2-1

C H A P T E R 2

M E C H A N I C A L P R O P E R T I E S

2.1 MECHANICAL PROPERTIES 2.1.1 Stress and Stra in

2.2 THE TENSILE TEST 2.2.1 E last ic Deformat ion 2.2.2 P last ic Deformat ion 2.2.3 Y ie ld Strength 2.2.4 Ul t imate Tens i le St rength 2.2.5 True Stress -True Stra in Curve 2.2.6 Duct i l i ty 2.2.7 (Tens i le) Toughness

2.3 HARDNESS AND HARDNESS TESTS

2-2

2.1 MECHANICAL PROPERTIES

• The properties of a material determine its performance in

service. The materials for any application are selected on

the basis of their properties in the service environment.

• The properties of a material are also important

considerations in certain manufacturing processes, in

which the material is deformed under a force to produce

the final shape of a component; e.g. forming, machining.

• The properties required of a product in service may be very

different from those needed to facilitate its manufacture –

e.g. high strength and stiffness are usually desirable in

most engineering components, while low strength and

good ductility are preferred for processing purposes.

• The mechanical properties of a material reflect how the

material responds to an applied force or load.

• Important mechanical properties include stiffness,

strength, ductility, toughness and hardness, as well as

those related to fatigue, creep and wear.

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• Mechanical properties are dependent on the ambient

temperature and the rate at which the force is applied.

• The mechanical properties of materials are determined

through laboratory tests using standardized testing

techniques.

2.1.1 Stress and Strain

• Stress may be thought of as the intensity of a force

experienced by a material. The force may be applied in

tension, compression or shear (Fig. 2.1-1).

Fig. 2.1-1 Schematic illustration of the deformation produced by forces in (a) tension, (b) compression, and (c) shear.

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• When a force (either tensile or compressive), F, is applied

in the direction perpendicular to a cross section of area, A0,

the engineering stress, !, is defined as:

! =

!

normal forceoriginal cross-sectional area

=

!

FA

0

(N/m2 = Pascal, Pa)

• Strain is the deformation (change in shape) produced by a

stress. For a normal stress, the engineering strain, ", is

defined as:

" =

!

change in lengthoriginal length

=

!

"ll0

=

!

length after force is applied - original lengthoriginal length

=

!

l - l0

l0 (m/m)

• For a shear force, F, applied parallel to surfaces of area A,

the shear stress, #, is defined as:

# =

!

shear forcesurface area =

!

FA (Pa)

2-5

2.2 THE TENSILE TEST

• The tensile test is commonly used to determine several

important mechanical properties of metals and polymers.

[Note: different tests are used for ceramics.] It measures how a material

responds to a static or slowly applied force.

• Test specimens may either be cylindrical or flat (Fig. 2.2-1).

The choice of specimen geometry and size depends on the

shape of the end product that is to be made from the

material tested: the cylindrical specimen is preferred when

the final product has a thick cross-section, while the flat

specimen is chosen for a thin cross-section.

• The specimen geometry is specified by established

standards, e.g. ASTM E8M, ISO 6892:1992.

Fig. 2.2-1 Specimen geometries used in the tensile test: (a) cylindrical, and (b) flat. The gauge length is the portion from which measurements would be taken.

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• The specimen is gripped by its ends in the test machine (Fig.

2.2-2), which elongates the specimen at a constant rate,

usually until fracture occurs. [Note: testing is destructive.]

• The machine automatically and continuously measures the

instantaneous applied force (with a load cell) and the

resulting elongation (using an extensometer).

• The output of the tensile test is recorded as load versus

elongation (Fig. 2.2-3a), which is then normalized to

engineering stress versus engineering strain (Fig. 2.2-3b).

Fig. 2.2-2 Schematic illustration of the tensile test.

2-7

!

(a) (b)

Fig. 2.2-3 (a) Load versus elongation diagram, and (b) stress versus strain diagram obtained by normalizing the curve in (a).

2.2.1 Elastic Deformation

• During the initial part of the tensile test, the material

returns to its original length when the load is removed; its

deformation is non-permanent and reversible; i.e. elastic.

• When deformation is elastic, most metals exhibit a linear

relationship between stress and strain (Fig. 2.2-4). This is

known as Hooke’s law:

! = E" where E is the modulus of elasticity

or Young’s modulus (Pa)

2-8

• E corresponds to the slope of the linear segment of the

stress-strain curve (Fig. 2.2-4).

Fig. 2.2-4 The portion of the

stress-strain curve corresponding to elastic deformation.

• E may be thought of as stiffness (whether rigid or floppy),

or a material’s resistance to elastic deformation. A stiff

material has a high modulus, and its deformation (strain)

under an elastic load is small (Figs. 2.2-5).

Fig. 2.2-5 The effect of modulus of elasticity on elastic deflection: ESteel > EAluminium > EPolystyrene. (All beams have the same length and cross-section).

2-9

Fig. 2.2-6 Typical elastic moduli of various engineering materials.

• A high E is generally preferred, especially where adjacent

components in an assembly are in relative motion,

requiring correct alignment and fit of the parts.

• In metals and ceramics, E depends on the nature of the

bonding of atoms within the material (Sec. 3.8.3). Stiffness

may only be altered by physically combining 2 or more

materials of different stiffness together as a composite.

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2.2.2 Plastic Deformation

• At some point during the tensile test, the stress-strain

behaviour becomes non-linear and no longer obeys

Hooke’s law. The specimen does not return to its original

length the load is removed, although there is recovery of

the small elastic component (sometimes called springback)

(Fig. 2.2-7); its deformation is now permanent and non-

reversible; i.e. plastic.

• Plastic deformation follows upon elastic deformation when

the applied stress exceeds the critical value of the elastic

limit.

Fig. 2.2-7 Stress-strain curve showing permanent plastic deformation upon

removal of load.

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2.2.3 Yield Strength

• The point at which plastic deformation begins is known as

yielding, which is close to the initial departure of the

stress-strain curve from linearity.

• In most materials, the transition from elastic to plastic

deformation is gradual, making it difficult to determine the

yield point precisely.

Fig. 2.2-8 Determining the 0.2% offset yield strength.

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• The yield strength, !y, is thus specified as the stress level at

which a noticeable yet safe amount of plastic deformation

has occurred, which is usually a strain of 0.2% (0.002).

This stress is known then as the 0.2% offset yield

strength or the 0.2% proof stress.

• This is found by locating 0.2% strain (on the x-axis) and

constructing a line parallel to the elastic (linear) portion of

the stress-strain curve. Intersection of this line with the

stress-strain curve gives the 0.2% offset yield strength (Fig.

2.2-8).

• The yield strength of a material is an important

consideration in component design. The primary design

concern is to keep any deformation elastic, such that the

component recovers its original shape when the load is

removed. Thus, the maximum applied stress allowable

must be below the yield strength.

• In designing for strength, a safety factor must also be

incorporated, to account for variations in material

properties, due to inhomogeneity and internal flaws.

• The strength of a material generally refers to the yield

strength.

2-13

Fig. 2.2-9 Typical yield strengths of various engineering materials.

• Yield strength in all classes of materials depends on the

characteristics of atomic bonding; but, unlike the modulus

of elasticity, it is also sensitive to internal microstructure.

The strength of metals, in particular, may be altered over a

wide range by variations in composition and structure (Sec.

6.3).

2-14

2-15

2.2.4 Ultimate Tensile Strength

• The ultimate tensile strength (UTS), or simply, tensile

strength (TS), is the maximum stress on the stress-strain

curve (Fig. 2.2-10); it represents the highest stress a material is

able to withstand before necking.

• All deformation up to the UTS is uniform throughout the

gauge length of the tensile specimen. At the UTS, a small

constriction or neck begins to form at some point (due to

some internal microscopic flaw), and all subsequent

deformation is confined to this small region (non-uniform

deformation), leading to final fracture at the neck (Fig. 2.2-11).

Fig. 2.2-10 The correlation of the stress-train behaviour with the deformation

of the tensile specimen at various points during the tensile test. The UTS is the maximum stress on the stress-strain curve.

2-16

Fig. 2.2-11 The development of plastic strain during tensile testing.

• For design purposes, the yield strength rather than the UTS

is used, because by the time the UTS has been reached,

the excessive plastic deformation would have rendered the

component useless.

• However, the UTS can be a measure of the quality of a

material. The presence of pores (tiny internal holes) or

harmful inclusions (foreign particles) may result in lower

UTS than normal (Sec. 7.1).

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2.2.5 True Stress-True Strain Curve

• The calculation of engineering stress and engineering strain

is based on the original (and hence, constant) dimensions

of the tensile specimen, and does not take into account the

continuous change in dimensions as the test progresses.

Fig. 2.2-12 Comparison between engineering stress-strain

and true stress-strain curves.

• During the tensile test, the cross-sectional area of the

tensile specimen constantly decreases; thus, the actual or

true stress at any instant is higher than that depicted by

the engineering stress-engineering strain curve (Fig. 2.2-12).

2-18

• True stress, !t, is defined as the force, F, divided by the

instantaneous minimum cross-sectional area, Ai,

!t =

!

normal forceinstantaneous minimum cross-sectional area =

!

FA

i

• True strain, "t, is related to the differential change in

length, dl, divided by the instantaneous length, l:

d"t =

!

dll ! "t =

!

dlll

0

l

" = ln

!

ll0

"

#

$ $

%

&

' '

• The true stress-strain curve and engineering stress-strain

curve are very close up to yielding. The difference between

the two curves becomes much greater only after necking

begins.

• The true stress-strain curve implies that the strength of the

material actually rises with increasing plastic deformation.

In metals, this is known as strain hardening (Sec. 6.3.5).

• In design, the engineering stress-strain curve is sufficient

since it underestimates the true strength of the material. In

manufacturing (forming and shaping), however, the true

stress-true strain curve is more relevant because it portrays

the real stress required to deform and shape a material.

2-19

2.2.6 Ducti l ity

• Ductility is a measure of the amount of plastic deformation

that has been sustained at fracture.

• Ductility may be expressed as either percent elongation or

percent reduction in area.

Fig. 2.2-13 Tensile specimens at start and end of test.

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• The percent elongation is the percentage of plastic strain

after fracture:

%EL =

!

final gauge length " original gauge lengthoriginal gauge length

#

$ % %

&

' ( ( x 100%

=

!

lf" l

0

l0

#

$

% %

&

'

( ( x 100%

• The percent reduction in area is defined as:

%RA =

!

orig. x -sect. area " x -sect. area at fracture siteoriginal cross-sectional area

#

$ % %

&

' ( ( x 100%

=

!

A0"A

f

A0

#

$

% %

&

'

( ( x 100%

• Both lf and Af are measured after fracture, by fitting the two

broken ends of the tensile specimen back together. This

reflects the amount of plastic deformation only, by taking

into account the elastic recovery (springback) that occurs

after the removal of stress.

• The values of ductility from the two different definitions are

not, in general, equal. While %EL is easier to determine,

%RA is a more fundamental measure of ductility. %RA is

based on the minimum diameter at the fracture site and so

is a measure of the highest strain along the gauge length.

%EL is an average over an arbitrarily chosen gauge length;

its value varies with different gauge lengths (hence the

need for standardized tensile test specimens).

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• Brittle materials are typically those that exhibit strains of

less than 5% at fracture.

• The ductility of a material is sensitive to the ambient

temperature. Materials that are ductile at room tempera-

ture may become brittle at low temperatures (Sec. 7.1.4).

• Ductility is generally of minor concern in component

design, but it becomes an important consideration in the

manufacture of components through forming processes,

such as rolling, drawing and extrusion, in which large-scale

deformation takes place. A ductile material may undergo

large changes in shape before it fractures.

• Like the UTS, ductility can also give some indication of

defects in a material. Porosity, inclusions, or improper

processing (e.g. overheating), may lower ductility.

2-22

2-23

2.2.7 (Tensile) Toughness

• One measure of toughness is the ability of a material to

absorb energy up to fracture.

• In the tensile test and other loading situations in which the strain rate (i.e. rate of elongation) is low, toughness is the area under the engineering stress-strain curve up to the point of fracture (Fig. 2.2-14), which gives the work done per unit volume in causing the material to fracture. [See Sec. 7.1 for

other measures of toughness.]

Fig. 2.2-14 The stress-strain behaviour of brittle and ductile materials; ductile materials are generally tougher than brittle materials because the more energy is absorbed per

unit volume up to fracture (area under the stress-strain curve is greater).

• A tough material must display both strength and ductility (Fig. 2.2-15).

• A tough material will exhibit much plastic deformation before fracture, allowing preventive measures to be taken.

2-24

Fig. 2.2-15 The toughness of a material depends on a combination of strength and ductility.

Fig. 2.2-16 Summary of the mechanical properties obtained from the tensile test.

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2.3 HARDNESS AND HARDNESS TESTS

• Hardness is a measure of the resistance of a material to

surface indentation (a dent or a scratch).

• Hardness testing involves pressing a hard indenter with a

definite shape and definite load against a material. The

material undergoes local plastic deformation under the

indenter, leaving a depression (Fig. 2.3-1). Hardness is related

to the size or depth of the depression. The larger or deeper

the depression, the softer the material.

Fig. 2.3-1 Schematic illustration of the hardness test.

• Since hardness depends on the ease with which a material

deforms plastically, a relationship between hardness and

strength can be determined empirically (Fig. 2.3-2). Hardness

testing is much simpler than the tensile test and is used

extensively in industry as a relatively inexpensive and non-

destructive method of quality control.

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Fig. 2.3-2 Relationships between hardness and tensile strength.

• Hardness testing is also the easiest way to determine the strength of brittle materials such as ceramics.

• Hardness becomes an important consideration when the surface of a component rubs against another surface in service, leading to wear. Generally, a harder surface would experience less wear.

• The 4 most common tests are the Brinell and Rockwell hardness tests, and the Vickers and Knoop microhardness tests. The hardness number for each of these tests depends on the shape of the indentation and applied load (Fig. 2.3-3).

2-27

Fig.

2.3

-3 H

ardn

ess

test

ing

met

hods

.

2-28

• There is no absolute scale for hardness; each hardness test

method has its own scale. For the same material, different

values are given by different techniques. There are no

simple theoretical relationships between the various scales;

conversion data are determined experimentally (Fig. 2.3-4).

Fig. 2.3-4 Comparison of various hardness scales.