Module 1 Physical and Mechanical Properties of Metals

bulgefetaUrban and Civil

Nov 29, 2013 (3 years and 6 months ago)

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Physical and Mechanical Properties of Metals

Engineering
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Module 1


Physical and Mechanical
Properties of Metals



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Physical and Mechanical Properties of Metals

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1.1

Physical Properties


1.1.0

Introduction


The evaluation of materials for particular engineering applications and ultimately the
selection of materials will and should include the physical prope
rties of materials.
Physical properties evaluation should include density and weight, color, electrical
properties such as electrical conductivity, chemical properties such as corrosion
resistance, thermal properties such as thermal expansion coefficients
, melting point,
magnetic properties, and optical properties


1.1.1 Exploration: Physical Properties of materials



Student Exercise: Physical properties of materials


Specimens:

1.

Block of wood

2.

Aluminum Block or plate

3.

Steel or stainless steel plate

4.

Block or

plate of plastic


Apparatus:

1.

Magnet

2.

Mechanical Balance

3.

Slotted mass set

4.

Dial calipers

5.

1 liter beaker

6.

Water

7.

Flash Light


Procedure:


Select two specimens of the ones available and define and quantify two physical
properties for each specimen.


Data:


Speci
men No.1:


Material:


Property No. 1:




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Property No. 2:







Specimen No.2:


Material:


Property No. 1:






Property No. 2:






Questions:


1.

List several potential applications for the material that you just studied and
describe the value of those proper
ties in this application.








1.1.2 Density


1.1.2.1 Dialog: Density


Density of materials is defined as mass per unit volume. Thus the equation for
density is:


V
m





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Where:

3
3
3
3
3
,
,
,
,
/
,
/
,
/
,
in
m
volume
V
slug
kg
mass
m
ft
lbs
in
slug
m
kg
density






Table 1.1.2
-
1 Densities of some co
mmon materials


Material

Density,
3
/
m
kg

Density,
3
/
ft
lbs

Aluminum

2700

169

Brass

8520

532

Ceramics

2300
-
5500

144
-
343

Copper

8970

560

Cast Iron

7190

449

Glass

2400
-
2700

150
-
169

Lead

11350

710

Nickel

8910

556

Plasti
c

900
-
2000

56
-
125

Titanium

4510

282

Wood
-
Pine

544

34

Wood
-
Oak

800

50



1.1.2.2 Exploration: Density



Student Exercise: Density of materials


Specimens:

1.

Block of wood

2.

Aluminum Block or plate

3.

Steel or stainless steel plate

4.

Block or plate of plastic


App
aratus:

1.

Mechanical Balance

2.

Slotted mass set

3.

Dial calipers


Procedure:

1.

Using the mechanical balance and the mass set determine the mass of each
of the four (4) specimens listed above.


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2.

Using the dial calipers determine the dimensions of each of the four (4)
specimens and then calculate the volume of each.

3.

Using the data from steps 1 and 2 calculate the density of each of the
specimens.


Data:


Specimen

Mass

Dimensions

Volume

Density

Wood





Aluminum





Steel





Plastic






Questions:

1.

How did your cal
culated densities compare to the theoretical densities that
were given in table 1.1.2
-
1?









2.

Is the density of steel the same on earth as it is on the moon? Why or Why
not?







1.1.3 Thermal Properties of Materials


1.1.3.1 Exploration: Thermal Condu
ctivity in various types of cups/glasses


Student Exercise: Physical properties of materials


Specimens:

1.

Glass cup

2.

Ceramic cup

3.

Styrofoam cup

4.

Metal cup

5.

Plastic


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Apparatus:

1.

Coffee Maker

2.

Water

3.

Thermometer


Procedure:

1.

Fill coffee maker with plain water at lea
st five cups per lab group

2.

Heat water in coffee maker

3.

Using thermometer measure the temperature of the water Pour water in each
of the five (5) types of cups

4.

After 1 minute measure the temperature of the water in each of the cups

5.

Repeat step 4 after 2 minu
tes, 3 minutes, 4 minutes and 5 minutes.

6.

Plot the temperature in each cup as a funtion of time


Questions:

1.

Rank the cups in terms of the best to worst insulators









2.

For a product application of a coffee cup, which material would be the best
material i
n based on our exploration?








3.

Name an application where metal would be the preferred material when heat
transfer is one of the property requirements.





1.1.3.2 Dialog: Thermal Conductivity


Thermal conductivity is the transfer of heat through a mate
rial. Different materials
will transfer heat through them at different rates depending upon the type of material

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the molecular and/or the grain structure, the density. There are many factors in a
materials ability to transfer heat. Some materials will b
e chosen for design
applications where heat transfer is wanted, such as boiler tubes. Other design
applications will require materials that do not transfer heat. An example of this
would be exterior building material for a house. When two materials at
different
temperatures are in contact, heat will transfer from the higher temperature material
to the lower temperature material until equilibrium is reached. Depending upon the
mass of the two objects the equilibrium temperature will be at a temperature
between the temperatures of the two objects. The thermal resistance of that
material to heat transfer controls the rate of heat transfer or conductivity. Home
insulation materials are purchased by “R
-
value” or thermal resistance values.


In the example o
f the Styrofoam cup from the previous exploration, air is the main
insulating material. Styrofoam traps the air particles and prevents or at least limits
the molecular motion of the air. Air is a great insulator if it does not move.
Fiberglass insulatio
n prevents air motion better than the average coffee cup
therefore it is a better insulator.


1.1.4 Electrical and Magnetic Properties of Materials


1.1.4.1 Exploration: Electrical and Magnetic Properties of Various Materials


Student Exercise: Physical pr
operties of materials


Specimens:

1.

Block of wood

2.

Aluminum Block or plate

3.

304 stainless steel plate

4.

1020 mild steel

5.

Cast Iron

6.

Block or plate of plastic


Apparatus:

1.

Magnet


Procedure:

1.

Place the 1
st

specimen flat on a table

2.

Slowly move the magnet toward the sp
ecimen

3.

Observe the reaction of the material to the magnet

4.

Repeat with the opposite end of the magnet

5.

Repeat for each specimen





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Data:


Specimen

Reaction to 1
st

end of
magnet

Reaction to 2nd end of
magnet

1. Wood



2. Aluminum



3. 304 stainless ste
el



4. 1020 mild steel



5. Cast Iron



6. Plastic




Questions:


1.

Did all ferrous materials react the same? Explain







2.

Which materials did the magnet not affect?







1.1.4.2 Dialog: Electrical and Magnetic Properties of Materials


Different ma
terials are either magnetic or not. Ferrous materials are generally
magnetic but at elevated temperatures they are normally not magnet. Non
-
ferrous
materials are normally not magnetic. Magnetic properties of materials are related to
the orbit and spin o
f electrons in the atomic structure of the material. Different
materials just react differently to this magnetic field. Therefore some materials are
very magnetic and other materials are weaker or non
-
magnetic.


Electrical conductivity is a measure of th
e flow of electricity through a material.
Electrical conductivity is similar to thermal conductivity, which was the flow of heat
through a material. Materials, which have high conductivity, are therefore
considered good conductors and materials with low
conductivity are considered
insulators. Steel or copper materials are examples of a good conductor and
ceramics a good example of an insulator.



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1.2 Mechanical Properties of Metals


1.2.0

Introduction


One of the enduring requirements of engineers is the proper

selection of materials
for product applications. In the selection of parts for the aeronautical industry a
physical property such as density may be of prime importance due to weight
restrictions. In structural applications such bridge design the mechani
cal properties
of tensile strength and ductility may determine actual material selection. Subjecting
a material or specimen to a load or force and observing its response most commonly
determine mechanical properties.


1.2.1

Elastic Testing of Engineering Materi
als


1.2.1.1. Exploration: Hooke’s Law


English scientist Robert Hooke (1635
-
1703) gave a lecture
Of Spring

in 1678 in
which he describes his general law of elasticity. Hooke’s discoveries were a result
of his studies of the balance springs in clocks. In

this exploration we will investigate
the relationship between force and the resulting displacement in springs.


Student Exercise: Hooke’s Law Exercise


Specimens: At least three different springs having different spring constants


Apparatus:

1.

Pasco Model

No. ME
-
9827 Hooke’s Law Apparatus

2.

Pasco mass and hanger set or slotted mass set

3.

Mechanical Balance

4.

Graph paper or computer with
Microsoft Excel


Procedure:

1.

Select one of the springs and hang spring from notch on the support
arm of the Pasco Hooke’s law a
pparatus.

2.

Connect the Stretch or displacement indicator, which is a florescent
disc, to the bottom loop of your spring.

3.

Align the transparent scale plate to zero value using the stretch
indicator.

4.

If the mass of the hanger is not known, weigh and record th
e mass
hanger using the mechanical balance.

5.

Connect the mass hanger to the clamp on the bottom of the stretch
indicator.


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6.

Pick even increments of mass from the mass set for each spring. Use
different increments depending upon the spring constants that are
used.

7.

Place the first mass on the mass hanger and record the displacement
of the spring. Don’t forget to add the mass of the mass hanger to the
mass.

8.

Repeat this step for at least four increments of mass.

9.

Repeat the last
three steps for each spring.

10.

Using

Microsoft

Excel enter your data points and plot the force on the
Y
-
axis and the displacement on the x
-
axis.

11.

Using y= mx+b determine the equation for the line for each of the
springs. Use the appropriate units in your graph and your equation.

12.

Using the fo
llowing equation determine the spring constant for each
spring.


)
(
o
X
X
K
F







Where:

F = force, Newton’s

K = spring constant, N/m



o
X
X
Change in length of the spring


0
X
Reference point for zero force app
lication

13.

Compare your calculated spring constant against the known spring
constant.



Data:


Spring No. 1:


Spring Constant (if known): ____________________


Mass
-

gm

Force
-

Newtons

Displacement
-

cm





















Spring No. 2:


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Spring Consta
nt (if known): ____________________


Mass
-

gm

Force
-

Newtons

Displacement
-

cm

















Spring No. 3:


Spring Constant (if known): ____________________


Mass
-

gm

Force
-

Newtons

Displacement
-

cm


















Questions: Hooke’s L
aw Exercise


1.

How did the calculated spring constants compare to the factory or given
constants?



2.

How does force vary with displacement in the displacement of a spring?


__________________________________________________________________





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1.2.1.2 Dialog:

Stress and Strain


Stress is defined as the load on a specimen divided by the cross sectional area
through which the force acts. Engineering stress uses the original cross sectional
area of the material. True stress is defined as the force divided by th
e actual cross
sectional area as the material is deformed by the stress. In our work we will use
engineering stress that is given by the following formula:


A
P
S





Where:

S = stress in lbs/
2
in

or N/
2
m

P = Force in lbs or N

A = Cross sectional area in
2
in
or
2
m


The material subjected to the stress as defined in the previous equation will elongate
due to the application of this load. This phenomenon is calle
d strain, which is the
measure of the change in length per unit length. The formula for strain is as follows:


o
o
L
L
L
e




Where:


e
Unit strain, in/in or m/m


e
0
L
L


= Change in lengt
h, in


o
L
Original length, in


Type of Engineering Stress:


Tension Testing:

Tension or tensile testing of materials represents one of the most common forms of
the testing of materials. Many mechanical properties may be determined from
a
tensile test. In this test, a specimen is loaded usually to failure by applying a tensile
load uniaxially along its longest axis.


Compression Testing:

This type of test is very similar to tensile testing except that a compressive force is
applied to

the specimen. In terms of displacement the specimen decreases in size
with increasing levels of compressive stress.




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Shear Testing:

Shear testing involves the application of forces acting parallel to a cross sectional
area but opposite in direction,
which produce a sliding in the specimen.

Some typical parts subjected to shear forces include bolts, rivets, pins, and shafts.

Torsion Testing:

Forces that tend to produce a twisting in the specimen. These forces tend to turn
one end about the longitudi
nal axis while the other end of the specimen is held
constant or is turned in the opposite direction. Typical parts that are subjected to
torsion include shafts, axles, pulleys and gears.




1.2.1.3 Exploration: Calculation
of Stress and Strain


Student Exercise: Stress and Strain Calculations


A mountain climber weighs 150
-
lb has the choice of two ropes, one ¼” and one ½”
rope. Calculate the stress in each rope.



Calculation of stress in ¼” rope:







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Calculation of str
ess in ½” rope:









A brass bar 2
-
ft in length is subjected to a tensile force. It elongates a total of .154
in. Calculate the strain in the bar.


Calculation of the strain in the brass bar:








A steel bar 3.5
-
m in length is subjected to a tensil
e load that causes a total
elongation is the bar of .65
-
mm. Determine the strain in the bar.


Calculation of the strain in the steel bar:











1.2.1.4 Dialog: Elasticity


Elasticity is a property of materials that allows a material to return to its
original size
and shape after a load is removed. While loaded the material will experience
elongation but after removal of the load there is no measurable elongation. A
material can be described as performing “elastically” under these conditions.
However
, as the load is increased there is a point where the materials no longer

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perform elastically and the material does not return to its original size and shape.

This area will be studied in later sections.


Robert Hooke in the seventeenth century is credit
ed with the discovery that stress is
proportional to strain. This is known as Hooke’s Law and can be expressed as:



e
S



1.2.1.5 Exploration: Tensile Test of wire


Student Exercise: Ten
sile test of wire


Specimens:

1.

Soft Copper Bare Wire

2.

Piano Wire

3.

Soft Steel wire

4.

Aluminum wire



Apparatus:

1.

Tensile Testing Apparatus

2.

Mass Hanger (2)


50g

3.

Slotted weight set

4.

Hooked Mass set

5.

Dial Caliper

6.

Tape measure

7.

Universal clamp with holder

8.

Table clamp

9.

Gage holding rod

10.

Swivel Post snug

11.

Dial Indicator with slot back

12.

Small level




Procedure:


Set up the tensile tester with a mass hanger placed on the specimen side of the load
lever and add enough slotted weights to balance the load lever. See figure
1.2.1.5
-
1 for to see the tensile tester as shown with an aluminum wire shown on the
tester.


Mount the wire on the tensile tester. Wind the wire around the bolt at the bottom
mounting plate and tighten the wing nut. Pull the wire around the upper mounti
ng

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plate and tighten allowing for the load lever to remain nearly level. A small level may
aid in this process.


Place the 50g
-
mass hanger in the outer mass multiplier position (5
th

position) and
place a total of 125
-
gm on the load lever to pre
-
load the
wire. This load should be
sufficient to straighten the wire, cable or fishing wire.


Attach table clamp to table and mount the gage holding rod and the swivel post snug
on the rod. Attach the dial indicator to the swivel post snug. Set the gage clamp
ar
rangement over the mounting plate for the cable and zero the gage.


Apply the load to the wire in even increments and record the displacement in the
wire from dial indicator. Record each load and each increment of displacement.
Remember to multiply the a
ctual load by the load multiplier. If 500
-
gm is place in the
1
st

position it is just 500
-
gm if 500
-
gm is placed in the 2
nd

position it would be 500 x 2
or 1000
-
gm, etc. Apply at least 5 increments of load to each wire.

Plot the stress versus the strain u
sing strain on the x
-
axis and stress on the y
-
axis.
Determine the slope of the line that is produced. Convert values to common units.
Example if displacements are in inches and mass in grams, convert mass to units of
force in pounds or Newton’s; or conv
ert displacement and length to meters.



Figure 1.2.1.5
-
1: Tensile Testing Apparatus


Data:



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Diameter:


Initial length of the wire:


Preload:


Area of wire:


Mass

Load

Displacement

Stress

Strain












































1.2.1.6 Dialog: Young’s Modulus and Yield Point


Robert Hooke stated that stress was proportional to strain but it wasn’t until 1802
that the English physicist, Thomas Young evaluated the constant of proportionality.
This constant

is known as either
Young’s modulus

or the
modulus of elasticity
. The
modulus of elasticity is given by the symbol E. By modifying Hooke’s law we have
the following equation:


Ee
S


Where:

S = stress, lbs/in
2
or N/m
2

E = modulus of elasticity, lbs/in or N/m
2

e

= Unit strain, in/in or m/m


As a practical application the modulus of elasticity could be called the modulus of
stiffness.


The yield strength
is the maximum load that the material can hold and still exhibit
elastic characteristics. Beyond the yield point the material will experience
permanent deformation and not return to its original size or shape this is called
plastic deformation.



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The mod
ulus elasticity only applies when the material behaves elastically.
Therefore, the stress must be below the yield strength to measure or determine the
modulus of elasticity of a material.


The modulus of elasticity and yield strength values for some commo
n engineering
materials:


Material

Young’s
jodu汵猬=
xNM
9
=
丯k
2
=
v楥汤=
p瑲tng瑨Ⱐ
xNM
6
=
丯k
2
=
Young’s
jodu汵猬=
xNM
6
=
p獩
=
v楥汤=
p瑲tng瑨Ⱐ
歳k
=
A汵l楮um
=

=
㈴2
=

=

=
B牡獳
=
㄰N
=
㄰N
=

=

=
䍯Cper
=
ㄲN
=
㈴2
=

=

=
p瑥e氬⁈l
=
㈰2
=
㈴2
=

=

=
p瑥e氬⁃l
=
㈰2
=
㐴Q
=

=

=
䍡獴⁉牯r
=
㄰N
=
=

=
=
tood
=
QM
捯mpF
=
=
N⸷
=
R⸸
捯mpF
=
=
1.2.1.7 Exploration: Modulus of elasticity and yield strength


Using the data from the previous ex
ploration (1.2.3) determine the following:


For each material:


Did the stress exceed the yield strength? ____________________________


Compare the value for Young’s Modulus for each material tested and calculate the
percent error:


Material

Theoretical
Yo
ung’s Modulus
=
Calculated Young’s
jodu汵l
=
me牣敮t=
=
b牲or
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
1.2.1.8 Application: Modulus of Elasticity


OBJECTIVE: To study the practical applications of the property: modulus of
elasticity.


SPECIMENS:

1.

Vega
-
Modulus of Elasticity Kit:


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2.

1 x
1 x 13 aluminum bar

3.

1 x 1 x 13 heat treated carbon steel

4.

1 x 1 x 13 cold rolled carbon steel

5.

Deflection gaging block


APPARATUS:

1.

Universal testing machine
-

Vega, 20k machine

2.

Transverse loading fixture


REFERENCES:


1.

Manufacturing Processes,
H. V. Johnson,

Bennett & McKnight, 2nd Ed.,
1984,Unit 14, pp. 80
-
81.

2.

Material and Processes in Manufacturing
; Degarmo, Black and Kohser,
Prentice

Hall, Ch. 2, pp. 38
-
45, 7
th

Ed., 1997.

3.

Materials Testing Laboratory Manual,
Vega Enterprises Inc., 1975, Seventh
Printing,
pp. 34
-
37.

4.

Modern Materials and Manufacturing Processes
, R. G. Bruce, M. M. Tomovic,
J. E. Neeley, and R. R. Kibbe, Prentice Hall, 2
nd

Ed., 1987, pp 55
-
60.


BACKGROUND INFORMATION:


Another important mechanical property to study is the modulus of elasticit
y. From a
tensile test, if we plot the stress versus strain curve we find a straight
-
line portion of
the curve at lower values of stress and strain. This linear portion of the curve
represents the elastic portion of the materials response to a mechanical

load. The
material in this linear portion obeys
Hook’s law
, which states that stress is
proportional to strain. The proportionality constant is known as
Young’s Modulus

or
the Modulus of Elasticity.


The practical application of the modulus of elastici
ty is that for similar designs with
different materials under identical loading and cross sectional area but having
different values of modulus of elasticity, the materials will demonstrate different
stiffness. Stiffer materials will deflect less than mat
erials having lower values of
stiffness. The modulus of elasticity values will give a relative measure of stiffness for
different engineering materials. Comparing the Modulus of elasticity for steel and
aluminum, the steel having a modulus of 30,000,000
psi and aluminum 10,000,000
psi, these relative values and their implied stiffness, would indicate that the
aluminum would defect approximately three times that of the steel for the same
mechanical loading.



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The values for the modulus of elasticity remain
nearly constant regardless of the
processing methods or heat
-
treating methods. Carbon content and alloying
methods for steel have negligible effects on the modulus of elasticity values for steel.


This laboratory activity is designed to demonstrate the c
orrelation between text book
values for the modulus of elasticity and the practical effects of stiffness.


Procedure:


Attach the center
-
loading cylinder under the upper platen in the compression section
of the Vega Universal testing machine. On the lower

platen mount the transverse
bar and place the support cylinders on 12
-
inch centers.


Place one the test bars on the lower support cylinders and position the gage block
under the center of the bar. Slowly apply the load until the bar defects just enough
t
o contact the gage block. As you apply the load slowly move this gage block until
interference is detected. Record the load at the point of interference.


Caution: Do not load the bar without the gage block in position
.


Rotate the bar 180 degrees and r
epeat the procedure. Average the values and
record below.






Material

1
st

Side

2
nd

Side

Average

1 x 1 x 13 aluminum bar




1 x 1 x 13 heat treated
carbon steel




1 x 1 x 13 cold rolled
carbon steel









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Figure 1.2.1.8
-
1 Vega UTM with Modulus Demonstration kit










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1.2.2

Tensile Testing of Engineering Materials


1.2.2.1 Exploration: Tensile Test Fishing Line


Student Exercise: Tensile test of Fishing Line


Specimens:

1.

6
-
lb Fishing Line


Apparat
us:

1.

Tensile Testing Apparatus

2.

Mass Hanger (2)


50g

3.

Slotted weight set

4.

Hooked Mass set

5.

Dial Caliper

6.

Steel Rule

7.

Small level


Procedure:


Set up the tensile tester with a mass hanger placed on the specimen side of the load
lever and add enough slotted weigh
ts to balance the load lever. This set
-
up is
similar to exploration 1.2.1..


Mount the fishing line on the tensile tester. Wind the wire around the bolt at the
bottom mounting plate and tighten the wing nut. Pull the wire around the upper
mounting plat
e and tighten allowing for the load lever to remain nearly level. A small
level may aid in this process.



Do not

attach and or use the table clamp and dial indicator for this set
-
up. The
fishing line will be tested to failure and could result in damage

to the dial indicator.


Apply the load to the wire up to the amount specified by the fishing line weight limit.
Convert values to common units so that the weight will equate to the test limit of the
fishing line. Continue to load the fishing line until

failure and record the load.


Data:


Diameter:


Initial length of the fishing line:



-

23

-
23



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
23


Preload:


Area of fishing wire:


Load required for failure:


Questions:

1.

Did the fishing line meet the specified line limit?





2.

What percentage was the failure load over
the test limit of the fishing line?








1.2.2.2 Dialog: Universal Testing Machine


A universal testing machine is often used in the testing of materials for their
mechanical properties. This machine can apply tensile and compressive loads used
to meas
ure tensile, compressive, shear and flexure strengths, modulus of elasticity
and hardness. See figure 1.2.2.2
-
1 for a picture of the Baldwin & Swasey Universal
testing machine and figure 1.2.2.2
-
2 or the Vega Universal Testing.


In early mechanical testin
g the load was applied by a complicated method of weights
and levers. The weight and lever system relied upon a shifting of weights taking
advantage of the mechanical advantage. In modern universal testing machines the
load is applied by hydraulic pressur
e, or by a mechanical screw. Screw operated
machines may have between one and four screws driving a gear train to apply the
load to the machine. Hydraulic machines utilize a single hydraulic ram to apply
loads between a few pounds to several million poun
ds of force. The hydraulic force
may be produced by a hand operated pump or an electric hydraulic pump.



-

24

-
24



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
24



Figure 1.2.2.2
-
1: Baldwin & Swasey Universal Testing Machine


Simple load measurement is done by the use a bourdon tu
be, which is linked to a
rack and pinion, which directly indicates load through its pointer. A more accurate
method of reading the load is done by use of a load cell. This load cell is a hydraulic
chamber, which relates the hydraulic pressure on the cell

to the force application to
a specimen.



-

25

-
25



Physical and Mechanical Properties of Metals

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Materials


Page
25



Figure 1.2.2.2
-
2: Vega Universal Testing Machine


Comparison of Brittle and Ductile Materials:


Ductility is a measure of a material's ability to deform plastically without fracture
.
Ductility is commonly evaluated by percent elongation and/or percent area reduction.
Ductility in an engineering material permits the twisting, bending of materials into
various shapes and sizes without fracturing.


Brittleness is essentially the opp
osite of ductility, it allows for little or no bending or
deformation without fracture. Brittle materials fracture at very small values of strain.
Brittleness should not be confused with strength. A brittle material may exhibit large
values of compressi
ve strength but have little or no ductility. Brittle materials fracture
with values of strain that are 5% or less.


Brittle materials fracture with little or no warning however, ductile materials deform
greatly prior to fracture. Brittle materials fractur
e abruptly and catastrophically. Many
engineering materials are subjected to some type of shock or impact loading
therefore, brittle materials are not often desired for these types of applications.


-

26

-
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Physical and Mechanical Properties of Metals

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26




Some typical ductile materials are structural steel, bra
ss aluminum.

Glass, concrete, cast iron, cast aluminum and hardened steel are some examples of
brittle materials.


1.2.2.3 Application: Tensile testing of Ductile Materials


OBJECTIVE: To study and observe the common techniques of measuring the
Ulti
mate Tensile strength and Ductility.


SPECIMENS:

1.

Steel, hot rolled

2.

Steel, cold rolled

3.

Aluminum

4.

Brass
-
Free Cutting


APPARATUS:

1.

Universal testing machine
-

Vega, 20k machine

2.

Dial Calipers

3.

Gage marking device


REFERENCES:


1.

Manufacturing Processes,
H. V. John
son, Bennett & McKnight, 2nd Ed.,
1984,Unit 14, pp. 80
-
81.

2.

Material and Processes in Manufacturing
; Degarmo, Black and Kohser,
Prentice

3.

Hall, Ch. 2, pp. 38
-
45, 7
th

Ed., 1997.

4.

Materials Testing Laboratory Manual
, Kazanas and Wallace, Bennett, 1st Ed.,
1974
, Laboratory Activity Number 1, pp. 8
-
11.

5.

Materials Testing Laboratory Manual,
Vega Enterprises Inc., 1975, Seventh
Printing, pp. 19
-
24.

6.

Modern Materials and Manufacturing Processes
, R. G. Bruce, M. M. Tomovic,
J. E. Neeley, and R. R. Kibbe, Prentice Hall,

2
nd

Ed., 1987, pp 55
-
60.


BACKGROUND INFORMATION:


A tensile test is a very common destructive test performed on engineering materials.
The tensile tester is most commonly a universal testing machine, which is used to
pull the specimen in tension until i
t breaks. A tensile test is performed to determine
the following mechanical properties:




Ultimate Tensile Strength



Modulus of Elasticity


-

27

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Physical and Mechanical Properties of Metals

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27




Ductility



Proportional Limit



Yield Strength



Fracture Strength


This laboratory exercise is concerned with the determin
ation of ductility and ultimate
tensile strength.


Ductility is a measure of a material's ability to deform plastically without fracture.
The two most common methods of Ductility measurement are:




a. Percent elongation is de
termined by setting a gage length (usually 2") on
a specimen prior to loading and after tensile failure measuring the final
distance of these gage marks. Then a percent elongation value is
calculated.



100
*
(%)
ngth
OriginalLe
ngth
OriginalLe
h
FinalLengt
Elongation







b. Percent area reduction is calculated by putting the two ends of the
fractured specimen together and measuring the diameter at the break.
Calculate the area at the break at this point of fracture. This final area is
then compared with
the original area of the specimen and a percent
reduction in area is then calculated.




100
*
Re
%
ea
OriginalAr
FinalArea
ea
OriginalAr
rea
ductionInA






Ultimate Tensile Strength or tensile strength is the maximum tensile load divided by
the original specimen cross sectional area. It is
one of the most important properties
determined by tensile testing.




)
(
.)
(
)
(
2
in
ea
OriginalAr
lbs
d
MaximumLoa
psi
gth
nsileStren
UltimateTe




PROCEDURE:


Measure and record the original diameter of the specimen(s) and record on your
data sheet. Calculate the original cross
-
sectional area.



-

28

-
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Physical and Mechanical Properties of Metals

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28


Using

the center punch, carefully mark the gage length on the specimen. Place the
specimen in the anvil of the center punch making sure that the specimen is
centered. Strike the arm lightly to ensure that the marks do not go too deep.


Select the proper grips

for specimens and the Universal Testing Machine.
Specimens must be threaded into the grips at least two diameters

(for the 3/8"
tensile specimens used on the Vega Universal Testing machine this would be .3/4")
to prevent thread stripping. Caution must be

exercised that the bolts for the threaded
grips are properly threaded into the grips. See Figure below for the threaded tensile
specimen equipment setup.


Apply the load slowly. Observe the specimen, record the maximum load and
continue loading until fai
lure is reached. Record the breaking load, which must be
observed from the load dial at the instant of fracture.


Measure and record the final gage length and the diameter of the specimen at the
failure point. Observe and record the type of failure in t
he specimen.



Steel




CR

HR

Aluminum

Brass

Original Diameter, in.





Original Area, sq. in.





Maximum Load, lbs.





Ultimate Tensile Strength, psi





Breaking Load, lbs





Original Gage Length, in.





Final Gage Length, in.





Percent El
ongation, %





Break Diameter, in.





Area at Break, sq. in.





Area Reduction, %





Type of Failure






Which materials was the most ductile?





Which material was the least ductile?




-

29

-
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Physical and Mechanical Properties of Metals

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29




Figure 1.2.2.3
-
1: Tensile

Test for Threaded Specimens










1.2.2.4 Application: Tensile testing of Brittle Materials


OBJECTIVE: To study the tensile testing of Brittle materials, determine the
mechanical properties and compare these results to the tensile testing of ductile

materials.


-

30

-
30



Physical and Mechanical Properties of Metals

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Materials


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30



SPECIMENS:

1.

Tensile specimen


cast iron

2.

Tensile specimen


cast aluminum


APPARATUS:

1.

“Vega”


Universal Testing Machine; 20K

2.

Dial calipers

3.

Gage length marking device

4.

Universal grips with V jaws


REFERENCES:


1.

Manufacturing Processes
, H. V.

Johnson, Bennett & McKnight, 2
nd


Edition, 1984, Unit 14, pp. 80
-
81.

2.

Material and Processes in Manufacturing
; Degarmo, Black and Kohser;
Prentice Hall; Chapter 2; pp. 38
-
45, 7
th

edition; 1997.

3.

Materials Testing Laboratory Manual
, Kaza
nas and Wallace, Bennett, 1
st

edition 1974, Laboratory activity number 1, pp. 8
-
11.

4.


Materials Testing Laboratory Manual
, Vega Enterprises Inc., 1975, 7
th

printing, experiment 6, pp. 30
-
33.


BACKGROUND INFORMATION:


Brittle materials differ from ductile ma
terials in that they have little or no ability to
deform or elongate prior to failure. Cast iron, glass, concrete, brick, some plastics,
some high strength steels are some examples of materials that have very limited
ductility or a high degree of brittlen
ess. The ductility of iron based alloys, from steel
to cast iron, is affected by the composition of the alloy, the manufacturing process,
and the temperature of the process.


In application 1.2.2.2, tensile testing of ductile materials, we observed the
"cup
-
cone”
failure mode generally associated with the tensile failure of ductile materials. Brittle
materials often give little warning prior to failure. The ends of the specimen at the
point of failure will appear flat and distinctly granular.


Note:

T
ensile testing of Brittle Materials requires some addition care compared to
the tensile testing of ductile materials.


1.

Apply the load slowly to prevent shock or impact loading.

2.

Special attention must be given to axial loading to prevent bending stresses,
w
hich will cause premature failure in the specimen.


PROCEDURE:


-

31

-
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Physical and Mechanical Properties of Metals

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31



1.

Measure and record the original diameter of the specimen(s) and record on your
data sheet. With cast specimens, take measurements in at least three locations
and average. Using this diameter

calculate the original area of the specimen(s).

2.

Using the center punch, carefully mark the gage length on the specimen. Center
the punch on the specimen and do not allow the marks to go very deep.

3.

Use the V
-
grooved grips in the jaws on the Vega Universal

Testing Machine.

4.


Mount the specimen in the grips. Care should be exercised to properly align and
install the specimen in the grips.

5.

Apply the load
slowly
.

6.

Carefully observe the specimen and record the maximum load and the breaking
load.
Warning
: the

specimen will give little warning prior to failure.

7.

Record the final gage length and the diameter of the specimen at the point of
failure. Observe and record the type of failure in the specimen(s)


Cast Iron

Cast Aluminum

Original diameter, in.



Origi
nal area, sq. in.



Maximum load, lbs.



Ultimate tensile strength, psi



Breaking load, lbs.



Original gage length, in.



Final gage length, in.



Percent elongation, %



Break diameter, in.



Area at break, sq. in.



Area reduction, %






-

32

-
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Physical and Mechanical Properties of Metals

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32





Figure 1.2.2.4
-
1: Tensile Test Setup for Unthreaded Specimens








-

33

-
33



Physical and Mechanical Properties of Metals

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33


1.2.2.5 Dialog: Stress
-
Strain Curve


A tensile test is one of the most commonly performed tests for the determination of
mechanical proper
ties. One tool in the analysis of this data is the construction of a
stress
-
strain curve. A tensile specimen is loaded to failure while observing the
changing displacements at a given load. Then corresponding values of stress and
strain are calculated.
Stress is plotted on the y
-
axis and strain is plotted on the x
-
axis.


The shape of the stress
-
strain curve will be different depending upon the type of
material tested, the process used such as heat treatment, the temperature of the
material and the histo
ry of load application to the specimen.


Some typical mechanical properties derived from the stress
-
strain curve include
modulus of elasticity, ductility; yield strength, ultimate tensile strength, and
toughness.


A typical stress
-
strain curve is as show
n below:


Stress-Strain Curve
0
10000
20000
30000
40000
50000
60000
70000
0
0.1
0.2
0.3
0.4
0.5
Strain, e,in/in
Stress, S, psi




-

34

-
34



Physical and Mechanical Properties of Metals

Engineering
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34


Tensile tests are performed among other purposes, to determine the following
mechanical properties:

1.

Ultimate tensile strength is the maximum tensile load divided by the
original specimen cross sectional area. This
is one of the most important
properties determined by tensile testing.

2.

Modulus of Elasticity is the slope of the stress
-
strain curve for the elastic
portion of curve. This property is often referred to as the "stiffness" of a
material. This property is th
e ratio of the force or load divided by the strain
prior to reaching the proportional limit.

3.

Proportional limit is the maximum stress that a material can undergo prior
without permanent deformation.

4.

Yield Stress is an area of the stress
-
strain curve beyond

the proportional
limit where the strain increases without a proportional increase in the
stress. The yield point or yield point stress is often determined by the .2%
offset method.

5.

Ductility is a measure of a material's ability to deform plastically with
out
fracture. Ductility is often determined by the (1) percent elongation
method and (2) percent reduction of area method.

6.

Fracture strength is the load required to fracture divided by the original
cross
-
sectional area of the specimen.

7.

Toughness is evalua
ted using the area under the stress
-
stain curve.



1.2.2.6 Application: Stress
-
Strain Curve


OBJECTIVE:


To become familiar with the techniques of tensile testing and to
measure various properties associated with tensile testing.


SPECIMENS:


1


cold roll
ed threaded end tensile specimen


APPARATUS:

1.

Universal testing machines Baldwin/Warner & Swasey, 60
-
k machine

2.

Extensometer



3.

Dial Calipers

4.

Gage Length Marking device


REFERENCES:


1.

"
Manufacturing Processes
," by H. V. Johnson, Pub. Bennett & McKnight, 2nd
E
d., 1984, Unit 14, pp. 80
-
81.

2.

"
Material and Processes in Manufacturing
;" Degarmo, Black and Kohser,
Macmillan, Ch 2, pp 38
-
45, 7th ed., 1988.

3.

"
Materials Testing Laboratory Manual
," Kazanas and Wallace, Bennett, 1st
Ed., 1974, Laboratory Activity Number 1
, pp. 8
-
11.


-

35

-
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Physical and Mechanical Properties of Metals

Engineering
Materials


Page
35


BACKGROUND INFORMATION:





EQUATIONS:


Stress:


A
P
S





Where:

S = stress in lbs/
2
in

or N/
2
m

P = Force in lbs or N

A = Cross sectional area in
2
in
or
2
m


Strain:


o
o
L
L
L
e




Where:


e
Unit strain, in/in or m/m

0
L
L


= Change in length, in


o
L
Original length, in


Stress
-
Strain Curve Procedure:


A stress
-
stain curve show
s the graphical relationship of stress vs. strain for a
standard tensile test. Several mechanical properties may be determined from this
curve. Modulus of Elasticity, yield stress, proportional limit, and ultimate tensile
strength are several of these me
chanical properties.


To accurately prepare a stress
-
strain curve, you must carefully determine the values
of load and elongation at multiple points during the test. Elongation values are small;
therefore precision is required for this measurement. An ext
ensometer is a very
accurate instrument used for this determination.


Measure and record the diameter of the specimen. Mark the two
-
inch gage length on
the specimen. Select the proper grips for specimens and the Universal Testing
Machine.
Specimens mus
t be threaded into the grips at least two diameters.

Caution must be exercised that the bolts for the threaded grips are properly threaded
into the grips.


-

36

-
36



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
36



Attach the extensometer to the specimen. Finger tighten the clamping screws to the
specimen. Load

the specimen to approximately 100 lbs. on the load dial. Zero the
dial of the indicator on the extensometer.


Gradually apply the load, recording the load and displacements at regular intervals.
After the yield point has been reached, remove the exten
someter to prevent
damage. Continue to load and record values until failure.


Calculate actual stress and strain values and record such values on the chart below.


-

37

-
37



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
37



Data:



Load

Elongation

Stress

Strain






































































































Initial diameter of the tensile specimen:

Initial gage length:


From the data derived from this procedure, plot a stress
-
strain curve.


-

38

-
38



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
38


1.2.3 Compression Testing


1.2.3.1 Explor
ation: Compression Testing


Student Exercise: Compression Testing


Specimens:

1.

Marshmallow


Apparatus:

1.

Two aluminum plates approximately 2” x 2”

2.

Dial Calipers

3.

Steel rule


Procedure:

1.

Measure and record the approximate height and diameter of a marshmallow.

2.

Place one of the aluminum plates on a flat surface, place the marshmallow on
the plate and place the other plate on top of the marshmallow.

3.

Load the marshmallow by placing a slotted mass on top of the plate; record
the new diameter and height.

4.

Increase the

load increment in even steps and record each diameter and the
new heights.

5.

Plot the load versus displacement for the marshmallow.


Data:


Mass

Force

Height

Displacement

Diameter

Initial

0






























Questions:

1.

In your own words de
scribe compression loading and stress.










-

39

-
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Physical and Mechanical Properties of Metals

Engineering
Materials


Page
39


2.

Compare compression loads/stresses to tension loads/stresses.









3.

How does the displacement in compression compare to the displacement in
tension?









4.

What happen to the cross
-
sectional area of the spe
cimen in tension?
Describe the effect of compression loading on the cross
-
sectional area of a
specimen?










1.2.3.2 Dialog: Compression Testing


Compression stresses result from forces that tend to crush a material. In many
applications compression
stresses are assumed to be similar to those of tensile
stresses. In the elastic range of a material those assumptions are quite valid. In the
plastic range materials will normally behave quite differently.


Under compression loading materials will defo
rm elastically to the yield point. When
the load is released the material will return to its original size and shape. After the
yield point the material will increase in cross
-
sectional area and the


Compression testing is done to verify the material fo
r anticipated service conditions.
However, compression testing is often difficult to perform. Cross
-
sectional area of

-

40

-
40



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
40


specimens needs to be increased to avoid buckling and bending of specimens.
Frictional end conditions may affect test results. Most ma
terials have nearly equal
results in compression and tension; however cast iron and concrete are considerably
stronger in compression than in tension.



1.2.3.3 Application: Compression Testing of Ductile Materials



OBJECTIVE:

To study the effects of t
he compressive testing of ductile
materials.


SPECIMENS:

1. Steel
-

hot rolled


2. Steel
-

cold rolled


3. Wrought aluminum


4. Brass
-

free cutting


APPARATUS:

1. "Vega"
-

Universal Testing Machine


2. Hardened compression test discs


3. Raising Bl
ock


4. Dial Calipers


REFERENCES:



1.
Manufacturing Processing
, H. V. Johnson; Bennett & McKnight; 2nd
Edition; 1984; Unit 14; pp. 80
-
81.


2.
Material and Processes in Manufacturing
; Degarmo, Black and Kohser;
MacMillian; 6th Edition; Chapter 2, p.

47.


BACKGROUND INFORMATION:



There are four types of stresses that are studied for determining the strength of
materials: tension, compression, shear and torsion. In the last few sections we have
been studying tension. It is often stated that material
s behave the same in tension
and compression. That is true for most ductile materials.


A compression test is most commonly performed on a universal testing machine.
The compression space is the lower portion of the machine. Prior to the yield point
te
nsion and compression results are similar. The major difference with the
compression test compared to the tensile test is that the specimen compresses or
the area increases after the yield point is reached. Typically the compression test is
more difficult

to perform than the tensile test. The compressive specimen must have

-

41

-
41



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
41


a larger cross sectional area to prevent the effects of column buckling. For some
ductile materials the specimen will compress until a flat slug is reached. A
compression test is perfor
med to determine the following mechanical properties:




Ultimate Compressive Strength (brittle materials)



Modulus of Elasticity



Proportional Limit



Yield Strength


PROCEDURE:


1.

Attach compression test plates in the lower platen on the Vega Universal
testing m
achine.

2.

Place the raising block on the lower compression plate.

3.

Using the dial calipers, measure the diameter of a specimen. Using either the
dial calipers or an external spring caliper set the diameter of the calipers to
just fit freely over the specimen
.

4.

Place the specimen on the raising block. Make sure that the specimen is
centered on the machine.

5.

Gradually apply the load until the diameter is increased enough to be
detected by the calipers.

6.

Remove the specimen and measure the diameter of the specim
en. If the
diameter is the same as the original measurement the yield point has not be
used.

7.

Return the specimen to the universal testing machine and increase the load
by 200 pounds.

8.

Repeat the procedure until permanent deformation is measured.

9.

Record th
e load that first produced this permanent deformation.

10.

Repeat this procedure for each specimen.

11.

Calculate the yield strength for each specimen.


Specimen

Original

Diameter

Area

Yield

load

Yield
Strength

psi.

Steel
-

hot rolled





Steel
-

cold rolled





Wrought Aluminum





Brass
-

free cutting









-

42

-
42



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
42





Figure 1.2.3.3
-
1: Vega
-

Compression Testing


-

43

-
43



Physical and Mechanical Properties of Metals

Engineering
Materials


Page
43


1.2.3.4 Application: Compression Testing of Materials



OBJECTIVE: To study and observe the techniques

of the compression testing of
various common materials.


SPECIMENS: 1. Concrete cylinders; 2" in diameter x 4" high

2. Short wood column; 1" x 1" x 4"

3. Gray Iron cylinder;


APPARATUS: 1. Universal testing machine
-

Vega
-

20k machine


2. Dial Calipers

3.

Hardened compression test plates and raising block


REFERENCES:


5.

Manufacturing Processes,
H. V. Johnson, Bennett & McKnight, 2nd Ed.,
1984,Unit 14, pp. 80
-
81.


6.

Material and Processes in Manufacturing
; Degarmo, Black and Kohser,
Prentice

Hall, Ch. 2, pp. 38
-
45, 7
th

Ed., 1997.


7.

Materials Testing Laboratory Manual
, Kazanas and Wallace, Bennett, 1st Ed.,
1974, Laboratory Activity Number 1, pp. 16
-
20.


8.

Materials Testing Laboratory Manual,
Vega Enterprises

Inc., 1975, Seventh
Printing, pp. 46
-
51.


9.

Modern Materials and Manufacturing Processes
, R. G. Bruce, M. M. Tomovic,
J. E. Neeley, and R. R. Kibbe, Prentice Hall, 2
nd

Ed., 1987, pp. 55
-
60.


BACKGROUND INFORMATION:


It is often stated that materials behave
the same in tension and compression. That
is true for most ductile materials. However, there are some materials that are very
weak in tension and extremely strong in compression. Concrete, wood and cast iron
are materials that are mostly tested in compr
ession.


Gray Iron

or cast iron has very high compression strength and very low tensile
strength. Gray iron consists of tiny graphite flakes, which tend to weaken the matrix
structure in tension. However, these graphite flakes are very strong in compres
sion.
Gray iron tends to fail in diagonal shear.



-

44

-
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Physical and Mechanical Properties of Metals

Engineering
Materials


Page
44


Concrete

like gray iron is a brittle material, which is weak in tension and very strong
in compression. The diameter of the specimen should be at least three times the
size of the largest aggregate. Th
e specimen height should be at least twice the
diameter. When concrete specimens are tested in compression they should have
flat square ends. Specimens should be capped in paraffin or plaster which squares
the ends and helps to reduce the effects of end
friction on compression results. If
capped specimens are not available, a 1/8" layer of thick paper, cardboard or
fiberboard may be used to distribute the load evenly on the specimen. This is not a
recommended practice but may be used for demonstration p
urposes.


Wood

is an organic material composed of cells that are aligned in tubes or columns
in the general direction of the grain structure. This results in both good tension and
compression strength in the direction of the grain but poor results across
the grain.
Wood is difficult to grip in tension. Wood is most commonly tested in compression.
Wood specimens have square ends with a length four times the thickness.


PROCEDURE:


Gray Iron
-
Compression
:


1.

Attach compression test plates in the lower plate
n on the Vega Universal
testing machine.

2.

Place the raising block on the lower compression plate.

3.

Using the dial calipers, measure the diameter of the gray cast iron specimen.

4.

Place the gray cast iron specimen on the raising block. Make sure that the
speci
men is centered on the machine. Gradually apply the load and observe
the specimen. Record the maximum load that the specimen resists.
Continue to apply the load and observe until the specimen fails.

5.

Calculate the area of the specimen. Use this area and

the maximum load to
calculate the compressive strength.

6.

Sketch the type of failure for the gray Iron.



Specimen Diameter, in.


Specimen Area, sq. in.


Maximum Load, lbs.


Ultimate Compressive Strength, psi




Concrete
-
Compression
:


1.

Use three concrete

specimens that are 2" diameter x 4" height. If capped
specimens are not available use 1/8" layer of cardboard, paper or fiberboard
at each end of the specimens to evenly distribute the load.


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2.

Measure the diameter of each specimen. Measure in several loca
tions both
horizontally and vertically.

3.

Place the concrete specimen between the compression plates (raising block
is not needed) with the appropriate cushioning material.

4.

Slowly apply the load. Observe and record the highest load reached.

5.

When the load be
gins to decrease, remove the load and sketch the type of
failure in the specimen.

6.

Repeat the process for each of the specimens.

7.

Calculate the ultimate compressive strength for each specimen



Specimen


1

2

3

Diameter, in.




Area, sq. in.




Maximum lo
ad, lbs.




Ultimate Strength, psi




Average ultimate strength




Wood
-
Compression
:


1.

Obtain or prepare wood specimens with lengths four times their thickness.
Specimens of size 1" x 1" x 4" with ends sawed square is recommended for
this procedure.

2.

Cen
ter the specimen between the compression plates.

3.

Observe the specimen, as the load is gradually applied.

4.

Record the maximum load and continue loading until complete failure.

5.

Repeat for each specimen.

6.

Observe and describe the type of failure for each specim
en.



Specimen


1

2

3

4

Type of Wood





Dimensions, in.





Cross sectional area, sq. in.





Maximum load, lbs.





Ultimate Compressive strength, psi







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1.2.4 Shear Testing


1.2.4.1 Exploration: Paper Punch


Student Exercise: Paper Punch


Sp
ecimens:

1.

Several sheets of paper


Apparatus:

1.

Single paper punch

2.

Steel Rule

3.

0
-
1” Micrometer


Procedure:

1.

Using the paper punch, punch a single hole in one sheet of paper.

2.

Fold the paper and punch a single hole in the doubled sheet of paper.

3.

Fold the paper ag
ain and punch a single hole in the sheet of paper.

4.

Repeat this procedure twice.


Questions:


1.

Was the same force required to punch a hole in the single sheet of paper
versus the folded paper?







2.

If it was harder to punch the paper, why was it harder?








3.

What would be the area from which the stress would be calculated?







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1.2.4.2 Dialog: Shear Testing


In tension and compression testing we have analyzed forces that act parallel to the
material and perpendicular to the cross
-
sectional area. There are

many products
where the force acts perpendicular to the material and parallel to the cross
-
sectional
area. The forces are slightly offset in effect creating a sliding effect on the material.
This type of load produces a shear stress in the material. The

shear strength of a
material is normally less than the tensile or compressive strength of a material.
Products subjected to shear stress include pins, bolts, rivets, and punches. Shear
stress is calculated using the following equation:


A
P




Where:





Shear Stress, psi, Mpa

P= Force, lbs, N

A= Area,
2
2
,
m
in


The difficult part of analyzing shear applications is determining the area over which
the shear force acts. For a punching action for a circu
lar hole is the outside of a
cylinder. Thus the area is the circumference of a circle times the thickness.
Products such as bolts are either subjected to single or double shear. In double
shear the area is twice the cross
-
sectional area of the bolt. Sh
ear testing is difficult
to accurately perform due to bending and frictional effects in the material.


1.2.4.3 Application: Shear Strength Testing


OBJECTIVE: To perform shear strength tests on various materials.


SPECIMENS:

1.

3/8" diameter rods of stee
l and aluminum.


APPARATUS:

1.

Vega
-

Universal testing machine

2.

Hardened Plates

3.

Double
-
shear test fixture


REFERENCES:


1.
Materials testing Laboratory Manual
, Vega Enterprises Inc., 1975, 7th printing,
pp. 52
-
56.


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2.
Materials Testing Laboratory Manual
,
Kazanas and Wallace, Bennett, 1st edition,
1974, Laboratory Activity Number 10, pp. 35
-
37.


PROCEDURE:


1. Attach on hardened plate to the upper platen in the compression space on the
universal testing machine and place the other hardened plate on the low
er
platen.

2. Measure and record the diameter of each of the shear specimens.

3. Insert the specimen in the appropriate holes in the shear test fixture.

4. Do not center the specimen in the shear test fixture, but allow one end to just
project a short

distance to allow for a second test of the specimen.

5. Before testing, mark the position of the punch relative to the holder to allow for
observation of bending during the shear testing.

6. Position the shear
-
testing fixture between the hardened steel
plates on the
universal testing machine,

7. Gradually apply the load, observe the maximum load reached and any bending
present at this maximum load.

8. After the specimen has failed, continue loading until the sheared slug has passed
into the relieved ar
ea in the lower portion of the shear
-
testing fixture.

9. Remove the shear fixture from the Universal Testing Machine (UTM). Remove
the sheared slug from the fixture by sliding the center plate sideways.

10. Perform a second shear test on the remaining p
ortion of the shear specimen.

11. Repeat this process for the other shear specimen.

12. Record the appropriate data and calculate the required information.


Data:


Material

Specimen
Diameter

Max load
-

1st
test

Max load
-

2nd test

Shear
Strength, psi

Steel





Aluminum







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Figure 1.2.4.3
-
1: Vega UTM with Shear Testing Fixture



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1.2.5 Torsion Testing


1.2.5.1 Exploration: Torsion Testing


Student Exercise: Torsion testing of materials


Specimens:

1.


3” x 3” x 12” block of Styrofoam


Procedure:

1.

Ma
rk, if not marked, several longitudinal lines along the axis of the Styrofoam
block

2.

Working in pairs, pull the Styrofoam block in tension and observe the reaction
of the material to the tension in the block.

3.

Push down on the block creating compression in t
he block and observe the
block.

4.

Working in pairs, having one person hold one end of the block, twist the other
end of the block in torsion.


Questions:

1.

Describe the displacement in the Styrofoam when subjected to torsion.






2.

How would you suggest the qua
ntification of this displacement?








1.2.5.2 Dialog: Torsion Testing


Applications where the product is subjected to twisting type forces produces torsion
in the member. Power transmission in generators; transmissions, axles, shafts in
cars; and prope
llers on ships, are all examples of parts that are subjected to torsion.

This phenomenon produces torsional shear in the microstructure of the material.


The maximum torsional stress is given by the following equation:



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J
Tc




Where:



=
Shear stress, psi, Mpa

T = Torque, ft
-
lb, in
-
lb, n
-
m

C = Distance, usually the radius of the shaft, in, m, mm

J = Polar moment of inertia,
4
4
4
,
,
mm
m
in


The polar moment of inertia is a measure of the difficulty of rotation; the further that
the

mass is from the center of gravity the harder it is to rotate. As an example if you
take a 1
-
kg weight in your hand, hold your arm in toward your body and rotate just
the part of your arm from the elbow to your wrist. Repeat this action; however rotate
your arm from your shoulder. There is more difficulty in the second action due to the
polar moment of inertia. The polar moment of inertia for a solid circular shaft of
diameter D is given by the following equation:


32
4
D
J




The modulus
of Rigidity, G, or shear modulus is the ratio shear stress to the shear
strain. The modulus of rigidity is measured in pounds per square in or in newtons
per square meter.


With the application of torsion a shaft will experience angular displacement along

the
longitudinal axis of the shaft or angular displaced as viewed from the end of the
shaft. The displacement is given by the following equation:


JG
TL




Where:

T = Torque, ft
-
lb, in
-
lb, n
-
m

J = Polar moment of inertia,
4
4
4
,
,
mm
m
in

G=Modulus of Rigidity, psi, Mpa,


=Angular displacement, radians


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1.2.5.3 Application: Torsion Testing
-
Part I


Specimens:

1.

Brass Rod


3.96mm in diameter

2.

Steel Rod


2.02mm in diameter

3.

Steel Rod


2.76mm in diameter

4.

Steel Rod


3.96mm in diameter



Apparatus:

1.

CENCO Advanced Torsion Apparatus, CP74050
-
01

2.

Mass Hanger

3.

Meter Stick

4.

Dial Caliper

5.

4
-
100gm Slotted Weights

6.

500gm Slotted Weight

7.

1kg slotted Weight

8.

2kg slotted Weight


Procedure:

1.

Attach the two table clamps of the advanced t
orsion apparatus to a lab bench
and align the clamps so that the large diameter steel rod remains straight.

2.

Check to assure that the large diameter steel rod is rotating freely.

3.

Place the mass hanger on the steel cable and zero the vernier arm.

4.

Load the
hanger so that the rod is twisted 45

.

5.

Remove the weights, if the assembly is properly installed the vernier should
return to zero.

6.

Measure the diameter of the rod in multiple points and record the average
value in the data table.

7.

Measure the length of

the rod between the bushings and record.