Repeatability and reproducibility of compression strength ......ASTM International standard test...

NIST Technical Note XXXXRepeatability and reproducibility ofcompression strength measurements

conducted according to ASTM E9

William LueckeLi Ma

Stephen GrahamMatthew Adler


conducted according to ASTM E9William E Luecke

Li MaMetallurgy Division

Materials Science and Engineering Laboratory

Stephen M GrahamUnited States Naval Academy

Mechanical Engineering Department

Matthew A AdlerMarshall Space Flight Center

Jacobs ESTS GroupICRC

Sept 2010

US Department of CommerceGary Locke Secretary

National Institute of Standards and TechnologyPatrick D Gallagher Director

Certain commercial entities equipment or materials may be identified in thisdocument in order to describe an experimental procedure or concept adequately Such

identification is not intended to imply recommendation or endorsement by theNational Institute of Standards and Technology nor is it intended to imply that theentities materials or equipment are necessarily the best available for the purpose

National Institute of Standards and Technology Special Publication XXXXNatl Inst Stand Technol Spec Publ XXXX 38 pages (Sept 2010)

CODEN NSPUE2

Monday 27th September 2010 WERB Version Technical Note 1

Abstract

Ten commercial laboratories participated in an interlaboratory study to estab-lish the repeatability and reproducibility of compression strength tests conductedaccording to ASTM International Standard Test Method E9 The test employed acylindrical aluminum AA2024-T351 test specimen Participants measured elasticmodulus and 02 offset yield strength YS(02 offset) using an extensome-ter attached to the specimen The repeatability and reproducibility of the yieldstrength measurement expressed as coefficient of variations were cvr= 0011 andcvR= 0020 The reproducibility of the test across the laboratories was among thebest that has been reported for uniaxial tests The reported data indicated that us-ing diametrally opposed extensometers instead of a single extensometer doubledthe precision of the test method Laboratories that did not lubricate the ends ofthe specimen measured yield stresses and elastic moduli that were smaller thanthose measured in laboratories that lubricated the specimen ends A finite elementanalysis of the test specimen deformation for frictionless and perfect friction couldnot explain the discrepancy however The modulus measured from stress-straindata were reanalyzed using a technique that finds the optimal fit range and appliesseveral quality checks to the data The error in modulus measurements from stress-strain curves generally increased as the fit range decreased to less than 40 of thestress range

Keywords compression testing ILS ASTM E9 yield strength elastic modulus


1 IntroductionCompression testing is a conceptually simple method to establish the uniaxial stress-strain and mechanical behavior of materials Because the test specimens can be rightcircular cylinders they are easy to fabricate The short gauge length of the test spec-imen sometimes makes it the only possible geometry for establishing uniaxial proper-ties for example normal to the plane of a plate Compression tests can also be used toestablish the strength of brittle materials [1 2] that would be difficult to grip in tensionKuhn [3] and Chait [4] have reviewed the methods for compression testing and havedemonstrated that although the test is conceptually simple the user must overcomemany experimental difficulties to translate the measured load and displacement curvesinto accurate stress-strain behavior

Much of the literature see Table 1 on implementing the compression test focuseson tests to large strains [5 7 8 10 12 13 17 18] to establish work hardening behaviorbeyond the strains at which tension test specimens neck Other studies are devotedto modelling processes such as upsetting [5 14 15 17 18] A common theme inthese and other studies has been to quantify the effect of friction [18 7 12] or optimallubricant [4 6 12 13] and barreling [5 11 17 9] on interpreting the stress-strainbehavior of the test specimen

ASTM International standard test method E9 [2] first established in 1924 is a con-sensus standard for conducting compression tests to establish the strength of materialsIt contains methods for testing cylindrical test specimens as well as methods for test-ing sheets with lateral support The standard contains requirements for calibrating andqualifying the testing machine including extensometers and aligning the fixtures andtest specimen It recommends but does not require specific test specimen geometriesand lubricants In addition it suggests several fixture designs It does not require theuse of an extensometer in contact with the test specimen to measure strain and moststudies that reference E9 infer the test specimen strain and stress from the displacementof the actuator

Although the first version of E9 was released eight decades ago its precision hasnever been formally evaluated as required [19] Such evaluations require a formalinterlaboratory study which can benefit both end user and testing laboratories Usersneed the results of interlaboratory tests to determine the uncertainty that should beassociated with the value of a material parameter obtained using a test method Labo-ratories that employ test methods use interlaboratory studies to identify the deficienciesin their test methods and improve their implementation of them

This manuscript reports the results of an interlaboratory study to establish the preci-sion of ASTM International standard test method E9 for determining the yield strengthand elastic modulus in compression The results of this study were incorporated intothe Precision and Bias statement of E9 in 2009 This report goes beyond the researchreport [20] that documents the calculation of the precision by comparing the results toother interlaboratory studies of uniaxial test methods Sec 41 analyzing some of thepossible sources for the variabilitySec 42 and presenting a method to evaluate theelastic modulus measured in the test Sec43


Table 1 Summary of literature that analyzes the compression testReference Content emax Materials Lubricant

Banerjee 1985[5] b 16 Al teflon MoS2 oilnone

Carter 1985[6] F 035 Al MoS2 noneChait 1975[4] r NACook 1945[7] f 07 Cu noneGunasekera 1982[8] f 12 1022 steel teflonHsu 1969[9] bfF NA Cu teflonKamaluddin 2007[10] F 08 Al greaseKobayashi 1970[11] b 14 1040 steel graphiteLovato 1992[12] f 1 Al Nb brass

steelMoS2 teflonBN none

Male 1966[13] f 08 Al Ti brass graphite lanolinparaffin

Mescall 1983[14] F NA 4340 steelPapirno 1983[15] 0 NA steel teflonRay 1983[16] f NA steel teflonSchey 1982[17] b 1 1020 steel 6061

AlMoS2 teflon

Woodward 1977[18] f 12 steel teflon

emax maximum strain in testNA not availableKey to content of referenceb barreling analysisf friction analysisF finite element analysisr review article

2 Experimental ProcedureThis interlaboratory study followed the methods of ASTM E691 [21] and uses statis-tical terms in accord with ASTM E177 [22]

21 ParticipantsUsing the ASTM International [23] and American Association for Laboratory Accred-itation [24] laboratory directories the organizers contacted and discussed the interlab-oratory study with twenty-five possible laboratory participants From this original list


Table 2 List of participants in this studyParticipant URL

AADFW Inc Euless Tx httpwwwaadfwinccom

Alcoa Pittsburgh Pa httpwwwalcoacom

Exova Glendale Hts IL httpwwwexovacom

Dickson Testing Company IncSouth Gate Ca

httpwwwdicksontestingcom

Imperial College MechanicalEngr London England

httpwwwimperialacuk

MAR-TEST Inc (Cincinnati)Cincinnati Oh

httpwwwmar-testcom

MAR-TEST Inc (Stuart) StuartFl

httpwwwmar-testcom

Metcut Research Inc CincinnatiOh

httpwwwmetcutcom

Stork Climax Research ServicesWixom MI

httpwwwstorksmtcomcrs

Westmoreland MechanicalTesting Youngstown Pa

httpwwwwmtrcom

thirteen laboratories agreed and were able to participate and ten ultimately completedthe test program Table 2

22 Instructions and methodThe participants followed ASTM Standard Test Method E9 [2] to establish the elasticmodulus E and 02 offset yield strength YS(02 offset) At the time of the studythe version of E9 in use was E9-89a but the only non-editorial difference between E9-89a and the current version E9-09 was the addition of the precision statement to the lat-ter which was the purpose of the interlaboratory study The participants also returnedelectronic traces of the stress-strain curves to the organizers All compression fixtureswere required to be qualified according to ASTM E9 [2] Section 66 using at least fiveof supplied test specimens unless the participant had already qualified the test setup ac-cording to Section 66 The participants conducted the compression tests using at leastone extensometer at a nominal strain rate of dedt = 0005 minminus1 = 833times10minus5 sminus1No laboratory reported strain measured from actuator displacement Each participantreported ten items as required in sections 1011ndash1019 and 10113 of standard methodE9 Material (test specimen ID) configuration description test specimen dimensionsas tested fixture and lubricant description testing machine description speed of test-ing (required in section 87 report actual value) stress-strain diagram modulus ofelasticity E yield strength YS(02 offset) and any anomalies


Figure 1 Schematic of the location of test specimen blanks in the original plate

23 Test SpecimenThe material tested was aluminum alloy AA2024-T351 which is solution heat-treatedand stress-relieved by controlled stretching It was supplied as a plate with thicknesst = 222 mm (0875 in) from which the organizers cut and distributed test specimenblanks which were distributed throughout the plate Figure 1 describes the location ofthe test specimens in the original plate and their numbering scheme Only test speci-mens in rows 1 and 2 were used in this study Test specimens number 1-50 came fromrow 1 test specimens 51ndash100 came from row 2 Figure 2 shows the test specimen withdimensions and tolerances The drawing provided to the participants showed the di-


Figure 2 Dimensions of the test specimen used

mensions in non-SI units Participants machined their own test specimens from sawedblanks that the organizers supplied

Test specimens were tested with the loading axis transverse to the rolling direc-tion in the plane of the plate the so-called long-transverse (ldquoLTrdquo) orientation Mil-Handbook-5J [25] Figure 14123(a) The test specimen ID takes the form ldquoLT-NN-L-Xrdquo where ldquoLTrdquo identifies the orientation relative to the rolling direction ldquoNNrdquo identi-fies the test specimen number (1ndash250) ldquoLrdquo identifies the laboratory that received thetest specimen blank (A-K) and ldquoXrdquo identifies the test order of the test specimen at agiven laboratory

24 Compression fixturesThe participants used a variety of loading fixtures some of which involved a sub-pressmounted in the testing machine to improve alignment Others used adjustable platensthat were aligned and then locked Three laboratories used diametrically opposed ex-tensometers instead of a single extensometer No laboratory reported strain from ac-tuator displacement Table 3 describes the specimen fixturing alignment capabilitynumber of extensometers and the lubricant used in each laboratory


Table 3 Descriptions of the compression setup extensometers and gauge lengths Gand lubricants for all laboratories

Lab test setup Extensometer Lubricant

A No sub-press Two opposedclass B-1G = 254 mm

Not reported

B Sub-press Single class notreportedG = 127 mm

Molybdenum disulfide

C No sub-press nospherical seat

Single classnot-reportedG = 254 mm

None

E sub-press Single class B-1G = 254 mm

Teflon tape

H No sub-press Single class B-2G = 127 mm


I No sub-press Two opposedclass B-2G = 254 mm

Not reported

J Precision groundsub-press aligned tocloser tolerance thanrequired for specimen nospherical seat

Two opposedclass B-1G = 254 mm

None

K No sub-press Platensaligned shimmed andthen locked No sphericalseat

Single classB-2G = 127 mm


L Sub-press Single class B-2G = 254 mm

WD-40

M Compression platensmounted in alignedhydraulic grips

Single classB-2 G notreported

None

3 Results

31 Stress-strain behaviorFigure 3 plots the engineering stress-strain curves by laboratory For conveniencecompressive strains and stresses are plotted as positive rather than negative valuesIn each case the stress-strain curve was shifted along the strain axis so that a linearfit to the stress-strain (S minus e) data in the range (50 lt S lt 175) MPa intercepts


Engineering Strain mm

Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M

Figure 3 Engineering stress-strain curves

the origin Figure 4 presents four views of the same stress-strain curves over differentstrain ranges

Table 4 summarizes the reported modulus E and yield strength YS(02 offset)for the laboratories Figure 5 plots the reported elastic modulus E by laboratoryFigure 6 plots the reported 02 offset yield strength YS(02 offset) by laboratory

32 Testing ratesFigure 7 plots the strain as a function of time for the laboratories that reported time dataThe interlaboratory instructions did not specify a control mode for the test Four lab-oratories (CHKL) conducted the test in strain control from the extensometer signalas indicated from the constant slope of the strain-time plot Figure 7 Three labora-



Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM

(b) Low-strain behavior


Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

(d) Plastic behavior

Figure 4 Engineering stress-strain curves (a) complete behavior (b) low-strain be-havior (c) yield behavior and (d) plastic behavior Dashed lines show the acceptedvalue for the modulus of 2024-T351 E = 752 GPa the 02 offset yield strengthdetermination and the e = 0008 total elongation

tories (AEJ) conducted the test in position control as indicated from the changingslope in the strain-time plot Figure 8 plots the strain rates in the elastic and plas-tic portions of the stress-strain curves calculated by linear regression The plasticstrain rate was calculated for strains greater than the strain at the 02 offset yieldstrength eYS002 lt e lt emax The elastic strain rate was calculated in the range0 lt e lt (eYS002 minus 0002) Laboratory J conducted the test in position control andset the elastic strain rate close to the specified value


Table 4 Reported data

Lab Sample E YSGPa MPa

A LT-85 756 3390A LT-1 729 3400A LT-40 768 3410A LT-26 751 3420A LT-66 738 3420A LT-78 747 3420A LT-82 763 3430B LT-28 731 3480B LT-39 765 3490B LT-54 750 3490B LT-9 750 3530B LT-80 834 3560C LT-68 720 3180C LT-84 728 3350C LT-90 715 3360C LT-16 724 3380C LT-77 714 3380C LT-27 707 3390C LT-58 729 3410E LT-25 683 3422E LT-31 670 3468E LT-87 693 3474E LT-71 686 3490E LT-17 705 3511E LT-8 709 3514E LT-41 706 3558


H LT-10 772 3450H LT-44 738 3470H LT-55 731 3470H LT-63 772 3470H LT-76 758 3470H LT-91 772 3470H LT-19 786 3540I LT-43 750 3480I LT-57 760 3490I LT-65 750 3490I LT-21 760 3500I LT-34 750 3500I LT-74 750 3500I LT-70 760 3510J LT-4 745 3405J LT-89 742 3416J LT-94 744 3416J LT-73 745 3421J LT-37 748 3425J LT-23 748 3431J LT-14 741 3434


K LT-24 758 3430K LT-42 807 3480K LT-51 876 3510K LT-56 841 3510K LT-5 800 3520K LT-13 765 3540K LT-83 NA NAL LT-79 730 3480L LT-45 842 3490L LT-69 784 3520L LT-12 842 3550L LT-36 757 3560L LT-6 775 3560L LT-92 858 3630M LT-18 690 3380M LT-11 720 3420M LT-59 710 3420M LT-62 700 3420M LT-86 720 3420M LT-33 720 3430M LT-81 680 3450

NotesYS=YS(02 offset)

4 Analysis and discussion

41 Expected variabilityTable 5 summarizes the mean and standard deviation sd and coefficient of variationcv of the reported n measurements of the elastic moduli and yield strengths Table 6defines the statistical parameters used in this section

The results of an interlaboratory study contain variability that arises within a givenlaboratory and variability that arises between laboratories The terms repeatability andthe reproducibility denoted by subscripted ldquorrdquo and ldquoRrdquo are often used to differenti-ate between the sources [22] In a general sense repeatability characterizes the abilityof an individual laboratory to repeat measurements while reproducibility characterizesthe ability of an individual laboratory to achieve the global mean or accepted value Forexample if the results from an individual laboratory are tightly grouped their repeata-


Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa

Figure 5 Reported elastic modulus E Dashed lines show the average reported mod-ulus and a commonly accepted value of the modulus (E=752 GPa) from Mil-HDBK-5J [25] and the average of all the measurements E = 749 GPa

bility is high but their mean value may still deviate significantly from the acceptedvalue in which case their reproducibility is low

Both the variability in the material and the variability of the test method influ-ence the repeatability The excellent repeatability of the measurements for both E andYS(02 offset) in laboratories A I and J Table 5 shows that the material variabilityin this study is quite low and therefore the implementation of the test method by theindividual laboratories is the major contributor to repeatability

Figure 9 and Table 7 compare the results for repeatability and reproducibility forthis study to the results of other interlaboratory studies of tensile tests at room [26 27]and elevated temperatures [28] to establish the 02 offset yield strength YS(02 offset) In Figure 9 the within-laboratory and between-laboratory standard deviations


Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa

Figure 6 Reported 02 offset yield strength YS(02 offset) The dashed line is theaverage of the results from all laboratories

sr Eq 4 and sR Eq 7 see Table 6 are divided by the mean value and expressed astheir respective coefficients of variation cvr Eq 5 and cvR Eq 8

The repeatability coefficient of variation of the yield strength measurements in thisstudy derived from the average of the standard deviations of the individual laborato-ries is cvr = 00111 Eq 5 while the coefficient of variation of the reproducibilitycvR = 00197 Eq 8 is about twice as large The repeatability and reproducibilityof compression tests established in this study are among the best measurements of allreported uniaxial measurements [26 27 28]


time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M

Figure 7 Reported strain as a function of time

42 Effect of test method implementationBecause the laboratories were free to implement the test method in different wayswhile still complying with the standard their result can be used to learn about the effectof different aspects of test method on the measurement In particular the results can beexamined to determine the effects of the number of extensometers and lubrication onthe quality of the measurement

421 Effect of number of extensometers

Some laboratories used a single extensometer while others used two opposed exten-someters to measure the strain Figure 10 plots the reported modulus and yield strengthfor the laboratories grouped by the number of extensometers used in the determinationThe three laboratories A I J with the best repeatability and reproducibility of E and


Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain

(a) elastic strain rate

Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain

(b) plastic strain rate

Figure 8 Calculated (a) elastic and (b) plastic strain rates for laboratories that re-ported time data Symbols differentiate between position-control and strain-controltests Dashed line indicates the requested rate dedt = 833times 10minus5 1s


Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000

alloy steelaluminumstainless steelsteelsuperalloyThis Study

(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility

Figure 9 Literature data [26 28 27] on (a) repeatability (within-laboratory) and (b)reproducibility (between-laboratory) of yield strength YS(02 offset) Table 7 sum-marizes the data


Table 5 Summary statistics for the modulus and yield strength dataLab n E sd(E) cv(E) YS sd(YS) cv(YS)

GPa GPa MPa MPaA 7 750 14 0018 3413 14 0004B 5 766 40 0052 3510 34 0010C 7 720 08 0011 3350 77 0023E 7 693 14 0021 3491 43 0012H 7 761 20 0026 3477 29 0008I 7 754 05 0007 3496 10 0003J 7 745 03 0004 3421 10 0003K 7 808 45 0056 3498 39 0011L 7 798 49 0062 3541 51 0014M 7 706 16 0023 3420 21 0006

Note YS= YS(02 offset)

Parameter Grand Average sr cvr sR cvR

E macrE= 750 GPa 27 GPa 0036 44 GPa 0059YS(02 offset) macrYS(02 offset)= 3462 MPa 38 MPa 0011 68 MPa 0020

Table 6 defines the parameters Because laboratory B tested only five specimens instead of seventhe mean values shown in Figures 5 6 10 and 12 differ from the Grand Average also known asthe average of cell averages Table 6 Eq2

YS(02 offset) are the only ones that used a system of two-opposed extensometers in-stead of a single extensometer In addition the measured elastic modulus in these threelaboratories was the closest to the accepted [25] valueE = 752 GPa Figure 10a Notethat the repeatability of the modulus and yield strength from the labs that used a singleextensometer is worse (ie larger variability) but also that for an individual laboratorythe values usually all lie above or below the grand average Using two extensometerswill tend to average the effect of non-axial loading since during bending one side ofthe test specimen will be displaced more and the other less Because the values foran individual single-extensometer laboratory are usually displaced to one side of theglobal mean value points toward the alignment of the compression fixture rather thanmachining of the test specimen as the source of the non-axiality If the ends of the testspecimen were not parallel the measured values would tend to encompass the meanvalue because no special relationship exists between the test specimen and the loadingfixture Conversely the extensometer is usually mounted on the test specimen with afixed relation to the orientation of loading fixture so bending induced by a slightly mis-aligned loading fixture is always in the same geometric relation to the extensometerwhich will tend to always over- or under-estimate the strain


Table 6 Definitions of repeatability and reproducibility statistics

Formula Description

n number of tests in a laboratory n asymp 7

p number of laboratories p = 10

Yij individual test result in lab j

1 lt i lt n 1 lt j lt p

Yj =1

n

nXi=1

Yij average test result in lab j (cell average) (1)

macrY =1

p

pXj=1

Yj average of cell averages (grand average) (2)

sj =

vuut 1

nminus 1

nXi=1

(Yij minus Yj)2 standard deviation measured in lab j (3)

sr =

vuut 1

p

pXj=1

(sj)2 repeatability (within-lab) standard deviation (4)

cvr =sr

macrYcoefficient of variation within laboratories (5)

sY =

vuut 1

pminus 1

pXj=1

(Yj minus macrY )2 standard deviation of cell averages (6)

sR =

rs2

Y+ s2

r(nminus 1

n) reproducibility standard deviation ((between-lab) (7)

cvR =sR

macrYcoefficient of variation between laboratories (8)

422 Effect of Lubricant

The standard allows the laboratory to choose whether to lubricate the ends of the testspecimen during the test Figure 11 shows the engineering stress-strain curves identi-fied by the use or omission of lubricants Several laboratories did not report lubricantuse Table 3 identifies the lubricants used Three laboratories used no lubricant andtheir stress-strain curves are the lowest in the collection Figure 12 plots the reportedmodulus E and yield strength YS(02 offset) identified by lubricant use The aver-age yield strength from the three laboratories that did not use lubricant was 106 MPalower (31 ) than the average of the laboratories that lubricated the specimen Simi-larly the average reported elastic modulus E from the three laboratories was 41 GPa(57 ) smaller Table 8 an analysis of variance shows that the reported yield strengthYS(02 offset) and modulus Eare both significantly different for the lubricated andunlubricated cases


Table 7 Literature data [28 26 27] for repeatability and reproducibility in mechanicaltesting

Source Material T YS cvr cvRC MPa

[26] EC-H19 aluminum 200 1584 00210 00210[26] 2024-T351 aluminum 200 3629 00140 00150[26] AISI A105 steel 200 4024 00140 00250[26] SS316 stainless steel 200 4801 00140 00410[26] Inconel 600 200 2683 00090 00220[26] SAE 51410 steel 200 9675 00090 00160[27] AA5754 Al 200 1057 NA 00160[27] AA51802-O 200 1264 NA 00100[27] AA6016-T4 200 1272 NA 00110[27] DX56 low-carbon steel 200 1620 NA 00230[27] HR3 steel plate 200 2286 NA 00410[27] ZStE 180 steel 200 2671 NA 00500[27] S355 steel plate 200 4276 NA 00310[27] SS316L stainless steel 200 2307 NA 00350[27] X2CrNi18-10 stainless steel 200 3038 NA 00330[27] X2CrNiMo18-10 200 3533 NA 00390[27] 30NiCrMo16 high strength steel 200 10399 NA 00100[27] Nimonic 75 CRM 661 200 3021 NA 00180[27] Nimonic 75 CRM 661 200 2981 NA 00200[28] SS304 stainless steel 3160 1273 00580 01040[28] Low-carbon steel 3160 2364 00110 00350[28] 225 Cr 1Mo steel 3160 4547 00230 00330[28] A286 stainless steel 3160 6995 00280 00300[28] SS304 stainless steel 5930 1014 00770 00990[28] Low-carbon steel 5930 1330 00390 01040[28] 225Cr 1Mo ferritic steel 5930 3379 00260 00670[28] A286 stainless steel 5930 6422 00260 00350This study Al 2024-T351 200 3462 00111 00197NotesYS= YS(02 offset)NA = data not available

Since most laboratories used an extensometer with a gauge lengthG = 254 mm onthe test specimen Fig 2 with length l asymp 48 mm and diameter d = 127 mm the endof the test specimen is approximately one test specimen diameter away from the exten-someter contact point That distance complies with the requirements of E9 and shouldminimize the effect of the non-uniform stress caused by friction at the specimen endsNo study has examined the sensitivity of the strain measurement to the non-uniformstress at the end of the specimen but the existence of non-uniform stresses caused byfriction is well known [29] Finite element analysis (FEA) using the commercial finite-


Table 8 Analysis of variance tables for assessing the effect of lubrication on modulusand yield strength

Table generated on 2010-09-22 190527Analysis of Variance Table

Model 1 E ˜ 1Model 2 E ˜ LubricatedResDf RSS Df Sum of Sq F Pr(gtF)

1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1

Analysis of Variance Table

Model 1 YS02 ˜ 1Model 2 YS02 ˜ LubricatedResDf RSS Df Sum of Sq F Pr(gtF)

1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1

Key to parameters in tableE E elastic modulusYS02 YS(02 offset) 02 offset yield strengthData from laboratories that did not report the lubrication are omitted Model 1 is themean value of of the parameter and model 2 computes the mean value for the lubricated(ldquoYesrdquo) and unlubricated (ldquoNordquo) cases

element modeling software AbaqusStandard 610[30] was used to analyze the effectof friction and gauge length on the response of the specimen By exploiting the axialand radial symmetry of the specimen and platens it was only necessary to model theupper-right quadrant the specimen with radius r = 63 mm and length l = 2425 mmThe specimen mesh Figure 13 was constructed with 1542 quadrilateral four-nodeaxi-symmetric (CAX4) elements The platens were modeled as non-deforming rigidplanes of infinite elastic modulus Roller boundary conditions were applied on the axialcenterline and the specimen midplane The specimen material was modeled as a ho-mogeneous elastic-plastic time-independent material exhibiting strain hardening Theplastic deformation was modeled by the J2 (or von Mises) flow plasticity theory withisotropic hardening[30] The uniaxial stress-strain curve was taken from specimen LT-14 of the experimental results down-sampled to 58 points with the Youngrsquos modulusset to the accepted value E = 752 GPa and Poissonrsquos ratio=ν = 033 This materialmodel yields at a true stress σ = 1904 MPa at a true strain ε = 00026 and not at the


value of the 02 offset value YS(02 offset)=3434 MPa All of the stress-straincurves Fig 4a exhibited this behavior

Two limiting cases of zero friction and complete friction at the specimen-plateninterface were modeled The simulation was performed by pushing the rigid platenincreasingly to displacement of 0485 mm which is e = 002 deformation for the zerofriction case The effect of extensometer gauge length was tested by following theaxial displacement of two nodes Figure 13 located l = 635 mm and l = 127 mmabove the center plane of the specimen These nodes correspond to the contact pointsof extensometers with G = 127 mm and G = 254 mm respectively To calculatethe stress-strain behavior the force on the platen the displacement of the platen thedisplacement of the two extensometer contact points and a surface corresponding to thelength between the platens see Figure 13 were recorded The stresses were calculatedfrom the measured radii at those points

Figure 14 shows the computed true stress-strain curves for strain measures acrossthree gauge lengths (G = 127 mm G = 254 mm and G = 485 mmndashacross theloading platens) and for the two limiting friction cases frictionless (f = 0) and perfectfriction (f = 1) It also shows the true stress-strain curve used as the input model Inthe figure the true stresses are calculated from the load P and the instantaneous areaA by by assuming conservation of volume in deformation

A0l0 = Al (9)

where A0 and l0 are the original area and gauge length respectively This calculationmimics what would be done in analysis of an actual experiment where the instanta-neous load-bearing area A is calculated from the strain For the frictionless case allthe strain measures yield the same stress-strain behavior as the input model as theyshould For the case of perfect friction f = 1 the strains measured across the two ex-tensometer gauge length G = 127 mm and G = 254 mm differ by less than 05 MPaeach other and from the frictionless cases The difference between the average ofyield strengths measured by laboratories that lubricated and those that did not was wastwenty times this large ∆ YS(02 offset)=104 MPa Figures 11 and 12 The truestress calculated from the displacement of the loading platen a common method thatuse the displacement of the actuator corrected for machine compliance is about 6 MPaor 14 above all the other curves Note that no laboratory measured strain this wayeach laboratory used an extensometer on the test specimen with contact points remotefrom the test specimen end faces The agreement between the extensometer methodsfor the frictionless and complete friction cases eliminates friction as the source of thedifference in yield behavior between the laboratories that lubricated and those that didnot

The finite-element analysis also determined the evolution of the stress distributionsin the test specimen Figure 15 shows the von Mises stress evolution for four strainsStresses less than the yield stress of the material model σ = 1904 MPa are shownin white Consistent with other analyses [29 6] a non-deforming cap forms at the testspecimen end As the specimen deforms a region of slightly higher stress developsthat extends just into the region that the longer G = 254 mm extensometer samplesFigure 16 shows the evolution of the shear stress σ12 for the same four strains The


bulk of the test specimen has zero shear stress Only at the test specimen ends wherefriction constrains the deformation does shear strain develop

43 Elastic ModulusThe elastic modulus measured in the test is very sensitive to the alignment and sensitiv-ity of the test setup As a result ASTM E 9 [2] requires that laboratories validate theircompression test fixture by measuring the elastic modulus of aluminum alloy 2024-T4 bar according ASTM E 111 [31] and obtaining measurements on five consecutivespecimens to within 5 of a stated value E=738 GPa The behavior of the reportedelastic modulus should be a good indicator of the quality of the compression test facil-ity

The interlaboratory study did not require laboratories to revalidate their test setupsbut they did report the measurements of elastic modulus Figure 5 made during thecompression tests of this study Most of the laboratories only used a ASTM E 83 [32]Class B-2 extensometer see Table 3 rather than the roughly twice-as-accurate classB-1 extensometer required by ASTM E 111 [31] when elastic modulus is the primaryparameter to be determined But because the primary parameter to be determined wasthe yield strength E 9 Section 92 permits the use of the class B-2 extensometer

The laboratories had wide latitude in the method to determine the elastic modulusto report To reduce the variability due to the interpretation of the individual labora-tory and to put each modulus measurement on a consistent basis we reanalyzed eachstress-strain curve to estimate the elastic modulus using a technique [33] based on themethod of Scibetta and Schuurmans [34] These reanalyzed moduli are denoted by thesymbol EGA to differentiate them from the moduli that the participants calculated andreported denoted by E In addition to estimating the modulus the method includessome checks on the quality of the data that may be useful for laboratories that seek toimprove their modulus measurement

Many of the following plots evaluate the quality of the measurements by employingthe absolute modulus error ∆EGA in a measurement which is defined as the absolutevalue of the difference between the accepted modulus [25] for 2024-T351 aluminumEacc

Al = 752 GPa and the calculated modulus EGA

∆EGA = |EaccAl minus EGA| (10)

Other references [35 36 37 2] recommend different values in the range 738 GPa ltE lt 761 GPa and differentiate [36] between longitudinal and transverse orientation

Method for analysis The method consists of nine steps

1 Find the knee of the stress-strain (s minus e) curve by the method of Scibetta andSchuurmans [34]

1 Find the point on the stress-strain curve (e1 s1) closest to s1 = 005 max(s)2 Create point (eo so) where eo = e1 and so = 02 max(s)

3 Find the point on the stress-strain curve (et st) that is on a line drawnthrough (e0 s0) that is tangent to the stress-strain curve


2 Truncate the stress-strain data at (et st) and normalize by these values Retainthe maximum values of the test record (emax smax)

3 Check digital resolution δ of stress and strain The digital resolution should beδe lt

3212

xmaxet

and δs lt 3212

xmaxst

No more than more than 25 of points shouldhave zero stress or strain change from the previous point

4 Use the Scibetta-Schuurmans [34] algorithm to determine optimum fit windowand calculate the slope which is the elastic modulus EGAin normalized formThe Scibetta-Schuurmans algorithm finds the optimal region for determining themodulus by performing a linear regression of stress on strain on every possiblesubset of data in the region eo lt e lt et that contains at least 20 of the dataThe regression with the lowest residual standard deviation is the optimum fitIn some cases more than one million fits were evaluated for each stress-straincurve

5 Check for excessive noise in optimum fit window defined as the standard errorof the regression in step 4 sj defined in Table 6 where n is the number of stress-strain pairs in the optimal region Yij is the normalized stress evaluated at pointj and Yj is the predicted normalized stress from the fit to the optimal regionPerform the complementary regression of strain upon stress as well In bothcases the standard error in strain or stress should not be greater than 001

6 Extend the range of fit to include all stress points whose deviation from the opti-mal fit line is less than one times standard error computed in Step 5

7 Refit the extended data set to determine modulus EGA

8 Examine the shape of the stress and strain residuals as a function of strain inthe extended fit If the slope of the residuals in the first or fourth quartile of theextended range is more than 005 the data exhibit excessive curvature At leastfive points must exist in each quartile to evaluate this curvature

9 Check that the stress range of the optimal fit is greater than 04st

The method employs four metrics to determine the quality of the modulus

bull Data quality 1 digital stress and strain resolution should be sufficient (Step 2)

bull Data quality 2 strain or stress signal should not have excessive noise (Step 5)

bull Fit quality 1 the stress and strain residuals in extended data range should nothave excessive curvature (Step 8)

bull Fit quality 2 the size optimal fit range Rf should be greater than or equal to40 of the total range used to determine the modulus (Step 9)

The rest of this section will examine the results of the modulus measurement EGAusing these four quality metrics


Data Quality 1 sufficient digital resolution Figure 17 summarizes the strain andstress resolution Estimating the digital resolution of a data set post-test is difficult andthe interested reader should consult the original reference by Graham and Adler [33]To create the figure the digital resolution was estimated from the data set by taking theabsolute value of the difference of each sequential pair of stress and strain points forexample |siminussi+1| Those differences expressed in units of δ from step 3 were binnedto create a histogram If too many of the points show no change between reading or ifthe most frequent change is many times larger than the digital resolution δ defined inStep 3 the stress-strain curve may have insufficient digital resolution This conditioncould arise for example if a load cell were used near the very lower limit of its workingrange or if the analog-to-digital converter had insufficient precision Figure 17 plotsthe index of the bin with the maximum fraction of the data in units of δ defined instep 3 against the fraction of the points in the ldquozerothrdquo bin which is the fraction ofpoints where the stress or strain value did not change between readings The symbolsshow the fraction of the points in the bin of maximum fraction broken into two groupsthose where the bin of maximum fraction contained less than 25 of the data ((0 25])and those that contained more than 25 of the data ((25 Inf) The method identifiesexperiments with insufficient digital resolution as those where the bin of maximumfraction is greater than 3 and either the fraction in the zeroth bin is gt 25 or thefraction in the bin of maximum fraction is gt 25 The first condition is identified bythe dashed lines The second ldquoorrdquo condition comprise those points identified by greencircles with y value greater than 3 No experiment demonstrated insufficient digitalresolution

Data Quality 2 excessive noise Excessive noise in the strain or stress signal willdegrade the quality of the measured modulus The method identifies experiments withexcessive noise in these signals as ones in which the standard error of the fit is greaterthan 001 Figure 18 plots the standard error of the fit for both strain and stress bylaboratory The symbols identify three levels of modulus error Eq 10 The noise in allthe experiments was sufficiently low No obvious relation exists between the absolutemodulus error ∆E and either the standard error of stress or strain

Fit Quality 1 Excessive curvature in extended data set Some metric of the curva-ture of the optimal fit range is necessary since the method only selects the best fit overan optimal region That fit might still be poor One method for examining the qualityof the fit is to examine the deviation from the fit line in the first and fourth quartiles ofthe optimal range Curvature of the stress-strain record frequently appears this way Ifthe slope of the residuals vs strain in the outer quartiles is greater than 5 of the slopein the optimal region the curvature of the fit is deemed excessive

Figure 19 shows the slope of the residuals in the outer quartiles Different symbolsshow the level of absolute error of the elastic modulus Eq 10 All but one of the testsfall inside the plusmn5 limits In addition linear regression of the absolute modulus erroragainst the absolute value of the residual slope reveals no relationship


Fit Quality 2 Final fit range The second measure of the quality of the fit to deter-mine the elastic modulus EGA is the size of the optimal fit range Rf Figure 20 plotsthe absolute modulus error Eq 10 against the fraction of the range of original stressdata The dashed line is the boundary of the minimum acceptable limit Rf ge 04The absolute modulus error Eq 10 increases as the size of the fit region decreases asexpected and the boundary between the two regions lies at the chosen final fit rangeminimum Rf = 04 The mean error for tests with fit region Rf lt 04 is 25 timeslarger (488 GPa vs 195 GPa) than that from the acceptable region

Conclusions from elastic modulus analysis Of the quality metrics the size of thefinal fit range is the best predictor of overall quality of the modulus measurement andthe level chosen Rf ge 04 is a good metric for identifying potential problems withmodulus measurement

5 ConclusionsFive conclusions can be drawn from this study

bull The repeatability of yield strength determined from compression tests conductedaccording to ASTM E9 can be expected to be about 11 of the mean valuecvr= 0011 Figure 6 and Table 5

bull The reproducibility of yield strength determined from compression tests con-ducted according to ASTM E9 can be expected to be about 2 of the meanvalue cvR= 0020 Figure 6 and Table 5

bull Despite the perceived difficulties with alignment in compression the repeatabil-ity and reproducibility of the compression test was among the best measured foruniaxial tests Figure 9

bull Using two diametrally opposed extensometers instead of a single extensometercan improve the precision of the strain measurement by more than two timesFigure 10

bull If the final fit range for estimating the modulus is less than 40 of the elasticregion the modulus measurement is frequently in error Figure 20

In addition although the reported data indicated that yield strengths measured on unlu-bricated conditions were 31 lower than those measured using lubricated specimensFig 12 a finite-element analysis of the deformation that incorporated test-specimen-end friction did not identify any mechanism by which friction could caused the dis-crepancy

Author contributionsWilliam Luecke supervised the interlaboratory study and analyzed the reported modu-lus and yield strength data Stephen Graham and Matthew Adler analyzed the stress-


strain curves to recalculate the modulus and the associated data and fit qualities Li Maconducted the finite element analysis of the specimen deformation under frictionlessand perfect friction

AcknowledgmentsThe authors could not have completed this study without the generous donation of thetesting services of the participants including those who volunteered but ultimatelycould not complete the testing in the brief time allotted Ray Schiltz (AADFW Inc)Rich Brazill (Alcoa) Rick Kapaun (Exova) Bill Swartz (Constellation TechnologyCorp) I Ahmed (Dickson Testing Company Inc) James Hartman (Honeywell Aero-space) Hugh MacGillivray (Imperial College Mechanical Engr) Matt Webb (MAR-TEST Inc (Cincinnati)) Frank Worpenberg (MAR-TEST Inc (Stuart)) Ken Broen-ner (Metcut Research Inc) Dennis Galloway (Stork Climax Research Services) andMike Self (Westmoreland Mechanical Testing)

WEL thanks the other two members of the organizing team Rich Brazill and JamesHartman for their assistance Rich Brazill supplied the aluminum plate the test speci-men blanks and the test specimen assignments

References[1] International Organization for Standardization Hardmetals-compression

test Standard 45061979 International Organization for Standardization1979 Available from httpwwwisoorgisoiso_cataloguecatalogue_tccatalogue_detailhtmcsnumber=10402

[2] ASTM International Standard test methods of compression testing of metallicmaterials at room temperature Standard E9-09 ASTM International W Con-shohocken Pa 2009 doi101520E0009-09

[3] Howard A Kuhn Uniaxial compression testing In Howard Kuhn and DanaMedlin editors Mechanical Testing and Evaluation volume 8 of ASM Hand-book pages 143ndash151 ASM International Materials Park Ohio USA 2000

[4] R Chait and C H Curll Evaluating engineering alloys in compression InA K Schmieder editor Recent Developments in Mechanical Testing ASTMSpecial Technical Publication 608 pages 3ndash19 American Society for Testing andMaterials 1975 doi101520STP608-EB

[5] J K Banerjee Barreling of solid cylinders under axial compression Journalof Engineering Materials and Technology 107(2)138ndash144 1985 doi10111513225789

[6] William T Carter Jr and Daeyong Lee A finite element analysis of cylinderand ring compression and its experimental verification Computers amp Structures21(1-2)1 ndash 19 1985 doi1010160045-7949(85)90225-1


[7] Maurice Cook and Eustace C Larke Resistance of Copper And Copper Alloysto Homogeneous Deformation in Compression Journal of the Institute of Metals71(12)371ndash390 1945

[8] J S Gunasekera J Havranek and M H Littlejohn The effect of specimen sizeon stress-strain behavior in compression Journal of Engineering Materials andTechnology 104(4)274ndash279 1982 doi10111513225076

[9] T C Hsu A study of the compression test for ductile materials Materials Re-search and Standards 12(9)20 1969

[10] Syed Kamaluddin J Babu Rao M M M Sarcar and N R M R BhargavaStudies on flow behavior of aluminum using vision system during cold upsettingMetallurgical and Materials Transactions B 38(4)681ndash688 2007 doi101007s11663-007-9070-1

[11] S Kobayashi Deformation characteristics and ductile fracture of 1040 steel insimple upsetting of solid cylinders and rings J Eng Ind Trans ASME 92391ndash399 1970 doi does not resolve 2010-08-03 doi10111513427752

[12] M L Lovato and M G Stout Compression testing techniques to determinethe stressstrain behavior of metals subject to finite deformation Metallur-gical and Materials Transactions A 23(3)935ndash951 1992 doi101007BF02675569

[13] A T Male Variations in friction coefficients of metals during compressive de-formation J Inst Metals 94(4)121ndash125 1966

[14] John Mescall Ralph Papirno and James McLaughlin Stress and deformationstates associated with upset tests in metals In Richard Chait and Ralph Pa-pirno editors Compression Testing of Homogeneous Materials and Compos-ites ASTM Special Technical Publication 808 pages 7ndash23 American Societyfor Testing and Materials 1983 A symposium sponsored by ASTM Commit-tee E-28 on Mechanical Testing Williamsburg VA 10-11 March 1982 doi101520STP808-EB

[15] Ralph Papirno John Mescall and Anna M Hansen Fracture in axial compres-sion tests of cylinders In Richard Chait and Ralph Papirno editors Compres-sion Testing of Homogeneous Materials and Composites ASTM Special Techni-cal Publication 808 pages 40ndash63 American Society for Testing and Materials1983 A symposium sponsored by ASTM Committee E-28 on Mechanical Test-ing Williamsburg VA 10-11 March 1982 doi101520STP808-EB

[16] K K Ray and A K Mallik On the Determination of Flow Properties from Com-pression Tests Metallurgical Transactions A-Physical Metallurgy And MaterialsScience 14(1)155ndash156 1983 doi101007BF02643750

[17] J A Schey T R Venner and S L Takomana Shape changes in the upsettingof slender cylinders Journal of Engineering for Industry 104(1)79ndash83 1982doi10111513185802


[18] R L Woodward A note on the determination of accurate flow propertiesfrom simple compression tests Metallurgical and Materials Transactions A8(11)1833ndash1834 1977 doi101007BF02646893

[19] ASTM International Form and Style for ASTM Standards ASTM International100 Barr Harbor Drive PO Box C700 West Conshohocken PA 19428-2959March 2009 Available from httpwwwastmorgCOMMITBlue_Bookpdf

[20] ASTM International Interlaboratory study to establish a precision state-ment for standard test methods of compression testing of metallic ma-terials at room temperature Research Report E28-1042 ASTM In-ternational 100 Barr Harbor Dr West Conshohocken Pa Nov 2009Available from httpwwwastmorgDATABASECARTRESEARCH_REPORTSRR-E28-1042_691htm

[21] ASTM International Standard practice for conducting an interlaboratory study todetermine the precision of a test method Standard E 691ndash09 American Societyfor Testing and Materials 2009 Annual Book of ASTM Standards Vol 1402doi101520E0691-09

[22] ASTM International Standard practice for use of the terms precision and biasin ASTM test methods Standard E177-08 American Society for Testing andMaterials 2008 doi101520E0177-08

[23] ASTM International Directory of testing laboratories wwwastmorgLABSsearchhtml 2009

[24] American Association for Laboratory Accreditation Directory of accredited or-ganizations wwwa2laorgdirsearchnewnewsearchcfm 2009

[25] US Department of Defense Metallic materials and elements for aerospace vehi-cle structures Handbook MIL-HDBK-5J United States of America Departmentof Defense Jan 2003 Available from httpwwweveryspeccomMIL-HDBKMIL-HDBK+(0001+-+0099)MIL_HDBK_5J_139

[26] ASTM International Interlaboratory study to establish precision statementsfor ASTM B557 standard test methods for tension testing wrought and castaluminum- and magnesium-alloy products and B557M standard test methods fortension testing wrought and cast aluminum- and magnesium-alloy products [met-ric] Research Report E28-1004 ASTM International 100 Barr Harbor Dr WestConshohocken Pa Mar 1984 Available from httpwwwastmorgDATABASECARTRESEARCH_REPORTSRR-E28-1004_6htm

[27] Malcolm S Loveday Tom Gray and Johannes Aegerter Tensile testing ofmetallic materials A review Technical report National Physical LaboratoryApril 2004 Project funded by the European Community under the rdquoCompetitiveand Sustainable Growthrdquo Programme (1998-2002) Project Number GRD1-2000-25021 contract Number G6RD-CT-2000-00412 Available from www


nplcoukadvanced-materialsmeasurement-techniquesmechanicaltensile-testing-standards-and-tenstand

[28] ASTM International Interlaboratory test data for E21 tests for elevated tem-perture tension tests for metallic materials Research Report E28-1015 ASTMInternational 100 Barr Harbor Dr West Conshohocken Pa Sep 1992 Availablefrom ASTM International Committee E28 wwwastmorg

[29] Klaus D Debschutz Bernhard Caspers Gerold A Schneider and Gunter Pet-zow Critical evaluation of the compression creep test Journal of The AmericanCeramic Society 76(10)2468ndash2474 1993 doi101111j1151-29161993tb03968x

[30] Dassault Systemes Simulia Corp 166 Valley ST Providence RI USAAbaqusStandard Userrsquos Manual and Theory Manual version 610 2010

[31] ASTM International Standard test method for youngrsquos modulus tangent mod-ulus and chord modulus Standard E111-04 ASTM International W Con-shohocken Pa 2004 doi101520E0111-04

[32] ASTM International Standard practice for verification and classification of ex-tensometer systems Standard E83-06 ASTM International W ConshohockenPa 2006 doi101520E0083-06

[33] Stephen M Graham and Matthew A Adler Determining the slope and quality offit for the linear part of a test record Journal of Testing and Evaluation 39(2)2011 Paper ID JTE103038 doi101520JTE103038

[34] M Scibetta and J Schuurmans Development and qualification of an algorithmfor the determination of the initial linear portion of a force versus displacementrecord Journal of Testing and Evaluation 32(6)500ndash503 NOV 2004 doi101520JTE12618

[35] J A Brammer and C M Percival Elevated-temperature elastic moduli of2024 aluminum obtained by a laser-pulse technique Experimental Mechanics10(6)245ndash250 1970 doi101007BF02324097

[36] Ralph F Benck and Gordon L Filbey Jr Elastic constants of aluminum al-loys 2024-T3510 5083-H131 and 7039-T64 as measured by a sonic techniqueMemorandum Report 2649 Army Ballistic Research Lab Aberdeen ProvingGround Md Aug 1976 Available from httphandledticmil1002ADB012953

[37] Ralph F Benck Gordon L Filbey Jr and Jr SE Allen Murray Quasi-staticcompression stress-strain curvesndashIV 2024-T3510 and 6061-T6 aluminum al-loys Memorandum Report 2655 Army Ballistic Research Lab Aberdeen Prov-ing Ground Md Aug 1976 Available from httphandledticmil1002ADB013221


Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa

Extensometersextensometers 1extensometers 2

(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)

Figure 10 Reported (a) modulus and (b) 02 offset yield strength YS(02 offset)identified by number of extensometers used



Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

NonotminusreportedYes

Figure 11 Effect of lubricant on stress-strain behavior


Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes

LubricantNonotminusreportedYes

(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes


(b) Yield strength YS(02 offset)

Figure 12 Effect of lubricant on (a) modulusE and (b) yield strength YS(02 offset)Dashed lines are the mean values for all data including ldquonot-reportedrdquo not lubricated(ldquoNordquo) and lubricated (ldquoYesrdquo) tests


Figure 13 Finite element mesh and boundary conditions of the upper-right quadrantof the test specimen


True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030

FEA f=0 G=allFEA f=1 G=127 mmFEA f=1 G=254 mmFEA f=1 G=plateninput f=0 G=all

(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205


(b) Expanded section

Figure 14 Computed true stress-strain curves for the cases of frictionless (f = 0) andperfect friction (f = 1) and different gauge lengthsG (a) full curve and (b) expandedsection that shows the small differences between the results at large strain


Figure 15 Von Mises stress distribution in the upper-right quadrant of the test specimenfor four true strains (a) ε = 0002 (b) ε = 0008 (c) ε = 0015 and (d) ε = 0022measured from the G = 127 mm extensometer for the case of perfect friction

Figure 16 Shear stress distribution in the upper-right quadrant of the test specimen forfour true strains (a) ε = 0002 (b) ε = 0008 (c) ε = 0015 and (d) ε = 0022measured from the G = 127 mm extensometer for the case of perfect friction


Strain resolution

Fraction in zero bin

bin

of m

axim

um fr

actio

n

5

10

20 40 60 80

in max bin(025](25Inf]

(a) strain resolution

Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100


(b) stress resolution

Figure 17 (a) Strain and (b) stress data resolution Dashed lines enclose the region ofinsufficient resolution Symbols denote the fraction of points in the bin of maximumfraction


Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M

Modulus Error GPa(0016944](44878](878132]

(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise

Figure 18 Noise in calculated modulus based on (a) strain and (b) stress calculatedin Step 5 Symbols denote three increasing levels of absolute modulus error Eq 10All measurements are below the acceptance limit of 001 Data have been jittered toprevent over-plotting of points


Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M


(a) 1st quartile slope

Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M


(b) 4th quartile slope

Figure 19 Slope of residuals in the (a) 1st and (b) 4th quartile of the extended fit formodulus Symbols denote three increasing levels of absolute modulus error Eq 10Dashed lines denote the acceptance limit Data have been jittered to prevent over-plotting of points


Final fit range fraction

Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM

Figure 20 Absolute error in modulus Eq 10 as a function of the fraction of the final fitrange Rf used to calculate the modulus Symbols identify the different laboratoriesPoints to the left of the dashed line are deemed to have insufficient fit range

Introduction

Experimental Procedure

Participants

Instructions and method

Test Specimen

Compression fixtures

Results

Stress-strain behavior

Testing rates

Analysis and discussion

Expected variability

Effect of test method implementation

Effect of number of extensometers

Effect of Lubricant

Elastic Modulus

Conclusions


conducted according to ASTM E9William E Luecke

Li MaMetallurgy Division

Materials Science and Engineering Laboratory

Stephen M GrahamUnited States Naval Academy

Mechanical Engineering Department

Matthew A AdlerMarshall Space Flight Center

Jacobs ESTS GroupICRC

Sept 2010

US Department of CommerceGary Locke Secretary

National Institute of Standards and TechnologyPatrick D Gallagher Director




CODEN NSPUE2


Abstract
















AlMoS2 teflon













httpwwwimperialacuk


httpwwwmar-testcom


httpwwwmar-testcom


httpwwwmetcutcom




httpwwwwmtrcom















Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions




CODEN NSPUE2


Abstract
















AlMoS2 teflon













httpwwwimperialacuk


httpwwwmar-testcom


httpwwwmar-testcom


httpwwwmetcutcom




httpwwwwmtrcom















Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Abstract
















AlMoS2 teflon













httpwwwimperialacuk


httpwwwmar-testcom


httpwwwmar-testcom


httpwwwmetcutcom




httpwwwwmtrcom















Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions














AlMoS2 teflon













httpwwwimperialacuk


httpwwwmar-testcom


httpwwwmar-testcom


httpwwwmetcutcom




httpwwwwmtrcom















Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions









httpwwwimperialacuk


httpwwwmar-testcom


httpwwwmar-testcom


httpwwwmetcutcom




httpwwwwmtrcom















Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions













Not reported





None


Teflon tape




Not reported



None





WD-40



None

3 Results




Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions



Eng

inee

ring

Str

ess

MP

a

0100200300400

0000 0015

A B

0000 0015

C E

H I J

0100200300400

K0

100200300400

L

0000 0015

M







Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions



Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020

E= 752 GPa

ABCEHIJKLM

(a) Complete


Eng

inee

ring

Str

ess

MP

a

50

100

00005 00010 00015 00020 00025

E= 752 GPa

ABCEHIJKLM



Eng

inee

ring

Str

ess

MP

a

260

280

300

320

340

360

0005 0006 0007

E= 752 GPa

ABCEHIJKLM

(c) Yield behavior


Eng

inee

ring

Str

ess

MP

a

340

360

380

400

420

0000 0005 0010 0015 0020

ABCEHIJKLM

















Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions














Laboratory

EG

Pa

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa






Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

346 MPa





time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


time s

Eng

inee

ring

Str

ain

mm

0000

0005

0010

0015

0 100 250

A B

0 100 250

C E

H I J

0000

0005

0010

0015K

0000

0005

0010

0015L

0 100 250

M






Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Laboratory

elas

tic s

trai

n ra

te 1

s

3eminus05

4eminus05

5eminus05

6eminus05

7eminus05

8eminus05

A B C E H I J K L M

ModePositionStrain


Laboratory

plas

tic s

trai

n ra

te 1

s

000010

000015

000020

A B C E H I J K L M

ModePositionStrain




Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Yield Strength MPa

cv r

000

002

004

006

008

010

200 400 600 800 1000


(a) Repeatability

Yield Strength MPa

cv R

000

002

004

006

008

010

200 400 600 800 1000


(b) Reproducibility












Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions











Formula Description





Yj =1

n

nXi=1


macrY =1

p

pXj=1


sj =

vuut 1

nminus 1

nXi=1


sr =

vuut 1

p

pXj=1


cvr =sr


sY =

vuut 1

pminus 1

pXj=1


sR =

rs2

Y+ s2

r(nminus 1


cvR =sR













1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions










1 52 1180162 51 97131 1 20885 10966 000171 ---Signif codes 0 0001 001 005 01 1



1 52 265552 51 12239 1 14316 59653 3939e-10 ---Signif codes 0 0001 001 005 01 1







A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions





A0l0 = Al (9)



















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions

















3212

xmaxet

and δs lt 3212

xmaxst













































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions
































































Laboratory

EG

Pa

65

70

75

80

85

A B C E H I J K L M

752 GPa749 GPa


(a) Modulus

Laboratory

YS

(02

o

ffset

) M

Pa

300

320

340

360

380

400

A B C E H I J K L M

346 MPa


(b) YS(02 offset)




Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions



Eng

inee

ring

Str

ess

MP

a

0

100

200

300

400

0000 0005 0010 0015 0020




Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Laboratory

E G

Pa

70

75

80

85

A B C E H I J K L M

749 All723 No

764 Yes


(a) Modulus E

Laboratory

YS

(O=

02

offs

et)

MP

a

320

330

340

350

360

A B C E H I J K L M

3460 All3397 No

3503 Yes







True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions




True strain

Tru

e st

ress

MP

a

0

100

200

300

400

500

0000 0005 0010 0015 0020 0025 0030


(a) Full curve

True strain

Tru

e st

ress

MP

a

426

428

430

432

434

00195 00200 00205








Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions





Strain resolution


bin

of m

axim

um fr

actio

n

5

10

20 40 60 80



Stress resolution


bin

of m

axim

um fr

actio

n

5

10

0 20 40 60 80 100





Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Laboratory

Sta

ndar

d E

rror

of s

tres

s fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(a) strain noise

Laboratory

Sta

ndar

d E

rror

of s

trai

n fr

om fi

t

00000

00005

00010

00015

A B C E H I J K L M


(b) stress noise



Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions


Laboratory

Firs

t qua

rtile

slo

pe o

f res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M



Laboratory

Fou

rth

quar

tile

slop

e of

res

idua

ls

minus006

minus004

minus002

000

002

004

006

A B C E H I J K L M






Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions



Abs

(Mod

ulus

err

or)

GP

a

0

5

10

02 03 04 05 06

mean error488 GPa

mean error195 GPa

LabABCEHIJKLM


Introduction


Participants


Test Specimen


Results


Testing rates





Effect of Lubricant

Elastic Modulus

Conclusions

Repeatability and reproducibility of compression strength ......ASTM International standard test...

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Transcript of Repeatability and reproducibility of compression strength ......ASTM International standard test...