Measuring Strain

Required course for undergraduate geology majors

Students need to have been introduced to the concept of strain and how it is measured (i.e. angular strain, shear strain, stretching). They also need to have heard of a Mohr strain diagram, and they need to be able to use a protractor to measure angles.

This is a stand-alone exercise that was meant to be done during a lab period.

The goals are to:
Understand the concept of using strain markers to estimate strain.
Understand what shear strain is, and be able identify principal strain axes as directions of zero shear strain.
Learn the concept of relative orientation (orientation of the long axis of a fossil relative to the page).

The main higher order thinking skill is for the students to actually use their own measurements of shear strain to determine the orientation of the finite strain ellipse for this deformed sample.

How to properly use a protractor - originally this was not a goal, but apparently using a protractor is not a skill everyone had mastered

This exercise uses strain markers to estimate strain. The students measure angular shear in 15 strain markers that were in different orientations prior to experiencing homogenous simple shear (done in Illustrator). They also measure the orientation of each strain marker, and lengths of particular lines in the strain markers. They then use this data to determine the orientation of the principal axes of the finite strain ellipse; the lengths of these lines before deformation (assuming plane strain and that all strain markers were the same size originally); and from that they calculate stretching and quadratic elongation and construct a Mohr strain diagram first using their points, and then again using the strain equations with their calculated S1 and S3.

Detailed, step-by-step instructions are found in the downloadable file, which is attached as a Word file as well as a pdf with the deformed 'fossils.'

Measuring Strain pdf with deformed 'fossils' (Acrobat (PDF) 167kB May4 12)
Measuring Strain word document (Microsoft Word 2007 (.docx) 230kB May4 12)
Deformed spirex pdf (Acrobat (PDF) 17kB May4 12)

I tried to write step-by-step instructions. Most of the confusion was on the measurement of long axis orientation on the page. Specifying that they measure the acute angle between the flat edge of the fossil and a line parallel to the long edge of the page seemed to help, but for many students the very idea of orienting something on the page was confusing.
The next confusing part was how to measure angular strain when they didn't have the originally perpendicular line already drawn in for them. Once we got past that it went pretty smoothly for those who were adept at using a protractor.

Because the fossils are numbered it is pretty easy to grade this exercise because they should all have the same numbers within +/- 5˚.

If their Mohr strain diagram is not roughly circular, they missed something.