NIST Technical Note 1679
 

Repeatability and reproducibility of 

compression strength measurements 

conducted according to ASTM E9 

William E. Luecke 

Li Ma 

Stephen M. Graham 

Matthew A. Adler 

http://dx.doi.org/10.6028/NIST.TN.1679 
NIST Technical Note 1679 

Repeatability and reproducibility of 

compression strength measurements 

conducted according to ASTM E9 

William E. Luecke 

Li Ma 

Metallurgy Division

Materials Science and Engineering Laboratory

Stephen M. Graham 

United States Naval Academy

Mechanical Engineering Department

Matthew A. Adler 

Marshall Space Flight Center

Jacobs ESTS Group/ICRC

http://dx.doi.org/10.6028/NIST.TN.1679 

September 2009 

U.S. Department of Commerce 

Gary Locke, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Director
Certain commercial entities, equipment, or materials may be identified in this document in order 

to describe an experimental procedure or concept adequately. Such identification is not intended 

to imply recommendation or endorsement by the National Institute of Standards and Technology, 

nor is it intended to imply that the entities, materials, or equipment are necessarily the best 

available for the purpose. 

National Institute of Standards and Technology Technical Note 1679 

Natl. Inst. Stand. Technol. Technical Note 1679, 40 pages (September 2009) 

http://dx.doi.org/10.6028/NIST.TN.1679 

CODEN: NTNOEF 
i 

Abstract 

Ten commercial laboratories participated in an interlaboratory study to establish the repeatability and reproducibility of compression strength tests conducted 

according to ASTM International Standard Test Method E9. The test employed a 

cylindrical aluminum AA2024-T351 test specimen. Participants measured elastic 

modulus and 0.2 % offset yield strength, YS(0.2 % offset), using an extensometer 

attached to the specimen. The repeatability and reproducibility of the yield strength 

measurement, expressed as coefficient of variations were cvr= 0.011 and cvR= 0.020 

The reproducibility of the test across the laboratories was among the best that has 

been reported for uniaxial tests. The reported data indicated that using diametrally 

opposed extensometers, instead of a single extensometer, doubled the precision of 

the test method. Laboratories that did not lubricate the ends of the specimen measured yield stresses and elastic moduli that were smaller than those measured in 

laboratories that lubricated the specimen ends. A finite element analysis of the test 

specimen deformation for frictionless and perfect friction could not explain the discrepancy, however. The modulus measured from stress-strain data were reanalyzed 

using a technique that finds the optimal fit range, and applies several 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 the stress range. 

Keywords: compression, testing, ILS, ASTM, E9, yield strength, elastic modulus 
1 

1 Introduction 

Compression testing is a conceptually simple method to establish the uniaxial stress-strain 

and mechanical behavior of materials. Because the test specimens can be right circular 

cylinders, they are easy to fabricate. The short gauge length of the test specimen sometimes makes it the only possible geometry for establishing some uniaxial properties, for 

example those normal to the plane of a plate. Compression tests can also be used to establish the strength of brittle materials [1, 2] that would be difficult to grip in tension. 

Kuhn [3] and Chait [4] have reviewed the methods for compression testing, and have 

demonstrated that although the test is conceptually simple, the user must overcome many 

experimental difficulties to translate the measured load and displacement curves into accurate stress-strain behavior. 

Much of the literature, see Table 1, on implementing the compression test focuses on 

tests to large strains [5, 7, 8, 10, 12, 13, 17, 18], to establish strain-hardening behavior 

beyond the strains at which tension test specimens neck. Other studies are devoted to 

modelling processes such as upsetting [5, 14, 15, 17, 18]. A common theme in these and 

other studies has been to quantify the effects of friction [18, 7, 12] and barreling [5, 11, 

17, 9] on interpreting the stress-strain behavior of the test specimen, or finding the optimal 

lubricant [4, 6, 12, 13]. 

ASTM International standard test method E9, [2] first established in 1924, is a consensus standard for conducting compression tests to establish the strength of materials. 

It contains methods for testing cylindrical test specimens as well as methods for testing sheets with lateral support. The standard contains requirements for calibrating and 

qualifying the testing machine including extensometers, and aligning the fixtures and test 

specimen. It recommends, but does not require, specific test specimen geometries and 

lubricants. In addition, it suggests several fixture designs. It does not require the use 

of an extensometer in contact with the test specimen to measure strain, and most studies 

that reference E9 infer the test specimen strain and stress from the displacement of the 

actuator. 

Although the first version of E9 was released eight decades ago, its precision has 

never been formally evaluated, as required [19]. Such evaluations require a formal interlaboratory study, which can benefit both end user and testing laboratories. Users need the 

results of interlaboratory tests to determine the uncertainty that should be associated with 

the value of a material parameter obtained using a test method. Laboratories that employ 

test methods use interlaboratory studies to identify the deficiencies in their test methods 

and improve their implementation of them. 

This manuscript reports the results of an interlaboratory study to establish the precision of ASTM International standard test method E9 for determining the yield strength 

and elastic modulus in compression. The results of this study were incorporated into the 

Precision and Bias statement of E9 in 2009. This report goes beyond the research report [20] that documents the calculation of the precision by comparing the results to other 

interlaboratory studies of uniaxial test methods, Sec. 4.1, analyzing some of the possi­
2 

Table 1: Summary of literature that analyzes the compression test.
 

Reference Content emax Materials Lubricant 

Banerjee, 1985[5] b 1.6 Al teflon, MoS2, 

oil, none 

Carter, 1985[6] F 0.35 Al MoS2, none 

Chait, 1975[4] r NA 

Cook, 1945[7] f 0.7 Cu none 

Gunasekera, 1982[8] f 1.2 1022 steel teflon 

Hsu, 1969[9]  ̈ bfF NA Cu teflon 

Kamaluddin, 2007[10] F 0.8 Al grease 

Kobayashi, 1970[11] b 1.4 1040 steel graphite 

Lovato, 1992[12] f 1 Al, Nb, brass, MoS2, teflon, 

steel BN, none 

Male, 1966[13] f 0.8 Al, Ti, brass graphite, 

lanolin, paraffin 

Mescall, 1983[14] F NA 4340 steel 

Papirno, 1983[15] 0 NA steel teflon 

Ray, 1983[16] f NA steel teflon 

Schey, 1982[17] b 1 1020 steel, 6061 MoS2, teflon 

Al 

Woodward, 1977[18] f 1.2 steel teflon 

Key Key to content of reference 

emax : maximum strain in test b: barreling analysis 

NA : not available f: friction analysis 

F: finite element analysis 

r : review article 
3 

Table 2: List of participants in this study. 

Participant URL 

AADFW, Inc, Euless, Tx
 

Alcoa, Pittsburgh, Pa
 

Exova, Glendale Hts, IL
 

Dickson Testing Company Inc.,
 

South Gate, Ca
 

Imperial College Mechanical
 

Engr., London, England
 

MAR-TEST, Inc. (Cincinnati),
 

Cincinnati, Oh
 

MAR-TEST, Inc. (Stuart), Stuart,
 

Fl
 

Metcut Research Inc., Cincinnati,
 

Oh
 

Stork Climax Research Services,
 

Wixom, MI
 

Westmoreland Mechanical Testing,
 

Youngstown, Pa
 

http://www.aadfwinc.com 

http://www.alcoa.com 

http://www.exova.com 

http://www.dicksontesting.com/ 

http://www.imperial.ac.uk/ 

http://www.mar-test.com/ 

http://www.mar-test.com/ 

http://www.metcut.com 

http://www.storksmt.com/crs 

http://www.wmtr.com 

ble sources for the variability, Sec. 4.2, and presenting a method to evaluate the elastic 

modulus measured in the test, Sec. 4.3. 

2 Experimental Procedure 

This interlaboratory study followed the methods of ASTM E691 [21], and uses statistical 

terms in accord with ASTM E177 [22]. 

2.1 Participants 

Using the ASTM International [23] and American Association for Laboratory Accreditation [24] laboratory directories, the organizers contacted and discussed the interlaboratory 

study with twenty-five possible laboratory participants. From this original list thirteen 

laboratories agreed and were able to participate, and ten ultimately completed the test 

program, Table 2. 

2.2 Instructions and method 

The participants followed ASTM Standard Test Method E9 [2] to establish the elastic 

modulus, E, and 0.2 % offset yield strength, YS(0.2 % offset). At the time of the study, 

the 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 latter, 
4 

which was the purpose of the interlaboratory study. The participants also returned electronic traces of the stress-strain curves to the organizers. All compression fixtures were 

required to be qualified according to ASTM E9 Section 6.6 [2] using at least five of the 

supplied test specimens, unless the participant had already qualified the test setup according to E9 Section 6.6. The participants conducted the compression tests using at least 

one extensometer at a nominal strain rate of de/dt = 0.005 min−1 = 8.33 × 10−5 s−1. 

No laboratory reported strain measured from actuator displacement. Each participant reported ten items as required in sections 10.1.1–10.1.9 and 10.1.13 of standard method 

E9: Material (test specimen ID), configuration description, test specimen dimensions as 

tested, fixture and lubricant description, testing machine description, speed of testing (required in section 8.7; report actual value), stress-strain diagram, modulus of elasticity, E, 

yield strength, YS(0.2 % offset), and any anomalies. 

2.3 Test Specimen 

The material tested was aluminum alloy AA2024-T351, which is solution heat-treated 

and stress-relieved by controlled stretching. It was supplied as a plate with thickness, 

t = 22.2 mm (0.875 in), from which the organizers cut and distributed test specimen 

blanks, which were distributed throughout the plate. Figure 1 describes the location of the 

test specimens in the original plate and their numbering scheme. Only test specimens in 

rows 1 and 2 were used in this study. Test specimens number 1-50 came from row 1; test 

specimens 51–100 came from row 2. Figure 2 shows the test specimen with dimensions 

and tolerances. The drawing provided to the participants showed the dimensions in U.S.­

Customary units, rather than SI units. Participants machined their own test specimens 

from sawed blanks that the organizers supplied. 

Test specimens were tested with the loading axis transverse to the rolling direction 

in the plane of the plate, the so-called long-transverse (“LT”) orientation, Mil-Handbook5J [25] Figure 1.4.12.3(a). The test specimen ID takes the form “LT-NN-L-X” where “LT” 

identifies the orientation relative to the rolling direction, “NN” identifies the test specimen 

number (1–250), “L” identifies the laboratory that received the test specimen blank (A-K) 

and “X” identifies the test order of the test specimen at a given laboratory. 

2.4 Compression fixtures 

The participants used a variety of loading fixtures, some of which involved a sub-press 

mounted in the testing machine to improve alignment. Others used adjustable platens 

that were aligned and then locked. Three laboratories used diametrically opposed extensometers instead of a single extensometer. No laboratory reported strain from actuator 

displacement. Table 3 describes the specimen fixturing, alignment capability, number of 

extensometers, and the lubricant used in each laboratory. 

3 Results 

3.1 Stress-strain behavior 

Figure 3 plots the engineering stress-strain curves by laboratory. For convenience, com­
5 

Figure 1: Schematic of the location of test specimen blanks in the original plate.
 
6 

Table 3: Descriptions of the compression setup, extensometers and gauge lengths, G, and 

lubricants for all laboratories. 

Lab test setup Extensometer Lubricant 

A No sub-press 

B Sub-press 

C No sub-press, no spherical 

seat 

E sub-press 

H No sub-press 

I No sub-press 

J 

K 

L 

Precision ground 

sub-press, aligned to 

closer tolerance than 

required for specimen, no 

spherical seat 

No sub-press. Platens 

aligned, shimmed and 

then locked. No spherical 

seat 

Sub-press 

M Compression platens 

mounted in aligned 

hydraulic grips 

Two, opposed, 

class B-1 

G = 25.4 mm 

Single, class not 

reported 

G = 12.7 mm 

Single, class 

not-reported 

G = 25.4 mm 

Single, class B-1 

G = 25.4 mm 

Single class B-2, 

G = 12.7 mm 

Two opposed, 

class B-2, 

G = 25.4 mm 

Two opposed, 

class B-1 

G = 25.4 mm 

Single, class B-2, 

G = 12.7 mm 

Single, class B-2 

G = 25.4 mm 

Single, class B-2, 

G not reported 

Not reported 

Molybdenum disulfide 

None 

Teflon tape 

Molybdenum disulfide 

Not reported 

None 

Molybdenum disulfide 

WD-40 

None 
7 

Figure 2: Dimensions of the test specimen used. 

pressive strains and stresses are plotted as positive, rather than negative, values. In each 

case the stress-strain curve was shifted along the strain axis so that a linear fit to the stressstrain (S − e) data in the range (50 < S < 175) MPa intercepts the origin. Figure 4 

presents four views of the same stress-strain curves over different strain ranges. 

Table 4 summarizes the reported modulus, E, and yield strength, YS(0.2 % offset), for 

the laboratories. Figure 5 plots the reported elastic modulus, E, by laboratory. Figure 6 

plots the reported 0.2 % offset yield strength, YS(0.2 % offset), by laboratory. 

3.2 Testing rates 

Figure 7 plots the strain as a function of time for the laboratories that reported time data. 

The interlaboratory instructions did not specify a control mode for the test. Four laboratories (C,H,K,L) conducted the test in strain control from the extensometer signal, as 

indicated from the constant slope of the strain-time plot, Figure 7. Three laboratories 

(A,E,J) conducted the test in position control, as indicated from the changing slope in the 

strain-time plot. Figure 8 plots the strain rates in the elastic and plastic portions of the 
8 

Engineering Strain/ m/m

Engineering Stress/MPa

0

100

200

300

400

0.000 0.015

A B

0.000 0.015

C E

H I J

0

100

200

300

400

K

0

100

200

300

400

L

0.000 0.015

M

Figure 3: Engineering stress-strain curves.
 
9 

Engineering Strain/ m/m

Engineering Stress/MPa

0

100

200

300

400

0.000 0.005 0.010 0.015 0.020

E= 75.2 GPa

A

B

C

E

H

I

J

K

L

M

Engineering Strain/ m/m

Engineering Stress/MPa

50

100

0.0005 0.0010 0.0015 0.0020 0.0025

E= 75.2 GPa

A

B

C

E

H

I

J

K

L

M

(a) Complete (b) Low-strain behavior 

Engineering Strain/ m/m

Engineering Stress/MPa

260

280

300

320

340

360

0.005 0.006 0.007

E= 75.2 GPa

A

B

C

E

H

I

J

K

L

M

Engineering Strain/ m/m

Engineering Stress/MPa

340

360

380

400

420

0.000 0.005 0.010 0.015 0.020

A

B

C

E

H

I

J

K

L

M

(c) Yield behavior (d) Plastic behavior 

Figure 4: Engineering stress-strain curves: (a) complete behavior, (b) low-strain behavior, 

(c) yield behavior, and (d) plastic behavior. Dashed lines show the accepted value for the 

modulus of 2024-T351, E = 75.2 GPa, the 0.2 % offset yield strength determination, and 

the e = 0.008 total elongation. 
10 

Laboratory

E/GPa

70

75

80

85

A B C E H I J K L M

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●●●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

75.2 GPa

74.9 GPa

Figure 5: Reported elastic modulus, E. Dashed lines show the average reported modulus 

and a commonly accepted value of the modulus (E=75.2 GPa) from Mil-HDBK-5J [25] 

and the average of all the measurements, E = 74.9 GPa. 
11 

Laboratory

Y

S(O=0.2% offset)/MPa

320

330

340

350

360

A B C E H I J K L M

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

346 MPa

Figure 6: Reported 0.2 % offset yield strength, YS(0.2 % offset). The dashed line is the 

average of the results from all laboratories. 
12 

time /s

Engineering Strain/ m/m

0.000

0.005

0.010

0.015

0 100 250

A B

0 100 250

C E

H I J

0.000

0.005

0.010

0.015

K

0.000

0.005

0.010

0.015

L

0 100 250

M

Figure 7: Reported strain as a function of time.
 
13 

Table 4: Reported data
 

Lab Sample E YS Lab Sample E YS Lab Sample E YS

GPa MPa GPa MPa GPa MPa 

A LT-85 75.6 339.0 H LT-10 77.2 345.0 K LT-24 75.8 343.0 

A LT-1 72.9 340.0 H LT-44 73.8 347.0 K LT-42 80.7 348.0 

A LT-40 76.8 341.0 H LT-55 73.1 347.0 K LT-51 87.6 351.0 

A LT-26 75.1 342.0 H LT-63 77.2 347.0 K LT-56 84.1 351.0 

A LT-66 73.8 342.0 H LT-76 75.8 347.0 K LT-5 80.0 352.0 

A LT-78 74.7 342.0 H LT-91 77.2 347.0 K LT-13 76.5 354.0 

A LT-82 76.3 343.0 H LT-19 78.6 354.0 K LT-83 NA NA 

B LT-28 73.1 348.0 I LT-43 75.0 348.0 L LT-79 73.0 348.0 

B LT-39 76.5 349.0 I LT-57 76.0 349.0 L LT-45 84.2 349.0 

B LT-54 75.0 349.0 I LT-65 75.0 349.0 L LT-69 78.4 352.0 

B LT-9 75.0 353.0 I LT-21 76.0 350.0 L LT-12 84.2 355.0 

B LT-80 83.4 356.0 I LT-34 75.0 350.0 L LT-36 75.7 356.0 

C LT-68 72.0 318.0 I LT-74 75.0 350.0 L LT-6 77.5 356.0 

C LT-84 72.8 335.0 I LT-70 76.0 351.0 L LT-92 85.8 363.0 

C LT-90 71.5 336.0 J LT-4 74.5 340.5 M LT-18 69.0 338.0 

C LT-16 72.4 338.0 J LT-89 74.2 341.6 M LT-11 72.0 342.0 

C LT-77 71.4 338.0 J LT-94 74.4 341.6 M LT-59 71.0 342.0 

C LT-27 70.7 339.0 J LT-73 74.5 342.1 M LT-62 70.0 342.0 

C LT-58 72.9 341.0 J LT-37 74.8 342.5 M LT-86 72.0 342.0 

E LT-25 68.3 342.2 J LT-23 74.8 343.1 M LT-33 72.0 343.0 

E LT-31 67.0 346.8 J LT-14 74.1 343.4 M LT-81 68.0 345.0 

E LT-87 69.3 347.4 

E LT-71 68.6 349.0 

E LT-17 70.5 351.1 

E LT-8 70.9 351.4 

E LT-41 70.6 355.8 

Notes: 

YS=YS(0.2 % offset) 

stress-strain curves calculated by linear regression. The plastic strain rate was calculated 

for strains greater than the strain at the 0.2% offset yield strength: eYS002 < e < emax. 

The elastic strain rate was calculated in the range 0 < e < (eYS002 −0.002). Laboratory J 

conducted the test in position control and set the elastic strain rate close to the specified 

value. 

4 Analysis and discussion 

4.1 Expected variability 

Table 5 summarizes the mean and standard deviation, sd, and coefficient of variation, cv, 

of the reported n measurements of the elastic moduli and yield strengths. Table 6 defines 

the statistical parameters used in this section. 
14 

Laboratory

elastic strain rate /1/s

3e−05

4e−05

5e−05

6e−05

7e−05

8e−05

A B C E H I J K L M

● ● ●

●●

●

●

Mode

Position

Strain ●

(a) elastic strain rate 

Laboratory

plastic strain rate /1/s

0.00010

0.00015

0.00020

A B C E H I J K L M

● ●●

●

● ●●●●

Mode

Position

Strain ●

(b) plastic strain rate 

Figure 8: Calculated (a) elastic and (b) plastic strain rates for laboratories that reported 

time data. Symbols differentiate between position-control and strain-control tests. Dashed 

line indicates the requested rate, de/dt = 8.33 × 10−5 1/s. 
15 

Table 5: Summary statistics for the modulus and yield strength data. 

Lab n E ̄ sd(E) cv(E) YS ̄ sd(YS) cv(YS)
 

GPa GPa MPa MPa
 

A 7 75.0 1.4 0.018 341.3 1.4 0.004 

B 5 76.6 4.0 0.052 351.0 3.4 0.010 

C 7 72.0 0.8 0.011 335.0 7.7 0.023 

E 7 69.3 1.4 0.021 349.1 4.3 0.012 

H 7 76.1 2.0 0.026 347.7 2.9 0.008 

I 7 75.4 0.5 0.007 349.6 1.0 0.003 

J 7 74.5 0.3 0.004 342.1 1.0 0.003 

K 7 80.8 4.5 0.056 349.8 3.9 0.011 

L 7 79.8 4.9 0.062 354.1 5.1 0.014 

M 7 70.6 1.6 0.023 342.0 2.1 0.006 

Note: YS= YS(0.2 % offset)
 

Parameter Grand Average sr cvr sR cvR

E E

 ̄ ̄= 75.0 GPa 2.7 GPa 0.036 4.4 GPa 0.059 

YS(0.2 % offset) YS ̄ ̄ (0.2 % offset)= 346.2 MPa 3.8 MPa 0.011 6.8 MPa 0.020 

Table 6 defines the parameters. Because laboratory B tested only five specimens instead of seven, 

the mean values shown in Figures 5, 6, 10, and 12 differ from the Grand Average, also known as 

the average of cell averages, Table 6, Eq. 2. 

The results of an interlaboratory study contain variability that arises within a given 

laboratory and variability that arises between laboratories. The terms repeatability and 

the reproducibility, denoted by subscripted “r” and “R,” are often used to differentiate 

between these sources [22]. In a general sense, repeatability characterizes the ability 

of an individual laboratory to repeat measurements, while reproducibility characterizes 

the ability of an individual laboratory to achieve the global mean or accepted value. For 

example, if the results from an individual laboratory are tightly grouped, their repeatability 

is high, but their mean value may still deviate significantly from the accepted value, in 

which case their reproducibility is low. 

Both the variability in the material and the variability of the test method influence the 

repeatability. The excellent repeatability of the measurements for both E and YS(0.2 % 

offset) in laboratories A, I, and J , Table 5, shows that the material variability in this 

study is quite low, and therefore the implementation of the test method by the individual 

laboratories is the major contributor to repeatability. 

Figure 9 and Table 7 compare the results for repeatability and reproducibility for this 

study to the results of other interlaboratory studies of tensile tests at room [26, 27] and 
16 

Table 6: Definitions of repeatability and reproducibility statistics.
 

Formula Description 

n number of tests in a laboratory, n ≈ 7

p number of laboratories, p = 10

Yij individual test result in lab j

1 < i < n ; 1 < j < p

n

= Yij n

i=1

p

 

 

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

1 Y

 ̄ ̄ Y ̄ = j average of cell averages (grand average) (2)

p j=1

1

 n

n − 1

i=1

 (Yij − Y ̄j )2 sj = standard deviation measured in lab j (3)

 

p

p j=1

sr

1 (sj )

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

coefficient of variation within laboratories (5) 

sr =

cvr = Y

 ̄ ̄

 p

p − 1

j=1

1 (Y ̄j − Y

 ̄ ̄ )2 sY ̄ = standard deviation of cell averages (6)

 n − 1 2 sR = s + s2( ) reproducibility standard deviation ((between-lab) (7) Y ̄ r n

cvR =sR coefficient of variation between laboratories (8) Y

 ̄ ̄

elevated temperatures [28] to establish the 0.2 % offset yield strength, YS(0.2 % offset). 

In Figure 9 the within-laboratory and between-laboratory standard deviations, sr, Eq. 4, 

and sR, Eq. 7, see Table 6, are divided by the mean value and expressed as their respective 

coefficients of variation, cvr, Eq. 5, and cvR, Eq. 8. 

The repeatability coefficient of variation of the yield strength measurements in this 

study, derived from the average of the standard deviations of the individual laboratories, is 

cvr = 0.0111, Eq. 5, while the coefficient of variation of the reproducibility, cvR = 0.0197, 

Eq. 8, is about twice as large. The repeatability and reproducibility of compression tests 

established in this study are among the best measurements of all reported uniaxial measurements [26, 27, 28]. 
17 

Yield Strength/ MPa

c

vr

0.00

0.02

0.04

0.06

0.08

0.10

200 400 600 800 1000

● ●

●

alloy steel

aluminum

stainless steel

steel

superalloy

This Study

●

●

(a) Repeatability 

Yield Strength/ MPa

c

v

R

0.00

0.02

0.04

0.06

0.08

0.10

200 400 600 800 1000

●

●

●

alloy steel

aluminum

stainless steel

steel

superalloy

This Study

●

●

(b) Reproducibility 

Figure 9: Literature data [26, 28, 27] on (a) repeatability (within-laboratory) and (b) reproducibility (between-laboratory) of yield strength, YS(0.2 % offset). Table 7 summarizes 

the data. 
18 

Table 7: Literature data [28, 26, 27] for repeatability and reproducibility in mechanical 

testing. 

Source Material T YS cvr cvR ◦C MPa 

[26] EC-H19 aluminum 20.0 158.4 0.0210 0.0210 

[26] 2024-T351 aluminum 20.0 362.9 0.0140 0.0150 

[26] AISI A105 steel 20.0 402.4 0.0140 0.0250 

[26] SS316 stainless steel 20.0 480.1 0.0140 0.0410 

[26] Inconel 600 20.0 268.3 0.0090 0.0220 

[26] SAE 51410 steel 20.0 967.5 0.0090 0.0160 

[27] AA5754 Al 20.0 105.7 NA 0.0160 

[27] AA51802-O 20.0 126.4 NA 0.0100 

[27] AA6016-T4 20.0 127.2 NA 0.0110 

[27] DX56, low-carbon steel 20.0 162.0 NA 0.0230 

[27] HR3 steel plate 20.0 228.6 NA 0.0410 

[27] ZStE 180 steel 20.0 267.1 NA 0.0500 

[27] S355 steel plate 20.0 427.6 NA 0.0310 

[27] SS316L stainless steel 20.0 230.7 NA 0.0350 

[27] X2CrNi18-10 stainless steel 20.0 303.8 NA 0.0330 

[27] X2CrNiMo18-10 20.0 353.3 NA 0.0390 

[27] 30NiCrMo16 high strength steel 20.0 1039.9 NA 0.0100 

[27] Nimonic 75 CRM 661 20.0 302.1 NA 0.0180 

[27] Nimonic 75 CRM 661 20.0 298.1 NA 0.0200 

[28] SS304 stainless steel 316.0 127.3 0.0580 0.1040 

[28] Low-carbon steel 316.0 236.4 0.0110 0.0350 

[28] 2.25 Cr 1Mo steel 316.0 454.7 0.0230 0.0330 

[28] A286 stainless steel 316.0 699.5 0.0280 0.0300 

[28] SS304 stainless steel 593.0 101.4 0.0770 0.0990 

[28] Low-carbon steel 593.0 133.0 0.0390 0.1040 

[28] 2.2.5Cr 1Mo ferritic steel 593.0 337.9 0.0260 0.0670 

[28] A286 stainless steel 593.0 642.2 0.0260 0.0350 

This study Al 2024-T351 20.0 346.2 0.0111 0.0197 

Notes: 

YS= YS(0.2 % offset) 

NA = data not available 
19 

4.2 Effect of test method implementation 

Because the laboratories were free to implement the test method in different ways, while 

still complying with the standard, their results can be used to learn about the effect of 

different aspects of test method on the measurement. In particular, the results can be 

examined to determine the effects of the number of extensometers and lubrication on the 

quality of the measurement. 

4.2.1 Effect of number of extensometers 

Some laboratories used a single extensometer, while others used two opposed extensometers to measure the strain. Figure 10 plots the reported modulus and yield strength for 

the laboratories, grouped by the number of extensometers used in the determination. The 

three laboratories, A, I, J, with the best repeatability and reproducibility of E and YS(0.2 % 

offset) are the only ones that used a system of two-opposed extensometers instead of a 

single extensometer. In addition, the measured elastic modulus in these three laboratories was the closest to the accepted [25] value E = 75.2 GPa, Figure 10a. Note that 

the repeatability of the modulus and yield strength from the labs that used a single extensometer is worse (i.e. larger variability), but also that for an individual laboratory, the 

values usually all lie above or below the grand average. Using two extensometers will 

tend to average the effect of non-axial loading, since during bending, one side of the test 

specimen will be displaced more, and the other less. Because the values for an individual, 

single-extensometer laboratory are usually displaced to one side of the global mean value 

points toward the alignment of the compression fixture, rather than machining of the test 

specimen as the source of the non-axiality. If the ends of the test specimen were not parallel, the measured values would tend to encompass the mean value, because no special 

relationship exists between the test specimen and the loading fixture. Conversely, the extensometer is usually mounted on the test specimen with a fixed relation to the orientation 

of loading fixture, so bending induced by a slightly misaligned loading fixture is always 

in the same geometric relation to the extensometer, which will tend to always over- or 

under-estimate the strain. 

4.2.2 Effect of Lubricant 

The standard allows the laboratory to choose whether to lubricate the ends of the test 

specimen during the test. Figure 11 shows the engineering stress-strain curves, identified 

by the use or omission of lubricants. Several laboratories did not report lubricant use. 

Table 3 identifies the lubricants used. Three laboratories used no lubricant, and their 

stress-strain curves are the lowest in the collection. Figure 12 plots the reported modulus, 

E, and yield strength, YS(0.2 % offset), identified by lubricant use. The average yield 

strength from the three laboratories that did not use lubricant was 10.6 MPa lower (3.1 %) 

than the average of the laboratories that lubricated the specimen. Similarly the average 

reported elastic modulus, E, from the three laboratories was 4.1 GPa (5.7 %) smaller. 

Table 8, an analysis of variance, shows that the reported yield strength, YS(0.2 % offset), 

and modulus, E,are both significantly different for the lubricated and unlubricated cases. 
20 

Laboratory

E/GPa

65

70

75

80

85

A B C E H I J K L M

●

●

●

●

●

●

● ●

●

●

●●●

75.2 GPa

74.9 GPa

Extensometers

extensometers: 1

extensometers: 2 ●

(a) Modulus 

Laboratory

Y

S(0.2% offset)/ MPa

300

320

340

360

380

400

A B C E H I J K L M

●

●●

●

●

●●●

●

●●●●

 346 MPa

Extensometers

extensometers: 1

extensometers: 2 ●

(b) YS(0.2 % offset) 

Figure 10: Reported (a) modulus and (b) 0.2 % offset yield strength, YS(0.2 % offset), 

identified by number of extensometers used. 
21 

Engineering Strain/ m/m

Engineering Stress/MPa

0

100

200

300

400

0.000 0.005 0.010 0.015 0.020

No

not−reported

Yes

Figure 11: Effect of lubricant on stress-strain behavior.
 
22 

Laboratory

E /GPa

70

75

80

85

A B C E H I J K L M

●

●

●

●

●

●

● ●

●

74.9 : All

72.3 : No

76.4 : Yes

Lubricant

No

not−reported

Yes

●

(a) Modulus, E

Laboratory

Y

S(O=0.2% offset)/MPa

320

330

340

350

360

A B C E H I J K L M

●

●●

●

●

●

●

●

●

346.0 : All

339.7 : No

350.3 : Yes

Lubricant

No

not−reported

Yes

●

(b) Yield strength, YS(0.2 % offset) 

Figure 12: Effect of lubricant on (a) modulus E and (b) yield strength YS(0.2 % offset). 

Dashed lines are the mean values for all data, including “not-reported,” not lubricated 

(“No”) and lubricated (“Yes”) tests. 
---

---

23 

Table 8: Analysis of variance tables for assessing the effect of lubrication on modulus and 

yield strength. 

% Table generated on 2010-09-22 19:05:27

Analysis of Variance Table

Model 1: E  ̃ 1

Model 2: E  ̃ Lubricated

Res.Df RSS Df Sum of Sq F Pr(>F)

1 52 1180.16

2 51 971.31 1 208.85 10.966 0.00171 **

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Analysis of Variance Table

Model 1: YS02  ̃ 1

Model 2: YS02  ̃ Lubricated

Res.Df RSS Df Sum of Sq F Pr(>F)

1 52 2655.5

2 51 1223.9 1 1431.6 59.653 3.939e-10 ***

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Key to parameters in table: 

E: E, elastic modulus 

YS02: YS(0.2 % offset), 0.2 % offset yield strength 

Data from laboratories that did not report the lubrication are omitted. Model 1 is the mean 

value of of the parameter, and model 2 computes the mean value for the lubricated (“Yes”) 

and unlubricated (“No”) cases. 

Since most laboratories used an extensometer with a gauge length G = 25.4 mm on 

the test specimen, Fig. 2, with length l ≈ 48 mm and diameter d = 12.7 mm, the end 

of the test specimen is approximately one test specimen diameter away from the extensometer contact point. That distance complies with the requirements of E9, and should 

minimize the effect of the non-uniform stress caused by friction at the specimen ends. No 

study has examined the sensitivity of the strain measurement to the non-uniform stress 

at the end of the specimen, but the existence of non-uniform stresses caused by friction 

is well known [29]. Finite element analysis (FEA), using the commercial finite-element 

modeling software Abaqus/Standard 6.10 [30], was used to analyze the effect of friction 

and gauge length on the response of the specimen. By exploiting the axial and radial 

symmetry of the specimen and platens, it was only necessary to model the upper-right 
24 

Figure 13: Finite element mesh and boundary conditions of the upper-right quadrant of 

the test specimen. 

quadrant the specimen with radius r = 6.3 mm and length l = 24.25 mm. The specimen mesh, Figure 13, was constructed with 1542 quadrilateral four-node axi-symmetric 

(CAX4) elements. The platens were modeled as non-deforming, rigid planes of infinite 

elastic modulus. Roller boundary conditions were applied on the axial centerline and 

the specimen midplane. The specimen material was modeled as a homogeneous elasticplastic time-independent material exhibiting strain hardening. The plastic deformation 

was modeled by the J2 (or von Mises) flow plasticity theory with isotropic hardening.[30] 

The uniaxial stress-strain curve was taken from specimen LT-14 of the experimental results, down-sampled to 58 points, with the Young’s modulus set to the accepted value 

E = 75.2 GPa, and Poisson’s ratio ν = 0.33. This material model yields at a true stress 

σ = 190.4 MPa at a true strain E = 0.0026, and not at the value of the 0.2 % offset 

value YS(0.2 % offset)=343.4 MPa. All of the stress-strain curves, Fig. 4a, exhibited this 

behavior. 

Two limiting cases of zero friction and complete friction at the specimen-platen interface were modeled. The simulation was performed by pushing the rigid platen increasingly to displacement of 0.485 mm, which is e = 0.02 deformation for the zero friction 

case. The effect of extensometer gauge length was tested by following the axial displacement of two nodes, Figure 13, located l = 6.35 mm and l = 12.7 mm above the center 
25 

plane of the specimen. These nodes correspond to the contact points of extensometers 

with G = 12.7 mm and G = 25.4 mm respectively. To calculate the stress-strain behavior, the force on the platen, the displacement of the platen, the displacement of the 

two extensometer contact points and a surface corresponding to the length between the 

platens, see Figure 13, were recorded. The stresses were calculated from the measured 

radii at those points. 

Figure 14 shows the computed true stress-strain curves for strain measures across 

three gauge lengths (G = 12.7 mm, G = 25.4 mm, and G = 48.5 mm–across the loading 

platens) and for the two limiting friction cases: frictionless (f = 0) and perfect friction 

(f = 1). It also shows the true stress-strain curve used as the input model. In the figure, 

the true stresses, are calculated from the load P and the instantaneous area, A, by by 

assuming conservation of volume in deformation: 

A0l0 = Al (9) 

where A0 and l0 are the original area and gauge length respectively. This calculation 

mimics what would be done in analysis of an actual experiment, where the instantaneous 

load-bearing area, A, is calculated from the strain. For the frictionless case, all the strain 

measures yield the same stress-strain behavior as the input model, as they should. For the 

case of perfect friction, f = 1, the strains measured across the two extensometer gauge 

length, G = 12.7 mm and G = 25.4 mm differ by less than 0.5 MPa from each other 

and from the frictionless cases. The difference between the average of yield strengths 

measured by laboratories that lubricated and those that did not was was twenty times this 

large: Δ YS(0.2 % offset)=10.4 MPa, Figures 11 and 12. The true stress calculated from 

the displacement of the loading platen, a common method that use the displacement of 

the actuator, corrected for machine compliance, is about 6 MPa, or 1.4 %, above all the 

other curves. Note that no laboratory measured strain this way; each laboratory used an 

extensometer on the test specimen, with contact points remote from the test specimen end 

faces. The agreement between the extensometer methods for the frictionless and complete 

friction cases eliminates friction as the source of the difference in yield behavior between 

the laboratories that lubricated and those that did not. 

The finite-element analysis also determined the evolution of the stress distributions in 

the test specimen. Figure 15 shows the von Mises stress evolution for four strains. Stresses 

less than the yield stress of the material model, σ = 190.4 MPa, are shown in white. 

Consistent with other analyses [29, 6], a non-deforming cap forms at the test specimen 

end. As the specimen deforms, a region of slightly higher stress develops that extends 

just into the region that the longer, G = 25.4 mm extensometer samples. Figure 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, where friction constrains 

the deformation, does shear strain develop. 
26 

True strain

True stress/MPa

0

100

200

300

400

500

0.000 0.005 0.010 0.015 0.020 0.025 0.030

FEA f=0 G=all

FEA f=1 G=12.7 mm

FEA f=1 G=25.4 mm

FEA f=1 G=platen

input f=0 G=all

(a) Full curve 

True strain

True stress/MPa

426

428

430

432

434

0.0195 0.0200 0.0205

FEA f=0 G=all

FEA f=1 G=12.7 mm

FEA f=1 G=25.4 mm

FEA f=1 G=platen

input f=0 G=all

(b) Expanded section 

Figure 14: Computed true stress-strain curves for the cases of frictionless (f = 0) and 

perfect friction (f = 1) and different gauge lengths, G: (a) full curve, and (b) expanded 

section that shows the small differences between the results at large strain. 
27 

Figure 15: Von Mises stress distribution in the upper-right quadrant of the test specimen 

for four true strains: (a) E = 0.002, (b) E = 0.008, (c) E = 0.015, and (d) E = 0.022, 

measured from the G = 12.7 mm extensometer for the case of perfect friction. 

4.3 Elastic Modulus 

The elastic modulus measured in the test is very sensitive to the alignment and sensitivity 

of the test setup. As a result, ASTM E 9 [2] requires that laboratories validate their 

compression test fixture by measuring the elastic modulus of aluminum alloy 2024-T4 bar, 

according ASTM E 111 [31] and obtaining measurements on five consecutive specimens 

to within 5 % of a stated value, E=73.8 GPa. The behavior of the reported elastic modulus 

should be a good indicator of the quality of the compression test facility. 

The interlaboratory study did not require laboratories to revalidate their test setups, 

but they did report the measurements of elastic modulus, Figure 5, made during the compression 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 class B-1 extensometer required by ASTM E 111 [31] when elastic modulus is the primary parameter 

to be determined. But because the primary parameter to be determined was the yield 

strength, E 9 Section 9.2 permits the use of the class B-2 extensometer. 

The laboratories had wide latitude in the method to determine the elastic modulus 

to report. To reduce the variability due to the interpretation of the individual laboratory, 

and to put each modulus measurement on a consistent basis, we reanalyzed each stressstrain curve to estimate the elastic modulus using a technique [33] based on the method 
28 

Figure 16: Shear stress distribution in the upper-right quadrant of the test specimen for 

four true strains: (a) E = 0.002, (b) E = 0.008, (c) E = 0.015, and (d) E = 0.022, measured 

from the G = 12.7 mm extensometer for the case of perfect friction. 

of Scibetta and Schuurmans [34]. These reanalyzed moduli are denoted by the symbol 

EGA, to differentiate them from the moduli that the participants calculated and reported, 

denoted by E. In addition to estimating the modulus, the method includes some checks 

on the quality of the data that may be useful for laboratories that seek to improve their 

modulus measurement. 

Many of the following plots evaluate the quality of the measurements by employing 

the absolute modulus error, ΔEGA, in a measurement, which is defined as the absolute 

value of the difference between the accepted modulus [25] for 2024-T351 aluminum, 

Eacc 

Al = 75.2 GPa and the calculated modulus, EGA. 

ΔEGA = |Eacc 

Al − EGA| (10)

Other references [35, 36, 37, 2] recommend different values in the range 73.8 GPa <

E < 76.1 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 − e) curve by the method of Scibetta and Schuurmans [34]. 

1. Find the point on the stress-strain curve (e1, s1) closest to s1 = 0.05 max(s)
29 

2. Create point (eo, so) where eo = e1 and so = 0.2 max(s). 

3. Find the point on the stress-strain curve (et, st) that is on a line drawn through 

(e0, s0) that is tangent to the stress-strain curve. 

2 Truncate the stress-strain data at (et, st) and normalize by these values. Retain the 

maximum values of the test record: (emax, smax). 

3 Check digital resolution, δ, of stress and strain. The digital resolution should be 

3	 xmax 3 xmax δe	 < 212 and δs < 212 . No more than more than 25 % of points should et	 st

have zero stress or strain change from the previous point. 

4 Use the Scibetta-Schuurmans [34] algorithm to determine optimum fit window and 

calculate the slope, which is the elastic modulus EGA, in normalized form. The 

Scibetta-Schuurmans algorithm finds the optimal region for determining the modulus by performing a linear regression of stress on strain on every possible subset of 

data in the region eo < e < et that contains at least 20 % of the data. The regression 

with the lowest residual standard deviation is the optimum fit. In some cases, more 

than one million fits were evaluated for each stress-strain curve. 

5 Check for excessive noise in optimum fit window, defined as the standard error of 

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 point j, and Yj

is the predicted normalized stress from the fit to the optimal region. Perform the 

complementary regression of strain upon stress as well. In both cases, the standard 

error in strain or stress should not be greater than 0.01. 

6 Extend the range of fit to include all stress points whose deviation from the optimal 

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 in the 

extended fit. If the slope of the residuals in the first or fourth quartile of the extended 

range is more than 0.05, the data exhibit excessive curvature. At least five points 

must exist in each quartile to evaluate this curvature. 

9 Check that the stress range of the optimal fit is greater than 0.4st. 

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

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

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

•	 Fit quality 1: the stress and strain residuals in extended data range should not have 

excessive curvature (Step 8) 
30 

•	 Fit quality 2: the size optimal fit range, Rf , should be greater than or equal to 40 % 

of the total range used to determine the modulus (Step 9) 

The rest of this section will examine the results of the modulus measurement, EGA, using 

these four quality metrics. 

Data Quality 1: sufficient digital resolution Figure 17 summarizes the strain and 

stress resolution. Estimating the digital resolution of a data set post-test is difficult, and 

the 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 the absolute value of the difference of each sequential pair of stress and strain points, for example 

|si − si+1|. Those differences, expressed in units of δ from step 3, were binned to create 

a histogram. If too many of the points show no change between reading, or if the most 

frequent change is many times larger than the digital resolution, δ defined in Step 3, the 

stress-strain curve may have insufficient digital resolution. This condition could arise, 

for example, if a load cell were used near the very lower limit of its working range, or 

if the analog-to-digital converter had insufficient precision. Figure 17 plots the index of 

the bin with the maximum fraction of the data, in units of δ, defined in step 3, against the 

fraction of the points in the “zeroth” bin, which is the fraction of points where the stress 

or strain value did not change between readings. The symbols show the fraction of the 

points in the bin of maximum fraction, broken into two groups: those 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 identifies experiments with insufficient 

digital resolution as those where the bin of maximum fraction is greater than 3 and either 

the fraction in the zeroth bin is > 25 % or the fraction in the bin of maximum fraction 

is > 25 %. The first condition is identified by the dashed lines. The second “or” condition comprise those points identified by green circles with y value greater than 3. No 

experiment demonstrated insufficient digital resolution. 

Data Quality 2: excessive noise Excessive noise in the strain or stress signal will degrade the quality of the measured modulus. The method identifies experiments with excessive noise in these signals as ones in which the standard error of the fit is greater than 

0.01. Figure 18 plots the standard error of the fit for both strain and stress by laboratory. 

The symbols identify three levels of modulus error, Eq. 10. The noise in all the experiments was sufficiently low. No obvious relation exists between the absolute modulus 

error, ΔE, and either the standard error of stress or strain. 

Fit Quality 1: Excessive curvature in extended data set Some metric of the curvature 

of the optimal fit range is necessary, since the method only selects the best fit over an 

optimal region. That fit might still be poor. One method for examining the quality of 

the fit is to examine the deviation from the fit line in the first and fourth quartiles of the 

optimal range. Curvature of the stress-strain record frequently appears this way. If the 

slope of the residuals vs. strain in the outer quartiles is greater than 5 % of the slope in the 

optimal region, the curvature of the fit is deemed excessive. 
31 

Strain resolution

Fraction in zero bin /%

bin of maximum fraction

5

10

20 40 60 80

●●●●●● ●●●●● ●●●●●●●●●●●●●●●● ●●

●●●●●

●●●●●●

% in max bin

(0,25]

(25,Inf] ●

(a) strain resolution 

Stress resolution

Fraction in zero bin /%

bin of maximum fraction

5

10

0 20 40 60 80 100

●●●● ●●●●●●●●●●●●●●●

●

● ● ● ●●● ● ●

●

●

% in max bin

(0,25]

(25,Inf] ●

(b) stress resolution 

Figure 17: (a) Strain and (b) stress data resolution. Dashed lines enclose the region 

of insufficient resolution. Symbols denote the fraction of points in the bin of maximum 

fraction. 
32 

Laboratory

Standard Error of stress from fit

0.0000

0.0005

0.0010

0.0015

A B C E H I J K L M

●

●

●

●

●

●

●

Modulus Error /GPa

(0.0169,4.4]

(4.4,8.78]

(8.78,13.2]

●

(a) strain noise 

Laboratory

Standard Error of strain from fit

0.0000

0.0005

0.0010

0.0015

A B C E H I J K L M

●

●

●

●

●

●

●

Modulus Error /GPa

(0.0169,4.4]

(4.4,8.78]

(8.78,13.2]

●

(b) stress noise 

Figure 18: Noise in calculated modulus based on (a) strain, and (b) stress, calculated in 

Step 5. Symbols denote three increasing levels of absolute modulus error, Eq. 10. All 

measurements are below the acceptance limit of 0.01. Data have been jittered to prevent 

over-plotting of points. 
33 

Figure 19 shows the slope of the residuals in the outer quartiles. Different symbols 

show the level of absolute error of the elastic modulus, Eq. 10. All but one of the tests 

fall inside the ±5 % limits. In addition, linear regression of the absolute modulus error 

against 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 determine 

the elastic modulus, EGA, is the size of the optimal fit range, Rf . Figure 20 plots the 

absolute modulus error, Eq. 10, against the fraction of the range of original stress data. 

The dashed line is the boundary of the minimum acceptable limit Rf ≥ 0.4. The absolute 

modulus error, Eq. 10, increases as the size of the fit region decreases, as expected, and 

the boundary between the two regions lies at the chosen final fit range minimum Rf =

0.4. The mean error for tests with fit region Rf < 0.4 is 2.5 times larger (4.88 GPa vs. 

1.95 GPa) than that from the acceptable region. 

Conclusions from elastic modulus analysis Of the quality metrics, the size of the final 

fit range is the best predictor of overall quality of the modulus measurement, and the 

level chosen, Rf ≥ 0.4, is a good metric for identifying potential problems with modulus 

measurement. 

5 Conclusions 

Five conclusions can be drawn from this study. 

•	 The repeatability of yield strength determined from compression tests conducted 

according to ASTM E9 can be expected to be about 1.1 % of the mean value, cvr= 

0.011 , Figure 6 and Table 5. 

•	 The reproducibility of yield strength determined from compression tests conducted 

according to ASTM E9 can be expected to be about 2 % of the mean value, cvR= 

0.020 , Figure 6 and Table 5. 

•	 Despite the perceived difficulties with alignment in compression, the repeatability and reproducibility of the compression test was among the best measured for 

uniaxial tests, Figure 9. 

•	 Using two diametrally opposed extensometers instead of a single extensometer can 

improve the precision of the strain measurement by more than two times, Figure 10. 

•	 If the final fit range for estimating the modulus is less than 40 % of the elastic 

region, the modulus measurement is frequently in error, Figure 20. 

In addition, although the reported data indicated that yield strengths measured on unlubricated conditions were 3.1 % lower than those measured using lubricated specimens, 

Fig. 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 discrepancy. 
34 

Laboratory

First quartile slope of residuals

−0.06

−0.04

−0.02

0.00

0.02

0.04

0.06

A B C E H I J K L M

●

● ● ●

●

●

●

Modulus Error /GPa

(0.0169,4.4]

(4.4,8.78]

(8.78,13.2]

●

(a) 1st quartile slope 

Laboratory

Fourth quartile slope of residuals

−0.06

−0.04

−0.02

0.00

0.02

0.04

0.06

A B C E H I J K L M

●

●

●

● ● ● ●

Modulus Error /GPa

(0.0169,4.4]

(4.4,8.78]

(8.78,13.2]

●

(b) 4th quartile slope 

Figure 19: Slope of residuals in the (a) 1st, and (b) 4th quartile of the extended fit for modulus. Symbols denote three increasing levels of absolute modulus error, Eq. 10. Dashed 

lines denote the acceptance limit Data have been jittered to prevent over-plotting of points. 
35 

Final fit range, fraction

Abs(Modulus error) /GPa

0

5

10

0.2 0.3 0.4 0.5 0.6

●

● ●

●

●

● ● ●

●

● ● ●

mean error

4.88 GPa

mean error

1.95 GPa

Lab

A

B

C

E

H

I

J

K

L

M

●

●

Figure 20: Absolute error in modulus, Eq. 10, as a function of the fraction of the final 

fit range, Rf , used to calculate the modulus. Symbols identify the different laboratories. 

Points to the left of the dashed line are deemed to have insufficient fit range. 
36 

Author contributions 

William Luecke supervised the interlaboratory study and analyzed the reported modulus 

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 Ma conducted the finite element analysis of the specimen deformation under frictionless and 

perfect friction. 

Acknowledgments 

The authors could not have completed this study without the generous donation of the 

testing services of the participants, including those who volunteered, but ultimately could 

not complete the testing in the brief time allotted: Ray Schiltz (AADFW, Inc), Rich 

Brazill (Alcoa), Rick Kapaun (Exova), Bill Swartz (Constellation Technology Corp.), I. 

Ahmed (Dickson Testing Company Inc.), James Hartman (Honeywell Aerospace), Hugh 

MacGillivray (Imperial College Mechanical Engr.), Matt Webb (MAR-TEST, Inc. (Cincinnati)), Frank Worpenberg (MAR-TEST, Inc. (Stuart)), Ken Broenner (Metcut Research 

Inc.), Dennis Galloway (Stork Climax Research Services), and Mike Self (Westmoreland 

Mechanical Testing). 

WEL thanks the other two members of the organizing team, Rich Brazill and James 

Hartman for their assistance. Rich Brazill supplied the aluminum plate, the test specimen 

blanks, and the test specimen assignments. 

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