APPL 150

Four-point bending lab group project

Amy Oldenburg, 3/29/09

 

Goal: You will use a 4 point bending tester to determine the mechanical properties of acrylic (also known as plexiglass), plaster of Paris, and finishing cement.  You will measure the elastic modulus at low strain, and where possible, the maximum stress before failure, and the strain at failure.  You will learn how reinforcements and stress raisers such as notches and scratches affect these properties. 

 

This lab is somewhat labor-intensive and I recommend splitting the work up between group members or possibly pairs – you should also check on each other’s work because you are each responsible for the entire report.  The main group tasks will be:

1.      Preparing the plaster and cement samples

2.      Testing all of the samples

3.      Analysis of the test data including linear fits

4.      Computing the elastic moduli and standard errors

5.      Tabulating and plotting the results

I expect each of these steps may take 2 or more hours and culminate in your group lab report (guidelines detailed below).  In addition, each group member will write a summary of the main results in their own words, as described in the guidelines below.

 

Logistics: Each group will set up a time to get oriented on the system with me, at our mutual convenience (at minimum 2 group members need be present).  I expect you all to get started no later than Tues, April 14th, and preferably earlier.  Unfortunately, there is only 1 tester, and so after your “orientation”, lab use will be on a first-come first-served basis.  Also, it will take each of you some time to generate your plaster and cement samples (curing times are several hours to overnight).

 

Hint: You’ll want to bring a USB drive to save your data, and if you have access to Matlab on a different computer, copy the ProcessData.m and Read4Pt.m files and you can do your analysis elsewhere.

 

I also ask that if you’ve been running the tester for more than 2 hours and another group wants to get in some time, to hand it off.  Most of the time I won’t personally be in the lab, but you can ask the helpful staff general questions about where to find stuff.  They may not be able to answer specific questions about the lab work, in which case you’ll have to email me or ask before/after class.  So, don’t wait until the last minute expecting everything to go off without a hitch, because I may not be available to answer immediate questions.

 

Background:

Similar to the 3-point bending test we learned about in class, we will be using a 4-point bending test (Fig. 1).  The particular advantage of this test is that the maximum bending moment M is level in the region between the center two pressure points, meaning a larger portion of the sample is exposed to this maximum moment, in comparison to a single point in the 3-point test.  Thus, 4 point tests provide a more accurate assessment of the average material property.  

Fig. 1 Diagram of 4 point bending of a rectangular slab of thickness d.

 

As the force is increased, the sample tends to curve and the maximum tensile stress s is on the outer (bottom) portion of the slab.  It can be written as:

Where s is the stress, F the load (force), b the slab width and d the slab thickness as defined previously in class, and distance a between the load points as defined in Fig. 1.

 

The flexural strength (or maximum stress before failure) sfs can thus be written as:

Where Ff  is the load at failure (or maximum load).

 

Since the bottom portion of the slab is where the tension is greatest, the maximum strain is also here.  We write the maximum strain emax in the limit of small deflection as:

Where the deflection Dy and distances a and L are defined in Fig. 1.

 

The elastic (tensile) modulus can then be computed using Hooke’s law.

 

Note that, as the sample bends, the bottom portion is under tension, and the top portion under compression.  This may have consequences for the results you get depending on the orientation of your samples, so please pay attention to which way (up or down) you place your scratched and reinforced samples in the tester!

 

Samples to be tested:

 

Fig 2. Picture of the plexiglass samples you will be given to test: A) plain, B) rounded notch, C) sharp notch, D) large scratch, E) small scratches on each side.

 

Plexiglass:

Thinnest:           Sample A Quantity 3

2nd thinnest:       Sample A Quantity 9 – test 3 plain, 3 tape reinforced on the top, 3 tape reinforced on the bottom

Samples B and C Quantity 3 each

Samples D and E Quantity 6 each – test 3 with scratches on the top, 3 with scratches on the bottom

3rd Thinnest:      Sample A Quantity 3

Thickest:           Sample A Quantity 3

 

You will also prepare:

Portland cement Quantity 3

Plaster of Paris Quantity 3

Plaster of Paris w/ Al screen reinforcement Quantity 3, test with reinforcement on the

bottom only

Plaster of Paris w/ Al screen reinforcement under tension, Quantity 3, test with

reinforcement on the bottom only

Total number of data runs = 48 (16 unique samples ´ 3 each to get sampling statistics)

 

Procedures

Preparing the cement or plaster:

Mold Preparation: Spray a plastic mold with mold release.  If you are adding reinforcement, cut a section of screen (be careful working with the screen because it is sharp) and place it in the bottom of the mold.  When you pour the plaster in, you’ll want to push it into the screen using a stick.  Also, if the reinforcement is to be under tension, use the table clamps to clamp the screen down into the mold under tension.  An alternate, but possibly more difficult method, is to pour a bit of plaster down first, squish the screen down on top (and add tension if needed), then pour the rest of the plaster.  Given the short working time of the plaster this may not be easy.

Mixing and Setting: Mix cement at a ratio of 4 parts cement : 1 part water.  Mix plaster at a ratio of 2 parts plaster : 1 part water.  Use the measuring cup, and disposable plastic cups and popsicle sticks for mixing.  About ½ cup of cement/plaster before adding water can make 2-3 samples.  Keep in mind that the mixtures will start to solidify very rapidly so you don’t want to make too much.  Also, the exact water ratio will affect the mechanical properties, so mix carefully.  Once poured, even the top off with the spatula, and let it set about 2 hours or more.  The edges can be messy – it need only be a bit longer than the tester span, and everything else beyond that length shouldn’t affect the measurement.  After solidified, carefully peel/bend away the plastic (be careful, as the sample is prone to break at this stage).  These samples are extremely fragile and I recommend measuring them right away.

 

Test Procedure:

Computer:

  1. Log on to computer next to the spools of colored wire in 412 Taylor
  2. Username: undergrad
  3. Password: =5boblab
  4. Create a folder with your group’s name on it on the desktop into which you will save your data
  5. Click Start ® Programs ® Measurement Computing ® TracerDAQ ® TracerDAQ
  6. Choose “Strip Chart” and click “run”
  7. File ® Load Configuration® Named Configuration “APPL 150 Project.scc”

 

Hardware setup:

  1. Put on safety glasses
  2. Enclose the immediate area around the tester to block flying shards of test materials
  3. Plug in the power cord for the black box
  4. Plug in the USB cable for the minilab
  5. Do a test run on a test piece of plexiglass to make sure the strip chart is working

 

Run procedure:

  1. Record the thickness and width (b and d) of the sample using calipers
  2. Place the sample in the tester
  3. Lower the jaw to close to touching (but not quite)
  4. Press play on the strip chart
  5. Slowly and evenly apply pressure while watching Channel 1 (displacement).  Occasionally, Channel 1 will become very noisy, in which case, release pressure, stop, and restart. 
  6. Continue to add pressure to the sample until either it breaks, or Channel 0 (force) exceeds 1 Volt which corresponds to the maximum of the load cell (300 lbs).  After the end is reached, DO NOT swing the handle backwards much beyond the zero point before stopping the recorder, or the software may crash when you try to save.
  7. Stop recording.
  8. Save as a .txt file with a unique filename.
  9. Record the type of sample, whether it failed, the orientation of any defects or reinforcements (whether they were on the top or bottom surface when you tested it), the filename, and any other relevant observations.

 

Data analysis procedure:

1.      Start Matlab 2008a

2.      Open “ProcessData.m” located in the Desktop “APPL 150 Do Not Remove Until July 2009 / Matlab” folder.

3.      Click “run” (green pointer icon).  If it asks about adding to the path, click “add to path”.  Then, it will prompt you for the data file name.

4.      It should pop up a plot of force vs. displacement from your raw data, which were converted from the voltage readings.  Choose the minimum and maximum displacements over which to fit the elastic modulus (this should be the linear regime near the beginning of the run) and type these values into “dispmin” and “dispmax” in the ProcessData.m file.

5.      Run ProcessData.m again with these new values.  The best fit line will be displayed in red.  If the best fit line looks good, record the slope which is reported in lbs/in.  If the fit is not good, modify the min and max values and try again.

6.      If the sample was one that failed, use the crosshairs icon and click on the plot to determine the maximum force, the force offset (force at minimum displacement), the maximum displacement, and the displacement offset.  Note that the offsets tend to drift significantly over time and need to be recorded for each run.  Also note that sometimes the maximum force will occur before failure – this is the value I want you to record.  However, the maximum strain will always be the strain at failure. 

 

Computation and plotting:

I leave you on your own here.  Use the equations above to compute the maximum stress, strain, and elastic modulus.  For the elastic modulus, you’ll have to combine the equations to get it in terms of the “slope” you measured.  Use those calipers to get all of the values you need.  Use a data plotter like Excel or anything you are familiar with.

 

What your group report should contain:

All of your tables should report values in metric units and display ± standard deviation as computed from your 3 measurements.  Because all of the equations are linear in this project, you can assume the standard deviation scales proportionally.  For example, when you compute the stress from the force ± force deviation, you can plug both force and force deviation as “F” into the same equation to get the stress ± stress deviation.

1.      A table comparing the elastic moduli of cement, plaster of Paris with and without reinforcements, and acrylic with and without reinforcements.

2.      A table comparing the maximum stress and strain of cement, and plaster of Paris with and without reinforcements.

3.      A table comparing the maximum stress and strain of all of the acrylic samples that failed.

4.      A plot of the elastic modulus of acrylic versus thickness (with error bars), and a theoretical curve for one “best” value of the elastic modulus (justify your choice of this value).

5.      Classify the force vs. displacement curve shapes into a few distinct categories (exactly linear, curved, S-shaped, etc.)  Plot a representative data curve of each and state which samples tended to exhibit that shape.  The plots could be taken directly from matlab.

6.      All of the raw data you have taken (48 .txt files) should be submitted to me via email, USB drive, or CDR, so that I can verify your results and check any problem areas that you may encounter.

 

What your individual report should contain:

Typewritten preferred, approximately 1.5 pages. 

Discuss each of the results in your group report (points 1-5).  State whether there are any significant differences (greater than a standard deviation apart), and whether the observations match what you expected based on your knowledge of materials.  For point 1, this may include some very brief research into acrylic, plaster of Paris, and the finishing cement, as well as the ingredients listed on the plaster and cement containers.  For the other points, bring in as many concepts from class that are relevant to the discussion.  It is highly likely that some of the results will not turn out as you expected.  I value scientific integrity above all else; do not over-state your conclusions.  State what didn’t work, and why you think it didn’t.  It is possible that the result you were hoping to see was “in the noise”. 

In addition to points 1-5, discuss what sources of experimental or analytical error may have contributed to your results.  Discuss whether any of these errors may be easily improved upon. 

 

If you want to submit either of the reports electronically, please put them in PDF format (e.g., using the free downloadable “PDF creator”).

 

Acknowledgements:

Bob Dennis and Steve Emanuel for building the tester, tester electronics, and cutting out all of the acrylic.