One focus of my research is the question,"Why
do cracks wiggle?" If you look at any crack moving through
a material, let's say glass or plastic, it tends to go pretty straight
for a while and then, all of a sudden, it starts
to move erratically. You might at first think this is due to
impurities in the material or the size of the grains that the substance
is composed of, and this could be the case if we are talking about cracks
in the sidewalk. However, even in glasses and polymers, substances considered
homogeneous (uniform throughout) and isotropic (the same in all directions),
oscillations of the crack tip are seen that do
not correspond to the sizes of any of the components in the material.
This leads us to think that there may be something more basic going on.
In fact, there are additional aspects of crack wiggling that make it
even more fascinating. In 1957 A.N. Stroh made the argument that the highest
speed a crack could move should be the Rayleigh wave
speed, the same speed that a sound wave
would travel on the surface of the material. Although this conjecture
was later confirmed in more mathematically rigorous treatments of the problem,
careful experiments performed on cracks in homogeneous materials show that
the crack never seems to reach this speed.
In fact, what is seen is that when the crack starts to wiggle it stops
accelerating. In the end it only attains 30-50%
of the theoretical limiting speed.
This observation is very exciting to physicists because it looks very much like the signature of what we like to call a dynamic instability. A system is stable if when you give it a little kick it just returns to where it was. Consider, for example, a pendulum. If the pendulum is at rest and you give it a little shove it oscillates around the initial position and eventually comes to rest there again.
There are other systems, much more complex than a pendulum, which are also stable, for example the climate. Many things act as kicks to our planet's climate like a volcano erupting or some other catastrophic event. Usually, however, there may be a cold winter or a particularly dry summer, but things settle back down to the ordinary patterns. This is dynamic stability: stability arising from the interplay of many changing quantities. However, if a dynamical system experiences a big enough change, such as build up of pollution or a change in absorbed solar radiation in the case of the earth's climate, the normal stable state may cease to be stable. At that point any small kick will cause the system to change drastically and come to some possibly very different state, like an Ice Age. The point at which this occurrs would be the onset of a dynamic instability.
We suspect that the crack may, in fact, be reaching a point of dynamic instability at some speed less than the Rayleigh wave speed. If this is the case, understanding the forces at work near the crack tip may be the key to predicting the final crack velocity and understanding the onset of the wiggling.
Computer simulations are a key aspect of my research due to their unique ability to bridge the gap between theory and experiment. Computational scientists can now run simulations of cracks in pieces of material with more than a million molecules. This may seem big, but a million molecule simulation still means you are looking at something smaller than the thickness of a human hair. If we pull these computer models apart violently enough we can get similar behavior to that seen in experiment. However, unlike the experiment we can look at what happened frame-by-frame like a slowed-down movie. Then we can examine how stresses built up at each point in the material, how the material heated up, and other quantitative measures that might give us insight into the intricate workings of the system as it fails. The amount of detailed information you can obtain from a simulation is truly incredible. But the real challenge is, can we get the simulation to point us in the right direction in order to devise some theory of how cracks behave in general?
With a little hard work maybe we can crack this problem.
Credits & Sources:
Crack Photographic art by Scott Steffens, UNL
Volcano: Photograph of the Eruption of Crater Peak, Spurr Volcano Alaska <http://mojave.wr.usgs.gov/pub/spurr/Spurr.html>
