Posted: November 24th, 2014

engineering stress versus engineering strain graphs in the low strain (

?
Plot the engineering stress versus engineering strain graphs in the low strain (<1%) region to
determine Young’s Modulus (E), 0.1% proof stress and
strain at yield.
Note that a linear regression
line can be created easily in Excel for the elastic region by
creating an additional column of strain
values and adding the offset (0.001). By c
licking on the
new
line and selecting the linear fit option
thi
s will produce a regression line
.
The option to display
the regression equation
will provide you
with the slope (E).
?
Plot the engineering stress versus engineering strain and true stress versus engineering strain graphs
from zero strain up to failure.
?
De
termine the ultimate tensile strength, fracture stress
,
ductility
and work to fracture
.
?
Determine the relationship between Vickers hardness and Yield Strength
?
= x (VHN) g.
?
Examine the fracture surfaces and describe the fracture process.
?
Use
CES Edupack (
available in the Mechanical Engineering 5
th
floor cluster under
Programs/Mechanical/ CES Edupack )
to determine which material you have tested for A, B, C
and
discuss your results vs what was expected from the database
.
Deliverables:
–
Each student should p
roduce a
brief but concise
laboratory report
containing an abstract, introduction,
materials and methods, results, discussion and conclusion. Your report should include
results of using
the Materials Selector Database
(CES Edupack)
a
s a means to determine
which materials were used in
the study (A, B, C)
based on their appearance,
fracture
behaviour, and mechanical properties of your
experimental laboratory
.
Introduce all background material
initially
in the Introduction
of your report
.
The
mater
ials and
methods should be as brief as possible
. Y
o
u can include this laboratory procedure in
an appendix and refer to it in your materials and met
hods to keep this section brief. Also include a
brief description of the
on
–
line
Materials
Selector
Database
(CES E
dupack)
.
The
two
required graphs
for each material
in the Results section
are:
(a)
Engineering stress versus engineering strain up to yield.
(b)
Engineering stress versus engineering strain and true stress versus
engineering
strain from the
start up to fra
cture.
These may be presented together in a single figure.
The laboratory report accounts for
1
0
% of the overall module mark.
EXPERIMENTAL METHOD
Follow instructions carefully
–
ask for assistance when you do not understand!
Important Safety Notice:
?
Forc
es may reach in excess of 50kN
–
5Tonnes. Keep your hands clear of the machine
when the load is being applied.
?
Keep clear of the machine. The door is not a safety guard; it is only to stop
d
ebris.
?
Ensure you wear safety glasses at all times.
?
Keep the d
oor closed when the test is running.
?
Following every measurement interval, ensure the door is closed before you continue the
test.
?
If you need to stop the machine in an emergency, press the red stop switch.
Tensile test
protocol
:
1)
Familiarise yourself w
ith the software and the logos below:
Console settings
–
Here, you can reduce the jog speed of the cross head, or return it to
normal
Strain 1 settings
–
the settings for strain gauge, where you can calibrate or balance the
strain gauge.
Load cell
settings
–
The load cell is calibrated and balanced here. You do not need to
do this during this exercise, as it will be done prior to testing for you.
Crosshead settings
–
To balance or set limits on the crosshead. You do not need to do
this during t
his exercise, as it will be done prior to testing for you.
2)
On Bluehill’s first page
(see image below)
,
three boxes display the current status of the machine.
The far left box shows the extension, which needs to be zeroed before start of test. The load i
s
shown in the middle box, and the strain is shown on the right hand side.
click on
Test
.

Laboratory Notes
–
Read after you have completed the lab
In the first part of the lab you measured the initial diameter and the overall gage length. You
measured engineering strain, vs applied load in the elastic region. You then removed the strain gage.
–
from this you can calculate the eng stress, eng strain. Strain was measured directly by the strain
gage; when you removed it this goes to zero or negative, ignore this. You can plot eng stress v eng
strain and solve for the elastic modulus and the yiel
d strength (use a proof str
ess if needed).
In the second part of the lab the machine recorded the deformation. You measured the change in
diameter and load as necking occurred. You measured the final load and final area and final length.
–
you can est
imate the eng stress, eng strain, true stress, true strain. Stress is force/ area, strain is
the change in length / original length. This is an estimate as the change in length used to calculate
strain is measured by crosshead deformation in this part (s
train gage was already removed, ignore
this) and the overall cross sectional shape of the entire specimen is not constant, particularly at the
collars where the specimen is much larger.
You can do the calculations in Microsoft excel or any spreadsheet a
nd paste the results graphs into
microsoft word processor.
If using excel you can do the equations and copy them so the equation is applied to a whole row or
selected column. Look at the cells in the online sample and the equation will be there usually i
n the
form…
=b1*c1 this multiplies two cell locations
=b1/c1 this divides two cells
You can copy this equation down a row or across a column by highlighting the source cell with your
mouse, doing Ctrl C, then highlighting the destination cells and p
ressing Ctrl V.
If you place a $ value in front of any of the characters in the equation it keeps these constant, if you
do not they increment when copied.
To plot data, select the data with the mouse, then click insert a graph by selecting the format
d
esired. If you have the axes mixed up you can simply select the line in the graph and make the
corrections so it picks the right one.
Once you have drawn a line the right mouse button selection allows you to conduct a linear
regression of the line (only
choose the section of the line that is linear for this, you may have to
truncate the data selected for plotting the line to the linear part only) and select the option to show
the equation on the chart, the slope of the equation should be your elastic modu
lus.
To calculate an offset line copy the equation into a cell and vary the values by picking a range of
stress values (in ranges of 50 or 100 MPa for example) and solving for strain or vice versa, you can
then add the offset to the strain column using an
equation like =C4+0.01 this would add a 1% strain
offset value to a cell in c4. if the rest of the values were below you could copy this equation
downwards to get the entire set of new strain data. You then want to plot stress vs the new strain
value
s to get the offset line and then estimate where this crosses the experimental data line, by eye .
Note: spreadsheets like excel plot data, they do not know how one set of data is related to another
even if you have calculated the equation for the line.
Hence excel cannot find the point where two
lines intersect for you.
Learning how to use a spreadsheet
effectively is essential in engineering, and will take a lot of trial
and error to get it right, expect to spend many days on this if you have never used one before. You
do not have to use microsoft products, they are all similar, in fact many are much b
etter (Microcal
Origin for example can do good 3D surface plots, excel can only do 2D and is very poor in this area).

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