Time-dependent Brittle Failure

When Geologists and Engineers think about the formation and propagation of a fracture in a brittle solid such as a rock they envision the rock subjected to an effective stress behaving elastically until it reaches the "rock strength", then fracture(s) ensue propagating at high speed and seismic waves are detected. However, that is not the only way fractures form and propagate in brittle solids.

In fact, last April 10, 2018 I had a very common occurrence here in Houston, TX which prompted me to collect data, make observations, and ultimately draw some conclusions. As I was driving on the highway, a pebble hit my windshield. At first, no apparent damage was observed. I parked my car in the shade and after a two-hour meeting I went back to the car and found a rather long crack formed on the windshield. After the upset I decided to learn something and began monitoring the crack tip position starting on Apr. 11, 2018 every 24 hours at 2:30 PM. What I observed was rather interesting. The crack continued to propagate very slowly, for days instead of seconds or milliseconds. These kinds of fractures won't even generate seismic waves.

Here's the data I collected

In the table above, time is recorded in hours, the fracture cumulative length is expressed in mm from time zero (Apr 11, 2:30 PM). Interestingly the fracture remained (apparently) inactive at two different times intervals: Apr 15-19 and Apr 21-22. I also recorded the max and min outside temperature with the intent of studying the effects of diurnal temperature excursions on the apparent fracture propagation velocity and I also recorded the occurrence of rain (as total in inches). Notice that the propagation velocity is an "apparent" velocity calculated solely on the basis of the crack tip location over 24 hour periods.

Graphing the Fracture Cumulative Length as a function of Elapsed Time, ignoring the intervals of apparent inactivity (represented by the + in the graph below), I obtained the following plot which clearly indicates that the crack growth is following a logarithmic law.

The obvious questions are:

1. What caused the crack initially?
2. Why propagation occasionally stops and restarts?
3. Why does the crack continue to propagate through time?

The first question is simple to answer. The crack was initiated by the high velocity impact of a pebble on the windshield. According to the Griffith theory of brittle failure, the impact generated a stress field large enough to have at least one of the intrinsic glass defects (material scientists call them "dislocations") take off and develop in a true open crack. What stopped the propagation of the crack and what made it restart? The stress at the fracture tip dissipates with the deformation. However, during the apparent inactive time when the crack tip is not propagating there are other phenomena that take place. For one, the diurnal thermal excursions and the inherent difference in temperature between parts of the frame and the glass can induce thermal stresses at the fracture tip. Also, the presence of fluids, typically water, might contribute to the weakening of the stressed molecular bonds at the fracture tip. When these thermal stresses become large enough, tip propagation restarts and crack length grows.

Let's take a look at the outside temperature record through time. In the plot below DT=TMax-TMin notice that the diurnal temperatures excursions are decreasing with time, however the induced thermal stress cannot be quantified since the differences in temperature between the glass and it's frame have not been measured. We can only assume their occurrence.

If we plot the apparent propagation velocity (blue) versus elapsed time and we also highlight the occurrence of rain (red), we obtain the following

Which indicates: 1. the fracture is decelerating with time (and deformation); 2. there's no apparent clear correlation between occurrence of rain and the restarting of crack propagation. However, we can safely assume that in Houston moisture is always present in open fractures whether it rains or not, therefore the lack of correlation might be only apparent.

Conclusions: 1.Not all brittle fractures develop instantaneously and in a seismic fashion; 2.Some fractures are time-dependent and asismic

Please don't try to replicate this on purpose.

Comments? Thoughts?