MECHANICAL PROPERTIES

OF MATERIALS

Manufacturing Processes, 1311

Dr Simin Nasseri
Southern Polytechnic State University
 MECHANICAL PROPERTIES
OF MATERIALS
1. Stress‑Strain Relationships (Slide 4)
2. Tensile Test (Slide 7)
3. Compression Test (Slide 36)

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Prof Simin Nasseri
 Mechanical Properties in
Design and Manufacturing
Mechanical properties determine a material’s
behavior when subjected to mechanical stresses
 Properties include elastic modulus, ductility,
hardness, and various measures of strength
 Dilemma: mechanical properties desirable to the
designer, such as high strength, usually make
manufacturing more difficult

The manufacturing engineer should

appreciate the design viewpoint
And the designer should be aware
Manufa
cturing
e n gi ne e
r
of the manufacturing viewpoint Desig
n er

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Prof Simin Nasseri
Strain- Stress Relationship
 Stress‑Strain Relationships
Three types of static stresses to which materials
can be subjected:

1. Tensile - tend to stretch the material

2. Compressive - tend to squeeze it
3. Shear - tend to cause adjacent portions of
material to slide against each other

 Stress‑strain curve - basic relationship that

describes mechanical properties for all three
types

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 Various Tests

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 Tensile Test
Most common test for
studying stress‑strain
relationship, especially
metals
In the test, a force pulls the
material, elongating it and
reducing its diameter

Figure 3.1 Tensile test: (a) tensile

force applied in (1) and (2) resulting
elongation of material

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 Tensile Test Specimen
ASTM (American
Society for Testing and
Materials) specifies
preparation of test
specimen

Figure 3.1 Tensile test:

(b) typical test specimen

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 Tensile Test Setup

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 Tensile Test Sequence
Figure 3.2 Typical progress of a tensile test:

If pieces are put

back together as
(1) (2) uniform (3) continued (4) necking (5) in (6), final length
beginning elongation and elongation, begins, load fracture can be measured
of test, no reduction of maximum load begins to
load cross‑sectional reached decrease
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 Tensile Test

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 Different types of stress-strain graphs

Engineering  important in design

Stress-strain curves
True  important in manufacturing

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 Engineering Stress
Defined as force divided by original area:

F
e 
Ao
where
e = engineering stress (MPa) or Pa or psi,
F = applied force (N) or lb, and
Ao = original area of test specimen (mm2 or m2 or in2)
(Remember: N/ m2 = Pa, N/ mm2 = MPa,
lb/ in2 = psi, klb/ in2 = kips/ in2)

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 Engineering Strain
Defined at any point in the test as

L  Lo
e
Lo

where
e = engineering strain (it has no unit);
L = length at any point during elongation; and
Lo = original gage length

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 Typical Engineering Stress-Strain Plot

Figure 3.3 Typical engineering stress‑strain

plot in a tensile test of a metal.

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 Two Regions of Stress‑Strain Curve
The two regions indicate two distinct forms of
behavior:

1. Elastic region – prior to yielding of the

material
2. Plastic region – after yielding of the material

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 Elastic Region in Stress‑Strain Curve
 Relationship between stress and strain is linear
 Material returns to its original length when
stress is removed

Hooke's Law: e = E e

where E = modulus of elasticity, e = stress, e=strain

 E is a measure of the inherent stiffness of a
material
 Its value differs for different materials

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 Yield Point in Stress‑Strain Curve
 As stress increases, a point in the linear
relationship is finally reached when the
material begins to yield
 Yield point Y can be identified by the
change in slope at the upper end of the
linear region
 Y = a strength property
 Other names for yield point = yield
strength, yield stress, and elastic limit

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 Plastic Region in Stress‑Strain Curve
 Yield point marks the beginning of plastic
deformation
 The stress-strain relationship is no longer
guided by Hooke's Law (non-linear relationship)
 As load is increased beyond Y, elongation
proceeds at a much faster rate than before,
causing the slope of the curve to change
dramatically

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 Tensile Strength in Stress‑Strain Curve
 Elongation is accompanied by a uniform
reduction in cross‑sectional area, consistent
with maintaining constant volume
 Finally, the applied load F reaches a maximum
value, and engineering stress at this point is
called the tensile strength TS (or ultimate
tensile strength)

Fmax
TS =
Ao

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 Ductility in Tensile Test
Ability of a material to plastically strain without
fracture
 Ductility measure = elongation EL
Lf  Lo
EL 
Lo

where EL = elongation (expresses as a percent);

Lf = specimen length at fracture; and
Lo = original specimen length

Lf is measured as the distance between gage marks after

two pieces of specimen are put back together

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 Area reduction
defined as

expressed as a percent, where:

Af = area of the cross section at the point of fracture, mm2 or in2

A0  Af
A0 = original area

Therefore, ductility is measured by elongation (EL) or area reduction (AR).

AR 
A0

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 Lets compare!

Which material has the highest modulus

of elasticity?

Which material has the highest tensile

strength?

Which material has the highest

elongational rate?

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 Lets compare!
LOW - - - - - - - - - - - - - - - - - - - - - - - - > HIGH
Modulus of elasticity (measure of stiffness):
Polyethylene (0.03x106 psi), Nylon, Lead (3x106 psi),
Magnesium, AL & Glass, Copper, Cast Iron (20x106 psi),
Iron & Steel (30x106 psi), Alumina (50x106 psi), Tungsten,
Diamond (150x106 psi)

stress has lower E

strain
For a given force, the one with lower E, deforms more in
comparison with the one with higher E (which is stiffer).

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 Lets compare!
LOW - - - - - - - - - - - - - - - - - - - - - - - - > HIGH
Tensile Strength:
AL (10,000psi), Copper, Cast Iron (40,000psi), Mg, Low C Steel,
High C Steel(90,000psi), Stainless steel (95,000psi), Ti alloy

Elongation:
Metals: Cast Iron (0.6%), Mg, high C steel (10%), Ti, low C steel
(30%), Nickel, Stainless steel (55%).
Ceramics: 0%
Polymers: thermosetting polymer (1%), Thermoplastic polymer (100%)

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 True Stress
Stress value obtained by dividing the applied
load by the instantaneous area
F

A

In elastic
region they
are almost
the same

where
 = true stress;
F = force; and
A = actual (instantaneous) area resisting the load
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 True Strain or Hencky strain
Provides a more realistic assessment of
"instantaneous" elongation per unit length
L
dL L
   d    ln L  ln L0  ln
Lo
L Lo
L
  ln
Lo

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 True Stress-Strain Curve
Figure 3.4 ‑ True stress‑strain curve for the previous engineering
stress‑strain plot in Figure 3.3.

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 Strain Hardening in Stress-Strain Curve
 Note that true stress increases continuously in
the plastic region until necking
 In the engineering stress‑strain curve, the
significance of this was lost because stress was
based on an incorrect area value

 It means that the metal is becoming stronger

as strain increases
 This is the property called strain hardening

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 True stress versus Engineering Stress
True strain can be related to the
corresponding engineering strain   ln  1  e 
by:

True stress and engineering

stress can be related by the
 t   e  1 e
expression:

True stress versus true strain in

plastic region:
K is the strength coefficient and is
 t  K n Flow curve

in MPa. n is the strain hardening

exponent.

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 Flow Curve
True stress-strain curve a straight line in a log-log plot:

  K n
ln   ln  K  n 
ln   ln K  ln   n 
ln   ln K  n ln 
this is similar to: if  =1, then
Y  b  nX  K

Figure 3.5 True stress‑strain curve plotted

on log‑log scale.

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 Lets compare!
Engineering Stress & strain True Stress & strain
e 
F F
Ao Elastic region 
e = E e  t  E A
L  Lo L
dL L
e    ln
Lo  t   e  1 e Lo L Lo

TS =
Fmax   ln  1  e  Fmax
Ao TS =
A

Plastic region

 t  K n

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 Lets compare!

Toughness:
area under
strain-stress
graph
(combination of
ductility and
strength)

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Categories of Stress-Strain Relationship

 Perfectly elastic
 Elastic and perfectly plastic
 Elastic and strain hardening

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 Perfectly Elastic

 Behavior is defined
completely by modulus of
elasticity E

 Fractures rather than

yielding to plastic flow

 Brittle materials: ceramics,

many cast irons, and
thermosetting polymers
Figure 3.6 Categories of
stress‑strain relationship:
(a) perfectly elastic.

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 Elastic and Perfectly Plastic
 Stiffness defined by E
 K
 Once Y reached, deforms
plastically at same stress
level
 Flow curve: K = Y, n = 0
 Metals behave like this
when heated to
sufficiently high
temperatures (above Figure 3.6 Categories of
recrystallization) stress‑strain relationship:
 One example is Lead (b) elastic and perfectly plastic.

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 Elastic and Strain Hardening
 Hooke's Law in elastic   K n
region, yields at Y
 Flow curve: K > Y, n > 0
 Most ductile metals
behave this way when
cold worked

Figure 3.6 Categories of

stress‑strain relationship:
(c) elastic and strain hardening.

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Compression test
 Compression Test

Applies a load that

squeezes the ends of a
cylindrical specimen
between two platens

Figure 3.7 Compression test:

(a) compression force applied to
test piece in (1) and (2) resulting
change in height.
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 Compression Test Setup

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 Engineering Stress in Compression
As the specimen is compressed, its height is
reduced and cross‑sectional area is
increased

e = - F
Ao

where
Ao = original area of the specimen

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 Engineering Strain in Compression
Engineering strain is defined

h  ho
e
ho

Since height is reduced during compression, value

of e is negative
(the negative sign is usually ignored when
expressing compression strain)

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 Stress-Strain Curve in Compression
Shape of plastic region
is different from tensile
test because cross
section increases

Calculated value of
engineering stress is higher
In comparison to the true
stress

Figure 3.8 Typical engineering

stress‑strain curve for a
compression test.

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 Tensile Test vs. Compression Test
 Although differences exist between engineering
stress‑strain curves in tension and
compression, the true stress‑strain
relationships are nearly identical
 Since tensile test results are more common,
flow curve values (K and n) from tensile test
data can be applied to compression operations
 When using tensile K and n data for
compression, ignore necking, which is a
phenomenon peculiar to straining induced by
tensile stresses
 Barreling and edge fracture happen

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