|MadSci Network: Physics|
There are a lot of issues involved in determining the effects of impact. I have tried to find a primer on impact phenomena on the net and haven't been successful (maybe I'm just not looking in the right places). So, let's examine what happens in impacts at various velocities. At low speed, when one object hits another, forces at the surface of the impacting objects have enough time to spread from the surface through the materials. Under these conditions, relative hardness and strength of the surfaces is very important. Consider a water drop hitting a hard surface. As long as the speed of the droplet is quite low, the droplet splatters and the hard surface remains unchanged. Quite simply, the water molecules do not have enough energy to move around any atoms in the hard surface or break any bonds. Furthermore, there is enough time for the surface forces to spread through the material. As the speed of the moving object increases, there are several effects that can cause the target to be damaged: 1. The kinetic energy of the object is high enough that the force exerted by the moving object exceeds the local compressive strength of the target, 2. The kinetic energy of the object is high enough to melt or vaporize the surface of the target being hit, or to product other temperature related phenomena such as thermal shock, and 3. Stress waves are set up in the material, which can cause failures at discontinuities away from the point of impact. How a material reacts to impact depends in part on the ductility or brittleness of the material. A ductile material, such as a piece of copper, can have a hole punched through it without the bulk of the material fracturing or flying apart. That is why copper makes a good liner for shaped charge explosives. A brittle material, such as window glass, will often fracture into many pieces upon impact. However, under some conditions of speed and geometry, sometime a high speed object will leave a funnel shaped hole in the glass. The glass in the immediate impact area will be crushed and broken, but the remainder of the glass may remain intact. When impact velocities are high enough, the relative properties of the target and the object hitting the target don't matter much. Since the second world war, copper liners have been used in shaped charges to blow holes in steel armor. Because the copper is traveling at thousands of meters per second and can exert tremendous forces on the steel, it doesn't matter that the steel is much harder than the copper (which is likely in a liquid form anyway). See http://www.llnl.gov/str/pdfs/06_98.3.pdf for an interesting discussion about shaped charge research in which a shaped charge penetrated 3.4 meters of armor steel. In this article, because armor steel is not brittle, a hole from a shaped charge can be punched through it. Sapphire windows used on high speed missiles can be eroded and damaged by rain drops, even though the sapphire is much, much harder than liquid water. Sand in the inlet of a jet engine can cause enormous damage to the turbine blades because of high speed impact and erosion. High pressure water mixed with a small amount of abrasive can be used to cut almost any material (water-jet or abrasive-jet cutting). So the physics of high speed liquids and particles apply in a variety of applications. Now, to attempt to answer your question, we need to examine the materials involved. Chalk is a brittle, weak material. Under impact conditions, the chalk will undergo brittle fracture, turning essentially into dust. Whether the chalk is moving and the target is stationary, or the target is moving and the chalk is stationary doesn't matter; the forces on the chalk are the same. Say the chalk hit a ductile target such as copper; even though the impact might leave a hole in the copper, the forces to rupture the copper are much higher than those necessary to crush the chalk. At very high speeds, there is no mechanism that might magically increase the strength or ductility of the chalk, so after an impact, the chalk will be in the form of small bits. Diamond is likewise a brittle material, even though it is very hard. Diamond can be broken by applying force with a steel wedge and a mallet, even though the diamond is much harder than the steel. Thus, when subjected to a very high speed impact, it is likely that the diamond will also fracture. Because it is much stronger than chalk, the pieces of diamond remaining after impact may be larger than the chalk pieces. And. like window glass, it may be possible that a high speed projectile may punch a hole through the diamond, leaving behind a hole. But in any case, the chalk will be destroyed. At least that is how it see it. Thanks for an interesting question.
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