Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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358 Part C Materials Properties Measurement

for plastic behavior that employ each of these loading

modes and are the subject of this section on plasticity.

In uniaxial tension, a bar or sheet is pulled along its

long axis. The stress in the bar is calculated by dividing

the applied force by the cross-sectional area of the bar.

The strain is determined from the change in length of

an initial, ﬁducial length. In uniaxial compression abar

is subject to compressive loading along one axis and

the stress and strain are determined in much the same

way as for tension. Both tension and compression have

components of hydrostatic tension or pressure which

may affect the ultimate behavior, but not the yielding

or workhardening behavior. One of the great values of

tension and compression testing arises from the fact

that the stress and strain are uniform and simply calcu-

lated from applied forces, displacements, and specimen

dimensions.

In practice, shear results in some bending and bend-

ing results in some shear loading. The shear stress is

the tangential surface force divided by the surface area.

The shear strain is deﬁned as the change in angle that

results. Bending develops additional tensile and com-

pressive loading away from the neutral axis resulting in

mean stress effects. Pure shear and torsion (which gen-

erates pure shear) do not develop any signiﬁcant level

of mean stress.

Lastly, combinations of loading modes are used to

assess the effect of complex stress or strain states on

plasticity and ultimate behavior. Bulge testing or cup

testing is largely a biaxial tension test for sheet ma-

terial with a small component of bending. The ratio

of the stress or strain in the two orthogonal directions

can be adjusted by cut outs or specimen shape. One of

the most popular tests for plasticity, the hardness test,

is a complex multiaxial compression test with a high,

superimposed pressure (Sect. 7.3).

7.2.3 Standard Methods

of Measuring Plastic Properties

This section lists and brieﬂy describes standard tests

used to measure plastic behavior. Some of the most crit-

ical features of each method and their limitations are

discussed. As noted above, plasticity is highly sensitive

to the stress and strain state. Thus, the methods are clas-

siﬁed according to loading mode and listed in order of

importance or frequency of performance.

Hardness Tests

Whereas hardness is treated in detail in the next sec-

tion, Sect. 7.3, a glimpse of plasticity in hardness is also

made here. The hardness of a material as measured by

the indentation test methods quantiﬁes a material’s re-

sistance to plastic ﬂow. By deﬁnition, a soft material

deforms plastically more easily than a hard mater-

ial. Indentation tests are used industrially for quality

control. They are the most frequently performed me-

chanical tests because of their simplicity, rapidity, low

cost, and usually nondestructive nature. In the inden-

tation test, a spherical or pointed indenter is pressed

into the surface of a material by a predetermined force.

The depth of the resulting indentation or the force

divided by the area of the resulting indentation is

a measure of the hardness. However, these tests mea-

sure the resistance to plastic deformation in complex,

multiaxial, and nonuniform stress and strain ﬁelds at

varying strain rates. Thus, the interpretation of these

tests in terms of more common concepts is difﬁcult.

The yield strength, workhardening, or ultimate tensile

strength can only be estimated by empirical correla-

tion. The ductility cannot be estimated by any means.

It is extremely difﬁcult to use the results from these

tests analytically to accurately describe plastic defor-

mation in other applications. This drawback is being

addressed by instrumented indentation test standards

(ISO 14577 [7.62] and efforts underway at ASTM). The

commercial importance of hardness testing cannot be

underestimated and justiﬁes an entire Sect. 7.3 devoted

entirely to hardness.

Tension Tests

The uniaxial tension test is the most important test for

measuring the plastic properties of materials for speciﬁ-

cation and analytical purposes. It provides well-deﬁned

measures of yielding, workhardening, ultimate tensile

strength, and ductility. It is also used to measure the

temperature dependence and strain rate sensitivity of

these quantities. Versions of the tension test provide im-

portant parameters for predicting forming behavior. The

tension test is carried out on a bar, plate, or strip of ma-

terial that has a region of reduced cross-sectional area,

the gage section (Fig. 7.22). The reduced area causes all

plastic deformation to occur in the gage section. The

unreduced ends are held in grips (Fig. 7.4 of Sect. 7.1)

and the specimen is elongated parallel to its long axis.

Initially, the sample deforms elastically, as described

in Sect. 7.1, and in linear proportion to the applied stress

as shown schematically in Fig. 7.23. At some applied

force, nonlinear and unrecoverable deformation, i. e.,

plasticity begins. The proportional limit is the force

at the onset of plasticity divided by the initial cross-

sectional area of the sample.

Part C 7.2

Mechanical Properties 7.2 Plasticity 359

Fig. 7.22 Examples of tensile test specimens used to mea-

sure plastic behavior of metals

Various deﬁnitions of yielding are used. In the ﬁg-

ure, the 0.2% offset (plastic) yield stress is shown. As

the sample continues to elongate, it workhardens. At the

ultimate tensile strength (UTS), it breaks or becomes

unstable to continued uniform deformation. A region of

localized thinning or necking characterizes the latter in-

stability (Fig. 7.24). This ultimate behavior is covered

in Sect. 7.4 on strength.

There are many standards for performing uniaxial

tensile tests. Some standards are widely used: ASTM

E8[7.63], ISO 6892 [7.64], DIN EN 10002-1 [7.65],

JIS Z 2241 [7.66], and BS 18 [7.67]. Other standards are

modeled after these or are based in some way on them.

For example, ASTM E8M[7.68] is a metric version

of ASTM E8[7.53], SAE J416 [7.69] provides some

guidance in sample geometry for testing according to

ASTM E8[7.63], ASTM A 370 [7.70] describes ten-

sile testing of steel products, and ASTM B 557 [7.71]

provides for tensile testing lightweight metals, but all

reference ASTM E8[7.63]. ASTM E 345 [7.72] also

refers to ASTM E8[7.63] when testing metallic foils.

ASTM E 646 [7.73], ISO 10275 [7.74], and NF A03-

659 [7.75] refer to ASTM E8[7.63]orISO 6892 [7.64]

compliant tensile tests to measure workhardening be-

havior. ASTM E 517 [7.76] and NF A03-658 [7.77]

also require adherence to one of the standard tensile

test methods to measure the r-ratio. Frequently used

fastener test standards (e.g., SAE J429 [7.78], ASTM

F 606 [7.79], and ISO 898 [7.80]) refer to ASTM

E8[7.63]orISO 6892 [7.64] for details of ten-

sile testing fasteners and fastener materials. While the

ASTM tensile tests for plastics (ASTM D 638 [7.81],

ASTM D 882 [7.82], and ASTM D 1708 [7.83]) do

not reference ASTM E8[7.63]; the actual perfor-

mance of the test is very similar to that in ASTM

Stress

Strain

Onset of

plasticity

Elastic region

High strain rate

Work

hardening

Room temperature

tensile tests

Low strain

rate

Ultimate

tensile strength

Fracture

0.2% offset

yield stress

Fig. 7.23 Uniaxial engineering stress versus engineering strain

curves at two strain rates, showing elastic region, onset of plastic-

ity (proportional limit), offset yield stress, workhardening, ultimate

tensile strength, and fracture

E8[7.63]. The interpretation of results is somewhat

different.

In principle, all standards for tensile testing are

fairly similar, so only ASTM E8[7.63] will be de-

scribed in detail here. This standard ﬁrst discusses

the following acceptable testing apparatus: testing ma-

chines and by reference ASTM E4[7.84], gripping

devices, dimension-measuring devices, and extensome-

ters, which measure sample displacement for moni-

toring strain within the gage section, by reference to

ASTM E83[7.85]. Acceptable test specimen details are

then presented. These cover size, shape, location from

product, and machining. Testing procedure is described

in detail:

(1) preparation of test machine

(2) measurement of specimen dimensions

(3) gage length marking of specimens

(4) zeroing of the test machine

(5) gripping of the test specimen

(6) speed of testing

Fig. 7.24 Broken tensile specimen showing necking prior

to fracture

Part C 7.2

360 Part C Materials Properties Measurement

(7) determination of yield strength

(8) yield point elongation

(9) uniform elongation

(10) tensile strength

(11) elongation

(12) reduction of area

(13) rounding reported test data, and

(14) replacement criteria for unsatisfactory specimens

or tests.

Of these, (6) speed of testing and (7) method of de-

termining yield strength have the most signiﬁcant effect

on the actual measurement of plastic properties. Speed

of testing is deﬁned in terms of:

(a) rate of straining of the specimen

(b) rate of stressing of the specimen

ing machine during the test

(d) the elapsed time for completing part or all of the test,

(e) free-running crosshead speed.

Speed of testing can affect all test values because of

the strain-rate sensitivity of materials. Ideally, the actual

strain rate experienced by the gage section should be

known and reported. All other speed of testing measures

are relevant only so far as they affect this strain rate.

Unless the strain rate is controlled, two laboratories may

get signiﬁcantly different results even when following

the standard method.

According to ASTM E8[7.63], the yield strength

can be determined by:

(a) the offset method

(b) the extension under load method

(d) the halt-of-the-beam method. These methods may

produce different results with different uncertain-

ties, yet all are equally valid at this time.

In general, the quantities reported from this test are

yield point or yield strength, ultimate tensile strength

(UTS), elongation to fracture (total elongation divided

by initial gage length), and reduction in area (area de-

crease in the fracture plane divided by initial gage area).

It is not uncommon to ﬁnd data with no record of testing

speed or initial gage length. This is unfortunate since the

speed of testing (as noted above) can signiﬁcantly affect

the yield strength and the other properties to a lesser ex-

tent. The initial gage length can affect the elongation

due to the nonuniform deformation that occurs in the

necked region.

Other important quantities, such as workhardening,

strain-rate sensitivity, and temperature effects, can also

be determined in a tensile test. The measurement of

these is left to other standards that will be discussed

next.

Workhardening Behavior. After yielding, the stress–

strain curves of many materials exhibit workhardening,

that is, an increased stress to achieve additional plastic

strain. This is usually due to the increased concentration

of dislocations and their complex interactions. Various

standards address the measurement of workhardening

•

ASTM E 646 [7.73]

•

ISO 10275 [7.74]

•

NF A03-659 [7.75]

to mention a few. In general, a uniaxial tensile test is

performed according to ASTM E8[7.63] with some

added constraints with regard to rate of testing and

collection of data. The true stress/true strain (that is,

the applied force or elongation divided by the current,

instead of the initial, area or gage length) curve is de-

termined from the raw data. In ASTM E 646 [7.73], the

curve is ﬁt by the equation

σ = Nε

to ﬁnd n, the strain hardening exponent, where σ is the

true stress, ε is the true strain, and n is a constant. The

method is appropriate for materials whose stress–strain

curve can be reasonably ﬁt by the equation above. For

the most important exception, i. e., steel, which may

have a discontinuous stress–strain curve, it is recom-

mended that only the region that can be ﬁt reasonably

be used. In general, n is probably a function of strain.

This possibility is not covered in ASTM E 646 [7.73].

Strain-Rate Sensitivity. The only standard addressing

the measurement of this property is European Struc-

tural Integrity Society (ESIS) designation P7-00.2000,

Procedure for Dynamic Tensile Tests. (European Struc-

tural Integrity Society documents may be obtained from

Professor K.-H. Schwalbe, GKSS-Forschungszentrum

Geesthacht, 21502 Geesthacht, Germany.) Here the

tensile test data (σ and true strain rate, dε/dt, both

measured at the same strain ε) are ﬁt to an equation of

the form

σ = M(dε/dt)

Part C 7.2

Mechanical Properties 7.2 Plasticity 361

to ﬁnd m, the strain-rate sensitivity. This procedure is

relatively new. In time, this approach may be accepted

by other standards development organizations (SDOs).

The only issue may be that the form of the equation has

little physical basis. There are other ﬁts to strain-rate-

dependent plastic properties, e.g., the Johnson–Cook

model [7.86] or the Bodner–Partom model [7.87].

Temperature Effects on Plasticity. The movement of

dislocations and vacancies is strongly temperature-de-

pendent and, thus, so is plasticity [7.88]. It is important

to characterize this behavior for any application that

occurs at low or high temperatures. Examples of such

applications are cryogenic tanks, pipelines operating in

the arctic, steam plant components, nuclear power gen-

erators, jet engines, structures that might be exposed to

ﬁres – the list is a long one. Some standards addressing

tensile tests at low and high temperatures are

•

ASTM E 1450 [7.89]

•

ISO/DIN 19819 [7.90]

•

ISO 15579 [7.91]

•

ASTM E21[7.92]

•

DIN EN 10002-5 [7.93]

•

JIS G 0567 [7.94].

These standard tests are essentially the same as the

room-temperature ones, but have or refer to extensive

requirements related to controlling and/or determining

the temperature at which the test is performed (see,

for example, ASTM E 633 [7.95]). Additionally, in

elevated-temperature tests, the speed of testing is more

tightly controlled than in room-temperature tests. This

additional control is necessary because the plastic be-

havior becomes strongly time- or rate-dependent at high

temperatures due to the signiﬁcant amount of creep

strain that can accrue even in a short-term tensile test.

Time-Dependent Plasticity. Time-dependent plasticity

is called creep. This mode of plasticity is important in

any part or structure that is exposed to temperatures

above about 1/3 of its melting temperature, especially

if it must resist permanent deformation for signiﬁcant

lengths of time. Creep may also be noticed at room tem-

perature in very long, highly stressed components such

as bridge cables. The loosening of bolts is also due to

creep, but under a decreasing stress. This effect is called

stress relaxation.

The importance of time dependent plasticity, i. e.,

creep and stress relaxation, has necessitated the devel-

opment of many standard tests for metals

•

ASTM E 139 [7.96]

•

ASTM E 328 [7.97]

•

DIN EN 10291 [7.98]

•

DIN EN 10319 [7.99]

•

ISO 204 [7.100]

•

JIS Z 2271 [7.101].

At elevated temperatures, brittle materials that normally

exhibit extremely limited or no plasticity at room tem-

perature, begin to deform plastically by creep. For this

reason, there are tensile creep standards, similar to those

for metallic materials that apply to ceramics, compos-

ites, and plastics

•

ASTM C 1337 [7.102]

•

ASTM C 1291 [7.103]

•

ISO 899-1 [7.104]

•

JIS K 7115 [7.105].

Creep tests are performed by loading a standard uni-

axial tensile sample with a constant force or stress

and measuring the tensile strain that occurs with time.

Stress-relaxation tests apply a constant strain and mea-

sure the relaxation of stress with time. Both tests are

measures of time-dependent plasticity.

These tests are usually done at an elevated tem-

perature, but the term elevated is quite relative to the

material being tested. Signiﬁcant time-dependent plas-

ticity is usually observed at or above one-third of the

melting temperature of most materials. For solder al-

loys, this is below room temperature. For structural

ceramics, industrially relevant creep and stress relax-

ation rates require temperatures in excess of 1000

◦

For metals and alloys, it is usually found that creep

rates increase exponentially with temperature. They are

often modeled using an Arrhenius (or other thermal ac-

tivation) law [7.88]. Therefore, it is important to know

and tightly control the temperature to about ±1

◦

Cif

1% accuracy is desired. Furthermore, this temperature

must be applied uniformly to the gage section of the test

piece. The various standard methods require accurate

and uniform temperature environments for the test.

Another important parameter is the load. Since

a constant force, that may be greater than 10

N, is

generally required for a long time (up to 100 000 h or

more), it is customary to use dead or static loads. These

are most frequently applied by a complicated system of

levers, knife-edges, and weights. It is essential to con-

ﬁrm that the applied load is correct. This is dealt with

in the standards, see for example ISO 7500-2 [7.106]or

ASTM E4[7.84].

Part C 7.2

362 Part C Materials Properties Measurement

As the creep sample elongates under load, its

cross-sectional area usually decreases. Thus, a constant

applied force leads to an increasing stress on the sam-

ple. Loading systems have been designed that reduce

the load as the sample creeps to maintain a constant

stress [7.107, 108]. These are not covered by any stan-

dard. While this might seem to be an oversight, most

applications of creep-resistant materials can only tol-

erate a few percent strain. For these, the difference

between constant load and constant stress is negligi-

ble. However, if one is interested in creep forming or

superplastic forming (SPF) where large plastic strains

are required, the differences between the two loading

systems can be quite large [7.109].

Superplasticity. Superplasticity in metals is charac-

terized by extraordinarily large ductilities. It is not

uncommon to observe strains of 1000 to 3000%. While

at ﬁrst a laboratory curiosity, superplasticity is now used

to form complex and highly deformed shapes like small

boat hulls, fuel tanks, spare tire wells, aircraft doors,

to mention a few. Superplastic behavior is exhibited

by a number of alloys under particular conditions of

microstructure, temperature, and strain rate. Any test

for superplasticity is chieﬂy for the purpose of char-

acterizing this processing window. An ASTM standard

method of characterizing superplastic behavior in uni-

axial tension has been recently approved. A draft ISO

tensile test has also been proposed based on JIS H

7501 [7.110]. This Japanese standard speciﬁes the test

specimen geometry, the apparatus, and the procedure

for the evaluation of tensile properties of metallic su-

perplastic materials. In particular, it speciﬁes how the

stress–strain curves and the strain rate sensitivity are to

be determined. It has been noticed for some time that

superplastic materials have a strain rate sensitivity m

near unity. Some researchers have claimed that an m

near unity implies superplastic behavior despite limited

ductility in the actual test. Superplasticity, by deﬁnition,

requires very large ductilities, so these claims would

seem incorrect.

The main feature of any standard for measuring

superplasticity would be speciﬁcations to perform the

test over a range of temperatures, perform the test over

a range of commercially useful strain rates, and apply

and measure the large strains that will necessarily occur.

Plastic Strain Ratio r for Sheet Metal. Another im-

portant plastic property that can be obtained from the

tension test is the plastic strain ratio r.Itisdeﬁned

as the ratio of the true plastic width strain to the true

plastic thickness strain at some level of plastic ten-

sile strain in the length direction (usually 15 to 20%).

The plastic strain ratio quantiﬁes the ability of a sheet

metal to resist plastic thinning when subjected to ten-

sile strains in the plane of the sheet. It is a consequence

of plastic anisotropy and is related to the preferred crys-

tallographic orientations within a polycrystalline metal.

This resistance to thinning contributes to the forming

of shapes, such as cylindrical ﬂat-bottomed cups, by

the deep-drawing process. The r-value, therefore, may

be considered an indicator of sheet metal drawability.

Three standards for measuring the plastic strain ratio are

•

ASTM E 517 [7.76]

•

ISO 10113 [7.111]

•

NF A03-658 [7.77].

Basically, a tensile test is run according to one of the

tensile test standards mentioned previously. In addi-

tion to measuring the gage length, the width of the

gage is measured. While the thickness can be measured

directly, the changes in thickness are very small, espe-

cially in thin sheets. The standard permits calculating

the thickness from the width and length assuming con-

stant volume. These measurements should be done in

the unloaded condition as the deﬁnition of r is in terms

of true plastic strains, not total strains. Otherwise, some

adjustment for the elastic strains must be made.

Since r is strongly dependent on the crystallo-

graphic texture, it may depend on the direction within

the sheet the tensile sample was taken. The standards

have procedures for assessing this effect.

Compression Tests

Compression testing, like tension testing, is uniaxial. It

provides similar data on plasticity of materials: initial

plastic behavior, such as yield strength and workhard-

ening. It is sensitive to alignment and buckling can be

a problem. Friction between the sample and compres-

sion platens may also affect the results. Barreling, i. e.,

nonuniform changes in the cross sectional area along

the length also causes deviations from uniaxiality and

ambiguities in the measurement of stress and strain.

If not for these effects, the compression test could be

carried out to very high strains in a plastic material. In-

stead, it is usually limited to about the same amount of

strain as the tensile test, or less. Standard methods for

performing compression tests are

•

ASTM E9[7.112]

•

ASTM E 209 [7.113]

Part C 7.2

Mechanical Properties 7.2 Plasticity 363

•

DIN 50106 [7.114]

•

DIN EN 12290 [7.115]

•

ISO 604 [7.116]

•

JIS K 7132 [7.117]

•

JIS K 7135 [7.118].

The samples are typically short cylinders (height-to-

diameter ratios between 2 and 3) or plates. If the plates

are thin, anti-buckling guides are required. An increas-

ing axial compressive force loads the specimen and

the mechanical properties (mainly yield strength and

workhardening) in compression are determined. There

is much more attention paid to axial alignment issues in

these standards compared to those for tension. This is

because load alignment will only get worse as compres-

sion increases whereas it usually improves with tensile

strain. If one wishes to achieve as large a strain as

possible in these tests, it is essential to provide lubrica-

tion throughout the test. Some experimentalists machine

shallow, concentric grooves in the top and bottom of

the sample and ﬁll them with lubricant. This provides

a reservoir of lubricant throughout the test and has met

with a fair degree of success.

ASTM E 209 [7.113] is interesting because it pro-

vides guidance for performing compression tests under

a wide range of temperatures, strain rates, and heating

rates. This provides the basic data for determining, for

example, the strain-rate sensitivity or the temperature-

dependence of workhardening, but the standard does not

favor any one model for interpreting the results. This ap-

proach permits one to use or compare any of the many

constitutive laws that might apply.

Standard Tests Employing Other Loading Modes

As we shall see, standard tests for plasticity employing

modes of loading other than tension and compression

have been used chieﬂy as measures of ultimate strength

or ductility. This may be due to stress concentrations

obscuring the early yield behavior, poorly deﬁned gage

section to calculate the strain, difﬁculty determining the

stress directly from the applied load, or a combination

of these. The fact that these tests do provide certain im-

portant plastic properties and are easy to perform often

outweighs their other limitations.

Shear. Shear loading is applied as single shear or double

shear as shown in Fig. 7.25. In single shear, pulling the

ends of the sheet specimen in tension generates a state

of shear between the two slot tips. The slots are at 45

◦

the tensile axis and the radius of the slot tips are tightly

controlled. Yielding is very sensitive to the details of the

slot tip curvatures and the gage length for shear is not

well deﬁned.

In double shear, a bar of material is inserted in a cle-

vis grip and pull (or push) rod having close-tolerance

holes. The pull or push rod and clevis may be pulled

in tension or compressed to generate two regions of

shear (i. e., double shear) in the specimen. Again, the

gage length for the shear is poorly deﬁned. The onset of

yielding is also sensitive to the radius of curvature of the

edges of the holes in the pull/push rod and the clevis.

Standards for measuring plastic properties in shear

are

•

ASTM B831 [7.119]

•

ASTM B769 [7.120]

•

ASTM B565 [7.121]

•

DIN 50141 [7.122]

•

DIN EN 4525 [7.123]

•

DIN EN 28749 [7.124]

•

ISO 7961 [7.125]

•

ISO 84749 [7.126].

ASTM B 831 [7.119] is carried out in the single-shear

mode (Fig. 7.25a), while ASTM B 565 [7.121]isin

double-shear tension, and ASTM B 769 [7.120], DIN

50141 [7.122], and ISO 7961 [7.125] are in double-

shear compression. All of the standard shear tests are

used mainly to measure the ultimate shear strength. This

is due to the fact that load ﬁxture or specimen stress

concentrations limit their usefulness in accurately mea-

suring the early yield behavior and the poorly deﬁned

gage section over which the shear acts means that the

shear strain is not well deﬁned. These tests provide

a shear stress that can be used to assure that a compo-

Test

specimen

a) b)

Fig. 7.25a,b Shear loading modes. (a) single shear, in ten-

sion only for sheet and plates, and (b) double shear, in

tension or compression, for bars

Part C 7.2

364 Part C Materials Properties Measurement

nent does not fail plastically in shear even if the yield

stress in shear is exceeded.

Torsion. Torsion loading is generated by twisting a bar

that is usually round in cross section around its long

axis (Fig. 7.21). Torsion provides a pure shear loading

with principal stresses σ

=−σ

and σ

=0. Therefore,

the hydrostatic tension is zero throughout the test and

does not increase as it does in a tension test. Conse-

quently, the processes responsible for ductile fracture

are greatly reduced. When a solid bar is tested in tor-

sion, very large ductilities are possible if the material is

inherently ductile. No instabilities will intervene as oc-

cur in tension and compression testing. If a tube is tested

in torsion, however, buckling will occur and end the test

prematurely.

There are standards for torsion testing to measure

the shear modulus and standards to measure the ductil-

ity of wires in pure shear

•

ASTM E 143 [7.127]

•

ASTM A 938 [7.128]

•

ISO 7800 [7.129]

•

ISO 9649:1990 [7.130].

There are published procedures used by individual re-

searchers, notably Nadai [7.131], who developed an

analysis to obtain the shear stress/shear strain curve

from torsion tests on bars. Without such an analysis, the

stress in a solid bar cannot be determined. For this rea-

son, some researchers use tubes. As noted above, tubes

have a limited strain before buckling occurs.

At this time, the only standard torsion test that pro-

vides shear stress/shear strain data in the plastic region

is ASTM F 1622 [7.132]. This standard is not only lim-

ited to a narrow range of materials and components, but

it only determines the torsional yield strength. Never-

theless, since the entire plot of torque versus angle of

rotation is recorded, the data obtained by this method

could be analyzed to give the shear stress/shear strain

curve.

Bending. Bending, like torsion, requires an analysis

to convert the load–displacement or moment–curvature

data to stress–strain curves when more than a few tenths

of 1% plastic strain has accrued. The standards that

use bending to characterize room-temperature plastic-

ity are only for determining the ductility or resistance

to cracking under this mode of loading. No other data

are obtained. Room-temperature bend test standards

include

•

ASTM E 290 [7.133]

•

ASTM E 190 [7.134]

•

ASTM E 796 [7.135]

•

ISO 7438 [7.136]

•

ISO 7799 [7.137]

•

ISO 7801 [7.138]

•

ISO 7802 [7.139]

•

ISO 8491 [7.140].

There are more international standards that refer to

these and many more national standards that use bend-

ing as a means of determining plastic ductility of

a variety of materials and welds in various shapes.

They are all variations on the above methods. In

ASTM E 290 [7.133], ISO 7438 [7.136], and ISO

8491 [7.140], the sample is bent monotonically ei-

ther in three- or four-point bending, or as a cantilever.

In ASTM E 796 [7.135], ISO 7799 [7.137], and ISO

7801 [7.138], the bending is carried out by cumu-

lative cyclic, reversed bending. If the sample cracks,

the amount of cumulative cyclic strain in bending to

achieve cracking is reported. Other requirements might

be that the sample be bent to a certain level without

cracking, such as in ASTM E 190 [7.134]andISO

7802 [7.139]. In this case, the method is a pass or fail

test.

Bending is a favorite testing mode for brittle ma-

terials because of the simplicity of sample fabrication

and not having to grip the sample in any way. For this

reason, ceramics are often tested in bending. Bending

is also one of the customary ways to test ceramics and

brittle plastics at temperatures where they do exhibit

creep. As long as the creep strain is small, the elastic

stress analysis is approximately correct and there are

standards for these tests

•

DIN V ENV 820-4 [7.141]

•

ISO 899-2 [7.142]

•

JIS K 7116 [7.143].

It is important to note here that ceramics are well known

to have different creep behavior in tension and com-

pression. An added complication of using bending to

characterize creep in ceramics is the fact that it convo-

lutes compression and tension behavior. Thus, bending

obscures some important features in the plastic behavior

of ceramics at high temperature.

Ball Punch Deformation of Sheet Materials. These

tests are used to determine the ductility of mater-

ials under a particular biaxial strain state. In this test,

Part C 7.2

Mechanical Properties 7.2 Plasticity 365

a spherical punch is pressed into a sheet of material that

is held in a hold-down assembly. The ball is pressed into

the sheet forming a cup until the sheet fails in some way.

Ball punch tests tend to be equi-biaxial, that is ε

=ε

in the plane of the sheet. Due to conservation of vol-

ume, ε

=−(ε

+ε

). Exhaustion of ductility is deﬁned

at the onset of severe localization, cracking, or drop in

load on the punch. Standard methods for this test are

•

ASTM E 643 [7.144]

•

ASTM E 2218 [7.145]

•

ISO 20482 [7.146]

•

ISO 12004 [7.147].

ASTM E 2218 [7.145]andISO 12004 [7.147] provide

directions for achieving other states of plastic strain by

testing strips of different widths instead of square or

round sheets. The state of strain is determined from the

distortion of an array of squares, circles, or both printed

onto the surface of the sheet specimens. While the load

on the punch or the hold-down force may be measured

in these tests, the stress in the sheet is unknown. Fur-

thermore, only the endpoint condition is reported. In the

case of ASTM E 643 [7.144]andISO 20482 [7.146],

it is the limiting dome height. In the case of ASTM

E 2218 [7.145]andISO 12004 [7.147], it is the principal

in-plane strains ε

and ε

at failure.

Other Loading Modes. There are applications in which

highly complex plastic straining is required to make im-

portant parts or assure safe performance. The ability

of a material to sustain these modes of loading is so

important that standards have been developed just for

them. The following standard test methods are mainly to

determine the ductility of various materials under a par-

ticular complex strain history which is usually indicated

by the name of the test

•

ISO 8492 [7.148]

•

ISO 8493 [7.149]

•

ISO 8494 [7.150]

•

ISO 8495 [7.151]

•

ISO 8496 [7.152]

•

ISO 11531 [7.153]

•

ISO 15363 [7.154]

•

ISO/TS 16630 [7.155].

These tests are in some ways like the hardness test: they

are so speciﬁc and involve such a complex strain path

that no extended meaning in terms of more fundamental

quantities can be easily deduced from them. Neverthe-

less, they have signiﬁcant industrial and commercial

importance. The reader is referred to the standards

themselves for more information.

7.2.4 Novel Test Developments for Plasticity

Motivation for the development of new standards for

measuring plasticity may be better appreciated after

a brief discussion of the industrial needs in this area that

are not being met by existing standards.

Now, one can specify the yield strength in tension or

compression, the ultimate tensile strength, the elonga-

tion at fracture, and the reduction in area at fracture. The

workhardening exponent and the r-ratio can be spec-

iﬁed. The creep rate and stress relaxation behavior can

be speciﬁed. The critical plastic strain for localization or

fracture can be speciﬁed under a variety of strain states.

All these speciﬁcations can be checked by standard-

ized tests. Are there material properties associated with

plasticity that industry needs to specify that are not cov-

ered by standard tests? As will be shown below, there

are unsatisﬁed needs for standards to measure plastic

properties.

Data for New Forming Processes

New forming methods drive a need for speciﬁcation

of materials with particular properties. An example

mentioned previously was superplastic forming (SPF).

Currently, industry cannot specify the material for an

SPF operation by some standard means of testing to

determine whether it is superplastic enough for a par-

ticular application. User and supplier can easily end

up at odds. That is what is driving the development of

standards in this area.

Another issue stems from the desire to reduce the

weight of automobiles and other products. This has

driven industry to use high-strength steel and alu-

minum alloys. An impediment to the wider use of these

materials is that they do not form like the traditional au-

tomotive alloys. One particular problem is that, during

certain forming operations, they spring back so much

that conventional die-design methods do not work. This

problem, known as springback, arises from a complex

interaction of the elastic and plastic strain, the residual

stress, and the complicated shape of the workpiece. Two

standards for characterizing the tendency for materials

to springback are currently under consideration – one

by ISO, and another by ASTM. The ISO document is

based on JIS H 7702 [7.156] while the ASTM standard

is based on extensive industrial experience [7.157]has

just been approved.

Part C 7.2

366 Part C Materials Properties Measurement

Data for Crashworthiness

and Fire-Resistive Steel

Another driving force for the development of standards

for characterizing plastic behavior arises when mater-

ials are used under extreme conditions that can be

reasonably expected to occur. Two examples are: (1) au-

tomotive materials involved in high-speed collisions,

and (2) structural steel exposed to a ﬁre.

In case (1), an extensive topic called crashworthi-

ness has grown up in the last decade. Automobiles

are now designed to remain as safe as possible un-

der accident conditions. Their materials of manufacture

are expected to behave reproducibly in a certain

way at the high rates encountered under such con-

ditions. A review of existing standards for acquiring

data needed to predict structural behavior in an acci-

dent [7.158] identiﬁed the need for tests to measure

high-rate plastic-deformation properties. This need has

motivated the European Structural Integrity Society

(ESIS) to develop its procedure for high-rate ten-

sile tests mentioned previously. (European Structural

Integrity Society documents may be obtained from

Professor K.-H. Schwalbe, GKSS-Forschungszentrum

Geesthacht, 21502 Geesthacht, Germany.) Recently,

Japan has developed methods based on the Kolsky

bar to provide this sort of rate-dependent plastic

data [7.159]. It will not be long before these methods

are proposed to standards development organizations

(SDOs).

In the case of steel used in buildings, bridges, or

other structures subject to ﬁres, the reduction in yield

strength with increasing temperature and the onset of

creep result in large plastic strains that endanger the

load-carrying capacity of the structure. Japanese and

German steelmakers have begun making and selling

steel claimed to be ﬁre-resistive [7.160]. By this they

mean that the yield strength retains 2/3 of its room

temperature value at 600

◦

C. ASTM has now convened

a working group to decide what is meant by ﬁre-

resistive: is the arbitrary deﬁnition above satisfactory,

or should some combination of standard or modiﬁed

hot tensile and creep tests be used to deﬁne ﬁre resis-

tive, or, lastly, should a new type of standard test, such

as a tensile creep test conducted with a temperature

ramp, be developed? Other possibilities are also being

considered.

Finite Element Analysis

The impact of complex computer codes and powerful

computers has made the accurate prediction of form-

ing and performance possible if the needed inputs of

material properties are available. These programs ac-

cept plastic properties in a variety of forms from raw

stress–strain curves in tabular form to evaluated con-

stitutive laws such as the Voce equation [7.161]. The

traditional data provided by existing standards is barely

adequate for these analyses. One real problem that fre-

quently arises is the need for true stress/true strain

data well beyond the onset of necking and fracture in

tension tests, or beyond buckling and barreling insta-

bilities in compression tests. The current solution to

the lack of data is to make some simplistic assump-

tions, such as arbitrarily extending the stress–strain

curve as required. This need could be better ﬁlled by

data obtained in the torsion test [7.162], which can

probe these high strains easily. As mentioned earlier in

this chapter, torsion standards have been developed for

shear modulus measurements, fatigue testing, and duc-

tility testing. It should not be difﬁcult to go this next

step.

The other area that is left to assumption in these

advanced analyses is the multiaxial workhardening be-

havior. Most often, the yield surface is assumed to

expand in a self-similar way with strain (isotropic hard-

ening) [7.47]. However, it is known that, in many

cases, it is better to assume that the origin of the

yield surface moves in stress space (kinematic hard-

ening) [7.47]. Improved prediction would be possible

if there were a standard method for measuring exactly

what does happen. There have been developments re-

cently in measuring the stress during cup deformation

tests that would permit this to happen [7.163]. It may

take a decade or more for these developments to reach

the standards development organizations (SDOs).

7.3 Hardness

Hardness may be deﬁned as the resistance of a ma-

terial to permanent penetration by another material.

A hardness test is generally conducted to determine

the suitability of a material to fulﬁll a certain pur-

pose [7.164]. Conventional types of static indentation

hardness tests, such as the Brinell, Vickers, Rockwell,

and Knoop hardness, provide a single hardness num-

ber as the result, which is most useful as it correlates to

Part C 7.3

Mechanical Properties 7.3 Hardness 367

Table 7.5 First publications of hardness testing standards in different countries

Test method Germany UK USA France ISO Europe

Brinell (1900) 1942 1937 1924 1946 1981 1955

Rockwell (1919) 1942 1940 1932 1946 1986 1955

Vickers (1925) 1940 1931 1952 1946 1982 1955

Knoop (1939) 1969 1993

Hardness testing of metallic materials

Direct testing

Static

hardness testing

Dynamic

hardness testing

Measurement

of energy

Determination after

removal of test force

Determination under

test force

Hardness defined as

quotient of test force

and penetration surface

Hardness defined as

quotient of test force

and projection surface

of penetration

Hardness defined by

depth of penetration

Indirect testing

KEMAG

Instrumented indentation test

UCl

2,3,4

Modified Vickers method HVT

Shore

Brinell Rockwell Knoop

Determination of Martens hardness

indentation hardness

indentation modulus

Not standardized

Hardness value by revaluation

Ultrasonic contact impedance

Combined electromagnetic method

Rockwell (Bm; Fm; 30Tm)

Modified Brinell method HBT

Vickers

Rebound hardness

(e.g. Leebs, Scleroscope)

Fig. 7.26 Overview of the hardness testing methods (after [7.165])

other properties of the material, such as strength, wear

resistance, and ductility. The correlation of hardness to

other physical properties has made it a common tool

for industrial quality control, acceptance testing, and

selection of materials.

With the rising interest in the testing of thin coatings

and in order to obtain more information from an inden-

tation test, the instrumented indentation tests have been

developed and standardized. In addition to obtaining

conventional hardness values, the instrumented indenta-

tion tests can also determine other material parameters

such as Martens hardness, indentation hardness, in-

dentation modulus, indentation creep and indentation

relaxation.

Hardness testing is one of the longest used and well-

known test methods not only for metallic materials,

but for other types of material as well. It has special

importance in the ﬁeld of mechanical test methods,

because it is a relative inexpensive, easy to use and

nearly nondestructive method for the characterization

of materials and products. In order to work with com-

parable measured values, standards of hardness testing

methods have been developed. This work started in the

1920s (Table 7.5). In some cases, national, regional and

international standards specify different requirements;

however, it is generally accepted to aim at the complete

alignment of hardness standards at all standardization

levels [7.166,167].

Hardness data are test-system dependent and not

fundamental metrological values. For this reason, hard-

ness testing needs a combination of certiﬁed reference

materials (reference blocks) and certiﬁed calibration

machines to establish and maintain national and world-

wide uniform hardness scales. Therefore, all hardness

Part C 7.3