

19

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212

TABLE 4

DENSITY

Material Density

8A1-lMo-lV Titanium 4.32 g/cm 3

410 Stainless Steel 7.57 gm/cm3

wave reflections occur in the specimen before a state of dynamic

equilibrium exists. This does not happen until some plastic

deformation has taken place. In addition, once necking occurs

in the specimen a uniform stress field no longer exists making

the equations for stress and strain invalid. This is a signifi-

cant factor for the small specimens.

However, the split-Hopkinson bar apparatus represents

the state-of-the-art technique for obtaining stress-strain

information at high strain rates. The curves are considered

most accurate in the range of 2 to 10 percent strain. The

yield stress values reported represent the point on the curves

where the load ceases to increase significantly for a rather

large increase in displacement. (The 0.2 percent offset method

obviously cannot be used because of the lack of data in the

elastic region.) The ultimate stress and ultimate strain values

from these tests were the final point of the curve. Although

the values front the iiigh strain rate tests cannot be used as

exact data points they are useful in establishing the trend

of the strain rate dependence of the subject materials over

nearly seven decades of strain rate.

22

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26

REFERENCES

1. Mardirosian, M.M., "Strain Rate Effects in Brittle and ToughMaterials," AMMRC-TR-74-34, December 1974.

2. Green, S.J. and S.G. Babcock, "Response of Materials toSuddenly Applied Stress Loads: Part I: High Strain-rateProperties of Eleven Reentry-vehicle Materials at ElevatedTemperatures," TR66-83 Part I, November 1966.

3. Eleiche, Abdel-Salam M., "A Literature Survey of the CombinedEffects of Strain Rate and Elevated Temperature on theMechanical Properties of Metals," AMFL-TR-72-125, September 1972.

4. 1977 Annual Book of American Society for Testing and MaterialsStandards, Part 10: Metals Physical, Mechanical, CorrosionTesting, pp. 154-173.

5. Nicholas, T., "Mechanical Properties of Structural Grades ofBeryllium at High Strain Rates," AFML-TR-75-168, October 1975.

6. Lindholm, U.S., "Some Experiments with the Split HopkinsonPressure Bar," Journal of the Mechanics and Physics of Solids,1964, Vol. 12, pp. 317-335.

7. Lindholm, U.S. and L.M. Yeakley, "High Strain-rate Testing:Tension and Compression, Experimental Mechanics, January 1968,pp. 2-9.

27

APPENDIX A

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HIGH STRAIN RATE CURVES ANDDIGITAL DATA

57

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