November 14, 1998
Modified September 30, 1999
The following image represents the flakes that Pelcin made from 1/2-inch thick glass cores with an external platform angle (EPA) of 55 degrees and angle of blow (AOB) of 70 degrees. (A detailed description of this core is located on the FEA page.) I selected this data to make my first FEA replication attempts because it represented the largest number of flakes created for a single set of conditions. This data is the same flakes indicated as the yellow diamonds in the image on the page describing Pelcin's Research.
Notice there is a very good, almost linear, correlation between flake mass and theoretical platform thickness (TPT) up to a TPT of about 23 millimeters. These are the energy-rich flakes. Above this value the mass values begin to flatten out and then rapidly drop (transition) around 27 millimeters to the energy-poor flake correlation. The reader should remember that these flakes, represented by the blue diamonds, were real flakes created by a dropping a 45 gram steel ball from a height of 125 centimeters. They were not created by the FEA software. As I wrote on the page about Pelcin's research, when I first saw this transition from energy-rich to energy-poor in the real data I was surprised. I did not expect it and at that time I could not explain it. However, I believed that if I could replicate these flakes along with the transition with the FEA model, then I would know why the transition was occurring.
After many months and many hours per day, I finally discovered how to replicate the flakes for this set of conditions, 55 degree EPA and 70 degree AOB. As I predicted, I now understand why the transition is occurring and I plan to share this with the reader. However, I want to postpone the explanation of the transition and first look at the replication results.
The red diamonds marked #1 through #4 indicate the flakes I created with the FEA software. These four FEA flakes are depicted next for the reader to get an appreciation for the difference.1
If the reader was asked to arrange the flakes into two groups, I am sure they would put #1, #2 and #3 in one group and #4 in the other group. Flakes #1 through #3 are long and narrow and get proportionally larger as the TPT gets thicker. However, flake #4 is definitely different. It is much shorter, thicker and does not have the mass of a flake with a similar TPT from the first group. Another way of describing the two flake groups is that #1 through #3 have the center of mass located away from the platform and #4 has it closer to the platform. So which group would make the best biface thinning flakes? Which group would be most desirable to turn the edge angle without removing significant mass? Obviously, the answers are energy-rich flakes and energy-poor flakes.2
To understand the mechanics of the formation of these flakes, I will begin with the concept of deflection (strain). When a force is applied against the platform, e.g. at 6 millimeters, the core is deflected. If the deflection is small and below the failure limit, the core will return to its original shape when the force is removed. This is identical to bending a paper clip. When the force is applied at a different location, e.g. 15-mm, the core will deflect to a different shape, but it again will return to its original shape if it is not deflected passed the failure limit. However, if the deflection is so large that the core cracks, then it will obviously never return to its original shape.
When the force is applied against the platform and the core is deflected, there is potential energy stored in the core. The more it is deflected the more potential energy is stored. When the force is removed, the core gives up that potential energy and returns to its original shape. If the force is applied at different location, the core will deflect differently and the amount of stored potential energy is different.
Realistically, to apply a force it must be done by way of an object and this object also deflects. Consider two pool balls. When one pool ball hits another, there is an instance when both balls deflect and potential energy is stored in both. This potential energy comes from the conversion of the kinetic energy of the moving ball. Then the balls convert their potential energy back into kinetic energy by returning to their original shape. When this happens the two balls move apart.
In most of Pelcin's research the object was a steel ball that applied the force to the core. So, the impact of the steel ball against the glass core caused both the glass core and the steel ball to deflect. The deflections are not in the same ratio as two identical pool balls because the steel ball and glass core are different materials and different shapes. However, both do deflect and there is an instant before they return to their original shape. If the glass core doesn't crack then the steel ball bounces off the core.
If enough potential energy is added to permanently deform the core, a crack (start of the flake) is initiated. It is at this instance that the difference between a energy-poor flake (Flake #4) and a energy-rich flake (Flake #3) occurs. I want to first describe the energy-poor flake because it is easier to explain.
When the energy-poor flake (Flake #4) first begins to crack, the core gives up some of its potential energy the steel ball has imparted to it. At this instance, the crack stops because there is not enough potential energy to continue to separate the rock. (Hence, the name is energy-poor.) When the steel ball rebounds (return to its original shape) it applies more force and the crack is continued. As the crack continues downward the lateral (horizontal component) force from the right is being amplified by the propagating of the crack (cantilever beam effect). Ultimately, the amplified lateral force (bending moment) changes the direction of the crack towards the edge and breaks the flake out.3
When the energy-rich flake (Flake #3) begins to crack, it does not stop and wait for the ball to help it. This flake cracks on its own because of the abundance of stored potential energy. (Its name is energy-rich.) This is similar to the crack that results from putting hot water on a frozen windshield. The crack occurs so rapidly that the ball does not have time to rebound before the crack finishes it downward travel.4 The crack stops its downward movement when the potential energy released per millimeter of crack length drops below the value to separate the glass. When the ball finally rebounds its lateral force immediately pushes the flake out, as it did with the energy-poor flake. The important point here is that the energy-rich flake crack is so fast that it reaches its total length before the ball pushes it out. This length is always longer than a energy-poor flake because there is no lateral (horizontal) force to break it out prematurely. Hence, it is a more massive flake.
If the reader is a knapper you are aware of the sound a good flake makes when it is created. To me this sound is a "snap". I believe that this "snap" is associated with energy-rich flakes as they are releasing their potential energy. I don't believe the energy-poor flake makes this type of sound. I would be interested in any knapper's comments on this speculation. My email is firstname.lastname@example.org.
At this point I want to remind the reader that all the flakes (energy-rich and energy-poor) discussed on this page were made from glass cores with an EPA of 55 degrees, AOB of 70 degrees, and 45-gram ball dropped from 125 centimeters. The only thing that was varied was the location of the blow (contact point of ball and glass). When the ball was dropped near the edge of the core (small TPT) it was able to store enough energy in the core to create a energy-rich flake. As the location of the blow was moved toward the center of the core, more energy was required to create the energy-rich flakes because the flakes were getting larger. Finally, a distance (TPT) was reach where the core stopped yielding energy-rich flakes and started yielding energy-poor flakes. Continually increasing the TPT even more ultimately resulted in the ball bouncing off the core. At this TPT, the core required more energy to make a energy-poor flake than the ball conveyed.
#1 The reader may have noticed that the masses of the FEA produced flakes tend to be higher than an average regression line through the real glass flakes. This disturbed me for a time until my son (William Baker) who is a mechanical engineer pointed out that ceramic materials (glass is one) tend to fail at values less than their know strength. This happens, "because the tensile properties of ceramics depend so critically on the size and geometry of the ever present flaws, there is considerable scatter in the values for the strength determined from a tensile, bending, or fatigue test" (Askeland 1994:436). The FEA model does not have any flaws in it. It will produce the biggest flake every time. On the other hand, Pelcin's real world flakes suffer from the properties of ceramics as do all flakes from either the archaeological record or the modern knapper. I found it very substantiating that Pelcin was aware of this real world problem as he conducted his research and that I, with the aid of my son, arrived at the same conclusion independently.
#2 The missing rectangular, lower right hand corner in all four images is where the core was clamped to the table so it was not part of the core under stress. Therefore, I eliminated it from the FEA model to reduce the number of nodes and elements to analyze.
#3 When I first began the FEA replication work, I had the full force that represented the ball attached to the core all the time the crack was occurring. This is the mechanics for creating the energy-poor flakes. Since I was trying to replicate the energy-rich flakes with the small TPT, the flakes would always be too short and lacked the mass. I tried tweaking the glass properties every way I could think of, yet nothing would work. I finally realized that the lateral force was breaking the flake out too soon. So I development a method to reduce the force as the crack propagated. I did this with springs that restrained the force with deflection and I began to successfully replicate the energy-rich flakes. When I finally attempted replicating a energy-poor flake, my results were now too long and massive. Then I remembered I had tweaked the glass properties early on in the research to replicate the energy-rich flakes (which had only help a little). So I returned to the published glass properties and I was able to create energy-poor flakes with the correct mass. Strange is the path of research.
#4 The speed of the energy-poor flake is equal to the rebound speed of the steel ball and the glass core. I do not know what this value is. I do know Crabtree made Mesoamerican blades in the energy-poor mode and his propag ation speed were 125 meters per second assuming a 10 centermeter blade (1968:474). Hutchings (1997:50) reported minimum velocities of 118 and 152 meter per second for metal and antler pressure flaki ng. It is possible steel balls could create energy-poor speeds as high as 200 meters per second, but I believe this would be the upper limit.