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. 

Week 6

This week I encourage you to re-read the manuscript from Fineberg et. al. You might also read the manuscript from Goldman on acquisition of inertia by a moving crack, in references. These papers, and citations therein, can form a basis for theory against which to evaluate your measurements.

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

Lecture notes

2022

week 1

week 2

Previous years

2021

week 1

week 2

week 3

2020

week 1

week 2

week 3

week 4

Groups

Group 1: Benjamin Colety, Cameron Bush, Filippo Brignolo, James Ziadeh

Group 2 : Algisi Colleen, Mi-Lane Bouchez, Syrielle Wicki, Guede Axel

Group 3 : Roy Aymeric, Soury-Lavergne Nathan, Assier de Pompignan Leo, Karim Azzouzi

Group 4 : Joao Barini Ramos, Joseph Bernaert, Julien Jeandroz, Victor Solelhac

Group 5 : Cassandre Pitz, Nicolas Avellan Marin, Kateryn Andrea Leon De la Torre, Abhijeet Singh

Group 6 : Joseph Bejjani, Dogukan Ustun, Pierre Garrabos, Alexandre Mehdi Clement 

Group 7 : L. Molefe, X. Wei, T. Yang

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

Acquisition of Inertia by a Moving Crack

Introduction to Continuum Mechanics by W. Michael Lai - Chapter 4 Stress and Integral Formulations of General Principles 

Student submissions

Group 1: General advice for noise resistant circuits

Group 5 : Resistance evolution during the crack

Group 2:  Making a buffer with OP37G: https://wiki.epfl.ch/me412-emem-2021/documents/Buffer with OP37G.pdf

Group 3: Relationships between resistance and crack length: https://wiki.epfl.ch/me412-emem-2021/documents/Group3_Relationships between the sample resistance and the crack length.pdf

Group 4: Voltage reference REF102 for improved output current