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

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398 Part C Materials Properties Measurement

a high-sensitivity strain detector is necessary because

the change in the elastic strain is very small. In other

words, this is a tensile test with extremely low strain

rates, and the strain rate decreases continuously while

the stress is held.

7.4.2 Dynamic Loading

Dynamic means that the loading or deformation speed is

high compared with the quasistatic case. Several kinds

of dynamic loading are found. These include high-speed

tension or compression tests such as the Hopkinson

split-bar method, impact tests, and fatigue tests. These

three tests are explained below.

Computer

memorizer

etc.

Compressor

Booster

Valver

Gun

Strike bar

Input bar

Output bar

Output

bar

Specimen

Absorber

Fig. 7.52 Schematic illustration of a high-speed tension

test using the Hopkinson split-bar method

Nominal stress (MPa)

Low carbon steel SUS310S

Nominal strainNominal strain

800

600

400

200

00.10.20.300.10.20.3

Strain rate

2 × 10

–1

4 × 10

–3

–1

4 × 10

–3

–1

2 × 10

–1

a) b)

Fig. 7.53a,b Flow curves observed under high-speed deformation

(the Hopkinson split-bar tension test): (a) low-carbon steel and

(b) austenitic steel

High-Speed Tension or Compression Tests

These testing methods include the split pressure-bar

tester, the one-bar method, the load-sensing block-type

tester, and the servo-hydrostatic loading machine. The

most popular method is the Hopkinson split-bar method

in which either tension or compression impact defor-

mation can be carried out. The outline of the test is

shown in Fig. 7.52, where the input bar and the out-

put bar are pictured. A specimen is set between them.

To avoid the reﬂected stress pulse, the specimen gage

length should be sufﬁciently short. Examples of ﬂow

curves obtained at a strain rate of 2× 10

−1

are pre-

sented in Fig. 7.53 [7.213,214]. As seen, the ﬂow stress

becomes higher at a high speed, similarly to the case

of lowering test temperature. Very-high-speed deforma-

tion occurs almost under adiabatic conditions, so that

the temperature of a specimen increases with plastic

deformation. Hence workhardening decreases in a low

carbon steel with a large temperature dependence of

ﬂow stress. Such workhardening behavior is the dif-

ference between the deformation at lower temperature

with a low strain rate and that at room temperature with

a high strain rate. These data are useful for the the safety

design of automobiles with respect to trafﬁc collisions

or the safety of infrastructures such as buildings with

respect to the occurrence of earthquakes.

The dislocation structure that evolves during plastic

deformation is strongly dependent on the test tempera-

ture and strain rate. As shown in Fig. 7.54 [7.213]for

the case of a low-carbon steel, the dislocation cell struc-

ture evolves at room temperature under a low-strain-rate

deformation. However, planar dislocation arrays are ob-

served either during low-temperature deformation with

a low strain rate or at room temperature with a high

strain rate.

Impact Test

Impact testing is performed to evaluate the toughness of

materials. There are several loading methods, including

tension, compression, bending, and torsion. The typi-

cal test is the Charpy impact test in which three-point

bending is employed. As shown in Fig. 7.55, a hammer

is dropped to hit a rectangular specimen. A V- or U-type

notch is introduced to allow easy fracture due to stress

concentration for ductile materials. In the case of brit-

tle materials such as ceramics, cast iron etc., a notch is

not introduced. Parts of the hammer before and after hit-

ting (breaking) a specimen are compared. The balance

is considered to show the resistance to fracture, and the

energy needed to bend and fracture the specimen. The

impact tester can impart 300 J for metallic materials use,

Part C 7.4

Mechanical Properties 7.4 Strength 399

a) b) c)

200 nm 200 nm 200 nm

Fig. 7.54a–c Dislocation structures evolved by tensile deformation (10%) in ferritic steels: (a) 77 K, 3.3×10

−3

−1

(b) 295 K, 2 × 10

−1

and (c) 295 K, 3.3×10

−3

−1

Hammer

Charpy

Specimen

Izot

= Absorbed

energy

Fig. 7.55 Outline of impact testing: Charpy and Izot tests

Charpy impact energy (J)

350

300

250

200

150

100

0 100 150 200 250 300

Test temperature (K)

Low carbon steel

Lower shelf energy

Upper shelf energy

Fig. 7.56 Ductile-to-brittle transition behavior observed

by the Charpy impact test

and 3 J for resin or plastics. The Izot tester is another

typical device but is now rarely used. The specimen is

held in a different way, as shown in Fig. 7.55. The ab-

sorbed energy K is calculated from the angle of the

hammer and the starting (α) and maximum (β) height

after hitting,

K = WR(cos β −cos α) , (7.67)

where W and R refer to the weight and the arm length,

respectively.

Some materials fracture in a ductile manner under

quasistatic testing but fracture in a brittle manner under

impact testing. As the fracture mode is strongly depen-

dent on the testing temperature, the Charpy impact test

is carried out at a variable test temperature. The ab-

sorbed energy is then plotted as a function of the test

temperature, as presented in Fig. 7.56 [7.208]. In the

case of ferrite steel, for example, the energy changes

at a certain temperature, known as the ductile-to-brittle

transition temperature (DBTT). At higher tempera-

tures, specimens fracture in a ductile mode so that the

fracture surface exhibits a dimple pattern. However, in-

tergranular or cleavage (transgranular) fracture facets

are observed in specimens fractured at lower tempera-

tures. The DBTT is determined either from the absorbed

energy or the percentage of dimple facet on the fracture

surface. The results of impact tests are often used for

material selection. It is difﬁcult to use the results quan-

titatively for machine design, e.g., for the determination

of design stress. On the other hand, the quantitative

resistance to fracture is determined by other tests us-

ing precracked specimens based on fracture mechanics

(see Sect. 7.4 for details).

Fatigue

Several fatigue testing methods have been utilized to

date.

Rotating (four-point) bending has been used to sim-

ulate a wheel axis, where a tension–compression stress

wave is repeated on the surface. The results are sum-

marized in a diagram of stress amplitude versus number

of cycles to fracture (S–N). As shown in Fig. 7.57,the

applied stress amplitude is plotted as a function of the

Part C 7.4

400 Part C Materials Properties Measurement

Stress (MPa)

1400

1200

1000

800

600

Number of cycles to failure

Spring steels

Conventional

fatigue limit

Fig. 7.57 Stress amplitude versus number of cycles to fail-

ure (S–N) curve for fatigue fracture

Stress amplitude σ

Mean stress σ

Yield stress UTS

Time

Stress

Fig. 7.58 Fatigue endurance-limit diagram where the in-

ﬂuence of mean stress is given

number of cycles to failure [7.215]. As can be seen, the

relationship is almost linear in the beginning and tends

to saturate at a certain stress level near 10

–10

cycles.

In general, the stress at 10

cycles is called the fatigue

strength or endurance limit σ

. At stresses higher than

, the number determines the time to fracture and is

called fatigue life. Thus, the fatigue strength and fatigue

life are utilized for the design of machines or structures.

Recent studies on very-long-life fatigue reveal that

some materials fracture even at stresses below the con-

ventional σ

. In the case of aged materials, this should

also be taken into consideration.

The inﬂuence of the mean stress on the fatigue stress

(stress amplitude) is discussed using the fatigue-limit

diagram shown in Fig. 7.58 where the stress amplitude

at 10

cycles is plotted as a function of the mean applied

stress. The diagram is constructed with consideration

of the yield strength σ

, tensile strength σ

,andthe

Extrusion and

intrusion

Slip

Free

surface

Crack

Striation

Final

fracture

Maximum tensile

stress direction

Stage 1 Stage 2

Fig. 7.59 Schematic illustration on fatigue fracture; crack

initiation, growth and ﬁnal fracture

true fracture strength, σ

, obtained by tension testing

that corresponds to a quarter cycle of the fatigue test.

A hatched area is evaluated to be safe for both fatigue

fractures and macroscopic yielding (failure of elastic-

ity).

The mechanism for fatigue fracture is illustrated

schematically in Fig. 7.59. In the usual case, a fatigue

crack is initiated on the surface or a stress-concentrated

region such as a ﬂaw, brittle inclusions etc. If a material

is nearly free from such defects, slip deformation occurs

preferentially near the surface. Because of cyclic loading

of small stress below the yield strength, slip occurs lo-

cally and repeatedly, resulting in intrusion and extrusion

at the surface. Since the intrusion is a kind of micro-

crack at which stress is concentrated (the ﬁrst stage of

fatigue cracking), plastic ﬂow occurs locally at the tip

of the micro-crack. The growth direction along the max-

imum shear stress then changes to be perpendicular to

the applied tensile stress. This crack-propagating regime

is called stage 2. When the crack length has increased

enough to satisfy the ﬁnal fracture condition given by the

fracture mechanics approach (a detailed explanation of

which is given in Sect.7.4)

max

≥ K

, (7.68)

then ﬁnal fracture takes place. Here, the left-hand side

of (7.68) is the maximum stress-intensity factor K

max

ασ

max

√

πc), where α, σ

max

,andc refer to a constant re-

lated to the specimen’s geometry, the maximum stress

applied to the specimen and the crack length, respec-

tively, and K

is the fracture toughness against fatigue.

The crack growth speed during stage 2 is measured

using a prepared specimen in which a sharp prenotch is

introduced. With repeated application of the stress, the

length of the crack is measured and the growth rate is

then plotted as a function of the amplitude of the stress-

intensity factor ΔK(= Δσ

√

πc), as shown in Fig. 7.60.

Part C 7.4

Mechanical Properties 7.4 Strength 401

Crack growth rate log (da/dN)

Amplitude of stress intensity factor log (ΔK)

Stage 2a

(Microstructure

sensitive)

Stage 2b

(Striation:

(microstructure

insensitive)

Stage 2c

Fig. 7.60 Fatigue crack growth rate as a function of stress-

intensity amplitude

The growth rate in the low-ΔK region can be meas-

ured by decreasing Δσ continuously. Here, the engineer-

ing lower limit for crack growth is determined as the

threshold intensity factor ΔK

, which is sensitive to mi-

crostructural parameters. In the middle of the curve, it is

approximated by a linear relationship described by Paris’

equation [7.216,217]

dc/dN = CΔK

, (7.69)

where C and m are constants. The crack growth rate dur-

ing this stage 2 is insensitive to microstructure.

–200 0 200 400 600 800 1000 1200 1400

Temperature (°C)

Shear stress

at 300 K

(MN/m

)

Ferrite

Plasticity

Power law

Diffusional flow

Homologous temperature T/T

Creep

Austenite

(Boundary)

(Lattice)

(Lattice)(Boundary)

Phase

change

Phase

change

Low tempera-

ture creep

High tempera-

ture creep

High tempera-

ture creep

Dynamic

recrystallization

Curie

temperature

Normalized

shear stress

τ/μ

–1

–2

–3

–10

–4

–5

–6

0.2 0.4 0.6 0.8 1

–1

–2

–4

–6

–8

–9

–10

–5

–4

–3

–2

–4

–1

–7

–8

–10

1/s

Fig. 7.61 Deformation map for iron

(d = 0.1mm)

If the initial crack length c

in a material is known,

for example, by using nondestructive inspection such as

x-ray transmission, the fatigue life N

of the material can

be predicted by combining (7.68)and(7.69). That is, by

integrating (7.68), we obtain,



C(αΔσ

√

πc)

, (7.70)

where c

can be calculated by (7.68). In ductile materials,

the fracture surface during stage 2 consists of striation,

which is caused by repeated loading. Hence, the crack

growth speed is estimated from fractography.

7.4.3 Temperature and Strain-Rate Effects

Flow stress is inﬂuenced by the test temperature mainly

due to thermal activation mechanisms for dislocation

motion. The thermal vibration of atoms leads to the

vibration of the dislocation line. Therefore, the possibil-

ity per second of achieving a certain thermal activation

energy is proportional to the Boltzmann probability.

This means that the inﬂuence of temperature and strain

rate on strength should be understood simultaneously;

to achieve this, the deformation mechanism map has

been constructed for various materials [7.218]. As an

example, the deformation map for iron is presented

in Fig. 7.61. Because iron shows ferrite-to-austenite and

then austenite-to-ferrite transformations when heated,

Part C 7.4

402 Part C Materials Properties Measurement

Relative flow stress σ/E

Flow stress

Twinning

Phase transformation

Ferrite / pearlite

Austenite

Temperature

Dynamic strain

aging

Increase in

strain rate

Low temperature

deformation

Thermal

component

Athermal

component

High temperature

deformation

Relative temperature T/T

α–γ

Fig. 7.62a,b Effect of temperature on the yield strength

(schematic illustration): (a) general case and (b) mild steel

the curves for body-centered cubic (BCC, ferrite) is

interrupted by a face-centered cubic (FCC, austenite)

regime. Depending on the temperature and strain rate,

various deformation mechanisms become dominant.

Taking a look at the map near room temperature with

a strain rate of 10

–10

−5

−1

, the dominant mechanism

is slip, i. e. dislocation motion. A simpler illustration to

explain the effect of temperature on the yield strength

isgiveninFig.7.62. At 0 K, the enhancement by ther-

mal activation disappears and the strength corresponds

to the theoretical strength. At a certain temperature,

the strength is decreased through due to thermal ac-

tivation of dislocation motion. At higher temperatures

near T

/2, all the short-range barriers for dislocation

motion can be overcome, but some long-range barriers

remain. The stresses related to overcoming these two

kinds of barriers are called thermal stress (or effective

stress) and athermal stress (internal stress), respectively.

Thus, as shown in Fig. 7.62a, thermal stress becomes

zero at T

.BelowT

the temperature dependence of the

yield strength is ascribed to thermal activation mech-

anisms for dislocation motion. Therefore, if the strain

rate is increased, its effect is equivalent to decreasing

temperature. The inﬂuence of strain rate on the yield

strength is also drawn schematically in Fig. 7.62a. Flow

stress can also be discussed using this approach, al-

though the evolution of the dislocation structure must

also be taken into account. With increasing of plastic

strain, the dislocation density (ρ) increases by ρ

and

then workhardening occurs. At the same time, dislo-

cations are annihilated with recovery to be decreased

by ρ

−

, which is inﬂuenced by temperature. Therefore,

the total dislocation density (ρ

+ρ

−

) is determined as

a function of the strain as well as temperature and time,

i. e., strain rate. The ﬂow curve obtained at high strain

rate is therefore inﬂuenced by two thermal activation

mechanisms: dislocation motion and dynamic recovery.

When the test temperature is higher than T

,the

microstructure itself changes obviously during de-

formation, for example exhibiting to grain growth,

dynamic recovery and/or recrystallization. Such a re-

gion, as shown in Fig. 7.62a, is called high-temperature

deformation. As observed in Fig.7.61, creep deforma-

tion occurs strongly at high temperatures with small

strain rates.

The behavior of a real material is compli-

cated in comparison with that of the pure metal

in Fig. 7.62a. The example of mild steel is pre-

sented in Fig. 7.62b[7.219]. The curve in the lower-

temperature region corresponds to the deformation

of the BCC ferrite phase, while that in the higher-

temperature region corresponds to FCC austenite.

Moreover, due to the intrusion of deformation twinning

at cryogenic temperatures and dynamic strain aging

caused by solute carbon and nitrogen atoms in the

region slightly above room temperature, the typical be-

havior explained in Fig. 7.62a is not easy to discern.

7.4.4 Strengthening Mechanisms

for Crystalline Materials

As described above, ﬂow stress is controlled by the

motion of dislocations. Hence, there are two ways to

strengthen a material: remove dislocations thoroughly or

introduce a large number of obstacles to prevent disloca-

tion motion. The former approach has been achieved in

the form of single-crystal whiskers. When the diameter

of the whisker increases, the strength decreased rapidly

due to the inevitable introduction of defects including

dislocations. The latter approach has been used widely,

including solid-solution hardening, precipitation hard-

ening or dispersion particles hardening, workharden-

ing, grain-reﬁnement hardening and the duplex structure

(composite) hardening. These mechanisms to prevent

dislocation motion are described below.

Part C 7.4

Mechanical Properties 7.4 Strength 403

Solid-Solution Hardening

The interstitial or substitutional solute atoms hinder the

motion of dislocations due to the size effect and/or the

effect of an inhomogeneous elastic modulus. These are

elastic interactions and hence can be overcome by ther-

mal activation for dislocation motion. The amount of

hardening is given by

Δσ = Ac

, (7.71)

where A and c refer to a material constant and the con-

centration of solute atoms, respectively. The constant n

is about 0.5–1.0 from experimental or theoretical con-

siderations.

Workhardening

As explained in the previous sections, the dislocation

density is increased by plastic deformation and mobile

dislocations have to pass through the resulting dislo-

cation structure. There are two types of dislocation–

dislocation interactions: short-range interactions, in-

cluding elastic interactions, cutting, reactions etc., and

long-range interaction due to internal stresses caused

by the dislocation structure. The back-stress caused by

piled-up dislocations is a typical example. Either model

gives strengthening according to

Δσ = B

√

ρ, (7.72)

where B is constant. This equation was ﬁrstly proposed

by Bailey and Hirsch [7.220].

Precipitation or Dispersion Hardening

When small precipitates are dispersed in a matrix, a dis-

location line interacts with them. When the particle is

weak, the dislocation line cuts through such particles and

passes through, as shown in Fig. 7.63. The threshold con-

Orowan loop

Dislocation movement

Cross sectional view

b)a)

Fig. 7.63a,b Strengthening mechanisms for obstacles dis-

persion; (a) cut-through mechanism and (b) Orowan bypass

mechanism

dition is given by the following equation

Δσ =(aμb/λ)cos(φ/2) , (7.73)

where a is a constant, μ is the shear modulus, b is the

magnitude of the Burgers vector of a dislocation, λ is

the average distance between particles, and φ is the crit-

ical angle to cut the particle. If φ is 0

◦

, a dislocation line

passes through the particle, leaving a dislocation loop

known as an Orowan loop (Fig. 7.63b). This is the case

of a strong particle, leading to the following equation for

dispersion hardening (using φ = 0anda ≈2in(7.73))

Δσ =2μb/λ . (7.74)

Grain-Reﬁnement Hardening

When a dislocation moves towards a grain boundary,

it is stopped and induces internal stress, as is shown

in Fig. 7.64. When dislocations pile up at the grain

boundary, the back-stress generated hinders the further

motion of dislocations, as described for the case of

workhardening. Because the number of piled-up disloca-

tions depends on the applied stress and slip distance, i.e.,

grain diameter (d), the amount of strengthening (Δσ)is

given by theoretical relations such as

Δσ =kd

−1/2

. (7.75)

Other interpretations have been proposed for the effect

of grain size in this mechanism. For instance, the dislo-

cation density is increased due to the occurrence of many

Grain boundary

Grain

boundary

200 nm

Fig. 7.64a,b Strengthening mechanism for grain boundary

or interface: (a) dislocation pile-up model and (b) TEM mi-

crograph for a high-nitrogen-bearing austenitic steel

Part C 7.4

404 Part C Materials Properties Measurement

slip systems in the vicinity of a grain boundary due to

high local internal stresses. The amount of strengthening

is given by the Bailey–Hirsch relation (7.72). Because

the increase in the dislocation density is proportional to

the grain diameter d, the resultant equation exhibits the

same form as (7.75). Another interpretation for grain-

reﬁnement hardening is that newdislocations are emitted

from a grain boundary in the neighboring grain to relax

high local internal stresses. As (7.75) was ﬁrst proposed

by Hall and Petch [7.221–223] based on experimental

data, it is called the Hall–Petch relation. In fact, sev-

eral phenomena must be overlapping in this mechanism,

but the increase in strength can be expressed roughly

by (7.75).

Duplex Structure (Coarse Multiphase) Hardening

When the grain diameter of the second phase is compa-

rable to that of the matrix, the mechanism for dispersion

hardening such as the Orowan bypass model is no longer

applicable. Plastic ﬂow takes place preferentially in the

soft phase, resulting in stress partitioning between the

constituents, known as phase stress or averaged internal

stress. Such strengthening is similar to that for composite

materials. Many engineering materials such as ferrite–

pearlite steel, dual-phase steels, α −β Cu-Zn alloys etc.,

belong to this category. Although micromechanics mod-

els have been developed to express the deformation of

a multiphase material, ﬂow stress is described roughly

by a kind of mixture rule. In the case of a two-phase alloy,

σ =σ

(1 − f )+σ

f , (7.76)

where σ

, σ

, f refer to the strength of the matrix, the

strength of the second phase and the volume fraction of

the second phase, respectively.

Usually the above strengthening mechanisms are su-

perposed. Hence, a suitable superposition rule has to be

used for real engineering materials. This may be simply

described by

σ =



i=1

. (7.77)

In the case of superposition of strong and weak obsta-

cles, the value of N is believed to be nearly unity but is

less than unity in other cases where both obstacles are

strong.

7.4.5 Environmental Effects

The environment where a material is used inﬂuences

its strength. Such inﬂuences include chemical reactions

such as corrosion and radiation damage in a nuclear

furnace. Here, two examples are explained because the

social impact of these fracture is serious: hydrogen em-

brittlement and stress corrosion cracking.

Hydrogen-Induced Embrittlement

The most difﬁcult barrier to the use of high-strength

steels is hydrogen embrittlement, or so-called delayed

cracking. Hydrogen atoms invade not only during the

processing of products but also during service. Cur-

rent topics in this area include the interaction of mobile

dislocation and hydrogen atoms and the diffusion of hy-

drogen atoms within materials. The fracture mechanism

is, however, not yet clear.

Figure 7.65 shows the fracture strength after 100 h

in water for various kinds of steels [7.224]. The frac-

ture strength is plotted as a function of the tensile

strength obtained using the conventional tension test.

It is clear the fracture strength increases with in-

creasing tensile strength up to approximately 1.0GPa.

However, steels in the 1.5 GPa (tensile strength) class

exhibit a large scatter in their fracture strength; some

remain strong while others can drop below 1.0GPa.

Therefore, the strengthening in a mild environment

is not necessarily valid under different environmen-

tal conditions. The occurrence of fracture depends

strongly on the microstructure, i. e., strengthening

mechanism.

Another fracture mechanism caused by hydrogen

atoms is hydrogen attack which is observed for ma-

terials subjected to high temperatures in chemical

Fracture stress (GPa)

2.5

1.5

0.5

0 0.5 1 1.5 2

Tensile strength (GPa)

Piano wire

NiCrCoMo

18Ni marage

04C-SiMnCrMo

SCM22

SCM4

Fig. 7.65 Hydrogen-induced embrittlement observed in

various kinds of steels. (Fracture stress at 100 h in water for

a notched specimen with a stress concentration factor of 10

versus tensile strength)

Part C 7.4

Mechanical Properties 7.4 Strength 405

atmospheres such as that in an oil plant. In the case of

carbon steel, the invading hydrogen atoms react with ce-

mentite particles to produce methane gas, resulting in

the formation of blisters that lead to rupture. The crit-

ical condition for hydrogen attack is summarized by

the so-called Nelson diagram, in which the dangerous

conditions are summarized in terms of temperature and

partial pressure of hydrogen.

Stress Corrosion Cracking

Stress corrosion cracking (SCC) is observed in many

alloys (not in pure metals) under certain combined

conditions of stress, chemical environment and mi-

crostructure, as shown in Fig. 7.66a. For instance, SCC

has been found for Al alloys in air and sea water, Mg

alloys in sea water, Cu alloys in water or ammonium at-

mosphere, carbon steels in NaOH solution, austenitic

stainless steels in hot water, and so on. External or

Stress

Material

Chemical

condition

Crack propagating rate log (da/dt)

2nd region

1st region

3rd region

Stress intensity factor K

SCC

ISCC

Fig. 7.66a,b Stress corrosion cracking: (a) inﬂuential fac-

tors of stress, microstructure and chemical environment for

stress corrosion cracking and (b) crack-propagation rate as

a function of stress-intensity factor

residual tensile stress always plays an important role in

fracture. Stress accelerates local corrosion (anode so-

lution) and ampliﬁes the stress at crack tips, leading

to fracture. SCC fracture occurs along either certain

crystal planes in grains or grain boundaries. Macro-

scopic crack propagation is summarized by using the

stress intensity factor K, as shown in Fig. 7.66b. The

threshold K is deﬁned as K

ISCC

, which is dependent on

the materials’s microstructure. In general, the stronger

the yield strength, the lower the value of K

ISCC

,so

that the balance between strength and toughness is

important.

When an austenitic stainless steel is exposed to

a high-temperature atmosphere, Cr carbide precipitates

along the grain boundaries, leading to the formation

of a low-Cr zone. Corrosion then concentrates in such

low-Cr zone in the vicinity of the grain boundary and

cracks are initiated along the grain boundary, inﬂuenced

by local corrosion and local stress concentration. The

concentration of carbon is, therefore, extremely reduced

in steel-making for this use; in a nuclear reactor, it is

known that stress corrosion cracking is a key problem

for safe operation. Thus, extensive investigations have

been made on SCC for austenitic stainless steels. It

is also known that radiation damage accelerates SCC

cracking. However, recent results have indicated that

stress corrosion cracking on shroud plates in a nuclear

reactor starts in the interior of grains at the surface,

although the reason for this is not clear.

7.4.6 Interface Strength:

Adhesion Measurement Methods

Most engineering materials consist of multiple phases.

For instance, inclusions or precipitates are usually intro-

duced into engineering materials, whether intentionally

or not. Some of these are harmful to the material proper-

ties but others are useful for improving properties such

as material strength. A typical example is a composite

material. In the case of electronics packaging, interfaces

between different materials are very important. In par-

ticular, for nanosized devices, performance is strongly

dependent on the situation of interfaces. To examine the

strength of an interface experimentally, several meth-

ods are employed depending on the requirements. The

tests are not easy and require careful analysis, some-

times with the help of FEM calculations. The strength

of an interface is theoretically predicted by means of

the molecular dynamics method, which is helpful for

understanding the mechanism as well as interface de-

sign.

Part C 7.4

406 Part C Materials Properties Measurement

Tensile Strength

The fracture strength perpendicular to the interface is

tested in a similar method to tension test. Figure 7.67

shows the tension test used to measure the interface

strength [7.225]. Here, one should note the inclination

of the interface with respect to the tensile direction.

If the interface is inclined, even at an angle less than

◦

, the shear stress component appears to inﬂuence the

fracture mode. The normal to the interface should be

carefully adjusted to be parallel to the tensile direction.

This test is quite simple and easy to apply to some artiﬁ-

Grip Interface

Grip

Fig. 7.67 Tension test to measure the normal separation at

the interface

Interface

Load

Fig. 7.68a–d Bending test to evaluate cleaving stress at

the interface:

(a) compact tension test, (b) three-point bend-

ing loading parallel to the interface, (c) three-point bending

loading perpendicular to the interface and

(d) peel-off test

cially bonded parts but is not easy to apply to multiphase

alloys.

Cleavage Strength (Bending)

Similar to fracture toughness testing, compact tension

testing, using a specimen shown in Fig. 7.68a, is em-

ployed to examine the cleaving features of the interface

where the fracture mode is tensile [7.225]. Simpler

methods based on three- or four-point bending are

showninFig.7.68b and c. The strength for the deco-

hesion can be evaluated by these tests, while Fig. 7.68d

shows the peeling test. Some modiﬁcations of these

tests are also used.

Shear Strength (Adhesive Strength)

The evaluation of shear strength at the interface, which

is a key issue for composite strengthening and several

mechanically bonded parts, is an interesting measure-

ment. To measure the adhesive shear strength, the most

popular test is shown in Fig. 7.69a[7.225]. The thick-

ness of the grip is the same as that of the specimen

containing the interface, so that a bending moment

can be avoided. Figure 7.69b exhibits the compression-

type shearing test, which is frequently employed to

evaluate the strength of wire bonding in electric de-

vices. As shown in Fig. 7.69c, a special tool is prepared

to push the bonded wire to measure the decohesion

stress [7.226].

The interface strength between inclusions or pre-

cipitated particles and the matrix in engineering ma-

terials cannot be measured directly. In the case of

ﬁber-reinforced materials, methods to measure the shear

strength between the reinforcement and the matrix based

on pulling or pushing the ﬁber have been attempted. To

realize such a test, a small jig to grip the ﬁber or a small

c)b)

Grip

Load

Interface

Tool

Bonded wire

Interface

Device

Load

Fig. 7.69a–c Shearing tests: (a) tension-type test for

shearing the interface, (b) compression-type test, (c) shear-

ing test for wire bonding

Part C 7.4

Mechanical Properties 7.4 Strength 407

Pull

out

Push

down

Matrix

Fiber

Matrix

Lc/2

Fig. 7.70a–d Shear strength of interface in a composite material: (a) model of short ﬁber-reinforced composite, (b) shear-

stress distribution under the applied stress when the matrix is yielded. (c) tensile-stress distribution corresponding to (b)

and (d) pull-out and push-down tests to evaluate the shear strength of the interface

indenter with a tiny tip must be prepared. The schematic

testing arrangement is illustrated in Fig. 7.70 [7.227].

The simple shear-lag model for composite strengthen-

ing is shown in Fig. 7.70a. When the matrix yields under

the external tensile stress, the load transfer from the ma-

trix to a ﬁber, i. e., the shear stress τ

, can be roughly

described as in Fig. 7.70b. Within a limited length L

shear stress is generated and the integrated tensile stress

inside the ﬁber is shown in (b). If the ﬁber is short,

a pull-out phenomenon occurs, but if the ﬁber is long

enough, the tensile stress reaches the fracture strength

. Hence, in order to use the strength of ﬁber efﬁciently,

the length should be larger than σ

d/(2τ

), where d is the

ﬁber diameter. This is called the critical length Lc

max

When a ﬁber is shorter than Lc

max

, fracture does not take

place. Figure 7.70d presents mechanical tests to mea-

sure the decohesion shear strength at the interface. If

the length of the ﬁber is shorter than Lc

max

, it can be

pulled out or pushed down and the interface strength

can be evaluated from the relevant load–displacement

curve. However, in most cases, the ﬁber fractures during

pulling, and suitable modeling has to be considered to es-

timate the shear stress. When a brittle phase is formed at

the interface, fracture occurs easily and the cracking of

the brittle layer plays the part of a notch in reducing the

ﬁber strength.

Scratch Test for Thin-Film Coatings

The decohesion strength of thin or thick ﬁlms is fre-

quently of concern for surface modiﬁcation. Various

surface treatment such as chemical vapor deposition

(CVD), physical vapor deposition (PVD) etc. have been

developed. For rough testing to evaluate the interface

strength, adhesive tape is stuck onto the ﬁlm and pulled

quickly, as shown in Fig. 7.71a. If the interface strength

Load

Thin film

Adhesive

tape

Substrate

Interface

Load

Scanning

Indenter

Film

Fig. 7.71a,b Tests to evaluate the strength of interface be-

tween the deposited ﬁlm and substrate: (a) peel-off test

using adhesive tape and (b) scratching test for thin ﬁlm on

a substrate to examine decohesion behavior, where a di-

amond indenter with a tip radius of several μmisused

is weak, the ﬁlm can be removed easily. However, this

test is not sufﬁcient to evaluate the reliability of bonding

and hence more quantitative tests are used. Figure 7.71b

shows a schematic illustration of such a test [7.226].

An indenter is pressed into the ﬁlm and pulled along to

scratch a zigzag route, during which the applied stress

is increased gradually. After this test, the position where

separation starts can be determined by observation with

a scanning electron microscope (SEM) and the applied

stress at that point can then be found. Sometimes, the

test is performed inside a SEM.

Part C 7.4