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438 Part C Materials Properties Measurement

which can be coupled with the value of V

to calcu-

late V

and V

As discussed above, the accuracy of gas solubility

measurements depends strongly on the calibration of the

transducers and the volumes, especially for low-sorbing

materials. Since the true volume of the sample cell in

the measurement is the difference between the sample

cell volume and the polymer sample volume, the accu-

rate measurement of gas solubility depends sensitively

on the measurement of polymer sample volume and,

therefore, polymer density, which is used to calculate

polymer sample volume. The following procedure has

been developed in our laboratory to estimate the effect

of these uncertainties on solubility values. After the vol-

ume calibration, a standard sorption experiment (i. e.,

a blank experiment) is performed using the gases of in-

terest while still keeping the nonsorbing volume (e.g.,

stainless-steel spheres) in the sample cell. Ideally, the

gas solubility estimated from this experiment should

be zero since these nonporous spheres sorb a negligi-

ble amount of gas. However, due to the uncertainties in

the pressure and volume values, a small nonzero sorp-

tion value is typically obtained. In studying gas sorption

in polymers, the sample should have a volume similar

to V

, and the pressure decay sequence is kept similar

to that in the blank experiments. The solubility values

obtained in this experiment are compared with those ob-

tained from blank experiments. The difference between

these two series of results is regarded as the true gas

sorption in the polymer samples. A principal rule of

thumb to judge the validity of the data is that the gas sol-

ubility values obtained using the polymer samples need

to be much larger (such as ten times larger) than the val-

ues from the blank experiments. In general, the polymer

sample volume (V

) or the added volume should be as

Vent

Feed gas

Water out

Reference

rod

Water-jacketed

sorption chamber

Quartz spring

CCD camera

Water in

Computer

Vacuum

Liquid N

trap

Fig. 7.112 Schematic of a McBain spring system for sorption mea-

surements (P: pressure transducer; GR: gas/vapor reservoir)

large as possible so that the gas pressure change in the

sample cell during each sorption step will be very pro-

nounced, which reduces the uncertainty in the solubility

values. In our laboratory, this technique has been used to

measure solubility as low as 0.10 cm

(STP)/(cm

atm)

with a standard deviation of less than 10%.

Koros and coworkers have used data from the tran-

sient region of the pressure decay experiments to obtain

gas diffusion coefﬁcients in polymers. They monitored

the pressure change in the sample cell as a function of

time and interpreted the results using an analytical so-

lution to (7.138)[7.299]. However, this method is not

commonly used for kinetic studies, partially because the

polymer sample is typically stacked in the small sam-

ple cell, and a uniform boundary condition during the

transient sorption process for the entire polymer sample

might be difﬁcult to achieve.

Gravimetric Technique

Unlike the barometric technique described above,

which is used mainly for high-pressure gas sorption

measurements, the gravimetric technique is often used

at subatmospheric pressures [7.265]. Lately, this tech-

nique has been extended for use at high pressures. For

example, ISOSORP, a commercial apparatus made by

Rubotherm (Bochum, Germany) and designed based

on the gravimetric method, can be operated at pres-

sures as high as 100 MPa. The basic principle is to

monitor the weight change of a polymer ﬁlm due to

penetrant uptake. Typically, the results yield informa-

tion about transient sorption kinetics and equilibrium

sorption. From these data, solubility, diffusivity and per-

meability can be calculated using a proper model. This

section focuses on the McBain spring balance appa-

ratus, the Cahn electrobalance, and the quartz-crystal

microbalance techniques.

A McBain spring balance is commonly used to

track the kinetics of mass uptake in a thin polymer

ﬁlm, as illustrated in Fig. 7.112. The polymer sam-

ple is suspended from a calibrated quartz spring in

a water-jacketed glass chamber, where the temperature

is controlled by circulation of water from a tempera-

ture bath [7.265,300]. The quartz spring typically obeys

Hook’s law over a wide range of loading

M = kx , (7.159)

where M is the weight, x is the spring extension, and

k is the spring constant. Generally, the spring con-

stant is calibrated by measuring the spring extension

when loaded with a series of known weights. Thus,

the penetrant uptake as a function of time can be ob-

Part C 7.6

Mechanical Properties 7.6 Permeation and Diffusion 439

tained by monitoring the spring extension with time,

which is typically measured as the displacement of

a certain point on the spring relative to the end of a ref-

erence rod using a cathetometer or a camera [7.300].

The experiment begins by degassing the polymer sam-

ple and then exposing the ﬁlm to a large amount of

gas or vapor at a ﬁxed pressure. The spring exten-

sion is monitored until the sorption reaches equilibrium

(i. e., until there is no further spring extension). The

pressure in the chamber can be increased sequentially,

and gas sorption isotherms can be obtained from such

data. Additionally, gas diffusion coefﬁcients can be

obtained from kinetic sorption data. One key design el-

ement of this apparatus is to make the sorption chamber

large enough so that the change in gas pressure dur-

ing the sorption or desorption process is negligible, and

thus the boundary condition remains C =C

at x = 0

and l.

Care must be taken to eliminate any external inter-

ference of the spring operation, which is very sensitive

to vibrations. For example, the system needs to be ﬁxed

in an area free of vibration, and the introduction of gas

or vapor into the chamber to start the experiment needs

to be slow.

One limitation of conventional McBain spring bal-

ance systems is that the penetrant needs to have vapor

pressure values high enough so that the pressure can

be measured using a pressure transducer. For example,

a pressure of 0.1 mmHg is probably the lowest practical

value that could be achieved using a system such as the

one in Fig. 7.112 [7.301]. However, the performance of

food packaging materials can depend upon the sorption

and diffusion of ﬂavor compounds (e.g., higher hy-

drocarbons, benzaldehyde, benzyl alcohol, etc.), which

are typically not very volatile (i. e., they have very

low vapor pressure values). Additionally, these ﬂavor

compounds may be present at low thermodynamic ac-

tivity, which requires the study of transport properties

of these compounds at very low pressure [7.301]. In

our laboratory, we have modiﬁed a McBain system to

avoid the requirement of low-pressure measurement by

employing gas chromatography to measure penetrant

activity [7.301]. A light gas such as helium (which

is essentially nonsorbing in the polymer at pressures

of one atmosphere or less) is bubbled through the

liquid penetrant at a controlled temperature and in-

troduced into the sample chamber. The concentration

of liquid penetrant in the gas phase can be adjusted

by controlling the temperature of the liquid or by di-

luting the gas mixture with another stream of light

gas. The concentration of the penetrant in helium is

measured using a gas chromatograph. Since the light

gas essentially does not sorb into the ﬁlm, the poly-

mer weight change is due only to the sorption or

desorption of the penetrant. In this way, the sorption

of penetrants with very low vapor pressure can be

studied.

Instead of a spring, other devices have been used to

monitor the weight change of a polymer sample dur-

ing sorption or desorption. Examples of such devices

include the Cahn electrobalance [7.302], the magnetic

suspension balance [7.303] and the quartz-crystal mi-

crobalance [7.304]. These systems have been tested at

high pressure, for example, up to 200 atm [7.304], and at

temperatures from room temperature to 120

◦

C[7.302].

The ﬁrst two balances are commercially available.

A quartz-crystal microbalance contains a piezo-

electric crystal which oscillates at its characteristic

frequency when an alternating current is applied to it.

By coating a polymer layer on the crystal and expos-

ing the polymer coatings to gas, the crystal oscillating

frequency changes as a result of the weight change by

the polymer due to penetrant sorption. The mass of gas

sorbed or desorbed (i. e., the mass change of the crystal,

Δm) is given by [7.305]

Δm =−Δ f /G , (7.160)

where Δ f is the frequency change due to sorption or

desorption, and G is a constant determined by the vi-

brational frequency, frequency constant of the crystal,

density of the quartz, and the effective area of the vibrat-

ing plate [7.305]. Special care is required for calibration

of the quartz-crystal microbalance, since the surface

properties of the coated crystal can signiﬁcantly affect

the frequency, thus introducing errors into the mass cal-

culation [7.304].

Inverse Gas Chromatography

Inverse gas chromatography (IGC) has been used to

measure gas sorption, though it is less widely used. IGC

is an indirect method, which uses a gas chromatograph

containing a solid support coated with a polymer ma-

terial of interest as the stationary phase [7.306]. The

penetrant of interest is introduced as the mobile phase,

and its passage through the GC column depends on its

interaction with the polymer. Typically, gas sorption in

the polymer is related to the gas’s retention time on

the polymer-coated column. IGC can easily be used to

study gas sorption as a function of temperature even

up to high temperatures. However, the column cannot

withstand high pressures.

Part C 7.6

440 Part C Materials Properties Measurement

Mixed-Gas Sorption Measurement

Mixed-gas sorption measurements are rarely reported,

partly due to the complexity of these measurements.

Additionally, gas sorption in polymers is often low, so

the mixed-gas sorption is typically assumed to be the

sum of the amounts of the components sorbed based on

pure-gas sorption measurements. In some cases, how-

ever, competitive sorption is expected, and the mixed-

gas sorption level could deviate from those estimated

based on pure-gas sorption. CO

and C

sorption in

glassy poly(methyl methacrylate) (PMMA)isanexam-

ple of such a system [7.314]. To understand the effect

of sorbing of one penetrant on the other in PMMA,

Sanders et al. designed a mixed-gas sorption system

based on barometric pressure decay principles such as

those described in Sect. 7.6.3. The design is similar to the

pure-gas measurement, except that the gas compositions

must be determined before and after the gas is introduced

into the sample cell using a gas chromatograph [7.314].

For details regarding the apparatus design and operation,

readers should consult [7.314].

Special Techniques

Advances in analytical equipment can potentially im-

prove methods to measure gas transport properties

in polymer ﬁlms. In addition to the more typical

systems discussed above, there are special tech-

niques available for certain situations. Crank and

Park reviewed various techniques to measure pene-

trant concentration directly as a function of time and

position [7.268]. These techniques include refractive-

index measurements, radiation absorption methods and

radiotracer methods [7.268]. From these techniques,

small-molecule transport properties such as solubility,

Table 7.16 A list of some ASTM International standards related to the measurement of gas transport properties in polymer

ﬁlms

Document number

Measurement Method Ref.

D1434-82 Gas permeability Constant-pressure variable-volume, constant-volume variable-

pressure

[7.307]

D3985-02 Dry O

permeability Continuous ﬂow with a coulometric detector [7.308]

F1307-02 Dry O

permeability Continuous ﬂow with a coulometric detector [7.295]

F1927-98 Humidiﬁed O

permeation Continuous ﬂow with a coulometric detector [7.309]

E96-00 Water vapor permeance Gravimetric cup method (desiccant method and water method) [7.310]

E398-03 Water vapor permeance Relative humidity measurement [7.311]

F1770-97 Water permeability,

solubility and diffusivity

Continuous ﬂow with a water-concentration-dependent

sensor; time lag

[7.312]

F1769-97 Vapor permeability,

solubility and diffusivity

Continuous ﬂow with a ﬂame ionization detector; time lag [7.313]

The numbers after the dash indicate the year of original adoption or last revision

diffusivity and permeability can be obtained when these

results are combined with ﬂux measurements. Fieldson

and Barbari applied Fourier-transform infrared (FTIR-

ATR ) spectroscopy to study small-molecule diffusion in

polymers [7.315]. Assink used nuclear magnetic reso-

nance (NMR) techniques to study ammonia sorption in

glassy polystyrene [7.316]. As discussed in Sect. 7.6.2,

glassy polymers exhibit two distinct sorption sites,

Henry’s law sites and Langmuir sites. It is commonly

assumed that gas sorbed into these two populations

of sorption sites can exchange rapidly (i. e., the lo-

cal equilibrium hypothesis), and gas sorbed into the

Langmuir sites is typically less mobile than that in

Henry’s law sites [7.316, 317]. To test that assump-

tion, Assink determined gas concentration in the ﬁlm

using NMR and obtained the relative concentration by

ﬁtting the data to (7.132). Based on the characteris-

tic exponential decay of the nuclear magnetization, he

was able to verify the validity of the local equilibrium

hypothesis [7.316].

7.6.6 Method Evaluations

In the USA, the American Society for Testing and

Materials (ASTM) has published guidelines for many

of the measurement techniques discussed above. Ta-

ble 7.16 provides a synopsis of relevant ASTM stan-

dards. Interested readers should consult the original

ASTM documents, which discuss equipment design,

operating procedures, and application of the techniques.

Some commercial instruments used for gas transport

property measurement are listed in Table 7.17.

In general, it is important to plan the experi-

ments needed to understand the transport of particular

Part C 7.6

Mechanical Properties 7.6 Permeation and Diffusion 441

Table 7.17 Some representative commercially available instruments

Model Measurement Method Company

OX-TRAN Model 2/21 O

permeability ASTM D3985 MOCON Inc., Minneapolis,

MN, USA

PERMATRAN-W Model 3/33 Water permeability ASTM F1249

PERMATRAN-C Model 4/41 CO

permeability Constant volume with an

infrared detector

ISOSORP 2000 Gas or vapor sorption Gravimetric method Rubotherm, Bochum, Germany

L100-5000 Gas permeability ASTM D1434 Lyssy AG, R

uti, Switzerland

OPT-5000 O

permeability

L80-5000 Water vapor permeability

Model 8500 O

permeability Continue ﬂow with a sensor Illinois Instruments, Inc.,

Johnsburg, IL,USA

Model 7000 Water vapor permeability

No. 869 Frazier-type permeator Air permeability Toyo Seiki Seisaku-Sho, Ltd.,

Tokyo, Japan

penetrants in a polymer. Permeability and selectivity

represent the inherent separation performance of a ma-

terial and are often of interest industrially. Pure-gas

studies are much easier to organize and perform than

mixed-gas measurements. However, mixed-gas trans-

port properties can, in some cases, yield results that

are different from the pure-gas results, especially when

one of the penetrants can interact strongly with the

polymer. For example, in studies of CO

and CH

permeation through cellulose acetate, CO

plasticizes

the cellulose acetate, leading to an increase in the

polymer free volume, chain ﬂexibility and CH

mixed-

gas permeability. At 35

◦

C, pure-gas CH

permeability

is about 0.12 Barrers at a pressure of 10 atm, but it

is 0.32 Barrers when the feed gas to the membrane

is a mixture of CO

and CH

with CH

and CO

partial pressures of about 10 atm and 24 atm, respec-

tively. Thus, the mixed-gas CO

/CH

selectivity was

20 while the pure gas selectivity was approximately

80 [7.318].

Gas permeability must be decoupled into solubility

and diffusivity components to understand the funda-

mentals of gas transport in polymers and polymer-based

materials of interest. For new materials, equilibrium

sorption and steady-state permeation are often stud-

ied independently to determine the transport param-

eters [7.319]. Transient transport or sorption studies

(i. e., the time-lag method or McBain spring system)

depend on speciﬁc assumptions of diffusion mod-

els, which cannot always be judged a priori for new

materials. The following sections give some gen-

eral guidelines regarding the selection of a proper

method.

A. Permeation

1. Pure-gas permeation is commonly measured using

a constant-volume variable-pressure or a constant-

pressure variable-volume device. The latter is suit-

able for polymers when the permeate gas ﬂow is

greater than 0.3cm

/min. At this and higher ﬂows,

the gas ﬂow can be accurately measured by a bubble

ﬂow meter. Otherwise, a constant volume/variable

pressure device can be used for a wide range of

ﬂux values, as long as an appropriate downstream

volume is chosen.

2. The time-lag method is most useful when the con-

centration dependence of the diffusion coefﬁcient

is known. In this way, both permeability and dif-

fusivity can be obtained in one single experiment.

From measurements of permeability and diffusivity,

solubility can be estimated according to S = P/D.

B. Sorption

1. The most common devices for sorption mea-

surements include the barometric pressure-decay

apparatus for high-pressure studies and the McBain

spring system for low-pressure studies (i. e., for

condensable vapors). The pressure-decay method

requires equation of the state information for the

desired gas (e.g., the second and third virial coef-

ﬁcients), while the McBain spring system does not.

2. Diffusion coefﬁcient can be obtained from transient

studies only when the dependence of the diffusion

coefﬁcient on penetrant concentration is known or

an assumption is made, as discussed in Sect. 7.6.1.

The McBain spring system is most widely used in

low-pressure studies.

Part C 7.6

442 Part C Materials Properties Measurement

3. If defect-free polymer ﬁlms are very difﬁcult to

prepare for permeation studies, a transient sorption

study could be very useful to obtain gas solubil-

ity and diffusion coefﬁcients, and these can be used

to estimate permeability. Solubility and diffusivity

values obtained from kinetic sorption studies are

virtually insensitive to pinhole defects in samples.

7.6.7 Future Projections

This chapter reviews basic models of gas transport in

polymer ﬁlms and measurement techniques to deter-

mine transport parameters. Guidelines for choosing one

method over another are provided. Although phenom-

ena such as non-Fickian diffusion are not discussed,

the basic principles of equipment design still apply, ex-

cept that the data analysis would be different [7.265].

Additionally, some polymers exhibit special properties

which need to be considered in the experimental design.

For example, poly(1-trimethlsilyl-1-propyne) (PTMSP)

ages rapidly (i. e., polymer ﬁlms become denser,

which decreases gas diffusion coefﬁcients over time)

during the measurement, so a standardized sample-

pretreatment protocol is required to obtain reproducible

results, along with rapid permeation tests and frequent

conﬁrmation of the polymer properties by measuring

the permeability of a marker penetrant.

The development of experimental techniques for

gas transport property measurement has beneﬁted from

other ﬁelds, such as gas absorption in liquids [7.320]

and adsorption [7.321]. For example, the dual-volume

pressure-decay method used to determine gas sorption

in polymers at high pressures is based upon a sim-

ilar principle as the one developed for gas sorption

in liquids [7.296, 320]. Similarly, the principles intro-

duced here can also be found in other applications,

such as H

storage (or H

sorption in solids) [7.322].

It might be fair to predict that the future development

of measurement methods would rely on knowledge

transfer from related ﬁelds and advancement in sen-

sors such as those for pressure and gas concentration

measurements. Recently, molecular simulations have

been extensively investigated to calculate gas solubility,

diffusivity and permeability in polymers [7.323, 324].

This approach often offers a detailed description of

complex polymer structure and transport mechanism,

although quantitative agreement between simulated and

experimental results is not always obtained [7.324].

Further information can be found in the following ad-

ditional references [7.238, 239, 241–244, 246, 247, 251,

325,326].

There is a growing interest in mixed gas solubility

measurements. Mixed gas solubility data are rarely re-

ported in the literature, probably due to the complexity

of such experiments. However, in many scenarios (such

as at high pressures, with highly sorbing penetrants,

etc.), mixed gas solubility can deviate substantially

from pure gas solubility [7.327, 328]. The capability of

measuring mixed gas solubility and calculating mixed

gas diffusivity is very valuable for developing a more in-

formed and fundamental understanding of the transport

of gas mixtures in polymers.

References

7.1 I.S. Sololnikoff: Mathematical Theory of Elasticity

(McGraw–Hill, New York 1956)

7.2 S.P. Timoshenko: HistoryofStrengthofMaterials

(Dover, New York 1983)

7.3 A.E.H. Love: A Treatise on the Mathematical Theory

of Elasticity (Dover, New York 1944)

7.4 S.P. Timoshenko, J.N. Goodier: Theory of Elasticity,

3rd edn. (McGraw–Hill, London 1982)

7.5 G. Galilei: Discorsi e Dimostrazioni Matematiche (El-

sevier, Leiden 1636)

7.6 R. Hooke: De Potentia Restitutiva (Martyn, London

1678)

7.7 E. Mariotte: Traité du Mouvement des Eaux (Michal-

let, Paris 1686)

7.8 T. Young: A Course of Lectures on Natural Philoso-

phy and the Mechanical Arts, Vol. 1 (Johnson, London

1807)

7.9 T. Young: A Course of Lectures on Natural Philosophy

and the Mechanical Arts, Vol. 2 (Johnson, London

1807)

7.10 C.L.M.H. Navier: Résumé des Lec¸ons sur l’Application

de la Mécanique, Vol. 3 (Carilian–Goeury, Paris 1864)

7.11 J.S. Smith, M.D. Wyrick, J.M. Poole: An evaluation

of three techniques for determining the Young’s

modulus of mechanically alloyed materials. In: Dy-

namic Elastic Modulus Measurements in Materials,

ASTM STP, Vol. 1045, ed. by A. Wolfenden (Ameri-

can Society Testing and Materials, Philadelphia 1990)

pp. 195–206

7.12 ASTM E 8-01: Standard test methods for tension

testing of metallic materials, Annual Book of ASTM

Standards (ASTM Int., West Conshohocken 2003)

7.13 ASTM E 74: Standard practice of calibration of

force-measuring instruments for verifying the force

Part C 7

Mechanical Properties References 443

indication of testing machines, Annual Book of ASTM

Standards, Vol. 03.01 (ASTM, West Conshohocken

1995)

7.14 E4-03: Standard practices for force veriﬁcation of

testing machines, Annual Book of ASTM Standards,

Vol. 03.01 (ASTM, West Conshohocken 1995)

7.15 ASTM E 111-04: Standard test method for Young’s

modulus, tangent modulus and chord modulus, An-

nual Book of ASTM Standards, Vol. 03.01 (ASTM, West

Conshohocken 1995)

7.16 ASTM E 132-04: Standard test method for Poisson’s

ratio at room temperature, Annual Book of ASTM

Standards, Vol. 03.01 (ASTM, West Conshohocken

1995)

7.17 ASTM E 143-02: Standard test method for shear mod-

ulus at room temperature, Annual Book of ASTM

Standards, Vol. 03.01 (ASTM, West Conshohocken

1995)

7.18 J.W. House, P.P. Gillis: Testing machines and strain

sensors. In: ASM Handbook, Mechanical Testing and

Evaluation, Vol. 8, ed. by H. Kuhn, D. Medlin (ASM

Int., Materials Park 2000)

7.19 ASTM E 83: Practice for veriﬁcation and classiﬁcation

of extensometers, Annual Book of ASTM Standards,

Vol. 03.01 (ASTM, West Conshohocken 1995)

7.20 ASTM D3379-75: Standard test method for tensile

strength and Young’s modulus for high-modulus

single-ﬁlament materials, Annual Book of ASTM

Standards, Vol. 15.01 (ASTM, West Conshohocken

2005)

7.21 ASTM D 638-03: Standard test method for tensile

properties of plastics, Annual Book of ASTM Stan-

dards, Vol. 08.01 (ASTM, West Conshohocken 2005)

7.22 ASTM 882-02: Standard test method for tensile prop-

erties of thin plastic sheeting, Annual Book of ASTM

Standards, Vol. 08.01 (ASTM, West Conshohocken

2005)

7.23 ASTM C 1341-00: Standard test method for ﬂexural

properties of continuous ﬁber-reinforced advanced

ceramic composites, Annual Book of ASTM Standards,

Vol. 15.01 (ASTM, West Conshohocken 2005)

7.24 ASTM C674-88: Standard test methods for ﬂexural

properties of ceramic whiteware material, Annual

Book of ASTM Standards, Vol.15.02 (ASTM, West Con-

shohocken 2006)

7.25 STM C 215-02: Standard test method for fundamental

transverse, longitudinal, and torsional frequencies

of concrete specimen, Annual Book of ASTM Stan-

dards, Vol. 04.02 (ASTM, West Conshohocken 2005)

7.26 ASTM 623-92: Standard test method for Young’s

modulus, shear modulus, and Poisson’s ratio for

glass and glass–ceramics by resonance, Annual

Book of ASTM Standards, Vol.15.02 (ASTM, West Con-

shohocken 2006)

7.27 ASTM C 747-93: Test method for moduli of elas-

ticity and fundamental frequencies of carbon and

graphite materials by sonic resonance, Annual Book

of ASTM Standards, Vol. 05.01 (ASTM, West Con-

shohocken 1998)

7.28 ASTM C 848-88: Test method for Young’s modu-

lus, shear modulus, and Poisson’s ratio for glass

and glass–ceramics by resonance, Annual Book

of ASTM Standards, Vol. 15.02 (ASTM, West Con-

shohocken 2006)

7.29 ASTM C 885-87: Standard test method for Young’s

modulus of refractory shapes by sonic resonance,

Annual Book of ASTM Standards, Vol. 15.01 (ASTM,

West Conshohocken 2005)

7.30 ASTM C 1198-01: Standard test method for dynamic

Young’s modulus, shear modulus, and Poisson’s

ratio for advanced ceramics by sonic resonance, An-

nual Book of ASTM Standards, Vol. 15.01 (ASTM, West

Conshohocken 2005)

7.31 ASTM E 1875: Standard test method for dynamic

Young’s modulus, shear modulus, and Poisson’s

ratio by sonic resonance, Annual Book of ASTM Stan-

dards, Vol. 03.01 (ASTM, West Conshohocken 1995)

7.32 ASTM E 1876-01: Standard test method for dynamic

Young’s modulus, shear modulus, and Poisson’s

ratio by impulse excitation of vibration, Annual

Book of ASTM Standards, Vol. 03.01 (ASTM, West Con-

shohocken 1995)

7.33 J.M. Ide: Some dynamic methods of determination

of Young’s modulus, Rev. Sci. Instrum. 6, 296–298

(1935)

7.34 F. Forster: Ein neues Messverfahren zur Bestimmung

des Elastizitätsmoduls und der Dämpfung, Z. Metal-

lkd. 29, 109–115 (1937)

7.35 C1419-99a: Standard test method for sonic veloc-

ity in refractory materials at room temperature and

its use in obtaining an approximate Young’s modu-

lus, Annual Book of ASTM Standards, Vol. 15.01 (ASTM,

West Conshohocken 2005)

7.36 W.E. Tefft: Numerical solution of the frequency

equations for the ﬂexural vibration of cylindrical

rods, J. Res. NBS 64b,237–242(1960)

7.37 R.E. Smith, H.E. Hagy: A low temperature sonic res-

onance apparatus for determining elastic properties

of solids, Int. Rep., Vol. 2195 (Corning Glass Works,

Corning 1961)

7.38 J.B. Wachtman Jr., W.W. Tefft, D.G. Lam Jr.,

C.S. Apstein: Exponential temperature dependence

of Young’s modulus for several oxides, Phys. Rev.

122,1754(1961)

7.39 A.H. Cottrell: Mechanical Properties of Matter (Wiley,

New York 1964)

7.40 J.L. Hay, G.M. Pharr: Instrumented indentation test-

ing. In: ASM Handbook, Mechanical Testing and

Evaluation, Vol. 8, ed. by H. Kuhn, D. Medlin (ASM

Int., Materials Park 2000)

7.41 A.C. Fischer-Crips: Nanoindentation (Springer,

Berlin Heidelberg 2002)

7.42 A.E.H. Love: Boussenisq’s problem for a rigid cone,

J. Math. 10, 161–175 (1939)

Part C 7

444 Part C Materials Properties Measurement

7.43 I.N. Sneddon: The relation between load and pene-

tration in the axisymmetric Boussinesq problem for

a punch of arbitrary proﬁle, Int. J. Eng. Sci. 3,47–56

(1965)

7.44 S.I. Bulychev, V.P. Alekhin, M.K. Shorshorov,

A.P. Ternovskii, G.D. Shnyrev: Determining Young’s

modulus from the indenter penetration diagram,

Zavod. Lab. 41, 1137–1140 (1975)

7.45 W.C. Oliver, G.M. Pharr: An improved technique for

determining hardness and elastic modulus using

load and displacement sensing indentation experi-

ments, J. Mater. Res. 7, 1564–1583 (1992)

7.46 R. Hill: The Mathematical Theory of Plasticity (Oxford

Univ. Press, Oxford 1950)

7.47 W.F. Chen, D.J. Han: Plasticity for Structural Engi-

neers (Gau Lih, Taipei 1995)

7.48 R. deWit: Theory of dislocations: An elementary in-

troduction. In: Mechanical Behavior of Crystalline

Solids, NBS Monogr., Vol. 59, ed. by R. deWit (US

Printing Ofﬁce, Washington 1962) pp. 13–34

7.49 E.R. Parker: Plastic ﬂow and fracture of crystalline

solids. In: Mechanical Behavior of Crystalline Solids,

NBS Monogr., Vol. 59, ed. by R. deWit (US Printing

Ofﬁce, Washington 1962) pp. 1–12

7.50 H.J. Frost, M.F. Ashby: Deformation-Mechanism

Maps: The Plasticity and Creep of Metals and Ce-

ramics (Pergamon, New York 1982)

7.51 F.D. Fischer, G. Reisner, E. Werner, K. Tanaka,

G. Cailletaud, T. Antretter: A new view on transfor-

mation induced plasticity (TRIP), Int. J. Plast. 16(7),

723–748 (2000)

7.52 O. Grassel, L. Krüger, G. Frommeyer, L.W. Meyer:

High strength Fe-Mn-(Al,Si) TRIP/TWIP steel devel-

opment – properties – applications, Int. J. Plast.

16(10), 1391–1409 (2000)

7.53 K.H. Roscoe, J.H. Burland: On the generalized stress

strain behavior of wet clay. In: Engineering Plastic-

ity, ed. by J. Heyman, F.A. Leckie (Cambridge Univ.

Press, Cambridge 1968) pp. 585–609

7.54 A.H. Cottrell: Dislocations and Plastic Flow in Crystals

(Oxford Univ. Press, London 1965)

7.55 E. Orowan: Private communication (1972)

7.56 R.W.K. Honeycomb: The Plastic Deformation of Met-

als (Edward Arnold, London 1968)

7.57 L.E. Levine (Ed.): Dislocations 2000: An international

conference on the fundamentals of plastic defor-

mation,Mater.Sci.Eng.A309, 1–284 (2001)

7.58 L.E. Levine (Ed.): Dislocations 2000: An international

conference on the fundamentals of plastic defor-

mation,Mater.Sci.Eng.A310, 285–567 (2001)

7.59 A.S. Khan (Ed.): Dislocations, Plasticity, and Metal

Forming: Proc. 10th Int. Symp. Plasticity and Its

Current Applications (Neat, Fulton 2003)

7.60 L.E. Levine, R. Thomson: The statistical origin of

bulk mechanical properties and slip behavior of fcc

metals,Mater.Sci.Eng.A400, 202 (2005)

7.61 P.W. Bridgman: Studies in Large Plastic Flow and

Fracture (McGraw–Hill, New York 1952)

7.62 ISO 14577: Metallic Materials – Instrumented Inden-

tation Test for Hardness and Materials Parame-

ters (International Organization for Standardization

(ISO), Geneva 2002)

7.63 ASTM E 8: Standard Test Methods of Tension Testing

Metallic Materials (ASTM Int., West Conshohocken

2004)

7.64 ISO 6892: Metallic Materials – Tensile Testing at Am-

bient Temperatures (International Organization for

Standardization (ISO), Geneva 1998)

7.65 DIN EN 10002-1: Metallic Materials – Tensile Testing

– Part 1: Method of Testing at Ambient Temperature

(Deutsches Institut für Normung (DIN), Berlin 2001)

7.66 JIS Z 2241: Method of Tensile Test for Metallic Materials

(Japanese Standards Association, Tokyo 1998)

7.67 BS 18: Methods for Tensile Testing of Metallic Mater-

ials (British Standards Institute (BSI), London 1987)

7.68 ASTM E 8M: Standard Test Methods for Tension

Testing of Metallic Materials (ASTM Int., West Con-

shohocken 2004)

7.69 SAE J416: Tensile Test Specimens (Society for Au-

tomotive Engineers (SAE International), Warrendale

1999)

7.70 ASTM A 370: Standard Test Methods and Deﬁnitions

for Mechanical Testing of Steel Products (ASTM Int.,

West Conshohocken 2005)

7.71 ASTM B557: Standard Test Methods of Tension Testing

Wrought and Cast Aluminum- and Magnesium-

Alloy Products (ASTM Int., West Conshohocken

2002)

7.72 ASTM E 345: Standard Test Methods of Tension Testing

of Metallic Foil (ASTM Int., West Conshohocken 2002)

7.73 ASTM E 646: Standard Test Method for Tensile Strain-

Hardening Exponents (n-Values) of Metallic Sheet

(ASTM Int., West Conshohocken 2000)

7.74 ISO 10275: Metallic Materials – Sheet and Strip –

Determination of Tensile Strain Hardening Expo-

nent (International Organization for Standardization

(ISO), Geneva 1993)

7.75 NF A03-659: Method of Determination of the Co-

efﬁcient of Work Hardening N of Sheet Steels

(Association Francaise de Normalisation (AFNOR),

Saint-Denis La Plaine Cedex 2001)

7.76 ASTM E 517: Standard Test Method for Plastic Strain

Ratio r for Sheet (ASTM Int., West Conshohocken

2000)

7.77 NF A03-658: Method of Determination of the Plastic

Anisotropic Coefﬁcient R of Sheet Steels (Association

Francaise de Normalisation (AFNOR), Saint-Denis La

Plaine Cedex 2001)

7.78 SAE J429: Mechanical and Material Requirements

for Externally Threaded Fasteners (Society for Au-

tomotive Engineers (SAE International), Warrendale

1999)

7.79 ASTM F 606: Standard Test Methods for Determining

the Mechanical Properties of Externally and Inter-

nally Threaded Fasteners, Washers, and Rivets (ASTM

Int., West Conshohocken 2002)

Part C 7

Mechanical Properties References 445

7.80 ISO 898: Mechanical Properties of Fasteners (In-

ternational Organization for Standardization (ISO),

Geneva 1999)

7.81 ASTM D638: Standard Test Method for Tensile Proper-

ties of Plastics (ASTM Int., West Conshohocken 2003)

7.82 ASTM D882: Standard Test Method for Tensile Prop-

erties of Thin Plastic Sheeting (ASTM Int., West

Conshohocken 2002)

7.83 ASTM D1708: Standard Test Method for Tensile Prop-

erties of Plastics By Use of Microtensile Specimens

(ASTM Int., West Conshohocken 2002)

7.84 ASTM E 4: Standard Practices for Force Veriﬁcation

of Testing Machines (ASTM Int., West Conshohocken

2003)

7.85 ASTM E 83: Standard Practice for Veriﬁcation and

Classiﬁcation of Extensometers (ASTM Int., West Con-

shohocken 2002)

7.86 G.R. Johnson, W.H. Cook: A constitutive model and

data for materials subjected to large strains, high

strain rates, and high temperatures, Proc. 7th Int.

Symp. Ballistics (1983) p. 541

7.87 S.R. Bodner, Y. Partom: Constitutive equations

for elasto-viscoplastic strain-hardening materials,

ASME J. Appl. Mech. 42,385(1975)

7.88 U.F. Kocks, A.S. Argon, M.F. Ashby: Thermodynamics

and Kinetics of Slip (Pergamon, Oxford 1975)

7.89 ASTM E 1450: Standard Test Method for Tensile Testing

of Structural Alloys in Liquid Helium (ASTM Int., West

Conshohocken 2003)

7.90 ISO/DIN 19819: Metallic Materials – Tensile Testing in

Liquid Helium (International Organization for Stan-

dardization (ISO), Geneva 2004)

7.91 ISO 15579: Metallic Materials – Tensile Testing at Low

Temperatures (International Organization for Stan-

dardization (ISO), Geneva 2000)

7.92 ASTM E 21: Elevated Temperature Tension Testing of

Metallic Materials (ASTM Int., West Conshohocken

2005)

7.93 DIN EN 10002-5: Tensile Testing of Metallic Mater-

ials, Method of Testing at Elevated Temperature

(Deutsches Institut für Normung (DIN), Berlin 2001)

7.94 JIS G 0567: Method of Elevated Temperature Tensile

Test for Steels and Heat-Resisting Alloys (Japanese

Standards Association, Tokyo 1998)

7.95 ASTM E 633: Standard Guide for the Use of Thermo-

couples in Creep and Stress Rupture Testing to 1800

◦

1000

◦

C (ASTM Int., West Conshohocken 2005)

7.96 ASTM E 139: Conducting Creep, Creep Rupture, and

Stress Rupture Tests of Metallic Materials (ASTM Int.,

West Conshohocken 2000)

7.97 ASTM E 328: Stress Relaxation for Materials and

Structures (ASTM Int., West Conshohocken 2002)

7.98 DINEN10291:Metallic Materials – Uniaxial Creep

Testing in Tension – Method of Test (Deutsches In-

stitut für Normung (DIN), Berlin 2005)

7.99 DIN EN 10319: Metallic Materials – Tensile Stress Re-

laxation Testing (Deutsches Institut für Normung

(DIN), Berlin 2005)

7.100 ISO 204: Metallic Materials – Uninterrupted Uniaxial

Creep Testing in Tension – Method of Test (In-

ternational Organization for Standardization (ISO),

Geneva 1997)

7.101 JIS Z 2271: Method of Creep and Creep Rupture Testing

for Metallic Materials (Japanese Standards Associa-

tion, Tokyo 1999)

7.102 ASTM C 1337: Standard Test Method for Creep

and Creep Rupture of Continuous Fiber-Reinforced

Ceramic Composites under Tensile Loading at Ele-

vated Temperatures (ASTM Int., West Conshohocken

2005)

7.103 ASTMC1291:Standard Test Method for Elevated Tem-

perature Tensile Creep Strain, Creep Strain Rate, and

Creep Time-to-Failure for Advanced Monolithic Ce-

ramics (ASTM Int., West Conshohocken 2005)

7.104 ISO 899-1: Plastics – Determination of Creep Behav-

ior – Part 1. Tensile Creep (International Organization

for Standardization (ISO), Geneva 2003)

7.105 JIS K 7115: Plastics – Determination of Creep Be-

havior – Part 1. Tensile Creep (Japanese Standards

Association, Tokyo 1999)

7.106 ISO 7500-2: Metallic Materials – Veriﬁcation of

Static Uniaxial Testing Machines – Part 2: Tension

Creep Testing Machines – Veriﬁcation of the Applied

Load (International Organization for Standardiza-

tion (ISO), Geneva 1996)

7.107 L.M.T. Hopkin: A simple constant stress appara-

tus for creep testing, Proc. R. Soc. B63, 346–349

(1950)

7.108 R.B. Grishaber, R.H. Lu, D.M. Farkas, A.K. Mukherjee:

A novel computer controlled constant stress lever

arm creep testing machine, Rev. Sci. Instrum. 68(7),

2812–2817 (1997)

7.109 A.K. Mukherjee: Deformation mechanisms in super-

plasticity, Annu. Rev. Mater. Sci. 9, 191–217 (1979)

7.110 JIS H 7501: Method for Evaluation of Tensile Prop-

erties of Metallic Superplastic Materials (Japanese

Standards Association, Tokyo 2002)

7.111 ISO 10113: Metallic Materials - Sheet and Strip

- Determination of Plastic Strain Ratio (Inter-

national Organization for Standardization (ISO),

Geneva 1991)

7.112 ASTM E 9: Standard Test Methods for Compression

Testing of Metallic Materials at Room Temperature

(ASTM Int., West Conshohocken 2000)

7.113 ASTM E 209: Standard Practice for Compression Tests

of Metallic Materials at Elevated Temperatures with

Conventional or Rapid Heating Rates and Strain

Rates (ASTM Int., West Conshohocken 2005)

7.114 DIN 50106: Testing of Metallic Materials – Com-

pression Test (Deutsches Institut für Normung (DIN),

Berlin 2005)

7.115 DINEN12290:Advanced Technology Ceramics – Me-

chanical Properties of Ceramic Composites at High

Temperature in Air at Atmospheric Pressure – De-

termination of Compressive Properties (Deutsches

Institut für Normung (DIN), Berlin 2005)

Part C 7

446 Part C Materials Properties Measurement

7.116 ISO 604: Plastics – Determination of Compressive

Properties (International Organization for Standard-

ization (ISO), Geneva 2002)

7.117 JIS K 7132: Cellular Plastics, Rigid – Determina-

tion of Compressive Creep under Speciﬁed Load and

Temperature Conditions (Japanese Standards Asso-

ciation, Tokyo 1999)

7.118 JIS K 7135: Cellular Plastics, Rigid – Determination of

Compressive Creep (Japanese Standards Association,

Tokyo 1999)

7.119 ASTM B831: Standard Test Method for Shear Testing

of Thin Aluminum Alloy Products (ASTM Int., West

Conshohocken 2005)

7.120 ASTM B769: Standard Test Method for Shear Testing

of Aluminum Alloys (ASTM Int., West Conshohocken

2000)

7.121 ASTM B565: Standard Test Method for Shear Test-

ing of Aluminum and Aluminum-Alloy Rivets and

Cold-Heading Wire and Rod (ASTM Int., West Con-

shohocken 2004)

7.122 DIN 50141: Testing of Metals: Shear Test (Deutsches

Institut für Normung (DIN), Berlin 2005)

7.123 DINEN4525:Aerospace Series – Aluminium and

Aluminium Alloys – Test Method; Shear Test-

ing (Deutsches Institut für Normung (DIN), Berlin

2005)

7.124 DINEN28749:Determination of Shear Strength of

Pins (Deutsches Institut für Normung (DIN), Berlin

1986)

7.125 ISO 7961: Aerospace – Bolts – Test Methods (In-

ternational Organization for Standardization (ISO),

Geneva 1994)

7.126 ISO 84749: Pins and Grooved Pins – Shear Test (In-

ternational Organization for Standardization (ISO),

Geneva 2005)

7.127 ASTM E 143: Standard Test Method for Shear Modulus

at Room Temperature (ASTM Int., West Conshohocken

2002)

7.128 ASTM A 938: Standard Test Method for Torsion Testing

of Wires (ASTM Int., West Conshohocken 2004)

7.129 ISO 7800: Metallic Materials – Wire – Simple Torsion

Test (International Organization for Standardization

(ISO), Geneva 2003)

7.130 ISO 9649: Metallic Materials – Wire – Reverse Torsion

Test (International Organization for Standardization

(ISO), Geneva 1990)

7.131 A. Nadai: Theory of Flow and Fracture of Solids,Vol.1,

2nd edn. (McGraw–Hill, New York 1950) pp. 347–

349

7.132 ASTM F 1622: Standard Test Method for Measuring the

Torsional Properties of Metallic Bone Screws (ASTM

Int., West Conshohocken 2005)

7.133 ASTM E 290: Standard Test Method for Bend Testing

of Materials for Ductility (ASTM Int., West Con-

shohocken 2004)

7.134 ASTM E 190: Standard Test Method for Guided Bend

Test for Ductility of Welds (ASTM Int., West Con-

shohocken 2003)

7.135 ASTM E 796: Standard Test Method for Ductility Test-

ing of Metallic Foils (ASTM Int., West Conshohocken

2000)

7.136 ISO 7438: Metallic Materials – Bend Test (In-

ternational Organization for Standardization (ISO),

Geneva 2005)

7.137 ISO 7799: Metallic Materials – Sheet and Strip 3mm

Thick or Less – Reverse Bend Test (International Or-

ganization for Standardization (ISO), Geneva 1985)

7.138 ISO 7801: Metallic Materials – Wire – Reverse Bend

Test (International Organization for Standardization

(ISO), Geneva 1984)

7.139 ISO 7802: Metallic Materials – Wire – Wrapping

Test (International Organization for Standardization

(ISO), Geneva 1983)

7.140 ISO 8491: Metallic Materials – Tube (in full section) –

Bend Test (International Organization for Standard-

ization (ISO), Geneva 1998)

7.141 DIN V ENV 820-4: Advanced Technical Ceramics –

Monolithic Ceramics; Thermo-mechanical Proper-

ties – Part 4: Determination of Flexural Creep

Deformation at Elevated Temperatures (Deutsches

Institut für Normung (DIN), Berlin 2005)

7.142 ISO 899-2: Plastics – Determination of Creep Be-

haviour – Part 2: Flexural Creep by Three-Point

Loading (International Organization for Standard-

ization (ISO), Geneva 2003)

7.143 JIS K 7116: Plastics – Determination of Creep Beha-

viour – Part 2: Flexural Creep by Three-Point Loading

(Japanese Standards Association, Tokyo 1999)

7.144 ASTM E 643: Standard Test Method for Ball Punch

Deformation of Metallic Sheet Materials (ASTM Int.,

West Conshohocken 2003)

7.145 ASTM E 2218: Standard Test Method for Determina-

tion of Forming Limit Diagrams (ASTM Int., West

Conshohocken 2002)

7.146 ISO 20482: Metallic Materials – Sheet and Strip –

Erichsen Cupping Test (International Organization

for Standardization (ISO), Geneva 2003)

7.147 ISO 12004: Metallic Materials – Guidelines for the

Determination of Forming-Limit Diagrams (Inter-

national Organization for Standardization (ISO),

Geneva 1997)

7.148 ISO 8492: Metallic Materials – Tube – Flattening

Test (International Organization for Standardization

(ISO), Geneva 1998)

7.149 ISO 8493: Metallic Materials – Tube – Drift-

expanding Test (International Organization for

Standardization (ISO), Geneva 1998)

7.150 ISO 8494: Metallic Materials – Tube – Flanging

Test (International Organization for Standardization

(ISO), Geneva 1998)

7.151 ISO 8495: Metallic Materials – Tube – Ring-

Expanding Test (International Organization for

Standardization (ISO), Geneva 1998)

7.152 ISO 8496: Metallic Materials – Tube – Ring Tensile

Test (International Organization for Standardization

(ISO), Geneva 1998)

Part C 7

Mechanical Properties References 447

7.153 ISO 11531: Metallic Materials – Earing Test (In-

ternational Organization for Standardization (ISO),

Geneva 1994)

7.154 ISO 15363: Metallic Materials – Tube Ring Hydraulic

Pressure Test (International Organization for Stan-

dardization (ISO), Geneva 2000)

7.155 ISO/TS 16630: Metallic Materials – Method of Hole

Expanding Test (International Organization for

Standardization (ISO), Geneva 2003)

7.156 JIS H 7702: Method for Springback Evaluation in

Stretch Bending of Aluminium Alloy Sheets for Auto-

motive Use (Japanese Standards Association, Tokyo

2003)

7.157 M.Y.Demeri,M.Lou,M.J.Saran:A Benchmark Test

for Springback Simulation in Sheet Metal Forming,

SAE Techn. Paper No. 2000-01-2657 (Society Auto-

motive Engineers (SAE Int.), Warrendale 2000)

7.158 R.J.Fields,T.J.Foecke,R.deWit,G.E.Hicho,

L.E. Levine: Standard Test Methods and Data for

Modeling Crashworthiness, NIST Rep. No. NISTIR 6236

(US National Institute of Standards and Technology,

Gaithersburg 1998)

7.159 A. Uenishi, H. Yoshida, Y. Kuriyama, M. Takahashi:

Material characterization at high strain rates for op-

timizing car body structures for crash events, Nippon

Steel Tech. Rep. 88, 22–26 (2003)

7.160 Y. Sakumoto, T. Yamaguchi, M. Ohashi, H. Saito:

High-temperature properties of ﬁre-resistant steel

for buildings, ASCE J. Struct. Eng. 118(2), 392–407

(1992)

7.161 U.F. Kocks: Laws for work-hardening and low-

temperature creep, J. Eng. Mater. Technol. 98,

76–85 (1976)

7.162 U.F. Kocks, M.G. Stout: Torsion testing for general

constitutive relations, Gilles Canova’s Master’s The-

sis, Model. Simul. Mater. Sci. Eng. 7, 675–682 (1999)

7.163 T. Foecke, M.A. Iadicola: Direct measurement of

multiaxial yield loci as a function of plastic strain,

Am. Inst. Phys. Conf. Proc., Vol. 118 (2005) p. 388

7.164 V.E. Lysaght: Indentation Hardness Testing (Rein-

hold, New York 1949)

7.165 VDI/VDE 2616: Hardness Testing of Metallic Materials,

Part 1 (VDI, Düsseldorf 2002)

7.166 A. Wehrstedt: Situation of standardization in the

ﬁeld of hardness testing of metals, ASTM J. Test. Eval.

23(6), 405–407 (1998)

7.167 A. Wehrstedt: Situation of standardization in the

ﬁeld of hardness testing of metals, Proc. Int. Symp.

Adv. Hardness Meas., ed. by Standard’s Press of

China (IMEKO, Beijing 1998)

7.168 ASTM E 10-01: Standard Test Method for Brinell Hard-

ness of Metallic Materials (ASTM, West Conshohocken

2003)

7.169 ISO 6506-1: Metallic Materials – Brinell Hardness Test

–Part1,TestMethod(ASTM International Organiza-

tion for Standardization, Geneva 2005)

7.170 ASTM E 18-03: Standard Test Methods for Rock-

well Hardness and Rockwell Superﬁcial Hardness of

Metallic Materials (ASTM Int., West Conshohocken

2003)

7.171 ISO 6508-1: Metallic Materials – Rockwell Hardness

Test – Part 1, Test Method (Scales A, B, C, D, E, F, G,

H, K, N, T) (International Organization for Standard-

ization, Geneva 2005)

7.172 ASTM E 92-82: e2 Standard Test Method for Vick-

ers Hardness of Metallic Materials (ASTM Int., West

Conshohocken 2003)

7.173 ASTM E 384-99: e1 Standard Test Method for Microin-

dentation Hardness of Materials (ASTM Int., West

Conshohocken 2003)

7.174 ISO 6507-1: Metallic Materials – Vickers Hardness Test

–Part1,TestMethod(International Organization for

Standardization, Geneva 2005)

7.175 S. Low: Rockwell Hardness Measurement of Metallic

Materials (NIST, Gaithersbourg 2001) pp. 960–965

7.176 H. Bückle: Mikrohärteprüfung und ihre Anwendung

(Berliner Union, Stuttgart 1965), (Note: very exten-

sive), (in German)

7.177 H. Bückle: Echte und scheinbare Fehlerquellen bei

der Mikrohärteprüfung: Ihre Klassiﬁzierung und

Auswirkung auf die Messwerte, VDI Ber. 11,29–43

(1957), (Note: extensive), (in German)

7.178 D. Dengel: Wichtige Gesichtspunkte für die

Härtemessung nach Vickers und nach Knoop im

Bereich der Kleinlast- und Mikrohärte, Z. Werk-

stofftech. 4, 292–298 (1973), (Note: short extract),

(in German)

7.179 E. Matthaei: Härteprüfung mit kleinen Prüfkräften

und ihre Anwendung bei Randschichten (DGM-

Informationsgesellschaft, Oberursel 1987), (Note:

overall view of sources), (in German)

7.180 ISO 4545-1: Metallic Materials – Knoop Hardness

Test (International Organization for Standardization,

Geneva 2005)

7.181 ISO: Guide to the Expression of Uncertainty in

Measurement (International Organization for Stan-

dardization, Geneva 1993)

7.182 EA 10-16: Guidelines on the Estimation of Uncertainty

in Hardness Measurements (European Cooperation

for Accreditation of Laboratories, Paris 2001)

7.183 ISO 14577-1: Metallic Materials – Instrumented

Indentation Test for Hardness and Materials

Parameters – Part 1: Test Method (Interna-

tional Organization for Standardization, Geneva

2002)

7.184 H.-R. Wilde, A. Wehrstedt: Martens hardness HM –

An international accepted designation for Hardness

under test force, Z. Materialprüf. 42, 468–470 (2000),

(in German)

7.185 E. Meyer: Untersuchungen über Härteprüfung und

Härte, Z. Ver. Dtsch. Ing. 52,645–654(1908),(in

German)

7.186

I.N. Sneddon: The relation between load and pene-

tration in the axisymmetric Boussinesq problem for

a punch of arbitary proﬁle, Int. J. Eng. Sci. 3,47–57

(1965)

Part C 7