Module 1 - Dynamic Fracture Mechanics with Analog Electronics

 

For this expeirment, we will be measuring the crack speed as a function of length along a brittle polymer material (PMMA). We will do this following the work of Fineberg et. al., which you will find a copy of in the `references' section below. Essentially, we will coat the PMMA with a thin layer of aluminum, which will form one resistor in a Wheatstone Bridge configuration. We will use a Universal Testing Machine to load the sample in tension, and monitor the output of an instrumentation amplifier circuit with an oscilloscope to record the test. This module will last 6 weeks, over which time you should become familiar with the key apparatus for the experiment. 

Readings

Week 1

A simple website introduction to the oscilloscope: How to Use an Oscilloscope - learn.sparkfun.com

I also encourage you to read the appendix of the Art of Electronics (AoE) on the oscilloscope. This is available in both the 2nd and 3rd (most recent) editions of the book.

Week 2

Read about transistors (AoE 2nd Ch. 2, through 2.05) and op-amps (AoE 2nd Ch. 4, through 4.22 - stop at comparators)

Week 3

Read chapters 4, 7 and 8 in the HBM handout on Wheatstone Bridge circuits (wikipedia Wheatstone bridge if you've never seen it before) *posted 5.10 - for those whose thirst for knowledge about how to practically drive bridge circuits isn't yet sated, I emphatically recommend this article by Jim Williams*

Read this short handout on instrumentation amplifiers. It should be clear after reading this why one would use an instrumentation amplifier - particularly in a Wheatstone Bridge circuit.

If you can find the 2nd edition of AoE, read 15.03 on measuring strain and displacement - it covers almost any type of tranducer that you'd ever be interested to use in measurement applications (!)

Week 4

For a general discussion of error analysis and general error propagation, this website has a great, concise summary - from Werner Boeglin. You should understand how error in measured quantities used to derive another quantity can be used to determine the error bounds on the derived quantity.

From the Keithley low level measurements handbook, 7. ed (link below in resources): section 1.2, 1.4, all of section 3.

Week 5

No reading for this week. 

Exercises

Week 1

Familiarize yourself with the oscilloscope and other bench-top instrumentation at your desk. A suggested starting point is to feed a sine wave from the function generator into the oscilloscope input, and monitor the wave on the scope. Set up a proper trigger for the experiment. Measure the frequency - does it exactly correspond to the frequency of the function generator? 

Week 2

Week 3

  1. Take a measurement of the resistance of the coating on a `typical sample.' Bear in mind that you'll have to carefully account for lead resistance (look up a 4-wire meausrement method - you can use your multimeter) First convince yourself why you'll need the 4-wire measurement for this task. Record the resistivity of the coating. 
  2. Take a measurement of the resistance of the artifically `cracked' coating (cut with a razor blade) to get a sense for the `minimal' value of resistivity that you should anticipate. Record this value of the resistivity. 
  3. These measurements provide a range of typical resistance values you should anticipate, within about 10%. Design a Wheatstone bridge architecture, specificying the values of each of the resistors. If you consider the above measured values as the upper-bound and lower-bound for the coating during the fracture experiment, you might obtain a useful range for your bridge design.
    • Bear in mind that precision resistors might be required, depending on your design.
    • Account for thermal loading - if too much current passes through the bridge, you can be in trouble, because you'll get Joule heating of the resistors, and they'll drift from their design values. If you stay below 1/8 W for each resistor, you should be fine.
    Once you have converged on a bridge structure, build a voltage source for the bridge, and build the bridge itself. Test the output, and develop a relationship between resistance and voltage. Now that you have the transfer function of the bridge, and given what you know about the resistivity of the `cracked' sample, can you come up with a relationship between output of the bridge and crack length? 
  4. Consider circuits that you might used to measure crack length & velocity. If you choose to measure the crack position as a function of time, and then digitally differentiate the recorded signal, you can do this; this is what the original paper describes. Can you think of another way to measure crack tip velocity, which is our quantity of interest? (hint: an passive high-pass filter, or even an active high-pass filter, are also called differentiator circuits). Build one of these circuits (use an INA to deal with common-mode for the position measurement), and measure its bandwidth. If you build the differentiator, compare it with the passive-version constructed using a high-pass filter.

Lecture notes

Current year

week 1

week 2

week 3

Previous year

week 1

week 2

week 3

week 4

Groups

1: Martel, Kahraman, Aymon, Geissenberger

2: Hollosi, Faugère-Beraud, Piccini, Chouvalidzé, Fontaine

3: Bashardoust, Allabban, Courtemanche, Avoni, LI

4: Terzi, Schneegans, Chappuis, Lemoine, de Christen

5: Windler, Simon, Bugnard, Scheidegger

References

Fineberg et. al. Instability in Dynamic Fracture

Keithley low level measurements handbook - a phenomenal reference for all precision electronics measurements

Workbench Top Equipment: Oscilloscope, Multi-meter, Power Supply, Function Generator, Elvis NI

LF411 datasheet

INA122 datasheet

Transistor datasheet: NPN BC 549

Voltage Reference REF102

Instrumentation Amplifier LT1102

Operational Amplifier OPA 37

 

Student submissions

Group 1: General advice for noise resistant circuits