The window on the right is used to display the Figures in this document. To load a Figure in the window the reader needs to click on the Figure number. So at this time, please click on Figure 1.
Percussion and pressure flaking are generally considered two different processes of flake manufacture. The loads are applied differently, so it is assumed that the processes are different. However, they are exactly the same and, in fact, pressure flaking is a subdivision of percussion flaking. The flake manufacturing process is also not size dependent. A tiny retouched flake from a projectile is created with the same process as a 12-inch blade from a huge prismatic core. Beginning at the time the impactor touches the core, all flakes are made by the first adding potential energy to the core and impactor, next the platform separates, and finally the crack propagates by releasing the stored potential energy in both the core and impactor.
Figure 1 represents a vertical, glass cantilever beam that is ¼-inch thick and 1-inch long and firmly anchor on the bottom. (Click on Figure 1 if you haven't previous done so.) This cantilever beam can be visualized as representing a ¼-inch by 2-inch wide biface that is firmly supported at the midline. If pressure is applied to the end of the biface, it will bend as shown in Figure 2. In the real world this large amount of bending is impossible because glass is too brittle and would break. However, bifaces do bend when force is applied and the bending can be seen with magnification. In the mathematically world, the amount of bending in Figure 2 is possible and it is shown here for instructional purposes.
When the pressure force is slowly removed from the biface, it returns to its unbent shape, which is depicted in Figure 1. Again, Figure 2 is the bent shape and Figure 1 is the unbent or "at-rest-position" shape. If the force is removed instantenously, the biface will vibrate as in Figure 3. This vibration is identical to a tuning fork or the pendulum of a grandfather clock. In the real world, this vibration would soon stop or dampen out just like a tuning fork becomes silent a few seconds after it is struck. However, in the mathematically world the damping portion of this biface has been omitted and it will vibrate until the reader clicks on another figure or turns the computer off.
Clicking on Figure 4 will cause the biface to vibrate for only one cycle. One cycle is the movement from the starting position to the starting position. Click on Figure 4 a few more times and watch the motion during one cycle. The thin, vertical black line in the middle of the Figure is the at-rest-position for the biface. At the beginning of the cycle, the end of the biface starts on the right with no velocity (speed). As it begins to move to the left and towards the at-rest-position it gains velocity. When it crosses the at-rest-position it is at maximum velocity and begins to slow down as it continues to move to the left. At the far left, it stops and then begins moving back to the right gaining velocity as it goes. Again as it crosses the at-rest-position it is moving at it greatest velocity. Moving further to the right, it begins to slow down and finally stops at the far right and the end of a single cycle. The period of this biface is 0.0004726 seconds which is the time it takes to complete one cycle. Or, it makes 2116 cycles per second which is its frequency. A frequency of 2116 cycles per second is well within the audible range of the human ear and, in fact, it lies within the range of the piano.
This period of this biface does not vary with the amount of initial displacement. Figure 5 compares the vibration of the biface for two different initial displacements. As can be seen the time of a complete cycle is the same, even though the red starting position is about half that of the black. This is extremely important because this means that the velocity of the end of the biface is faster for the larger initial displacement. A pendulum on a grandfather clock behaves the same way. The period is independent of the displacement but the velocity is not. The period of the biface is dependent on it shape, mass and material and removing flakes changes its shape and mass, and therefore its period. However, it does not change much with the removal of only a single flake.
Pressure flaking is the application of a slowly increasing force near or on the edge of the core. Pressure flaking is identically to the repetitious process of increasing the load incrementally by one pound, waiting a minute and then increasing it again. It applies the load so slow that the entire core is able to bend or deflect in a response to the force. In different words, there are no inertia effects, the entire core and supports feel the pressure flaking force and response to it. Figure 2 is an example of a load applied by pressure flaking. The entire core has experienced the force and the entire core has been deflected. Additionally, the amount of deflection is related to the amount of force that is applied. The more force, the greater the deflection. This is evident in Figure 5. The black response was created by mathematically applying a force that was twice that of the red response. It is the same cantilever beam in each response.
So what determines how much force the knapper applies to a biface? "Is it the economy?" "Is it the war?" No, it is the platform or force application location (FAL). The strength of the FAL determines how much force the knapper applies to the core. The strength of the FAL varies for a number of reasons. If it is an off-margin FAL, then the greater the distance from the margin the stronger the platform. If it is on-margin platform, then FAL preparation, such as grinding, determines its strength. If the FAL is weak, there is little force applied to the core, there is little deflection in the core, and a little flake is all that is possible. On the other hand, if the FAL is too strong, the knapper cannot muster (created) enough force in this hands and legs to initiate the crack. Platform strength must not be too weak nor too strong, it must be just right. Therefore, it is one of several critical variables a knapper must manipulate while performing either pressure or percussion flaking. This is the reason John Whittaker writes in his book "platforms are the key to successful knapping" (p98). Or, in Bob Patten's book, we find "preparing a stable platform is one of the most crucial skills a knapper can develop" (39).
Figure 6 is an animation of the core as the pressure force is applied to the FAL. The force is applied perpendicular to the FAL at the location of the crosshairs, which is the point-of-contact. The deflections are exaggerated 15,000 times. Click Figure 6 a couple more times and watch the movement of the FAL. In Figure 7, the crack initiation animation has been added. Finally, Figure 8 depicts the creation of the entire flake. Click Figure 8 as many times as necessary to determine what is the movement of the FAL after the crack begins to propagate.
If you have determined that the FAL does not move after the crack begins to propagate, then you are correct. The animation in Figure 8 represents a rigid impactor or pressure tool, which means it does not move after the crack begins. The crack is made to propagate by the core vibrating and pulling away from the stationary FAL. This is an example of the crack being created with only the potential energy that is stored in core. There is no additional energy added by the impactor after the crack initiates.
Inherent in Figure 8 is an assumption I have made in the research. I assume that after the FAL separates there is no restraining force at the crack tip during the propagation of the crack. Therefore, there is no force holding the flake to the core. the crack is created as the core pulls away or separates from the flake, which is held in place at the FAL by the impactor.1 With this assumption I can make a statement about the time it takes to make the flake or the speed of the crack. Notice in Figure 8, the crack finishes at the same time as the core returns to the at-rest-position. The time interval from the beginning of vibration (initiation of the crack) to the core reaching the at-rest-position is ¼ of the period (0.0004726 seconds) or 0.0001182 seconds. Since the core and therefore the flake is 1 inch long, the average velocity can be approximated by dividing the length of 1 inch by 0.0001182 seconds. This velocity is 215 meters per second.2
The flake in Figure 8 is made by a rigid impactor because the FAL never moves after the crack initiates. Rigid impactors do not exist in the real world and can only be created in the mathematical world as I have done here. In the real world, deflection always occurs when a force is applied to a solid object.3 Therefore, when an impactor applies force to a core, it also applies the same force to itself.4. This force on the impactor causes it to deflect, also, as shown in Figure 9. When the crack begins to propagate both the core and the impactor begin to un-deflect or move toward their un-deflected shapes. The un-deflecting of the impactor pushes the FAL away from the core. Watch the FAL (crosshairs) in Figure 10 and observe how it continues to move after the crack is initiated.5 This movement of the FAL is caused by the un-deflecting of the impactor and it assists in making the crack propagate. In the real world the crack is made by both the core and the impactor as they return to their at-rest-positions (or release their stored potential energy).
The relative amounts of un-deflecting contributed by the core and impactor depend on how much each was originally deflected. The original deflections of each are a function of their stiffnesses. If their stiffnesses are the same their un-deflections will be equal. If the impactor is stiffer than the core, its un-deflection will be less than the core; and conversely, if it is less stiff than the core its un-deflection will be greater than the core.6 The following Figures represent different impactor stiffness, which varying from rigid to 10,000 lbs/in. The core stiffness is constant at 50,000 lbs/in. As the reader views these various Figures, please observe the movement of the FAL (crosshairs).
Figure 11 -- Rigid Impactor (also Figure 8)
Figure 12 -- Stiffness=500,000 lbs/in
Figure 13 -- Stiffness=100,000 lbs/in (also Figure 10)
Figure 14 -- Stiffness=45,000 lbs/in
Figure 15 -- Stiffness=10,000 lbs/in
In Figures 11-15, the only parameter that is varying in the impactor stiffness. As can be seen, an impactor that is much stiffer than the core (50,000 lbs/in) is desirable for producing long flakes. As the impactor's stiffness approaches the core stiffness, the crummier the flakes become. When, impactor stiffness becomes less than that of the core, the flakes become undesirable.
|Quick and Dirty Overview|
|Force Application Location Strength|
|Three "Ps" -- Potential Energy, Percussion and Pressure Flaking|
Angle of Blow
1 This assumption is obviously not correct because chemical bonds are broken as the crack is made and this requires the consumption of energy. However, after hundreds of FEA runs, it appears the energy to break the chemical bonds is very minute compared to the energy required to flex and vibrate the core.
2 The average speed of 215 meters per second is too large because the calculation assumes the vibrating core thickness does not change as the flake is made. This is obviously an incorrect assumption because the core thickness is continually changing as the crack is made. Look again at Figure 8. The flake being removed is reducing the 0.25 inch thick core to a thickness of 0.195 inches. This changes the period of the core vibration. A core that is uniformly 0.195 inches thick and 1 inch long will have a period of 0.0006059 seconds or about 30% longer. With this longer period, the average speed of the crack would be 168 meters per second. So the actual average speed of the crack in Figure 8 lies between 168 and 215 meters per second.
3 There are two types of deflection. The temporary one, or the one that disappears when the force is removed, is called deflection. The permanent one is called deformation. Consider a paper clip. If bending it causes no permanent change, it was only deflected. However, if the bending is permanent, then it was deformed.
4 The concept of equal and opposite forces is Newton's 3rd law of motion, which says "whenever one body exerts a force on another, the second always exerts on the first a force which is equal in magnitude, opposite in direction, and has the same line of action" (Physic book page 22).
5 One of the first things to be noticed about Figure 10 is that the bulb of force on the flake is much larger than its scar on the core and, therefore, it looks like it didn't come from the core. This is a product of the software. I have caused the solfware to increase all deflections 15,000 times so they are visible and therefore, the various distance the bulb of force is move is multiplied 15,000 times.
6 Discuss Hook's Law here.