## Lab
Manual for Engrd 202, Virtual Torsion Experiment

(Aluminum module)

### Introduction

In
this module, you will perform data reduction and analysis for
circular cross section aluminum samples. By plotting the torque
vs. twist data for aluminum and performing analyses of the data
you can infer relations between sample geometry, strength and
stiffness. Seeing how the samples deform and fail will also help
you to better understand material behavior under torsional loading.
From the torque twist curve you can find quantities such as yield
torque (for ductile materials), ultimate torque (for brittle materials),
maximum torque, stiffness, and material properties such as shear
strength and shear modulus. If you need, you can review the theory
for data reduction and analysis for circular samples by going
through the chalk-talks on basic theory and on testing of engineered
materials.

### Procedure

Select
three data sets for aluminum. Each of the aluminum tests were
performed using the same material, machined to different lengths,
and inner and outer diameters. These geometries are labeled geometries
1-4 in the tables linked under "Test Data". You will
find the nominal dimensions for each geometry in the tables linked
under "Test Data". The actual, measured dimensions for
each sample (which may differ from the nominal dimensions) are
listed at the top of each individual data file. Data files are
named according to the following convention: Material_Geometry_Repeat.***,
where the stars are in place of the file type extension (For example
AL_1_2.txt would be the text file containing data for the second
test on an aluminum sample made using geometry 1).

Select one data set each from geometries 1, 2 and
3 of the aluminum tests (You may use any data set within a particular
geometry since there are repeats of nominally identical samples).
Plot the torque-twist curves for each data set; continue your
analysis by completing tables 1 and 2, then proceed to answering
the questions below and to writing your lab report. Step-by-step
directions for completing the data and comparison sheets, (tables
1 and 2) are given at the end of the module

### Lab Report

Your
lab report should include the completed data sheets, graphs and
a brief discussion of the lab procedure. The report should also
provide answers to the questions below and any other discussion,
observations or comments you wish to include.

### Questions

**1.** For the aluminum
tests, compare the elastic stiffness, ksample, from geometries
2 and 3 to that for geometry 1. Do the relative values (i.e. ratios
of ksample from one geometry to the other) agree with theory?

**2.** Compare torque at first yield, Ty, for aluminum geometries
2 and 3. Repeat for geometries 1 and 2. When are the values different?
Do the relative values of Ty agree with theory?

**3.** Calculate the shear modulus, G, and shear yield stress,
y, for the aluminum samples. Compare these to the reference values
for these materials. Discuss any discrepancies between your measured
values and the reference values. Do you notice any trend in the
G values for aluminum as the sample dimensions change? Suggest
a way to improve the measurement of G.

**4.** Review the virtual test for the aluminum and comment
on the deformation of the sample during the test. If you were
to replace this circular sample with a square sample of same length
and polar moment of inertia, what difference would it make in
the deformation?

Step by step instructions for completing Tables 1 and 2 for a
given data set and Sample ID

**a)**
Select the data file and open it. You may choose to use a text
file (.txt) or an Excel file (.xls). The Matlab GUI (VL_1_v10.m)
uses the .txt files

**b)** Enter the sample ID, material and the dimensions of
the test sample on table 1. Use the information given in the header
of the text file or Excel file. If you choose to use the Matlab
program, this information will be displayed on the GUI.

**c)** Calculate J (polar moment of inertia) and enter this
value on row 3 of table 1.

**d)** Plot the torque vs. twist for the sample. For this purpose,
you may choose to use the Matlab GUI. In the Excel files the plots
are provided to you. You may refer to 'Hints for graphing' in
case of any difficulty in plotting the data.

**e)** Now, plot the torque vs. twist curve in the linear region.
Find the stiffness (slope of the torque-twist curve). Denote this
value as , the total stiffness (slide 5 of chalk talk on engineered
materials). Enter this value in row 4 of table 1.

**f)** Calculate the sample stiffness, (slide 6, 7 of the chalk
talk on engineered materials). Using this value of stiffness,
calculate shear modulus for the sample and enter this value in
row 5 of table 1.

**g)** Calculate the shear modulus, G, using the relation given
in slide 7 of the chalk talk on engineered materials. Enter this
value in row 6 of table 1.

**h)** Calculate the yield torque (or ultimate torque for brittle
materials) and the maximum torque (refer to slide 9 of the chalk
talk on engineered materials) and enter these values into row
7 and 8 of table 1.

**i)** Now, calculate yield strength or ultimate strength (refer
to slide 10 of the chalk talk on engineered materials) and enter
these values in row 9 of table 1.

**j)** Look at the broken sample and comment on the type of
fracture. Write your comments in row 10 of table1.

**k)** Follow this procedure for three of the four aluminum
samples. Then transfer the data over to table 2 and complete the
suggested comparisons.