Journal of Nuclear Materials 393 (2009) 425–432

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Journal of Nuclear Materials

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Tensile–shear correlations obtained from shear punch test technique

using a modified experimental approach
V. Karthik *, P. Visweswaran, A. Vijayraghavan, K.V. Kasiviswanathan, Baldev Raj
Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India

a r t i c l e i n f o a b s t r a c t

Article history: Shear punch testing has been a very useful technique for evaluating mechanical properties of irradiated
Received 11 February 2009 alloys using a very small volume of material. The load–displacement data is influenced by the compliance
Accepted 23 June 2009 of the fixture components. This paper describes a modified experimental approach where the complianc-
es of the punch and die components are eliminated. The analysis of the load–displacement data using the
modified setup for various alloys like low carbon steel, SS316, modified 9Cr–1Mo, 2.25Cr–1Mo indicate
that the shear yield strength evaluated at 0.2% offset of normalized displacement relates to the tensile
YS as per the Von Mises yield relation (rys = 1.73sys). A universal correlation of type UTS = msmax where
m is a function of strain hardening exponent, is seen to be obeyed for all the materials in this study. The
use of analytical models developed for blanking process are explored for evaluating strain hardening
exponent from the load–displacement data. This study is directed towards rationalizing the tensile–shear
empirical correlations for a more reliable prediction of tensile properties from shear punch tests.
Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction ment. Finite element simulation and analysis of the shear punch
test by Toloczko et al. [4] revealed that the compliance in the test
The shear punch test is a very useful mechanical test technique frame and fixturing had a profound effect on the shape of the LDC.
for evaluating the mechanical properties viz. yield strength, maxi- To minimize the effects of test frame compliance on the LDC, the
mum strength and strain hardening exponent using very small vol- test setup was modified suitably to accommodate a displacement
umes of material [1]. The driving force for development of this sensor across the test fixture [5] or coupled to the moving punch
technique has been the material development programmes for fu- [6,7].
sion and fission reactors. The small volumes of specimens could be The other aspect that has caught the attention of many investi-
easily fitted into the existing irradiation space and permitted easy gators is the accurate measurement of the yield load from the LDC.
handling due to low radioactivity for mechanical property evalua- The point of deviation from linearity of the initial portion of LDC
tion [2]. As a spin-off, it has a variety of other applications in situ- was first used as an approximate measure of the shear yield load
ations where conventional mechanical tests are not possible such [2]. However, for materials exhibiting a very smooth transition
as weld joints [3], coatings and failure analysis. from the linear to the non-linear deformation, this method of locat-
The shear punch (ShP) test technique involves slow blanking of ing the yield load resulted in considerable scatter. In one of our
a thin disc material clamped between a set of dies at a constant earlier studies, it was shown that online acoustic emission moni-
speed as shown schematically in Fig. 1. The deformation occurs toring during the test led to accurate prediction of the yield load
in the small annular region of the punch–die clearance. The [8]. Researchers subsequently adopted the method of measuring
load–displacement curve (LDC) obtained during the blanking oper- yield stress at an offset shear strain analogous to the offset proce-
ation (Fig. 2) is very similar to that obtained in a conventional uni- dure used in tensile testing.
axial tensile test and the properties obtained by analyzing the ShP To rationalize the methodology for shear yield strength deter-
test curve can be correlated to the corresponding conventional ten- mination, Guduru et al. [9] carried out finite element analysis
sile properties. (FEA) of the initial stages of punch displacement. Based on the
Many investigators have evolved the experimental test setup development of plastic deformation zone completely through the
and the method of analyzing the LDC over a period of time. In specimen thickness, they concluded that an offset of 0.15% of initial
the initial period of its development, investigators used the cross- linear portion of FEA generated stress–normalized displacement
head movement as an approximate measure of punch displace- curve represent the shear yield stress. However, this corresponded
to an offset of 1% in the actual experiments due to the compliance
effects of the test fixtures. The shear yield strength corresponding
* Corresponding author. Tel.: +91 44 27480122; fax: +91 44 27480356.
E-mail address: karthik@igcar.gov.in (V. Karthik). to 1% offset in their study satisfied the relation rys = 1.77sys which

0022-3115/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnucmat.2009.06.027
426 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432

0.5% and 1% are compared with the tensile YS for the various mate-
rials. The offset criterion which produces the best fit between ten-
sile YS and shear yield strength is established and compared with
published results. The nature of correlations obtained for maxi-
mum strength in ShP test and the corresponding UTS is also inves-
tigated. It is found that UTS can be related to shear maximum
strength through a function involving the strain hardening expo-
nent without any alloy specific constants. Finally an attempt is
made to evaluate the strain hardening exponent from load–dis-
placement data using analytical models developed for blanking
process.

2. Experimental procedure

2.1. Shear punch test setup

Fig. 3 shows the schematic of the shear punch test fixture devel-
oped at the authors’ laboratory. The test fixture consists of a flat
Fig. 1. Schematic of the shear punch test technique. punch of 3 mm diameter made of a hardened tool steel (RC 62)
and a set of dies between which the specimen is clamped. The
diameter of the receiving hole in the lower die is 3.04 mm. The test
fixture is placed on the compression platens of a universal test ma-
chine for carrying out the test. The load during the punch operation
is measured using a standard load cell of 4 kN. A linear variable dif-
ferential transformer (LVDT) of range ±2.5 mm is fixed at the bot-
tom of the test fixture as shown in Fig. 4. The LVDT is coupled to
the center of the specimen bottom using a stiff tungsten carbide
rod to measure the specimen displacement. The test fixture, LVDT
and the connecting rod are placed in line for accurate measure-
ment of the specimen deformation. The experimental setup has
also provisions for positioning the LVDT at the top of the moving
punch as shown in Fig. 5. This was to enable the comparison of
the LDC’s obtained using the two methods of displacement mea-
surement. The load and displacement data are acquired through
a 16 bit resolution data acquisition system built in the test ma-
chine controller.

2.2. Materials

Six different materials namely low carbon steel, AISI SS316,

Fig. 2. Typical load–displacement plot obtained in a shear punch test. 2.25Cr–1Mo steel, modified (Mod) 9Cr–1Mo steel, aluminum and
copper were chosen for the present study. The chemical composi-

is in close agreement with the Von Mises yield relation. Studies by

Toloczko et al. [6] using a modified test setup also indicated that
the yield strength determined using the ‘‘1% offset” shear strain
correlated well with tensile yield strength as per the Von Mises
yield relation. It may be noted that both Toloczko et al. and Guduru
et al. have measured the punch displacement by a displacement
sensor coupled to the moving punch. The linear correlation be-
tween the ultimate tensile strength (UTS) and shear maximum
strength has been generally found to obey the linear relation of
type UTS = Asmax + B with a range of values for A and B for various
alloy classes [10].
In the present work, a modified shear punch experimental setup
has been used with an aim to eliminate the compliance effects of
punch and die components on the test data. In the modified test
setup, the displacement is measured using a sensor attached to
the bottom of the specimen. With this arrangement, the compli-
ance effect of the punch on the measured displacement is elimi-
nated. The LDC obtained from the modified setup is also
corrected for the compliances arising out of the dies and associated
fixturing through elastic loading tests with thick specimens. The
corrected LDC is analyzed for various materials like carbon steel,
chrome-moly steels, austenitic stainless steel, copper and alumi-
num alloys. The shear yield strengths evaluated at offsets of 0.2%, Fig. 3. Schematic of the shear punch test fixture.
 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432 427

perature (298 K) using a computer controlled universal testing ma-

chine as per ASTM E 8. Two tests were performed for each material
and the average value is reported.

2.4. Shear punch test

Small disc specimens of 8 mm diameter and 1.0 mm thickness

were EDM (electric discharge machining) wire cut from the various
materials and their surfaces were gently ground using SiC 600 grit
to a final thickness in the range of 0.3–0.8 mm (±0.005 mm). Shear
punch tests were performed using a universal test machine at
room temperature and at a constant crosshead speed of
1.6  103 mm/s. Tests were conducted on specimens of different
thicknesses to study the thickness effect on the LDC. Four samples
were tested for each thickness of the material and the average val-
ues are reported.
To determine the compliance of the test fixture and the compo-
nents of LVDT fixturing, a sufficiently thick specimen (3 mm thick-
ness) of high speed steel was elastically deformed to nominal peak
loads achieved in actual shear punch tests. The load–deflection
data obtained was used to compute the compliance of the test
setup.

Fig. 4. The experimental setup of shear punch tests showing the LVDT attachment
coupled to the bottom of the specimen clamped in the test fixture. 3. Results and discussion

3.1. Shear punch test curves and compliance correction

A typical load–displacement curve for AISI 316 obtained using

the modified test setup is shown in Fig. 6. The LDC obtained using
the LVDT positioned at the top of the moving punch is superim-
posed for comparison. The initial non-linearity and the effect of
the punch compliance can be observed in the latter curve. In the
modified setup, the initial loading of the punch on the specimen
instantaneously produces measurable displacement at its bottom
surface. This clearly reflects that the displacement measured clo-
sely represents the punch tip displacement. Thus the compliance
of the punch and the fixturing above the specimen plane are com-
pletely eliminated by this modified experimental setup.
The compliance of the fixture components below the specimen
plane like bottom die and the LVDT setup are deduced by analyzing
the load–displacement plots of elastic loading tests performed on
thick specimens. The compliance (C) which is the inverse of slope
of the LDC (Fig. 7) is estimated to be about 1.9  105 mm/N. The
actual displacement dc in the shear punch tests are corrected as
Fig. 5. The experimental setup where LVDT is coupled to moving punch for
measuring the displacements. dc ¼ d  ðP  CÞ; ð1Þ
where d is the displacement measured by LVDT and P is applied
load. Fig. 8 shows the two curves before and after correcting for
tion of the various steels and their thermo-mechanical conditions the compliance effects, respectively. The change in the slope of
are given in Table 1. the initial loading line as a result of the compliance correction can
be well observed.
2.3. Tensile tests
3.2. Effect of specimen thickness
Conventional flat tensile test specimens (25 mm gage length)
were machined from the various materials and tensile tests were Tests with specimens of different thicknesses ranging from 0.3
carried out at a nominal strain rate of 3  104 s1 at ambient tem- to 0.8 mm indicated a systematic shift in the LDC. The load–dis-

Table 1
Chemical composition of the various steels used in this study.

In wt.% C Si Mn Cr Mo Ni N Nb V Fe Condition
AISI type 1025 carbon steel 0.23 0.40 Bal Annealed
2.25Cr–1Mo steel 0.06 0.18 0.48 2.18 0.93 Bal Normalized and tempered
Mod 9Cr–1Mo steel 0.096 0.32 0.46 8.72 0.90 0.10 0.05 0.08 0.22 Bal Normalized and tempered
AISI 316 SS 0.06 1.0 2.0 17.0 2.4 12.0 – – – Bal Annealed
428 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432

placement data is converted to stress–normalized displacement

data using the following expressions:
P
Shear stress s¼ ; ð2Þ
2prt
dc
Normalized displacement d ¼ ; ð3Þ
t
where P is the applied load, t is the specimen thickness, r is the
average of punch and lower die radius and dc is the displacement
corrected for compliance effects. When the LDC for SS316 of varying
thickness samples are scaled to shear stress–normalized displace-
ment curves as shown in Fig. 9, the normalized curves overlapped
well except for thickness less than 0.5 mm. Though the shear max-
imum strength is the same for all thicknesses, there is a change in
slope of the initial loading line for specimen thickness less than
0.5 mm. Similar deviations of the normalized curves for lower
thickness specimens were noticed for all the materials studied. This
change in the initial slope of the normalized curves for lower thick-
ness is likely due to the loading caused by bending or compression
Fig. 6. Shear punch test load–displacement curve obtained for SS316 with the of thin specimens [7]. Based on these observations, the normalized
modified setup superimposed on that obtained using LVDT attached to punch top.
curves for thickness above 0.5 mm which overlapped irrespective of
the specimen thickness were only analyzed.

3.3. Tensile–shear strength correlations

The stress–normalized displacement curves for the various

materials studied are plotted in Fig. 10. The shear maximum
strength is computed from the peak points of the plots. The value
of shear stress at a specified offset from linearity is used to define
the shear yield strength. Using this operational definition, the
shear YS was computed at offsets of 0.2%, 0.5% and 1% of the nor-
malized displacement. The standard deviations for the measured
shear maximum and yield strengths were ±3% and ±6% of the
respective average values. These values are given in Table 2 along
with the corresponding tensile properties for the various materials
studied.

3.3.1. Yield correlation

The plot of the tensile YS with shear YS determined for the var-
ious offsets and the corresponding fit parameters namely the slope,
regression coefficient and the standard deviation of the fit are gi-
ven in Fig. 11. It can be seen that out of the three offset definitions
Fig. 7. Load–displacement plots of elastic loading tests carried out to compute the
for the shear YS, the 0.2% offset produces the best fit with a regres-
compliances of the experimental setup.
sion coefficient of R2 = 0.99 and a standard deviation of ±17 MPa.

Fig. 8. Comparison of the load–displacement plots obtained for SS316 using the
modified experimental setup before and after applying the compliance correction. Fig. 9. ShP test curves of SS 316 samples with different thicknesses.
 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432 429

Fig. 10. The stress–normalized displacement curves for various materials.

The offset definition of 0.2% is much less than the value of 1% re-
ported by Toloczko and Guduru. A larger percentage offset re-
quired in their experiments was due to the finite compliances of
the die and punch components. In the present investigation, these
compliances are eliminated through (i) the use of LVDT at bottom
of the specimen and (ii) corrections through elastic loading tests. Fig. 11. Linear fit between the tensile and shear yield strengths of various materials
This resulted in steeper loading curve enabling accurate evaluation for different offsets.
of shear YS at 0.2% offset. This offset is in close agreement with the
FEA offset of 0.15% obtained by Guduru et al. [9] with rigid punch,
die and holder components. The equation of linear fit obtained be- 3.3.2. Maximum strength correlation
tween tensile YS and 0.2% offset shear yield strength is The UTS and corresponding shear maximum strength (smax) of
rys = 1.73sys which is exactly the same as Von Mises yield relation various alloys is plotted in Fig. 12. The linear correlation through
for shear deformation. origin yields a slope of 1.29 with R2 = 0.96 and standard deviation
The nature of tensile–shear correlations obtained from shear of ±45 MPa. In the earlier work by Hamilton et al. [10], Hankin et al.
punch tests has been a subject of debate over a period of years. [11] on various alloy systems, correlation equations of type UT-
Early studies led to development of material specific correlations S = A1smax + B1 were established with slope (A1) ranging from 1.8
of type r = As + B for yield and maximum strength with a range to 2.9 and intercept B1 ranging from 38 to 425 for various alloy
of A and B values for various alloy class. With the insights provided classes. Similar linear correlations for tensile–shear maximum
by FEA and improvements in displacement measurement for com- strength obtained in our earlier works using different heat treated
pliance corrections, the yield correlation simplified into a universal and cold worked microstructural conditions of 2.25Cr–1Mo [5],
equation of type rys = Asys with a material independent value for A. Mod 9Cr–1Mo [12] and SS316 is reproduced in Fig. 13. The limited
This work establishes that the offset definition for shear yield strength range over which the data were obtained for each alloy
strength with the modified experimental setup is 0.2% and the class could not force a best linear fit through origin and hence re-
shear YS so computed matches with the Von Mises yield relation. sulted in an intercept parameter B1. Hamilton et al. suggested that
The experimentally obtained universal value of A = 1.73 for yield the differences in the fit parameters between various alloys could
correlation clearly shows that the deformation in shear punch test be partly due to the size of the data base for each alloy class and
is shear dominant in the early stages of deformation. This enables partly due to punch–specimen–die friction. Based on these obser-
direct estimation of tensile yield strength of irradiated alloys using vations, a single correlation equation with a slope (A1) of 2.2 for
shear punch tests using the 0.2% offset definition without requiring all alloy data sets [10] were arrived by Hamilton et al. only after
any other material specific constants. subtracting the intercept values B1 from the respective data sets.

Table 2
Tensile and shear punch test results of various materials studied.

Material Tensile properties Shear punch test properties

0.2% YS, MPa UTS, MPa Shear yield strength, MPa Shear maximum strength, MPa
0.2% offset 0.5% offset 1.0% offset
Cu 127.14 202.00 56.74 64.71 74.02 158.00
Al 172.53 267.40 99.07 139.24 149.80 189.50
0.25% C steel 290.50 432.87 164.41 178.84 198.07 348.97
2.25Cr–1Mo 431.62 574.57 261.35 281.75 303.98 416.17
Mod 9Cr–1Mo 514.00 671.32 289.92 325.10 357.20 472.92
SS316 211.10 583.07 125.18 155.96 185.73 511.00
430 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432

Fig. 14. Plot showing the excellent agreement between the experimental shear
maximum strength and that predicted using Eq. (4).
Fig. 12. The linear fit between UTS and shear maximum strength.

the experimentally obtained smax and plotted in Fig. 14. A standard

deviation of ±14 MPa indicates a good agreement between the
experimental and predicted smax. The Eq. (4) relating the tensile
and shear maximum strengths through strain hardening exponent
‘n’ is also found to be obeyed for all earlier data sets of 2.25Cr–1Mo,
9Cr–1Mo and SS316 generated in authors’ laboratory.
The maximum strength correlation can thus be expressed as
UTS = msmax, where the coefficient m = (1/sf). Depending on ‘n’ va-
lue say 0.01–0.6, ‘m’ ranges from 1.68–1.06, indicating that the
coefficient of the UTS correlation is always less than that of YS cor-
relation. For a brittle material whose n is low, the coefficient m is
close to 1.73 (same as yield correlation constant), while for a duc-
tile material the ‘m’ reduces to around 1.10. Thus the lower values
of UTS correlation coefficient ‘m’ as compared to yield correlation
constant could be associated with the strain hardening capability
of the material. For the materials investigated in the present study,
the correlation coefficient ‘m’ averages to around 1.29 (Fig. 12). The
Eq. (4) can also be used for predicting the ‘n’ value using UTS esti-
mated through correlation of type UTS = A1smax + B1 with known
Fig. 13. UTS–shear maximum strength correlation of type UTS = Asmax + B obtained values of A and B. The following section analyses the evaluation
for various alloys in authors laboratory [5,12]. of a strain hardening or ductility parameter from load–displace-
ment data of ShP test.
However, to use this constant A1 for predicting UTS from ShP data
requires a prior knowledge of the B1 parameter for the alloy.
It is seen that any attempt to predict UTS from shear punch test
using a universal correlation of type UTS = msmax (m-constant)
seems to be unreliable due to relatively poor R2 and high standard
deviation as compared to that of yield correlation. These observa-
tions suggest that the actual relation between the UTS and smax
could be more complex involving some geometrical measure of
deformation present in the shearing zone.
Ramaekars and Kals [13] studied the Von Mises equivalent
strain of the blanked specimen from microhardness measurements
on the specimen at various penetrations. The empirical relation-
ship relating smax to UTS was derived as
smax ¼ sf UTS; ð4Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s  n 
1 3
where sf is the shearing factor equal to ;
3 n
n is the strain hardening exponent:
To verify the applicability of the above equation to our experi-
mental data, smax estimated using Eq. (4) from known values of n
from log r  log e traces of tensile data and UTS is compared with Fig. 15. Plot of ‘n’ from tensile test with the parameter (dudy)/t of ShP test.
 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432 431

Fig. 16. Schematic of the shear deformation (a) pure shear and (b) with bending of the blank material fibers [16].

3.4. Strain hardening from shear punch test

One of the earlier approaches was to relate true strain in tensile

tests to ns obtained from ShP data using the semi-empirical
expression:
 n ns s 
s max
¼ ; ð5Þ
0:002 sys
where ns is the strain hardening exponent in ShP test [2]. The other
approach is based on relating the true plastic strain or strain hard-
ening exponent obtained in tensile test to the normalized displace-
ment in ShP test. Fig. 15 shows the plot of strain hardening
exponent ‘n’ from tensile data with (dudy)/t, where du/t and dy/t
are the normalized displacements at shear maximum strength
and shear yield strength respectively. No distinct trend line is pos-
sible through the data sets indicating that a direct universal corre-
lation of type n = B(d/t), (B-constant) may not be possible.
An attempt was made to use the analytical model of Atkins [14]
to analyze the LDC for strain hardening parameter. For the simple
geometry of punching shown in Fig. 16a, assuming a power law Fig. 17. Plot of ‘n’ estimated from shear punch test data using Eq. (9) compared
behavior r = Ken, where K is the strength coefficient and n is the with ‘n’ determined from tensile test.
strain hardening exponent, Atkins derived the punching force F
with friction modeled through an assumed proportion f of the
to include bending (Fig. 16b) and frictional component during
shear stress s as
the blanking process for estimating the Von Mises equivalent
 n
d stress and strain from force–displacement data. Analysis of the
F ¼ pD½ðt  dÞ þ 2f  dC 2 ; ð6Þ modified model with our ShP data reveals a trend almost similar
c
to Fig. 17, with good match for estimated ‘n’ with tensile ‘n’ for
where D: diameter of the punch; d: punch penetration; c: width of low carbon steel, modified 9Cr–1Mo and copper alloys, while large
the clearance zone; t: specimen thickness; C2: constant in the differences are observed for austenitic steels. The assumptions of
power law s = C2cn; c: shear strain. shear dominant deformation in punching with the simplified
Using the Von Mises’ expressions for equivalent stress and geometry of Fig. 16 and power law type of work hardening behav-
strain for assumed pure shear condition: ior needs further investigation for evolving an accurate analytical
r model for equivalent stress–strain values. The optimization of
s¼p ; ð7Þ
these analytical models together with finite element modeling of
3
p the non-linear deformation up to peak load form the basis for fur-
c ¼ 3e; ð8Þ
ther research work in authors’ laboratory.
the constants C2 and K are related through the expression C2 = K/
p
( 3)n+1. 4. Conclusions
This coupled with Ramaekars equation smax = UTS sf, where
UTS = K(n/e)n, e = 2.71, is used to derive an equation for du (dis- A modified shear punch experimental setup in which specimen
placement at peak load) in terms on ‘n’ and other parameters displacement is measured directly using an LVDT has been demon-
(assuming f = 0) as strated to eliminate the effects of punch and die compliances on
n
ðt  du Þðdu Þ ¼ tð1:1cÞn ðnÞn=2 : ð9Þ the load–displacement curve.
The shear yield strength evaluated using the 0.2% offset definition
An estimate of n (nest) obtained by solving the above equation produces the best fit with the tensile yield strength and satisfies the
with experimental values of du is compared with the strain harden- Von Mises yield relation rys = 1.73sys. The 0.2% offset definition for
ing exponent ‘n’ from log r  log e traces of tensile data as shown shear yield strength proposed in our experimental study is much less
in Fig. 17. A good match is seen for low carbon steel, Mod 9Cr–1Mo than 1% offset reported by earlier researchers due to the elimination
and copper, while nest is grossly underestimated for SS316. It may of compliances of the fixture components. The offset definition is in
be noted that this model is based on assumptions of pure shear. close agreement with the 0.15% offset criterion obtained in finite ele-
Klingenberg et al. [15,16] modified the analytical model of Atkins ment simulation studies by other investigators.
432 V. Karthik et al. / Journal of Nuclear Materials 393 (2009) 425–432

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AWS (2002) 265s.
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[4] M.B. Toloczko, Y. Yokokura, K. Abe, M.L. Hamilton, F.A. Garner, R.J. Kurtz, in:
in this study. The value of coefficient ‘m’ is found to be always less M.A. Sokolov, J.D. Landes, G.E. Lucas (Eds.), Small Specimen Test Techniques,
than the yield correlation constant. vol. 4, ASTM STP 1418, 2002, p. 371.
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