Kutz M. Handbook of materials selection

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628 CERAMICS TESTING

generated during machining would cause an internal error. Another example of

an internal error would be excessive specimen deﬂection during testing. Support

point frictional forces at large deﬂections will have a component aligned with

the applied force that will increase the applied moment. ‘‘External’’ errors are

those classiﬁed as being caused by incorrect test ﬁxture geometry. Improper

location of the inner load points is an example that causes external error. Another

example is the generation of torque on the test specimen. This can be caused

by an initially twisted test specimen, unparallel line loads, or nonuniform line

loads at the contact points.

5,6

External error can also occur from compressive

contact stresses at the support pins, which can result in localized crushing. This

error can be reduced by using support pins above a critical radius r

To minimize the errors associated with ﬂexure testing, the test specimen and

test ﬁxtures must adhere to certain restraints and standards. Test specimen ge-

ometry has been standardized based on error considerations. A common ge-

ometry in the United States is 3 by 4 by 50 mm for the test specimen and inner

and outer spans of 20 and 40 mm, respectively, for the ﬁxtures.

The test spec-

imen must be isotropic and homogeneous to apply the maximum tensile stress

equation previously given. In addition, the specimen should be as free as possible

of surface defects as the maximum tensile stress occurs on the surface.

In comparing the three- and four-point ﬂexure test methods, it is found that

the four-point method is more appropriate for determining fracture strength be-

cause no shear stresses are generated as in the three-point test method. The three-

point test method with its simpler geometry, however, may be more attractive

for tests in which stable crack growth must be induced into the test specimen.

Some of the ﬂexure test standards that are applicable to advanced ceramics

are listed here:

JISC, ‘‘Testing Method for Flexural Strength (Modulus or Rupture) of Fine

Ceramics,’’ R1601-1995

JISC, ‘‘Testing Method for Flexural Strength of Fin Ceramics at Elevated

Temperature,’’ R1604-1995

ASTM, ‘‘Standard Test Method for Flexural Strength of Advanced Ceramics

at Ambient Temperatures,’’ C1161-94

ASTM, ‘‘Standard Test Method for Flexural Strength of Advanced Ceramics

at Elevated Temperatures,’’ C1211-92

Comite´ Europe´en de Normalisation (CEN),* ‘‘Advanced Technical Ceram-

ics—Monolithic Ceramics—Mechanical Properties at Room Tempera-

ture—Part 1: Determination of Flexural Strength,’’ EN843—1:1995

CEN, ‘‘Advanced Technical Ceramics—Monolithic Ceramics—Thermo-

mechanical Properties—Part 1: Determination of Flexural Strength at

Elevated Temperature,’’ ENV820—1:1993.

2.2 Creep

Similar to the fracture testing methods previously discussed, the three test meth-

ods used to determine creep characteristics in ceramics are the tensile, com-

* Comite´ Europe´en de Normalisation, Brussels, Belgium.

2 MECHANICAL TESTING 629

Fig. 3 Schematic of typical test setup for creep testing in ﬂexure. (From Ref. 3 by courtesy of

Marcel Dekker Inc.)

pressive, and ﬂexural tests. The primary differences in the test ﬁxtures are that

the gauge section must be heated to the desired elevated temperature and an

alternate method of measuring deﬂection such as extensometers must be em-

ployed because of the increased temperature. Figure 3 shows a typical test setup

for a ﬂexure test that utilizes extensometers.

Flexure Creep

Flexure testing using four-point loading yields the maximum tensile stress of a

beam in bending given in the fracture strength section:

1.5P (L

⫺ L )

ƒo i

S ⫽

In addition, the maximum tensile strain equation is given as:

␦

center

␧ ⫽

max

(L )

Compared to the tensile and compressive creep tests, ﬂexure testing is less

expensive, easier to design, and requires less test specimen preparation. How-

ever, the nonuniform stress state induced in the ﬂexure testing results in difﬁculty

in determining the creep characteristics of a material if it deforms differently in

tension than in compression. This difference in tensile and compressive creep

behavior is a result of cavitation among other factors. Conducting an additional

test in either compression or tension allows for the determination of uniform

stress-state creep characteristics from the nonuniform ﬂexure test results. Ad-

ditional errors from twisting, friction between test specimen and load points,

and excessive contact stress at support points are also considerations.

630 CERAMICS TESTING

Tensile Creep

Tensile testing to determine creep characteristics yields a uniform stress state

characterized by the equation:

␴

⫽

The uniform stress state eliminates the problem of different deformations in

tension and compression. This results in the much simpler calculation of stress

and strain than with ﬂexure testing. The test setup, however, is more expensive

and difﬁcult to implement. The test specimens required for creep tensile testing

are also more difﬁcult and time intensive to design and manufacture. In addition

to stress gradients from the test specimen geometry, temperature differences

induce an unwanted temperature gradient in the specimen from the grip contact

portion of the specimen to the heated gauge section.

This temperature gradient

becomes larger and poses more of a problem when cold grips are used. Un-

wanted failure in the grip interface portion of the specimen can also be a prob-

lem. Various test standards are applicable to tensile testing of advanced ceramics.

ASTM C1291-95 directly applies to tensile testing for creep behaviors:

ASTM, ‘‘Standard Test Method for Elevated Temperature Tensile Creep

Strain, Creep Strain Rate, and Creep Time to Failure for Advanced Mon-

olithic Ceramics,’’ C1291-95

ASTM, ‘‘Standard Test Method for Tensile Strength of Monolithic Advanced

Ceramics at Elevated Temperatures,’’ C1366-95

ASTM, ‘‘Standard Test Method for Monotonic Tensile Strength Testing of

Continuous Fibre-Reinforced Advanced Ceramics with Solid Rectangular

Cross-Sections at Elevated Temperatures,’’ C1359-96

Compressive Creep

Compressive testing to determine creep behavior, like tensile testing, results in

a uniform stress state that allows for easy determination of creep characteristics.

It has been shown that creep in compression can vary signiﬁcantly from creep

in tension so it is of value to conduct both tests to ‘‘get the best picture’’ of a

material’s creep properties. Some advantages to the compressive test are the low

cost in preparing the material as well as the small geometry of the specimen,

which allows for more testing per sample material size.

There are some drawbacks to the compressive test as well. The test specimen

must be aligned to a greater accuracy than tension or ﬂexure tests to prevent

unwanted bending and buckling. End constraints on the test specimen can result

in shear stresses if the specimen ends are constrained, which results in a non-

uniform stress state. In addition, temperature gradients can have an adverse effect

on test result accuracy.

2.3 Hardness

Hardness is an important property to quantify in ceramics. Measured hardness

indicates the ability of the ceramic to resist deformation by a hard object. Usu-

ally, Knoop or Vickers diamond indenters are used in conjunction with a mi-

2 MECHANICAL TESTING 631

Fig. 4 Typical hardness versus load (force) plot. (From Ref. 8 ASM Handbook, Vol. 8: Mechani-

cal Testing and Evaluation, ASM International, Materials Park, OH 44073-0002, Fig. 3, page 245.)

croindentation hardness machine.

Rarely are the popular Rockwell and Brinell

indenters used for ceramics research. Vickers indenters are used to characterize

roughly 60% of the ceramic hardness values that are published.

The indentation force should always be included with the hardness value. For

the most accurate results, the entire force versus hardness curve should be mea-

sured as shown in Fig. 4.

Discrepancies can arise at different indentation forces. At higher forces, crack-

ing can complicate the measuring process or make measuring impossible.

Mea-

suring the hardness from the indentation, especially at small forces, is also a

signiﬁcant source of error in hardness testing. The hardness value can change

based on the force value applied to the test specimen at small forces. Volume 8

of the ASM Handbook

recommends forces greater than or equal to 9.8 N for

Vickers and Knoop indentations. Errors in the measurement of the indentation

diagonal length essentially double the hardness error as the hardness value is

proportional to the square of the diagonal length. A Versailles Advanced Ma-

terials and Standards (VAMS) round-robin test project conducted on alumina

ceramic samples resulted in uncertainty in the hardness values given by the

laboratories involved.

Although using numerous indentations can reduce some

of this uncertainty, engineers and scientists conducting hardness tests should

nevertheless keep this uncertainty in mind when considering their data.

Standards for measuring hardness for ceramics are listed below:

Vickers Hardness

ASTM, ‘‘Standard Test Method for Vickers Indentation Hardness of Ad-

vanced Ceramics,’’ C1427-97

CEN, ‘‘Advanced Technical Ceramics—Monolithic Ceramics—Mechanical

Properties at Room Temperature—Part 4: Determination of Vickers, Knoop

and Rockwell Superﬁcial Hardness Tests,’’ prEN834-4

JISC, ‘‘Testing Method for Vickers Hardness of High Performance Ceramics,’’

R1610:1991

632 CERAMICS TESTING

ISO, ‘‘Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—

Test Method for Hardness of Monolithic Ceramics at Room Temperature,’’

ISO 14705:2000

Knoop Hardness

ASTM, ‘‘Standard Test Method for Knoop Indentation Hardness of Advanced

Ceramics,’’ C1426-99

CEN, ‘‘Advanced Technical Ceramics—Monolithic Ceramics—Mechanical

Properties at Room Temperature—Part 4: Determination of Vickers, Knoop

and Rockwell Superﬁcial Hardness Tests,’’ prEN834-4

ISO, ‘‘Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—

Test Method for Hardness of Monolithic Ceramics at Room Temperature,’’

ISO 14705:2000

ISO, ‘‘Glass and Glass-Ceramics—Knoop Hardness Test,’’ ISO 9385-1990.

2.4 Fracture Toughness

The brittle nature of ceramics results in low resistance to fracture, quantiﬁcial

as fracture toughness, which is an important factor in many applications of

ceramics. Fracture toughness is a measure of a specimen’s ability to resist further

growth of a crack. Low fracture toughness values increase the risk of cata-

strophic failure of a ceramic component. Ceramic matrix composites (CMCs)

have better fracture toughness compared to monolithic ceramics as the additional

reinforcing elements help to deter crack growth. The concepts of the linear-

elastic fracture mechanics (LEFM) method commonly used for other materials

can be applied to monolithic ceramics for the purpose of analysis. For ceramic

matrix composites, ongoing research is being conducted regarding the applica-

tion of the concepts of elastic-plastic fracture mechanics (EPFM) methods.

There are various testing methods and setups for fracture toughness testing.

Some methods included in the testing standard, ASTM C1421, are the single-

edge precracked beam (SEPB) method, the surface crack in ﬂexure (SCF)

method, and the chevron notched beam (CNB) method.

The SEPB, SCF, and CNB methods all consist of a ﬂexural test of a beam in

which a short straight crack is induced into the tensile side. The primary differ-

ences are the methods by which the beam is deformed to introduce the prelim-

inary short crack. All three methods have good calibration characteristics but

have some drawbacks as well. With the SEPB method, it can be difﬁcult to

obtain straight-fronted cracks. Crack initiation in CNB testing can be difﬁcult

as a result of residual stresses from machining. SCF testing can only be per-

formed on materials that produce high-quality cracks from the indentation.

Standards organizations have introduced fracture toughness testing standards

utilizing various testing methods. For example, ASTM C1421 generally uses a

ﬂexure test of a cracked bend bar while JIS R1607 utilizes only two test methods,

SEPB and IF (indentation fracture). Standards that apply directly to fracture

toughness testing of ceramics are given below.

Japanese Industrial Standards Committee, ‘‘Testing Methods for the Fracture

Toughness of High Performance Ceramics,’’ JIS R1607-1990

2 MECHANICAL TESTING 633

Fig. 5 Test setup schematic for traditional split Hopkinson pressure bar testing. (From Ref. 11

ASM Handbook, Vol. 8: Mechanical Testing and Evaluation, ASM International,

Materials Park, OH 44073-0002, Fig. 1, page 497.)

American Society for Testing Materials, ‘‘Standard Test Methods for the De-

termination of Fracture Toughness of Advanced Ceramics at Ambient Tem-

perature,’’ ASTM C1421-99

International Organization for Standardization, ‘‘Fine Ceramics (Advanced

Ceramics, Advanced Technical Ceramics)—Test Method for Fracture

Toughness of Monolithic Ceramics at Room Temperature by Single Edge

Pre-Cracked Beam (SEPB) Method,’’ ISO DIS15732 (in 1999)

2.5 High Strain Rate

Split Hopkinson pressure bar (SHPB) testing has primarily been used in the past

to measure the plastic properties of metals. The fact that ceramics are brittle and

many ceramic compounds and alloys show only elastic strains before fracture

makes accurate testing and measurement more difﬁcult than with more ductile

materials such as metals.

A traditional SHPB test conﬁguration is shown in Fig. 5.

The test setup

consists of an incident bar, a transmission bar, and a striker bar. The ceramic

test specimen is placed in between the incident and transmission bars as shown.

The striker bar strikes the incident bar at a predetermined velocity by being

launched from a gas gun. When it impacts the incident bar, it generates a com-

pressive pulse that continues to travel to the test specimen. Part of the incident

pulse travels through the test specimen, and the remaining part is reﬂected back

into the incident bar. The stress pulses are measured by strain gauges placed at

midpoints on the transmission and incident bars. An oscilloscope displays the

measured pulses. The stress, strain, and strain rate equations are given as

␴

(t) ⫽ ␧ (t)

˙␧ ⫽⫺ ␧ (t)

␧ (t) ⫽ 冕 ˙␧ (t) dt

634 CERAMICS TESTING

Fig. 6 Incident bar and transmission bar protection using tungsten–carbide inserts. (From Ref.

11 ASM Handbook, Vol. 8: Mechanical Testing and Evaluation, ASM International,

Materials Park, OH 44073-0002, Fig. 3, page 499.)

where E is Young’s modulus, l is length, A is cross-sectional area,

␴

is stress, ␧

is strain, is strain rate, and t is time. Subscripts T, s, o, and R refer to the˙␧

transmitted pulse, specimen, bar, and reﬂected pulse.

Some of the inherent properties of ceramics such as brittleness and high

strength, conﬂict with assumptions that are made in deriving the stress, strain,

and strain rate equations.

An example is the assumption that the bar end sur-

faces remain ﬂat and parallel during the deformation of the test specimen. The

hard nature of ceramics can cause the test specimen to indent into the steel bar

ends, resulting in stress concentration around the test specimen end faces. These

stress concentrations result in nonuniform, nonuniaxial stress state in the test

specimen, which violates another assumption in using the equations, which is

that the stress state is uniform and uniaxial. The stress concentrations can con-

sequently lead to chipping and failure of the ceramic test specimen through

microcrack initiation.

One way to minimize the problem of test specimen damage is to place tung-

sten–carbide inserts in between the test specimen and bar ends as shown in Fig.

The high strength of the inserts prevents the ceramic test specimen from

indenting into the incident and transmission bars, thereby reducing stress con-

centrations. However, the tungsten–carbide inserts can have the adverse effect

of altering the incident, transmitted, and reﬂected stress-wave properties that can

result in inaccurate strain gauge measurements. This can be prevented by se-

lecting tungsten–carbide inserts with the same impedance as the bar material.

Selection of the diameter of the inserts can also help solve this problem. Typi-

cally, the insert lengths are one fourth of the test specimen length.

2.6 Fatigue

Fatigue testing is an important design tool for the designer of ceramic compo-

nents where reliability and lifetime estimates need to be made. Fatigue tests for

ceramics generally cover the three situations of cyclic fatigue, static fatigue, and

dynamic fatigue.

Cyclic fatigue is the periodic loading of a component under

various load ratios usually denoted as R:

2 MECHANICAL TESTING 635

Fig. 7 Failure stress versus time to failure. (From Ref. 14 ASM Handbook, Vol. 8: Mechanical

Testing and Evaluation, ASM International, Materials Park, OH 44073-0002.)

␴

min

R ⫽

␴

max

Common scenarios for the stress ratio include R ⬎ 0 (both minimum and max-

imum stresses in tension or compression) and R

⬍ 0 (minimum stress in

compression and maximum stress in tension). The simple loading scenario would

involve a sinusoidal loading that varied continuously with a minimum and max-

imum stress. In real-world examples, however, the loading can be much more

complicated.

Static fatigue testing involves slow crack growth of a test specimen with a

constant tensile force under the desired conditions. The length of time for the

test specimen to fail and the applied stress are measured and used to obtain the

fatigue characteristics by using various fatigue equations. Dynamic fatigue test-

ing involves applying a constant, increasing stress (i.e., constant nonzero stress

rate) to a test specimen under desired conditions. The stress rate and maximum

applied stress at failure are measured and used in conjunction with various fa-

tigue equations to determine the fatigue characteristics.

Fatigue testing can further be divided into the two categories of ‘‘direct’’ and

‘‘indirect.’’ Direct methods, also known as fracture mechanics methods, involve

running tests with test specimens with previously induced cracks and directly

observing crack growth. Indirect methods, also known as strength measurement

techniques, involve measuring the strength of the test specimen over time inter-

vals and using the data to estimate fatigue properties.

Indirect Methods

Static loading utilizing the indirect method involves subjecting a tensile or ﬂex-

ure test specimen to a constant load under the desired environment conditions.

The applied force stress and the amount of time for specimen failure are mea-

sured and used to estimate the fatigue properties of the ceramic material. A

typical plot of failure stress versus time to failure is shown in Fig. 7.

Uniaxial ﬂexural tests in three- or four-point loading situations are performed

under the directions given in JIS R1601, ‘‘Test Method for Flexural Strength

(Modulus of Rupture) of Fine Ceramics.’’ At least three levels of stress are

636 CERAMICS TESTING

Fig. 8 Failure stress versus stress rate. (From Ref. 14 ASM Handbook, Vol. 8: Mechanical Test-

ing and Evaluation, ASM International, Materials Park, OH 44073-0002.)

recommended. The fatigue strength can be related to the failure time with the

following equation

⫺

␴

t ⫽⫺1

冋冉冊册

␴␴

ƒƒ

where B is a variable determined from crack geometry, fracture toughness, load-

ing situation, and K and n, which are material and environment constants;

␴

the inert strength at which no crack extension occurs for noncorrosive conditions.

Indirect dynamic loading usually involves tensile or ﬂexure test specimens

subjected to a constant stress rate. The applied stress rate and the failure stress

are measured and used to estimate fatigue properties. Figure 8 shows a typical

plot of failure stress versus the stress rate.

The standard, ASTM C1368, gives guidelines for fatigue strength estimating

via dynamic loading. It involves four-point ﬂexure testing of a ceramic specimen

in accordance with ASTM C1161 ‘‘Standard Test Method for Flexural Strength

of Advanced Ceramics at Ambient Temperature.’’ The fatigue strength and ap-

plied stress rate are related by the equation

⫺

21/n

⫹

␴

⫽ [B(n ⫹ 1)

␴

]

ƒi

where the same variable deﬁnitions apply as in the static loading equation.

There are various methods for applying periodic loads to ceramics. With

bending fatigue tests, a periodic force with a speciﬁed frequency and stress ratio

is applied to three- or four-point ﬂexure test setups. Cyclic tensile fatigue tests

involve cyclically loading a test specimen with a testing apparatus with speciﬁed

load ratio and frequency. Various test specimen shapes can be used and tension–

compression cyclic fatigue (stress ratio

⬍ 0) has been performed utilizing a

button-head specimen and clamping ﬁxture. Rotary bending is also used for

fatigue testing ceramics and is especially useful for analyzing components such

as shafts that undergo similar stress states while in use.

3 THERMAL TESTING 637

Fig. 9 Double-cantilever beam test method. (From Ref. 14 ASM Handbook, Vol. 8: Mechanical

Testing and Evaluation, ASM International, Materials Park, OH 44073-0002.)

Direct Methods

Direct methods, also known as fracture mechanics methods, use fatigue tests

that employ test specimens with an induced crack.

Crack growth is observed

directly or via strain gauges or other measuring devices.

One testing technique is the double-cantilever beam method, shown sche-

matically in Fig. 9. For the conﬁguration shown, the stress-intensity factor and

fracture toughness can be found utilizing the equation

Pa h

K ⫽ 3.47 ⫹ 2.32

冉冊

3/2

兹Bb

where B is the thickness of the test specimen, b is the web thickness, a is the

crack length, h is half the specimen height, and P is the applied force. Some

standards that directly apply to fatigue testing of ceramics are given below.

●

Japanese Industrial Standards Committee, ‘‘Test Methods for Static Bend-

ing Fatigue of Fine Ceramics,’’ JIS R1632—1998

●

Japanese Industrial Standards Committee, ‘‘Test Method for Flexural

Strength,’’ JIS R1601—1995

●

American Society for Testing Materials, ‘‘Standard Test Method for De-

termination of Slow Crack Growth Parameters of Advanced Ceramics by

Constant Stress-Rate Flexural Testing at Ambient Temperature,’’ ASTM

C1368-99

●

American Society for Testing Materials, ‘‘Standard Test Method for Flex-

ural Strength of Advanced Ceramics at Ambient Temperature,’’ ASTM

C1161-99

●

Japanese Industrial Standards Committee, ‘‘Test Method for Bending Fa-

tigue of Fine Ceramics,’’ JIS R1621—1996

●

American Society for Testing Materials, ‘‘Standard Test Method for Flex-

ural Strength of Advanced Ceramics at Elevated Temperatures,’’ ASTM

C1211-95

3 THERMAL TESTING

3.1 Thermal Expansion

Thermal expansion is an important property that quantiﬁes the volume change

a material undergoes when it is subjected to temperature changes. Typically,