- -t

AMMRC TR 71-13 IADIiI~1

UTILIZATION OF THE BEND TEST FOR

DETERMININ-G STRSE S S* "-A-,N CURVES

z/ _.. .

/

I' / - ,~

' , AMPo \",/-1 "I CS OF MA ' IALS DIVIS,O"NJAI

NAP \\-/ ,

___ARCH D D C .

MOCT 20 1971

! Approved for public release; distribution unlimited. i

SReproduced by V I

NATIONAL TECHNICAL B :H•iS \INFORMATION SERVICE$S n g fi e ld , V a . 2 2 15 1,'

4 /

JulY MA97 IAL A1MECHNC DEEACHCETEWatetown Masachsets QZ720

EUI~5

~IWT Sumir

........ ...... .............

y .......... -..........-

Ij&S6hW,/AA-Ifl

IT iNA,. aod/o

The findings in this report are not to be construed asan official Department of the Army position, unless sodesignated by other authorized documents.

Mention of any trade names or manufacturers in this reportshall not be construed as advertising nor as an officialindorsement or approval of such products or companies bythe United States Government.

DISPOSITION INSTRUCTIONS

Destroy this report whes it is so looter seeded.Do sot reters it to the oritisator.

UNCLASSI FIEDsecurity Classification

DOCUMENT CONTROL DATA.- R & DIORIGINA TING £t T.1. C r (Corporelee author)2aREO TSC IY LStC&IN

Army Materials and Mechanics Research Center UnclassifiedWatertown, Massachusetts 021727.GRU

ITILIZATION OF THE BEND TEST FOR DETERMINING STRESS-STRAIN CURVES -

4 OtSC RIP TIVE NOTES (7~.pe of report and Inclusive dates)

5 AU THORIS) (First name,. middle initial, last ner..)I

John Camnpo

* REPORT DATE 741. TOTAL -ic OF PAGES 7b No. oi. Refs

July 1971 2S.CONTRACT OR GRANT NO. aORIGINATOR'S REPORT NUM'DERISI

b. e6ROJECT No. D/A Project 1JIT0621r.5A328 AM!I1RC TR 71-13

C*AMi41M Code 502E.11.294 thsb (Ayiternibeathtma e alea

d.Agency Accessior Number DA 0B4707 ______________________

10. CISTRIGUTION STATEMEZST IApproved for public release; distribution unlimited.j

It. SUPPLEMENTARY NOTES 1.SPONSOO.5G uILIIAt'Y ACTIVITY_______________________________{U. S. Army Materiel Commandt3 GSTACT-4Experimental verification of the utilization of the bend test for deter-

mining stress-strain curves for tension and compression is presented,i, is'repmnStress-strain curves are determined from independently performed tensicn, compression,and bend tests of AISI 4340 steel specimens (heat treated to three nominal yieldIstrength levels - 125,000, 175,000, and 225,000 psi, respectively, at 0.2% offset) andcompared. Fair agreement is found to exist among the curves uip to t!,', 2% strain limitof each test. (Author)

ro 11111F RELACES 00 FORM 147S. 1 JAN St. WHICH ISDD so.414713 OSSOLETE FO ARMY USE. UNCLALSSIF!.6DSeCurity Ctasslficatioen

UNCLASS IF IED

Securitq Cllastiicjatjen

'4LIMA( A LINK~ LIN ClK-E WOROS

ROLE WY ROLE vv A0L E ft

Bend testsTension testsCompression testsStatic testsStress-strain diagramsMeasuring instrumentsStrain gages

iINCLASS I FIEDe Wurltv Cle-tIfeafluon

MMRC TR 71-13

UTILIZAT!bON OF THE BEND TEST FOR DETERMINING STRESS-STRAIN CURVES

Technical Report by

.IOHN CA MPO

July 1971

D!A Project 1TO621O5A32PAMCMS Code 502E.1 1.294Metals Research for Army MaterielAgency Accession Number DA 084707

A~ow fo pubi- eiese; istrbutor vlintI:I

MECHANICS OF MATERIAL.S DIVISION 26ARMY MATERIALS AND MECHANICS RESEARCH CENTERWatertown, Massachuo-tts 02172j

-- N ' - - -- -7

ARMY MATERIALS AND MECHANICS RESEARCH CENTEk

UTILIZATION OF THE BEND TEST FOR DETERMINING STRESS-STRAIN CURVES

ABSTRACT

Experimental verification of the utilization of the bend test for determiningstress-strain curves for tension and compression is presented in this report.Stress-strain curves are determined from independently performed tension, compres-si>nn, and bend tests of AISI 4340 steel specimens (heat treated to three nominalyield strength levels - 125,000, 17,000, and 225,000 psi, respectively, at 0.2%off set) and compared. Fair agreement is found to exist among the curves up tothe 2% strain limit of each test.

I- -- --

CONTENTS

Pa3

ABSTRA(7.

I. NOMENCLATURE................. . . ... . .. .. .. .. .. .. .....

II. INTRODUCTION.................. . . ... . .. ... .. .. .. .. .....

II1. VALUES OF STRESSES AND STRAINS FROM BEND TEST DATA. .. .... .... 2

IV. VALUES OF STRESSES AND STRAINS FROM CONVENTIONAL TENSION AND

COMPRESSION TEST DATA ......................

V. SELECTION OF SPECIMEN SIZES .. ..... ........... .... 44

VI. SPECIMEN PREPARATION .. .. ......... ............. 4

VII. MEASURING DEVICES AND EXPERIMENTAL PROCEDURES. .. .......... 5

VIII. RESULTS AND DISCUSSION .. .. ......... ............ 7

IX. SUMM4ARY AND CONCLUSIONS .. ..... ........... ..... 20

ACKNOWLEDGMENTS .. .. ......... ........... ....... 20

LITERATURE CITED. .. ......... ........... ....... 21

No

I. NOMENCLATURE

Bend Tests

a = moment arm or distance between either support and its closer loadpoint (double point loading).

b,h = beam cross sectional dimensions, width and height, respectively.

P = applied load.

G1 0 2 = absolute values of extreme fiber stresses, compression and tension,respectively.

eit 2 = absolute values of corresponding extreme fiber strains.

6 deflection at midspan of neutral axis from its original horizontalposition.

Tension and Compression Tests

A = original cross sectional area.

P = applied load.

= P/Ao = absolute value of engineering stress.

E = absolute value of axial ordinary strain.

II. INTRODUCTION

interest in the bend test has undergone a revival in recent years becauseof the development and exploitation of such brittle materials as ceramics andcarbides and because of the greater use of high-strength materials with littleductility.

The tension test has normally been one of the most common m thods used fordetermining design data of a material. Sometimes, however, a tensile specimenmay not be feasible either because of size limitacions or because of difficultyin machining the particular material. The latter problem, usually with accom-panying extraordinary expenses, is particularly encountered when dealing withsuch limited ductility materials as those mentioned above. In such cases, abend test with its major advantage of employing a simple specimen with a rec-tangular cross section would be most welcome, provided that such a test couldbe used as a satisfactory substitute for the tension test.

Nadai,1 in an analysis of the bending problem, provides the foundation forderiving the tensile and compressive stress-strain curves from the bend test.Bluhm 2 has modified the form of the resulting equation extending it to consid-eration of cases other than pure bending, illustrated its application, andsuggested computational forms to facilitate the carrying out of the requiredoperations.

In the present investigation, experimental verification of the proposed for-i

mulation is attempted. Tension, compression, ant bend tests are independentlyperformed on AISI 4340 steel specimens heat treated to three nominal yield-strength levels (125,000, 15,000, and 225,900 psi, respectively, at 0.2% offset).Stress-strain curves determined from the bend tests are then compared to thosedetermined from the conventional tension and compression tests. The resultstend to substantiate, at least up to the 2.0% strain limit of each test, thatthe proposed method is valid in obtaining a stress-strain curve for either tensionor compression by utilization of the bend test.

Before continuing with the text, however, it should be brought out that:a) a steel, rather than some ceramic is chosen as the testing material in orderto minimize machining and testing costs; b) an arbitrary value of 2.0% strain isselected as an upper test limit since muny brittle materials will fracture belowthis strain value; and c) a computer program could obviously have been devisedfor automatic reduction of the test data.

III. VALUES OF STRESSES AND STRAINS FROM BEND TEST DATA*

Stresses

If bend tests are divided into three cases as noted below, and if, for easein manipulation, the values of tensile and compressive stresses computed fronthe bend test data are expressed in absolute terms, that is, numerical valuesonly, then the formulas presented by Bluhm become:

Case I. Different Stress-Strain Curves for Tension and Compression.

[__ '2+( ,i~~ 2) de,|+I I

2- [2 ] dp + d'

SIdentical = d ( 2 ( d 1( 2 d) 1

Case II. Identical Stress-Strain Curves for Tension and Compression.

el~[ + (.f 2aP

Case III. Identical Stress Strain for Tension and Conpression. Bean Pestricted A.to Pure Bending.

M

2r a b- +~ ((4 )

*See Nomenclature (Section I) for definition of tern and Figure IA for specimen1

configuration and loading arrangement.

2 2

stranaes,agin boue erm-s

Recaise t-his revort is c~c.-rr^- c v -* : t. ~mi~~~ ith e e xvres s i as fo r de ze r inn , = t sw: I - - m z±a. - n~sVt i:s t~ z.4rUt

the forrimaas, to b-e fcmd -- :-r~n~ As-t~ ~~:tL~l~r~~the basic coesiderztioc-. i--wolwe4 im cbe t~~ ~:tC~

1 . Ani ini tia;- a YS t ai j~t :re oen' ~ t~ w.z -!3-;~ S? I.. =iZ~ t-~I,by forces verveicaur to its z.c- L:-1rZt wit ;-f nzof inertia of the crs se-c-ti *rt ;-- a= t- ~tj = -- t't1 fa -

2. The crss scti, cm~- ixemscu ;-- ::i !,ta irnzt L.1 z.~irits length so that Shear -fr:~~ I.-~t~

4. For a be-a restiezed to t tizj, :s %=t z*qL tacu tnr*nxbeaw bems isito a cir-wT- *Iar c- F , aj gixtca. VMMzrnM:it is DeCessarY that oM1y trbe Vpt=i Qf the tC 4-.Aft 'U41 'r ~tz~Cross seticms w-er Ozsiarat --CrL (x= 3iNLj pe -1ftn 'Lli I Zt~!Xr

Stresses amd Strams

Sim~e dhe tctaI strai im =x~ -nie zec-luma==md :-M_ =nt s-=,= !:bitest results are fu-, caw-s. =., . ;' Z's~ S-u5F:rn- =ct 3'i~-Rim CgiMeeiffag stzz-c=~ r~tk -~ih±-ta&n :m~z-

the applied Icad. -7rtecrpn:mt n-am d tW2a1ie ofr sat6= tht cAaum.Ly UI ~ ~ui *Za

*Se %=SWn- t fit i z--r !=I *if 7-t-zi ant I~ +4

V. SELECTION OF SPECIMEN SIZES

B"ed Specien

.Yore than one experimenter has found that varying the size of test specimensleads to different bend test properties. From the data presented by Grobe and.Aberts' (when enploying the double-point loading system,) it may be seen thathigher bend-strength values are obtained from a 2-in. rather than a 4-in. span(distance between outermost supports) or from a 0.2SO-in. rather than a 0.500-in.bean widzh. Burghardt and Elder" remind us to maintain a reasonable span (theychose 0.500-in.) and keep the h/a ratio, that is, ratio of beam height to momentar*', snaller than 2/3 in order to prevent shear stresses from becoming tooPronounced. Duckworths also suggests that the h/a ratio be kept as small aspracticable to avoid pronounced shear stresses, and, in addition, that the b/hratio, that is, ratio of beam width to beam height, be kept reasonably small toavoid stiffening effect due to relatively wide beams. Because of the abovefindings and because of space requirements for the application of strain gagesand their leads, a 3-in. span was judged to be satisfactory, and a bar with a3 1/4-in, overall length, a 0.600-in. width, and a 0.!50-in. height was chogenas the bend specimen.

Tension Specimen

A threaded tensile specimen with a 0.357-in. uniform diameter was used inthis investigation.

Conpression Specimen

According to ASTM EN-61,' a compression specimen should be round, and, ifof nediun length, should have a length-to-diameter ratio of 3.0. A 5/8-in.diameter was selected in order to keep the applied load from exceeding the120,000 pounds capacity of the testing machine and, yet, to have ample spacealong the specinen for strain-gage application. In compliance with the recom-mended length-to-diameter ratio of 3.0, the specimen was made 2.0 in. long.

VI. SPECIMEN PREPARATIONFR

Material

AISI 4340 steel was chosen for the experimental work in this investigation.In order to insure uniform material properties, all specimens were taken from

rone plate, 12 x 12 x 3/4 in., and the length of each specimen was always in thelongitudinal direction of the plate. In addition, the width of each bend speci-men was taken in the transverse direction of the plate.

"See Figure IA for explanation of moment arm, a.

.I

Heat Treatment

Roughly cut blanks, all with the original 3/4-in. thickness were heattreated before machining, as indicated below, to three nominal yield strengthvalues (125,000, 175,000, and 225,000 psi, respectively, at 0.2% offset). Allblanks were normalized by heating at 1650°F for one hr and by air cooling. Theywere then austenitized at 1550=F for one hr and oil quenched. Double temperingfollo%%ed at the temperatures and for the periods of time indicated:

Level 1 - nominal yield strength of 125,000 psi - 1200°F (1+1) hr.

Level 2 - nominal yield strength of 175,000 psi - 950°F (1/2+1/2) hr.

Level 3 - nominal yield strength of 225,000 psi - 400*F (2+2) hr.

Tempering was performed in salt baths.

Surface Grinding

After heat treatment, the bend specimens were brought to within 0.010 or0.01S in. of the final dimensions by rough grinding and were then finished byfine surface grinding. A similar procedure was followed for the ends of theconpression specimens.

Nurmber of Specimens

Four tension, 4 compression, and 5 bend specimens in each of the threenominal yield-strength levels, or a total of 39 specimens in all, were tested.

VII. MEASURING DEVICES AND EXPERIMENTAL PROCEDURES

Bend Tests

Since strain gage readings on both the top and bottom surfaces were re-quired, double-point loading (see Figure 1A) was desirable. Longitudinal straingages (SR4, type FAE-25-PL) were mounted, one each of mid-span on both the topand bottom surfaces of each specimen. The strain gages were electricallyconnected to separate X-Y recorders so that simultaneous readings could be made.

The testing was performed on a Tinius Olsen testing machine, manuallyoperated at head speeds well within the limits recommended in ASTM standards.

6

Strain-rate effects were considered to be negligible. A signal from a pressuretransducer in the tc';ting machine, indicating the applied load, was also con-nected to the X-Y recorders, and, in this way, plots of load vs strain wereautographically recorded. Each test was continued until a total strain of 2.0%was indicated. Figure 2 shows the test setup.

In this setup, load and support points consisted of "rollers" that werefree to rotate in order to minimize friction effects.

4S

ABSOLUTE VALUE OF ITREME

- -FIFR STRAIN IN COMPRFSStON

• . ,.: - -I2.° I / ,o,,,

P ' P

A, RE AD TEST B. COTI RESSOP TEST

~Figure 1. Sketch of loading arrangementfor bend, compression, and tension test

~specimensSTAI GAGES _

110 APAAT--

SPAN. 3.0"

A. TENSTON TEST

tgo66-1250/AMC ,68(A(8 Figure 2 Bend test setup (A). employing "friction free" fixture

(B), showing specimen under load. Double point loading.

0.150 x 0.600 x 3.25-inch specimen

26TAN AE

Tension and Compression Tests

Since axial ordinary strains of the specimens were required in these tests,longitudinal strain gages (SR4, type PFA-50-12-L) were mounted at midspan and1800 apart (see Figures lB and 1C). These gages were connected to an X-Y re-corder so that average strain only could be recorded.

The testing was also performed on a Tinius Olsen testing machine, and,again, the head speeds were kept well within the limits recommended in ASTMstandards. The load signal of the testing machine was also connected to the X-Yrecorder, but the recorder was calibrated so that engineering stress (ratherthan applied load) could be indicated directly. For the tension and compressiontests, then, plots of engineering stress vs strain were autographically re-corded. Again, each test was continued until a total strain of 2.0% was reached.Figure 3 illustrates the testing arrangement for tension tests and Figure 4 thatfor compression tests.

VIII. RESULTS AND DISCUSSION

Recorded Data

Results were generally obtained in the form of X-Y recordings. Theserecordings consisted of applied load vs extreme fiber strains for the bend testsand engineering stress-strain curves, directly, for the tensile and compressivetests.

Auxiliary Curves for Bend Tests

When the extreme fiber strains of a bend test specimen were not equal, twoauxiliary curves had to be constructed before any stress-strain curve could bedetermined. These auxiliary curves consisted of two plots, one of applied loadvs sum of extreme fiber strains and one of extreme fiber strain in compressionvs extreme fiber strain in tension. No such auxiliary curve was required whenthe extreme fiber strains were equal.

Stress-Strain Curves for Each Specimen

The originally obtained X-Y recordings in the tensile and compressive testsconsisted of engineering stress-strain curves, directly, and no further treatmentof the data was required in determining these results. For the bend tests,however, to determine the required stress-strain curves, Eqs. (1) and (2) of thetext along with slope data of the auxiliary curves were employed when the ex-treme fiber strains were not equal, and Eq. (3) of the text along with slopedata of either of the originally obtained X-Y recordings were employed when theextreme fiber strains were equal.

Stress-Strain Curves for Each Yield Strength Level

In addition, because the stress-strain curves were essentially identicalfor any one strength level and for any one type of testing, stress-strain curvesfor each yield strength level were determined by averaging the individual test

7

F7!

Fiur 3. Teso etseu hwn

Fiue4 opeso etstpsoigspecimen under load. 037ic

uniform diameter x 4.25-inch threadedtype specimen

19.066-1 3761AMC.69

.... - = - --- _ k L LI_ _ - ____~m - --- =-= --

results. It was felt that a comparison of the stress-strain curves based on theaverage test results would be less bulky and just as indicative as a comparisonof the curves based on the individual test results themselves.

*Reported Rtsults

The average test data and corresponding values of stresses and strains forall three nominal yield-strength level specimens are summarized in Tables Ithrough IV. Stress-strain curves axe given in Figure 5 where the plotted valuesare taken from the aforementioned tables. In addition, pertinent values ofmechanical properties (including values of Young's moduli, yield strength at0.2% offset and flow stresses at both 1.0% and 2.0% of total strain - all de-termined from the stress-strain curves of Figure 5) are listed in Tables Vthrough VII. Maximum percentage scatter and percentage discrepancies (boththese terms are subsequently defined and discussed) are also included in thesetables.

Auxiliary curves, when required, and stress-strain curves, both in tensionand in compression, have been constructed for each bend specimen as well as foreach yield strength level. As typical examples, however, only those curves foryield strength level 1 are presented in Figures 6, 7, and 8. In fact, only thestress-strain curve in compression is depicted in the last figure.

Scatter

If scatter is defined as the amount that an individual test value differsfrom the average test value of a particular number of specimens tested, then

%scatter = individual test value - average test value X 100.average test value

Scatter is expected to be greater in stress-strain curves derived frombend tests than those derived from conventional tests. This is true because,as described above, in conventional tests, stress-strain curves may be obtaineddirectly, whereas, in bend tests, slope data must first be determined eitherfrom one of the originally obtained X-Y recordings or from auxiliary constructedcurves. The work involved in obtaining the required slope data introduces moreleeway for experimental error and, hence, greater scatter.

Discrepancy

If discrepancy is defined as the amount that a bend test value differs fromthe corresponding conventional test value, then

bend test value - conventional test value% discrepancy = conventional test value X 100.

Discrepancy values, then, indicate the degree of agreement, or rather, ofdisagreement, among results predicted by bend tests and those determined byconventional tests.

9

Y6 ILD STRENGTH LEVEL 5

COMP FROM COUP TEST-

COMPFROM SEND TF.ST1 TENS FROM BEND TEST

20 TENS FROM TENS TEST -

YIELD STR-ENGTH LEVEL 2

220 COMP FROM SEND TEST

-COMP FROM COMP TESTTENS FROM& SEND TEST

200 TENS FROM TENS TEST

ISO YIELD STRENGTH LEVEL I

COUP FRO BEND TEST

j 4 ENS FROM SEND TEST Figure 5. Stressstrain curve~s from bend,

£ 40COMP FROM CO-AP TEST tension, and compression testsZI2O-ENS FROM TENS TEST

b

t0 _ _ __ _

NOMINAL Y1IlLO STRENGTH LEVEL AT 0 2% OFFSET

so LEVEL I -25 kitLEVEL.2- 175 iiLEVEL)'- 225 hi,

40 NOTE. EACH CURVE REPRESENTS AVERAGE

40TYPE OF CURVE NMBUER OF TESTS

TENS TEST 4COUP TEST 4

20 SEND TEST 5

f0 2.000 4.000 6.000 8$PO~OO 1.000 O14-000 16.000 W'.o0o 20AW0

§600 dt gi 10

P2 12

18.000 1Vonb010

14,000- NOTE: CURVE REPRESENTSAVERAGE OF 5 TESTS

t 200LGN Figure 6. Plot of tensile strain vs

10.000 -P - APPLIED LOAD compressive strain for yield strengthb - WIDTH OF SPECIMEN level 1 bend specimens (auxiliary curve)

% It * THICKNESS OF SPECIMEN

6000 I * ASOLUTE VALUE Of EXTIREMEFIBER STRAIN IN COMPRESSION

*ABSOLUTE VAUE OF EXTREME

61000-FIBER STRAIN IN TENSION6.000 RATE OF CHARGE OF @It WITH

SRESPECT 70

4.00_ _ -4075,40.

0 2.000 4AW0 SAW0 "00 10. 20 M OO PO "6.00 141000 20.000

10 5

1100 P/2 P/2

1~0U b- 0.600"___ h-0.150"

900 P/2 P/2T

"TANGENT TO CURVE ATP •640 Ib

800 -

700Pz640 lb.

Figure 7. Plot of load vs sum of 600 -0.00

strains for yield strength level 1 LEGENDbend specimens (auxiliary curve) t P APPLIED LOAD

500 _ b " WIDTH OF SPECIMEN

h = THICKNESS OF SPECIMENa1. 400 ABSOLUTE VALUE OF EXTREME

FIBER STRAIN IN COMPRESSIONAT P- 640 Ib iE ASOLU (E VALUE OF EXTREME

300 P . 317-90b) FIBER STRAIN IN TENSIONd(e

1* 2 ) IO.000("Afint) d(P)

RATE OF CHANGE OF

.03179r 0b) d ('1* '2) WITH RESPECT TO (R1 + 2 )200 I n.fn)

NOTE CURVE REPRESENTS AVERAGEOF 5 TESTS

100

0 4.000 8000 12.000 ,00O 20,000 24D0X 2%,000 32$000 36000 4Q0(V .+ 4" 2 ) (IL i n /i4 - ..

80 P/2 W 2160 b - 0.600"

h - 0.150"

140 P/2 P/2 (0,2% OFFSET) 119 ki

120

,0 P -APLED L0-~~ - WIDTH OF SPECIMEN

Figure 8. Plot of stress vs strain b S0 , ABSOLUTE VALUE OF EXTREMEin compression for yield strength FIBER STRAIN IN COMPRESSION

'2 - ABSOLUTE VALUE OF EXTREMEeve 1 specimens 60 - FIBER STRAIN IN TENSION

E -YOUNG'S MODULUSys - SUBSCRIPT INDICATING YIELD

40 STRENGTH

E/300X106 NOTE. CURVE REPRESENTSAVERAGE OF 5 TEST!;

20

0 2.000 4.000 6.000 8,000 10.000 12.000 1400 16.000 18,000 2.00(I (FJ' n ) - -

11

-" '-----.--=-----' -

Table I. AVERAGE STRESS-STRAIN VALUES FROMYIELD-STRENGTH LEVEL 1 BEND SPECIMENS

E + 4 2 dPP 2 2 d( 1 +e2) 1 2

(Ib) - (pin/in) - (lb/pin/in) (lb/in) (lb/in2)

0 0 0 0 0.06614 0 0100 749 763 756 0.06614 22,433 22,015200 1498 1526 _ 1512 0.06614 44,866_ 44,030300 2247 2289 2268 0.06614 67,300 66.045400 2996 3052 3024 0.06614 89,733 88,060500 3745 3815 3780 0.06614 112,167 110,075520 3881 3953 3917 0.06063 113,287 ii1.74540 4055 41-31 4093 0.05423 1139 111.8321560 4240 t319 4280 0.05107 116,441 114270580 4433 4515 4474 0-04850 119.,194 116,972600 4657 4745 4701 0.04325 12.141 I17,901620 4927 J 5019 4973 0.03800 120,986 118 730640 5196 1 594 5254 0.03179 120,652 118,403660 5553 5,57 5605 0.02370 118,S74 116.363680 6004 6116 6060 0.01808 118.083 11i 81700 'o608 6732 6670 0.01550 120-.11 117.911720 7292 7428 7360 0.00962 18,268 116,063740 8372 8528 8450 0.00732 119,897 1i7,6621760 9947 10,133 10,040 0.00507 121,274 119013780 I12,242 12,470 12,356 j 0.00392 123,898 i21159800 15,406 15,694 [s 550 0.00287 126,319 123,964820 ... 19,260 19,620 19,440 0.00245 129,759 127,339

NOTES:

1) Circled numbers identify appropriate columns

2) E x 1 Eq. (1)

bh2 200 (D 103) -+1 Eq. (2)

de I

4) a 2.0 74.074bh 2 (.600) (.15O2)

-) = 1.019dc

1

6) Above value-s represent averages of five tests

12

i7Table II. AVERAGE STRESS-STRAIN VALUES FROM

YIELD-STRENGTH LEVEL 2 BEND SPECIMENS

00 02

P 4E C _e_+_6 dP 01 2 2 d(el+ E) 2

(lb) (Pin/in) - (lb/pin/in) (lb/in 2) (lb/in 2)

01 01 T_ 0 0,06717 0 0200 1478 1500 1489 0.06717 44,778 44,116400 2955 1 3000 2978 0.06717 89,555 88,232600 4433 4500 4467 0.06717 134,333 132,348800 5911 j _ 999 5955 0.06717 179,111 176064820 6052 6142 6097 0.06098 177,886 175,257840 6213 6306 J 6260 0.05917 180,663 1 177P993860 6396 6492 I 6444 0.05181 178,194 175,561880 6604 6703 I 6654 0.04608 1 177,114 I 174,49690- 698T 7002 6950 0.03788 173,629 171,063920 j 7084 7191 7138 0.03623 175,918 173 319940 7S20 7430 7375 0.03367 177,368 174 746I,60 7668 1 7783 7726 0.02494 172 049 169550798018015 8135 8075 0.02778 179 756 1

10G0 8402 8528 8465 0.02370 179,203 176,S551020 1 8769 8901 8835 0.02110 180,069 177,4081040 9281 9420 9351 0.01930 182.166 1741060 , 9851 9999 9925 0.01720 1 183695 180J980

'1080 10,484 10,642 110,563 0.01475 I 184244 181,7281100 11,232 11,400 11,316 0.01330 866491 12010 12,190 112,100 ! 0.01180 1 188,481 18S,69

12,8S413046 1 12,950 0.00975 189,001 186,2081 13,995 14,20 i14,100 0.00780 I189,556 186,75S1180 1S,533 15,767 IS,650 0.00580 1 189,674 186,8711200 17Y866 18,134 18,000 0.00400 I 189,858 187,0521210 18,821 19,104 _18,763 0.00330 1 189,944 187,137 J1220 20,261 20,564 120,413 0.00260j 190,017 187,209

NOTES:

1) Circled numbers identify apprcpriate columns

2) aO 0 xO I I Eq. (1)

3) (7 +Fh J o L~ 1 Eq. (2)a 1.0 "j dE2

4) =:: 74.074 S) d = 1.015bh 2 (.600)(.1502) deI

6) Above values represent averages of five tests

13

Table III. AVERAGE STRESS-STPAIM YAUES F iYIELD-STRENGTH LEVEL 3 BEND SPECI)Eh^S

- dPI:P• 4.. 7d =t I

(1b) I (ihn/in) (Ib/uin/in j (!b/in)

0 0 0. 1309So00 152 1 0. 13098

400 3054 I 0.13998 iT"600 4581 j 0.13098 12 3,33800 6108 0 . 1309S i 177 ,778840 1 6414 0. 1280 185,639880 6734 0.12640 19 w___920 7055 j 0.12!2 1 -199,634Z960 7402 1 0.11000 22S35

1000 7769 i O.40 20.- _,2

I 1040 18171 0. 10M8 215c,08-- 1080 i as554 10.0-C"70 ! 2.. uy01120 8991 0.02960 sn- ? 5

-1160 9446 0 .O06O i528 24S

1200 9942 1 0.0760 1 ;3$ -1240 10490 - 0.O725 _ .. "_1280 I 11.068 0.06950 ?.6,6.1320 11,607 j..610#1360 1 12,38 0 0.055649 ,..___

44 13,948 25;.15

_______t-14 14,936 G.04050___152 15Is875 J 0.036W0

1560 1 16V992 .0ZEJ _ __

15ism 17,S42 00

- ;~) Circled- numbers idm-fy7. Z.j gi -e -Z1600) !-T l'..16 1 0 " I - 11

120 ;2 03 i .0}

L (D4) yCiml ra~msza: i-Vemees z'24aa, filetss

-?L

-_'2 0

4mv -IIw Lim -

I - -

!f ~-!P U 'ULU" = -_

;ml..l 4 1 U _w Iimm 1: oI _ LiJi JiAiI- Z . UM1 AM Afav -

*~~~~~~;E A; U , it, ~ ~ * iI 'i -~~I

- -m

A -V611,1 - - 7

;:._-wrcxx u ~ 1 s -isi -air X=.

11111 2 1A*,Ij'f' mu V *ofV -

- - .

-atS

41 mnff Lit ,irUW __2z; wuia.im:I

-J It -1 aun-~ 7~I-~- -.-- =i

4hnxat at~Je h'xm:r~~ttls~~ur ~ ~ ~ ~ -

rCU Lf) -441

*L m ~ 0 0 't+ + +4.

:541)~~c, r--' %0' CAO -40C4~ O

4-JrJ . . .arn4LLjQ *.- 4)eo c;c Ors 4 OcN c -4 *-4 4 J *P O)tn C-; 0C C O 41)

O3.-LLI XCU'- + + + U- + a + I + + I+

2E 0

>. 0: 0 0tAJ.J ) $4 H4..-i V) 4 4 3 'C 44-4J. %C 0n

V) 0 0o 0 0) Cfl 0 0C 0r0 I G). -4 0 01-4 0D 0) 0

I- ~ ~ ~ ~ C CE-.- 0 C I E40 '

a CZ4a 0 4C) *L (nV x4

ujo. C4

= 1-- -4C' r-ir t:' 04CJ 't 0) 0 )>

o- = .-Q an 00 -0 40 0 *4 8 C.0 ~ 0 4 4 4 C 3+3 LCUL- +3 +1 V +C 1 ) 4.)

I _ _> U)

____ a- -4 0

___q- -- C4C C;co 4-

4j 4p2c 0 1C 0 4j QW> in 4

V) 043 00 .9-44-)4o

I - 4) 0 t 0

(a~0 4-43 tE- an) CU0>

a.c .u. a9. -0 .x mU: *S U;V 0ai C.> = 0 U. 0C cU; CU^ - n $44 a:: e(na. r4 *-4 Ow 43 43 g i) C)..4 44

L It I l$

-* 0- V) -4a do4) 44) ) 0 >4 I. *'4 >- n:

b- -- - I3 V43 1

1-4~~~~4 4) leh C4 ~ ) 4 4 1 .-

C. V n I '0 )4 -3 ~ ' 44 4) I) 4 0 0C ) 0

0~ es ~ 14a 43 $ 4C. r

I k~~~Ia fd=D ~ iJ L.i *\ 43 4L -4-1 -,4C4 U3 U3 >

16.10.b

- ~ ~ ~ ~ ~ ~ ~ ~ C - -- - -- - --- -- -

R-,0 _ -s- -

0D "T A . CU ) '0 NOo\0 -4 L '.0 '.P

+./ + +I + + +Cl)

Q0 CU: ) t)L 4 - , 0 C 1V~) +j

.,- 4J C) - 4 dQ) 0'- 0C\3 C;J V)CZ CUUi d 0)

CU U 0

0 0

0 0 0

,a ( 4 ) , -0 i-44- '0 0

0S (J 4-. 0 CO 0t C)~Lr OD XD * +X j

V) LA -1 -4 O C' .(/I - 40 *a -4 - 4 4 - - I0mC~ = C 41 C1 0~ 03 C4_jL 4) 41~ C0

.. JW0 0 0) 0 X (1-4

-_ - - x zLL E r=kr -4 0

z 4) Ln e C) -4 LCn eq Q ch :34 LA C14 00 .,-1'00 ~tnL * -4 4J \* C)' 00 00 C 0 a -4 4 -) \ -1 -4 0'-4 .4 0- C U c 41) 0L X al- + I +I + I + I XCU- + - + I >Ud.

CdL 0- 0o 0 M 4-

W_4V)lcd V

<W W EU) 4-0)C)D 04D 00 000 *HCDr- ) PC> > rU '0 $4' 0 )cUd 4-)Cfl $4I- 1-0 0 0, .0 0- 0 0 %0 > > >-4 3

u)( 4) = < - ).4 x CD H -4 < r_ r4 0W ~ -4 '.0 '. 0. o~l %D CA N. CO (nm004) 0 .J 4~.M uj j $.' 1- \ -4 %0 '-' -* In 0:1 0t(1- 0

0) 0E 44IU 4 V 41'L 1-4 0 C) t ClUX () ) > CU '-0 >00

> 4 C's CU > b4- - 0 > 0 $4

4.)4-) 0 4) >V) It

(1.4 *1-4 4140(- * .iwo m 0 CU CUi co 0:U$U=) 0 $4 $4Cl $4 k4 fA_j *r4 PP ONO4) ) 41) P. a)0

*; dp 0\ *-4 .0~ 0 ~ P o' I..0 0\ W, r_>8 0 E0 04.) * *0 4J) *'' ~ *

- ~ ~ ~ C 14 14 C. U C H 4 4) CU 44. -Ca 4.) 41 P0~0

I-V- ) U) rZ V ) t) 4-3 I$4 >..00 0 Vd) U) 4.) 0 0 CA In 4.) u-x.~ : $ 0 0) k4 M: 4 0 0 CU U) 0~l0 4-) k ;4 0D 4.) $4 4 u -4 > 4-)to U U 41) 4.) tn (f) ) 4.) 41) U) 0 Ou)6. - U U 0 -U) t/) 000 4 00 o U) CN 0%Q <4.P

r. :. 0.: LL)4 ~0 0H -4 14 0 *H '4 -',

>. >. L. LI. > > ElI. z C1 t4(J C)

17

4

c4 >4 4 -

5.' + + + + I-'- t I -LC.)

LU U)-

4-)CD M to j 4-0\ - - -

x M().. + I + a + a + I X co. + a + I + I + I a

0

00

'-0 4.44. 41J) 0 0) 0n 0) () 0 0

(D -.. LI) LI) aE.- ) L)Ur- U.. x 0 -f -n t ) X

ILI 5 ia . ('4 0' (' 4) ) t C-04*n ('4 (' (40I L) L) 0)a)O 0)4

-j 4- 4.)1q L a) a 0 X 4-4

)404 0C) <*C0

Xn ": 00 ' -

4J ~ 'C ~ Od a tI)(14 Ln) - \0 \O0 00 : > (n

it -41 - M + a + a + I + a Xcd'. + I + a + I + I> fU) 4.)< 4J a)

a- V)- - - - -

C 0a) cda tn44 aCLJ1 (D a) 0 0 4-4 0= 0 0 tA- a

0 P-- ('4 \0 0 to - 44-4 ) CO \-- ccnU ('1 0 -- 4) 414'-4.-4.. 0~ 4 - C) CIU) CO 0 OS )

C-) 0 r-E a- 04)-4 -4) 0) CO C4

(I.~5. CUh (1 W l

00 U) 0Ldj- X-i C14 V. P0 C14 .. 41o~ 0 .440 oC~ ~ a> 0d -.' >. U)bo..~

fr< NL U) r'4 Cd d )(4 U) C)> C d4-41 cc 0) >\ 0P 0 4

0A 0 E 0 0..4~) . *0 .) *4) 4 > C(D CU44 (4C) U 4 ' ) U )d

(n4 $4a t )4U~ ..4 4.) 4J V) .. 1. 4- .) C U

4)4 0U) U) 4) 0 1 a) ) U) >.5.;4 4) 4 rq54 4 )(U U ~) C) 4,) ,-) 0. U)ba4) 4. d U

0. C- E.) 0 k -l) Cd

4) 0 4-)

0- -3 Cd .4 0- 4J C4 CIS k s .-

- 1 k -j $4 p u -A > - ----- 1.-..

I______(n__U)___4_____)______(f)_____1__4-__

Acceptable Limits of Maximum Scatter

An experimental error analysis was made based on errors of + 1.0% in straingage indications, ± 0.5% in load indications, ± 0.001 in. in cross-sectionaldimensions, and ± 0.025 in. in X-Y chart readings. According to this analysis,experimental errors could be as high as ± 1.5% in conventional tests and ± 4.0%in bend tests. These values of maximum expected experimental errors, then, arethe acceptable limits of maximum scatter.

Comparison of Stress-Strain Curves

From Figure 5, it may be seen that stress-strain curves determined frombend tests agree fairly well with those determined from conventional tests. Alsofrom Figure 5, it may be noted from the conventional tests that, at any strainlevel, the corresponding values of stress in compression are generally higherthan those in tension. This same trend is brought out by the bend tests.

Observations concerning both scatter and discrepancies are best noted fromthe results reported in Tables V through VII.

Scatter, as expected, was generally higher in bend tests than in conven-tional tests. The acceptable limits of maximum-percentage scatter were neverexceeded in the bend tests and only once in the conventional tests - in thedetermination of Young's modulus in compression for yield strength level 1specimens. Even in this case, however, scatter was considered acceptable notonly because of the low value of scatter determined (-2.2%) but also because ofthe limited number of tests involved (four). Maximum percentage scatter, then,was generally within the computed allowable limits, and, therefore scatter wasnot deemed to be objec" .nable in any of the testing.

Discrepancy values, as mentioned earlier, are measures of agreement amongresults predicted by the bend tests and those determined by the conventionaltests.

Very close agreement was generally found among the values of Young's modulipredicted by the bend tests and those determined by the conventional tests. Thelargest value of discrepancy of -2.4% occurred for the value of Young's modulusin compression for yield strength level 3 specimens. Very good agreement, then,within 2.4%, was found in the elastic portions of the stress-strain curves pre-dicted by the bend tests and those determined by the conventional tests.

Beyond the elastic region, on the other hand, at least within the 2.0% oftotal strain to which all specimens were subjected, the flow stress values pre-dicted by the bend tests were generally higher than those determined by theconventional tests. The largest value of discrepancy of +9.8% occurred for thevalue of flow stress in tension at 2.0% of total strain for yield-strength level1 specimens. Fair agreement, then, (within 9.8%) was found to exist in theearly plastic portions of the stress-strain curves predicted by the bend testsand those determined by the conventional tests.

19

IX. SUMMARY AND CONCLUSIONS

1. Expressions from Nadail, adapted for experimental exploitation, havebeen presented that permit the calculation of the early portion of the stress-strain curve, both in tension and in compression, from bend tests. Theseexpressions are applicable to beams, whether or not subjected to pure bending,and are particularly adaptable to materials which fail with relatively smalldeformations. They are limited to the extent that shear stresses in the bendspecimen must be negligible.

2. Three of these expressions (two of which are applicable when the stress-strain curve in tension differs from that in compression and one of which isapplicable when the stress-strain curves in tension and in compression are equal)have been applied to bend specimens of steel, heat treated to three differentyield-strength levels. The bend tests were carried out to strain values of 2.0%.

3. Independent tension and compression tests were performed on specimensSmade from the same stock and subjected to the same heat treatment as the bend

specimens. These conventional tests were also carried out to 2.0% strain.

4. Stress-strain curves determined from the bend, tension, and compressiontests have also been presented. Mechanical properties derived from thesecurves, including Young's moduli, yield strengths at 0.2% offset, and flowstresses at both 1.0% and 2.0% total strain have also been presented. Maximumpercentage scatter and percentage discrepancies have been included with thesetabulated values.

5. Finally, a comparison of the results predicted by the bend tests andthose determined by the tension and compression tests of the specimens, atleast within the first 2.0% strain, indicated that:

a. Scatter was generally higher in bend tests than in conventionaltests, but not objectionable.

b. For the present tests, the observation from conventional teststhat, at any strain level, the corresponding value of stress in compressionwas generally higher than that in tension was confirmed in the bend-test results.

c. Also for the present tests, the results indicated that the bendtest could be regarded as a very good substitute for the conventional tests(within 2.4% agreement) for determining the elastic portions of stress-straincurves and a fair substitute (within 9.8% agreement) for determining the earlyplastic portions of stress-strain curves.

ACKNOWLEDGMENTS

The author wishes to acknowledge the invaluable aid provided by Mr. J. I.Bluhm, Chief of Theoretical and Applied Mechanics Research Laboratory and thehelpful suggestions offered by Messrs. R. Papirno, F. I. Baratta, andK. Robertson, also of Theoretical and Applied Mechanics Research Laboratory.

20

LITERATURE CITED

1. NADAI, A. Plasticity. McGraw-Hill Book Co., Inc., New York, 1931.

2. BLUHM, J. I. Mechanical Tests - Application of the Bend Test for Determi-nation of the Stress-Strain Curve. Watertown Arsenal Report No. WAL 110/19,1950.

3. GROBE, A. H., and ROBERTS, G. A. The Bend Test for Hardened High SpeedSteel. Transactions of the American Society for Metals, v. 40, 1948.

4. BURGHARDT, A. M., and ELDER, A. S. Mechanical Tests - Development of aStandard Bend Test for Cemented Carbides. Watertown Arsenal Report No.WAL 110/16, 1950.

S. DUCKWORTH, W. H. Precise Tensile Properties of Ceramic Bodies. Journalof the American Ceramic Society, v. 34, no. 1, 1951.

6. Standard Methods of Compression Testing of Metallic Materials. Book ofAmerican Society of Testing and Materials Standards, Part 30, 1966.

21