Introduction to Earth Sciences I
Geophysics Lab # 2
Deformation Properties of Earth (-Like) Materials
One of the most important ways in which we learn about the properties of materials is to subject them to stress and measure the amount and form of the deformation (strain) relative to the stress applied. These so-called stress-strain relationships are a principal guide to nature of the material.
The Earth includes materials that can deform in an elastic manner that is, they respond reversibly to deformation together with materials that behave in a plastic or ductile manner deformation is irreversible and materials that flow like a very thick fluid. In fact, in the Earth, the same material can exhibit different properties depending on how deep they are in the Earth and the time scale of the deformation.
The purpose of the lab is to investigate some simple properties of materials by deforming them in various ways.
A. Elastic materials.
You have numerous pieces of steel in the form of rods of different diameter and pieces with rectangular cross-section, and some pieces of wood. The object of the first part of the experiment is to deform them within their elastic limits. To do this either clamp the material at both ends over an open space, or at one end using the C clamps provided. To deform the materials under different stresses use the hanging scale provided to pull down on the middle (if clamped at two ends) or the end (if clamped at one end only) by different amounts. Measure the amount by which the material is deflected from horizontal as shown.
Build up data points of stress (the reading on the scale) and strain (the amount of deflection) for about ten incremental stresses of say one pound through ten pounds. Then plot these points on a stress-strain diagram. It should look something like this.
Each material should plot as a different slope on the stress-strain diagram. A very strong material will deform little for a given stress and have a steep slope, an easily deformed material should have a shallow slope. The slope of the line gives a measure of the material strength.
B. Going beyond the elastic limit.
At some large stress value all materials exceed their elastic limit. Some break, and others go into a different deformation domain. Usually the new domain is one in which deformation is irreversible the material changes shape when stressed but does not return (fully) to its original shape. We can explore this with the materials we have by subjecting them to high loads. So what we need to do is go well beyond the ten pound limit that we imposed on the previous experiments.
The pieces of wood should break. Watch the scale carefully and note the breaking stress.
The thinner pieces of metal should go into a domain where they bend but do not return to their original shape. Try to plot the points for deformation beyond the elastic limit on the same diagram as used for the elastic deformation and see if you can locate the stress point where the the material exceeds its elastic limit.
The thicker pieces of metal will probably be so strong that you will not be able to get them beyond their elastic limit.
All the metal rods are made from essentially the same material so it is clear that we are not measuring an intrinsic property of the material but one that is governed also by the size and shape of the materail.
Question:
If we are not measuring an intrinsic property of the metal, what are we measuring?
Finally, take one of the pieces of metal or other material and heat it in the center. Carry out the deformation experiment as before. You should find that the material reaches its elastic limit at lower stresses than when it was not heated.
Question:
Why do heated materials reach their elastic limit at lower stresses than the same material at colder temperatures? Whay is this important in the Earth?
C. Viscous flow.
This one is a little harder. What we will try to demonstrate is the time dependence of deformation in materials. You have a container that can be filled about half way with a mixture of corn starch and water. This proves to be a very interesting Earth-like material. Any of you who went to the Lamont Open House would have seen the properties of the mixture demonstrated quite graphically.
First, the extent of deformation depends on the rate at which stress is applied. If I slap the top of the mixture it will not splash out onto the floor. Try it!. However, if I gradually apply a force to the surface it will deform quite readily. You can push your fist into the mixture by applying a constant pressure. What you are observing is that the deformational response of the material depends on note only the size of the applied force but on the time frame over which the force is applied. This is very typical of earth materials on short time scales they behave elastically or somewhat like a rigid body, but if stress is applied over long (geological) time scales they will deform in a plastic or ductile manner. A measure of this is the viscosity.
Next, take a large beaker fill it with water and place it on the surface of the mixture. It will gradually sink. Measure the rate of sinking by taking measurements of the height of the top of the beaker at intervals of perhaps 30 seconds. It will eventually stop sinking. Then lift the beaker out and watch the material flow to fill the hole created by the beaker. You can make a plot of the height of the beaker top versus time like this
It will be much harder to measure the inflow rate but what you can do is see if the material takes the same total time to in-fill the depression caused by the beaker. From that you will know if the material deforms the in the same way under compression and tensional stresses.
Next, heat the material on the hot plate and repeat the beaker experiment. What you will see is that the beaker sinks faster and the hole in the mixture recovers faster. What you are observing, as in the Earth, is that the material becomes less viscous (flows more readily) as it gets hotter.
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