Impact Cratering Lecture 2

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Impact CrateringLecture 2

• Prelude to Impact Stress Waves in Solids

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To understand the impact process, it is essential
to understand how the effects of a sudden blow
are transmitted through matter.We start with
the simplest type of wave in solid matter, an
elastic wave. Elastic waves travel at constant
velocity
Perhaps familiar from sound waves, waves in
solids can be both longitudinal (compressional as
in sound) or transverse. Transverse waves, while
of great importance in seismology, play only a
limited role in impact and we will ignore them
hereafter
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It is, important, however, to understand how
elastic (and stronger) waves interact with
surfaces across which elastic properties change,
such as reflection from a free surfaceAt an
interface normal stress must be continuous. This
boundary condition determines the outcome of a
reflection.
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When two different materials meet, velocity must
be continuous as well, otherwise interpenetration
(or open cracks) would occur
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As waves become stronger, the velocity begins to
increase with the wave amplitude. This leads to
a new phenomenon--Shock Waves.The wave energy
piles up and the wave tries to break--but
unlike an ocean wave, there is material ahead of
it, so it just becomes very sharp
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Richard Courant, at Los Alamos, had an amusing
idea of how shock waves form
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Shock waves are probably most familiar in air or
gases
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The equations describing the jump in conditions
across a shock wave were first derived by P. H.
Hugoniot in his 1887 PhD thesisHe derived his
three equations from the conservation of mass,
momentum and energy--but not entropy
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The behavior of materials subjected to a strong
shock must be investigated experimentally,
generally by colliding one material with another
at high speed
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Explosives are sometimes still used to accelerate
the flyer plate, but most current work uses
light gas guns
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Although simple in principle, the actual
realization of a gun lab can be pretty complex
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as are the techniques used to measure the
response of the impacted materials
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The stress in a shock wave may get so strong that
it fractures the rock. This occurs at the
Hugoniot Elastic Limit
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This failure at the Hugoniot elastic limit takes
place typically at a few Gpa, but it varies
greatly from one material to another
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Crushing at the HEL may be responsible for
shatter cones, forming when a diverging stress
wave encounters an inhomogeneity
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The wave velocity depends upon shock pressure in
a complex way when failure occurs, first dipping,
then rising again
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The behavior of materials subject to a strong
compression can be described by a Hugoniot
curve. It can take one of two forms
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The velocity dip at the HEL allows an elastic
precursor to speed ahead of an intermediate
strength wave
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Such precursors are readily seen in the velocity
gauge records from large (nuclear, in this case)
explosions
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High pressure phase transitions show up as a
sudden decrease in volume at high pressure
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High pressure affects different materials in
characteristic ways, so that examination of a
material makes it possible to estimate the shock
conditions
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Crushing of porosity also reveals itself on the
Hugoniot curve
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Both porosity and phase transitions increase the
heat lost into the material and have a major
influence on how the material releases from high
pressure
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A better way to look at the release path is on a
Pressure vs. Entropy plot
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The pressure release occurs from any nearby free
surface. The release wave generally travels
faster than the shock in the compressed material
and so eventually catches up with it and sharply
weakens it.
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Here is how a real material--quartz--responds to
shock waves
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Quartz and Dunite Hugoniot Data
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Here is the high pressure behavior of Forsterite,
Mg2SiO4
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Shock and release curves on a P-T plot
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My favorite display Pressure vs. Entropy
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Porosity, as one might expect, plays a big role