mechanical properties

1
Chapter 3:
MECHANICAL
PROPERTIES OF
MATERIALS

Outline
 Terminology for Mechanical Properties
 The Tensile Test: Stress-Strain Diagram
 Properties Obtained from a Tensile Test
 True Stress and True Strain
 Shear stress diagram

3
Stress-Strain Test
specimen
machine

5
Important Mechanical Properties
from a Tensile Test
• Young's Modulus: This is the slope of the linear
portion of the stress-strain curve, it is usually
specific to each material; a constant, known value.
• Yield Strength: This is the value of stress at the
yield point, calculated by plotting young's modulus
at a specified percent of offset (usually offset =
0.2%).
• Ultimate Tensile Strength: This is the highest
value of stress on the stress-strain curve.
• Percent Elongation: This is the change in gauge
length divided by the original gauge length.

Terminology
 Load - The force applied to a material during
testing.
 Strain gage or Extensometer - A device used for
measuring change in length (strain).
 Engineering stress - The applied load, or force,
divided by the original cross-sectional area of the
material.
 Engineering strain - The amount that a material
deforms per unit length in a tensile test.

7
F
δ
bonds
stretch
return to
initial
1. Initial 2. Small load 3. Unload
Elastic means reversible.
F
δ
Linear-
elastic
Non-Linear-
elastic
Elastic Deformation

8
1. Initial 2. Small load 3. Unload
Plastic means permanent.
F
δ
linear
elastic
linear
elastic
δplastic
planes
still
sheared
F
δelastic + plastic
bonds
stretch
& planes
shear
δplastic
Plastic Deformation (Metals)

9
Typical stress-strain
behavior for a metal
showing elastic and
plastic deformations,
the proportional limit P
and the yield strength
σy, as determined
using the 0.002 strain
offset method (where there
is noticeable plastic deformation).
P is the gradual
elastic to plastic
transition.

10
Plastic Deformation (permanent)
• From an atomic perspective, plastic
deformation corresponds to the breaking of
bonds with original atom neighbors and
then reforming bonds with new neighbors.
• After removal of the stress, the large
number of atoms that have relocated, do
not return to original position.
• Yield strength is a measure of resistance
to plastic deformation.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
• Localized deformation of a ductile material during a
tensile test produces a necked region.
• The image shows necked region in a fractured sample

13
Permanent Deformation
• Permanent deformation for metals is
accomplished by means of a process called
slip, which involves the motion of
dislocations.
• Most structures are designed to ensure that
only elastic deformation results when stress
is applied.
• A structure that has plastically deformed, or
experienced a permanent change in shape,
may not be capable of functioning as
intended.

14
tensile stress, σ
engineering strain, ε
σy
εp = 0.002
Yield Strength, σy
tensile stress, σ
engineering strain, ε
Elastic
initially
Elastic+Plastic
at larger stress
permanent (plastic)
after load is removed
εp
plastic strain

Stress-Strain Diagram
Strain ( ) (∆L/Lo)
4
1
2
3
5
Stress(F/A)
Elastic
Region
Plastic
Region
Strain
Hardening Fracture
ultimate
tensile
strength
Slope=E
Elastic region
slope =Young’s (elastic) modulus
yield strength
Plastic region
ultimate tensile strength
strain hardening
fracture
necking
yield
strength
UTSσ
yσ
εEσ =
ε
σ
E =
ε
12
y
εε
σ
E
−
=

Stress-Strain Diagram (cont)
• Elastic Region (Point 1 –2)
- The material will return to its original shape
after the material is unloaded( like a rubber band).
- The stress is linearly proportional to the strain in
this region.
εEσ =
: Stress(psi)
E : Elastic modulus (Young’s Modulus) (psi)
: Strain (in/in)
σ
ε
- Point 2 : Yield Strength : a point where permanent
deformation occurs. ( If it is passed, the material will
no longer return to its original length.)
ε
σ
E =or

• Strain Hardening
- If the material is loaded again from Point 4, the
curve will follow back to Point 3 with the same
Elastic Modulus (slope).
- The material now has a higher yield strength of
Point 4.
- Raising the yield strength by permanently straining
the material is called Strain Hardening.

• Tensile Strength (Point 3)
- The largest value of stress on the diagram is called
Tensile Strength(TS) or Ultimate Tensile Strength
(UTS)
- It is the maximum stress which the material can
support without breaking.
• Fracture (Point 5)
- If the material is stretched beyond Point 3, the stress
decreases as necking and non-uniform deformation
occur.
- Fracture will finally occur at Point 5.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
The stress-strain curve for an aluminum alloy.

20
• Stress-strain
behavior
found for
some steels
with yield
point
phenomenon.

21
• After yielding, the stress necessary to
continue plastic deformation in metals
increases to a maximum point (M) and
then decreases to the eventual fracture
point (F).
• All deformation up to the maximum
stress is uniform throughout the tensile
sample.
• However, at max stress, a small
constriction or neck begins to form.
• Subsequent deformation will be
confined to this neck area.
• Fracture strength corresponds to the
stress at fracture.
Region between M and F:
• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are aligned and about to break.
Tensile Strength, TS

22
In an undeformed
thermoplastic polymer
tensile sample,
(a)the polymer chains
are randomly oriented.
(b)When a stress is
applied, a neck
develops as chains
become aligned locally.
The neck continues to
grow until the chains in
the entire gage length
have aligned.
(c)The strength of the
polymer is increased

23
• Tensile stress, σ: • Shear stress, τ:
Area, A
Ft
Ft
σ =
Ft
Ao
original area
before loading
Area, A
Ft
Ft
Fs
F
F
Fs
τ =
Fs
Ao
Stress has units: N/m2 or lb/in2
Engineering Stress

24
VMSE
http://www.wiley.com/college/callister/0470125373/vmse/strstr.htm
http://www.wiley.com/college/callister/0470125373/vmse/index.htm

Example 1
Tensile Testing of Aluminum Alloy
Convert the change in length data in the table to engineering
stress and strain and plot a stress-strain curve.

27
Engineering tensile strain, ε
Engineering
tensile
stress, σ
smaller %EL
(brittle if %EL<5%)
larger %EL
(ductile if
%EL>5%)
• Another ductility measure: 100% x
A
AA
AR
o
fo −
=
• Ductility may be expressed as either percent elongation (%
plastic strain at fracture) or percent reduction in area.
• %AR > %EL is possible if internal voids form in neck.
Lo Lf
Ao
Af
100% x
l
ll
EL
o
of −
=
Ductility, %EL
Ductility is a measure of the
plastic deformation that has
been sustained at fracture:
A material that
suffers very
little plastic
deformation is
brittle.

28
Toughness
Lower toughness: ceramics
Higher toughness: metals
Toughness is
the ability to
absorb
energy up to
fracture (energy
per unit volume of
material).
A “tough”
material has
strength and
ductility.
Approximated
by the area
under the
stress-strain
curve.

• Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve.
21
smaller toughness-
unreinforced
polymers
Engineering tensile strain, ε
Engineering
tensile
stress, σ
smaller toughness (ceramics)
larger toughness
(metals, PMCs)
Toughness

30
Linear Elastic Properties
Modulus of Elasticity, E:
(Young's modulus)
• Hooke's Law: σ = E ε
• Poisson's ratio:
metals: ν ~ 0.33
ceramics: ν ~0.25
polymers: ν ~0.40
σ
Linear-
elastic
1
E
ε
Units:
E: [GPa] or [psi]
ν: dimensionless
F
F
simple
tension
test
ν = εx/εy

31
Engineering Strain
Strain is dimensionless.

32
Axial (z) elongation (positive strain) and lateral (x and y)
contractions (negative strains) in response to an imposed
tensile stress.

True Stress and True Strain
 True stress The load divided by the actual cross-
sectional area of the specimen at that load.
 True strain The strain calculated using actual and not
original dimensions, given by εt ln(l/l0).
•The relation between the true stress-
true strain diagram and engineering
stress-engineering strain diagram.
•The curves are identical to the yield
point.

34
Stress-Strain Results for Steel Sample

Example 2:
Young’s Modulus - Aluminum Alloy
From the data in Example 1, calculate the modulus of
elasticity of the aluminum alloy.

• Use the modulus to determine the length after
deformation of a bar of initial length of 50 in.
• Assume that a level of stress of 30,000 psi is applied.
Example 2: Young’s Modulus - Aluminum Alloy - continued

37
0.2
8
0.6
1
Magnesium,
Aluminum
Platinum
Silver, Gold
Tantalum
Zinc, Ti
Steel, Ni
Molybdenum
Graphite
Si crystal
Glass-soda
Concrete
Si nitride
Al oxide
PC
Wood( grain)
AFRE( fibers)*
CFRE*
GFRE*
Glass fibers only
Carbon fibers only
Aramid fibers only
Epoxy only
0.4
0.8
2
4
6
10
20
40
60
80
100
200
600
800
1000
1200
400
Tin
Cu alloys
Tungsten
<100>
<111>
Si carbide
Diamond
PTFE
HDPE
LDPE
PP
Polyester
PS
PET
CFRE( fibers)*
GFRE( fibers)*
GFRE(|| fibers)*
AFRE(|| fibers)*
CFRE(|| fibers)*
Metals
Alloys
Graphite
Ceramics
Semicond
Polymers
Composites
/fibers
E(GPa)
Eceramics
> Emetals
>> Epolymers
109 Pa Composite data based on
reinforced epoxy with 60 vol%
of aligned carbon (CFRE),
aramid (AFRE), or glass (GFRE)
fibers.
Young’s Moduli: Comparison

Example 3: True Stress and True Strain
Calculation
Compare engineering stress and strain with true stress and
strain for the aluminum alloy in Example 1 at (a) the
maximum load. The diameter at maximum load is 0.497
in. and at fracture is 0.398 in.
Example 3 SOLUTION

39
THE SHEAR STRESS-STRAIN DIAGRAM
Like the tension test, this material when subjected to shear will
exhibit linear-elastic behavior and it will have a defined
proportional limit τpl. Also, strain hardening will occur until an
ultimate shear stress τu is reached. And finally, the material will
begin to lose its shear strength until it reaches a point where it
fractures, τf.

40
THE SHEAR STRESS-STRAIN DIAGRAM
For most engineering materials,
like the one just described, the
elastic behavior is linear, and so
Hooke's law for shear can be
written as
τ = G γ
Here G is called the shear modulus of
elasticity or the modulus of rigidity.
Furthermore, the three material constants, E, ν and G are actually
related by the equation
( )ν+
=
12
E
G
Provided E and G are known, the value of ν can be determined from this equation rather
than through experimental measurement.

mechanical properties

Recommandé

Recommandé

Contenu connexe

Tendances

Tendances (20)

En vedette

En vedette (20)

Similaire à mechanical properties

Similaire à mechanical properties (20)

Plus de Kum Visal

Plus de Kum Visal (20)

Dernier

Dernier (20)

mechanical properties