MadSci Network: Physics

Re: What would happen if you shot a piece of chalk at a diamond at mach 7?

Date: Tue Apr 3 15:44:26 2007
Posted By: Joseph Weeks, Engineer
Area of science: Physics
ID: 1173999860.Ph

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 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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