1. Chapter 7
Mechanical
Properties of
Solids

2. Mechanical Properties of Solids
Why study mechanical properties?
as a mechanical engineer…
how to measure mechanical properties &
what these properties represent.
-- may be used to design
components using predetermined
materials such that unacceptable levels
of deformation or failure will not occur.
as a structural engineer…
how to determine stresses & stresses
distributions within members that are
subjected to loads.
-- analyze & predict various stresses using
experimental & structural analysis.
as a materials & metallurgical engineer…
concerned with producing & fabricating
materials to meet service requirements as
predicted by these stress analysis.
-- understand relationship between
microstructure of the materials & their
mechanical properties.
Mechanical properties of materials…
- reflect the relationship between its response
or deformation to an applied load.
-- its behavior when subjected to external
load (shows elastic & plastic deformation
before failure).
- measure using various mechanical testing.
Concept of
elastic deformation
materials return to its original dimension after tensile force is removed.
Common mechanical properties… Hardness Ductility Yield strength Toughness Brittleness Tensile strength Modulus of Malleability Fracture strength elasticity Flexural strength
Elastic means reversible!
Concept of
plastic deformation
Some mechanical testing…
Tension test Hardness test
Compression test Impact test
Flexural test Fatigue test
Shear/Torsion test Creep test
will cover in Chapter 9: Failure of Materials
materials are deformed to such an extent such that it cannot return to its original dimension.
1. Initial
2. Small load
3. Unload
return to
initial F d
Linear-
elastic
Non-linear elastic
1. Initial
2. Small load
3. Unload
planes
still
sheared F d
elastic + plastic
bonds
stretch
& planes
shear
plastic
bonds
stretch
Elastic deformation F d
linear
elastic
plastic
Plastic deformation
elastic d F d
= deformation/elongation/deflection

3. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Consider: Linear elastic deformation
Typical tension test
Typical stress-strain curves for hypothetical materials
strain
Typical response of a metal
Neck – acts as stress concentrator  y
TS  F
specimen
extensometer
gauge
length
Adapted from Fig. 7.2,
Callister & Rethwisch 3e.
Concept of engineering stress
Concept of engineering strain q
90º
90º - q y x
1. Tensile stress, s: Ao F t s
2. Shear stress, t: d /2 L o w
1. Tensile strain: Ao F t e = d L o F t = F s A o s = t A o
2. Lateral strain:
original area
before loading
Stress has units: N/m2 or lbf /in2 - d e L = w o
3. Shear strain:
g = Dx/y = tan q

4. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Elastic deformation region
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers
Composites
/fibers
Based on data in Table B.2,
Callister & Rethwisch 3e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers.
E (GPa)
0.2 8
0.6 1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum G
raphite
Si crystal
Glass -
soda
Concrete
Si nitride
Al oxide PC
Wood( grain)
AFRE( fibers) *
CFRE
GFRE*
Glass fibers only
Carbon
fibers only A
ramid fibers only
Epoxy only
0.4
0.8 2 4 6 10 00
1200
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTF E
HDP
LDPE PP
Polyester PS
PET C
FRE( fibers)
FRE( fibers)*
FRE(|| fibers)*
1. Modulus of Elasticity, E
(also known as Young's modulus)
E values for selected materials s
Linear-
elastic E e  
E =
Units:
E: [GPa] or [psi]
n: dimensionless
2. Poisson's ratio,n eL e -n e n = - L
metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40

5. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Plastic deformation region
1. Yield strength, 
Stress at which noticeable plastic deformation has occurred.
when ep = 0.002
= 0.2% offset
Elastic+Plastic
at larger stress
Elastic initially sy
engineering stress, s
engineering stress, s
permanent (plastic)
after load is removed ep e
engineering strain, e
engineering strain, e p
= 0.002
plastic strain
Adapted from Fig (a),
Callister & Rethwisch 3e. y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts as stress concentrator
engineering
TS
stress
engineering strain
2. Tensile Strength, TS
Maximum stress on engineering stress-strain curve.
Metals: occurs when noticeable necking starts.
Polymers: occurs when polymer backbone chains
are aligned & about to break.

6. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Plastic deformation region
 & TS values for selected materials (room temperature)
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yield strength, s y
(MPa)
PVC
Hard to measure ,
since in tension, fracture usually occurs before yield.
Nylon 6,6
LDPE 70 20 40 60 50
100 10 30
200
300
400
500
600
700
1000
2000
Tin (pure) Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020) cd
(4140) qt
(5Al-2.5Sn) W
Mo (pure) cw
Hard to measure,
in ceramic matrix and epoxy matrix composites, since
in tension, fracture usually occurs before yield. H
DPE PP
humid
dry PC
PET
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
PVC
Nylon 6,6 10
100
200
300
1000 Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020)
(4140) qt
(5Al-2.5Sn) W cw L
DPE PP PC
PET 20 30 40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride H
wood
( fiber)
wood(|| fiber) 1
GFRE
(|| fiber)
( fiber) C
FRE A
FRE( fiber)
E-glass fib
Aramid
fib
strength, TS
(MPa)
Tensile

7. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Plastic deformation region
3. Ductility
4. Toughness
Plastic tensile strain at failure.
-- shows a significant plastic deformation
before rupture.
Energy to break a unit volume of material.
Approximate by the area under the stress-strain curve.
Engineering L - L
tensile
small toughness (ceramics) % EL = f o
x 100
stress, s L
large toughness (metals) o Lo Ao Af Lf A - A = o f % RA x
100 A
very small toughness o
(unreinforced polymers)
Engineering tensile strain, e
Adapted from Fig. 7.13, Callister & Rethwisch 3e.
Engineering tensile strain, e E
ngineering
tensile
stress, s
smaller %EL
larger %EL
Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

8. Stress-Strain curves for typical polymers
Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Tension test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
Surface area, Ao
Poisson’s ratio, v
Engineering stress, 
Engineering strain, 
True stress, T
True strain, T
Modulus of elasticity, E
Yield strength, 
Tensile strength TS
Fracture strength F
Ductility %RA)
Toughness (area under graph)
Stress-Strain curves for typical polymers
True Stress & Strain
Note: Surface area, A changes when sample stretched.
True stress
True strain
brittle polymer
plastic
elastomer
elastic moduli – less than for metals
Adapted from Fig. 7.22, Callister & Rethwisch 3e.
Fracture strengths of polymers ~ 10% of those for metals.
Deformation strains for polymers > 1000% – for most metals, deformation strains < 10%.
Adapted from Fig. 7.16, Callister & Rethwisch 3e. 8 8

9. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Flexural test [Universal Testing Machine (UTM)]
Load, F
Elongation, 
(deflection)
Modulus of elasticity, E
Flexural strength, fs
- ceramic materials are more brittle than metals.
Why is this so?
- consider mechanism of deformation
-- in crystalline, by dislocation motion.
-- in highly ionic solids, dislocation motion is
difficult.
* few slip systems.
* resistance to motion of ions of like charge (e.g., anions) past one another.
Flexural test…
- most common test for ceramics.
Flexural test…
- materials with room T behavior is usually elastic but with brittle failure.
-- show little plastic deformation before failure.
- 3-Point Bend Testing often used.
-- tensile tests are difficult for brittle materials.
Typical 3 point bend test F
L/2
d = midpoint
deflection
cross section R b d
rect.
circ.
Adapted from Fig. 7.18, Callister & Rethwisch 3e.
Determine elastic modulus according to:
Flexural strength:
(rect. cross section)
(circ. cross section)
Typical values: F x
linear-elastic behavior d
slope =
Si nitride
Si carbide
Al oxide
glass (soda-lime) 69
304
345
393
Material s fs
(MPa) E(GPa)
(rect. cross section)
(circ. cross section)
Data from Table 7.2, Callister & Rethwisch 3e.

10. Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Hardness test [hardness machine]
Hardness number (HN)
Covert to  , TS, E
Hardness…
- Resistance to permanently indenting the surface.
- Large hardness means:
-- resistance to plastic deformation or cracking in
compression.
-- better wear properties.
Type of hardness test
Brinell hardness test
Rockwell hardness test
Vickers microhardness test
Knoop microhardness test
General procedure…
Press the indenter that
is harder than the metal
Into metal surface.
Withdraw the indenter
Measure hardness by
measuring depth or
width of indentation.
Typical rockwell hardness tester
e.g.,
10 mm sphere
apply known force
measure size
of indent after
removing load d D
Smaller indents
mean larger
hardness.
increasing hardness
most
plastics
brasses
Al alloys
easy to machine
steels
file hard
cutting
tools
nitrided
diamond

11. Detail of hardness testing techniques & measurement
Mechanical Properties of Solids
mechanical testing
experiment data
experiment result
mechanical properties
Hardness test [hardness machine]
Hardness number (HN)
Covert to  , TS, E
Detail of hardness testing techniques & measurement
Table 7.5 11

12. Design or Safety Factors
• Design uncertainties mean we do not push the limit.
• Factor of safety, N
Often N is
between
1.2 and 4
• Example: Calculate a diameter, d, to ensure that yield does
not occur in the 1045 carbon steel rod below. Use a
factor of safety of 5.
1045 plain
carbon steel: s y
= 310 MPa
TS = 565 MPa
F = 220,000N d L o 5
d = m = 6.7 cm 12

13. Summary • Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure. 13

14. End of Chapter 7 14