Note: Descriptions are shown in the official language in which they were submitted.
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SOLID, SOFT, LIGHT METAL IMPACT SKIRTS FOR
RADIOACTIVE WASTE AND OTHER SHIPPING CONTAINERS
B~CKG~OUND OF THE INVEN~ION
~nis invention pertains to the art of impact
arrangements for casks or packages for shipping radioac~ive
waste.
Two categories of radioactive waste casks are
called type A and type B. Each category has re~uirements
for withstanding certain impact forces and other conditions
such as internal and external heat, for example. Type B
casks, with which this application mainly deals, must be
capable of withstanding impacts delivered by dropping a
cask 30 feet upon a substantially unyielding surface wi~h
the cask having the following orientations in the drops:
flat top end or bottom end drop
top or bottom end corner drop
side drop.
One cask end arrangement for absorbing impact
energy is disclosed in U.S. Patent 4,26~,755. This patent
discloses a fuel assembly shipping cask including "a shock-
absorbing piston member associated with the underside of :
the transfer cask, the piston member comprising twomutually spaced-apart metal plates, a multiplicity of
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hollow metal bodies stacked on top of one another there-
between and fastening elements for fastening the piston
member to the lifting devices. If the transfer cask should
then fall, a deformation of the hollow bodies would result.
Energy would consequently be consumed, so that the forces
generated upon impact to the cask would not be merely
temporarily but entirely reduced. The following transfer
cask would thus be gently decelerated and would not rebound
elastically...it is essential that a material with rela-
tively great deformation energy be used which can experi-
ence or withstand a great amount of plastic elongation or
expansion before it breaks, and that, through the herein
afore-mentioned cavities, space is provided for this
plastic elongation or expansion."
U.S. Patent 3,675,746 discloses a deformable
impact energy absorber for use with spent nuclear reactor
fuel shipping casks. The absorber includes a large diame-
ter tubulation 12 within which is packed a plurality of
smaller tubes 14. It is said "as the cross-sectional area
of the tubulation 12 decreases, the resistance to deforma-
tion increases due to progressive deormation of the tubes
14. This increase in resistance to deformation increases
at a readily predictable and somewhat linear rate with
deformations, as shown in Figures 3 and 4. The tubulation
~5 can contain stainless steel or other ductile, high strength
steels, metal or alloys."
U.S. patent 4,423,802 discloses a cask end cap
which includes a number of different compartmentalized
spaces formed by sheet metal members with part of the
compartments containing soft dampening materials such as
balsa wood, and the other compartments containing harder
dampening material such as hard wood.
It is my view that these approaches to absorbing
impact energy by the use of too easily crushable arrange-
ments as disclosed, as well as the use of foam materialsand honeycomb structures, are inferior to my approach in a
number o respects. With such materials and structures,
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pressure and energy absorption increase as a function of
displacement. A major fraction of the energy is absorbed
during the final stages of crushing when the pressure is
the highest. This results in high deceleration forces and
deceleration.
The aim of this invention is to provide impact
absorbing means for a cask in which the deceleration is as
relatively constant as is consistent with the constraints
of geometry of the impact absorbing means.
SUMMARY OF ~HE INVENTION
In accordance with the invention, a radioactive
waste material cask of generally tubular form and having
opposite closed ends is provided with an impact skirt
fitted to the cask at each end, each impact skirt compris-
ing a one-piece, monolithic, member of a solid, soft, light
metal material, such as aluminum, configured in the general
shape of a cap and fitting over an end of the cask. The
cap provides lapping axial and radial portions for adequate
distances, and of adequate thickness, to provide a volume
~O of material in excess of the volume of material subject to
be crushed in specified drop tests such as those required
for type B casks. The volume of material is such that the
displacement of the material with a specified impact will
be less than the material available in the direction of
displacement.
DRA~ING DESCRIPTION
Figure 1 is a somewhat schematic, broken, isomet-
ric view of a casX fitted with impact skirts of one form
according to the invention;
3Q Figure 2 is a graph illustrating the relation of
deceleration forces and crush distances for two different
types o~ deceleration;
Figure 3 is a fragmentary, schematic side view of
a cask with an impact skirt illustrating generally the
volume of the skirt subject to being crushed in a flat end
drop;
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Figure 4 is an end view of the skirt of Figure 3
and illustrating the area of the skirt subject to being
crushed;
Figure 5 is a fragmentary, schematic side view of
a cask with impact skirts, with the cask oriented for a
side drop and illustrating the portion of the skirt subject
to being crushed in such a drop;
Figure 6 is a view corresponding to one taken
along the line XI-XI of Figure 5 and illustrating the area
of the skirt subject to being crushed in a side drop;
Figure 7 is a fragmentary schematic view of the
part of the skirt subject to being crushed in a 45~ corner
drop;
Figure 8 is a view showing one half of the crush
area from a corner drop; and
Figure 9 is a somewhat schematic and fragmentary
view of a section of an impact skirt of a different form
somewhat optimized with respect to reducing the weight of
the skirt.
DESCRIPTION OF THE PREEERRED EMBODIMENTS
Most metals exhibit a pseudo material property
sometimes called "dynamic flow pressure" which is defined
as the energy necessary to displace a unit volume of the
material and has its dimensions in in-lb/in3 or psi for
most light and/or soft metals. The dynamic flow pressure
is relatively constant over a wide range of displacement of
the metal and has a value slightly higher than the compres-
sive yield strength of the metal which permits the absorbed
energy to be substantially directly related to the dis-
placement of the metal which significantly simplifies the
analysis of impact, although the dynamic flow pressure must
be determined experimentally.
The preferred impact skirts according to the
invention are constructed of solid, soft, light metal such
3~ as aluminum~ berylium, magnesium or an alloy of one of
these metals~
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Most type B radioactive waste containers are
cylindrical in shape because such a shape withstands impact
better than a rectangular shape. Referring to Figure 1, a
cylindrical cask generally designated 10 has a side wall 12
and opposite end walls 14. An impact skirt 16 in the form
of a very shallow cup is fitted to each of the opposite
ends of the cask. Each skirt comprises a one piece,
monolithic member of a solid, soft, light metal material
such as aluminum. As can be seen in Figure 1, the inside
corner of the skirt fits to the outside end corner of the
cask. For purposes of description, the axially extending
portion of the skirt which laps the side wall 12 is desig-
nated 18, and the radially extending part of the skirt
which laps the end of the cask is designated 20. The
skirts may be secured to the cask by any of various means.
In the Figure 1 example such means comprises rod and turn
buckle members 22.
It is believed the invention can be best under-
stood in terms of a mathematical analysis of the impact and
the absorption of energy. Therefore the following will
attempt for the most part to explain and describe the
invention in such terms.
The energy to be absorbed by the cask and skirts
will be:
KE = PE = (30 + d~ x 12 x W (1)
where:
~E = Kinetic Energy
~E = Potential Energy
d = displacement following impact
W = Weight of the shipping package
The velocity at impact of an object falling from
a given height ~neglecting aerodynamic drag, etc.) is:
V = ~ 2gD (2)
where:
V = Yelocity at impact
g = acceleration due to gravity
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D = fall distance
The lowest deceleration will occur when the
object is subjected to constant deceleration since the
deceleration will then be a function of the distance over
which the deceleration occurs. The relationship between
constant deceleration and distance and velocity is:
V = ~ 2a'D' (3)
where:
a' = constant deceleration
lOD' = deceleration distance
Since equations (2) and (3) equal each other, the following
relationship for a constant deceleration force is derived.
gD = a'D' (4~
For a 30 foot drop and g = 32.2 ft~sec2, the relationship
for a constant deceleration is:
a' = 360 g's (5)
In which D' is in inches.
For foam, light wood, honeycomb, or other rela-
tively easily crushable materials, the deceleration forcewill be a function of displacement and in an extreme case,
a' could be directly proportional to displacement and the
final deceleration could be twice the average deceleration.
In such ~ case, the follo~ing equation would apply in ~hich
a'' is the maximum deceleration and D'' is the displacement
distance:
2gD = a''D'' (6)
For the same drop distance and force of gravity as used to
obtain equation (5~, the equation for the maximum decelera-
tion is:
,, = 720 g-5 (7)
Figure ~ is a graphical illustration of the
deceleration forces as a function of the crush distance for
a constant deceleration, line 24, and for the deceleration
orce bein~ proportional to displacement, line 26.
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EOMETRY EFFECTS
For each of the drop orientations, that is end,
side, and corner drops, the volume of material crushed and
the projected crush area are the major factors used in
determining the deceleration forces, and these factors are
related to the geometry of the skirt.
Referring to Figures 3 and 4, a cask with impact
skirt is shown oriented for a flat end drop. For the flat
end drop the crushed volume is simply the product of the
crush area times the displacement. In most cases no credit
is taken for the skirt material which extends beyond the
projected area of the cask. In a high impact situation
this material could be displaced without crushing and
therefore would contribute little energy ~bsorption. The
principal equations for analyzing the flat snd drops are
the following:
Crush Volume = ~R21 - R2) ~ x d (8)
Crush Area = (R21 - R2) ~ (9)
The cross hatched area of Figure 3 and 4 represent the
crushed volume and the crushed area, respectively.
~ eferring to Figures-5 and 6, a cask is shown
oriented for a side drop, with the~crush volume and crush
~5 areas schematically shown by the cross-hatched portions.
The equations which apply for the side drop are 10-12
below~
Crush Volume = 2R32W ~18~0 ~ sin~ cos~) (lO~
Crush Area = 4R3 sin~ W (11)
Displacement = R3 (1 - cos~) (12)
~igure 7 includes a cross hatch~d part which represents a
section through the crushed volume along the plane of
maximum material displacement. In Figure 8, the cross
hatched part represents one half of the crushed area and as
projected ~rom Figure 7.
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For a corner drop at a 45 angle the following
equations apply:
Crush Volume = R33 (sin~ _ in~ _ ~rcos~) (13)
Crush Area = R3 [~ cos~ sin~ sin 1 (cosp)] (14)
Displacement = R3 (1 cos~) (15)
Only the flat bottom and flat top drops will give
a constant deceleration using a material with a constant
dynamic flow pressure. Eor both the side drop and the
corner drop the impact area increases as a function of
displacement and the deceleration will increase in direct
proportion to the impact area. In the case of the top and
bottom end drops, the deceleration will be substantially
constant and the displacement can be varied by increasing
or decreasing the inside diameter of the impact skirt. In
other words~ the part 20 of the skirt which laps the end in
a radial direction can be increased or decreased. Like-
wise, the displacement during the side drop can ba varied
by changing the distance the part 18 of the skirt extends
axially along the outer wall 12 of the cask.
Eor purposas of illustrating the concept by
applying the equations to a particular example, a type B
cask is assumed to have a weight of 48,000 lbs. (21770 kg)
and a radius ~Rl~ of 33 inches ~0.84 m). The impact skirt
of the example is~of solid aluminum with a dynamic flow
pressure (DFP) of 15,000 psi (1054 Pa3 with a skirt radius
(R3) of 39 inches ~0.99 m) with a radial overlap of part 20
of two inches (0.05 m3 and an axial overlap of part 18 of
six inches ~0.15 m). The drop distance is of course 30
feet ~9.15 m) with an allowance of half a foot ~0.15 m) for
the displacement. Applying equation (1) it is found that
the kinetic energy is 17.568 x 106 inch pounds (1.98 x 106
J3. Since the kinetic energy eguals the crushed volume
times DFP, the crush volume is determined to be 1171.2 in3
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(0.0192 m3). By inserting the known values of the crush
volume and R3 into equation 13, it can be determined that
the angle ~ for the corner drop is 40.12. The crush area
of the equation 14 can then be found, which in the example
is 446.6 in2 (0.288 m2).
Three other equations useful in determining the
suitability of the impact skirt of the example follow:
Deceleration Force (DF) = Area x DFP (16)
Deceleration (DEC) g's = DF . W (17)
Displacement (D') = R3 (1 s~) (18)
Solving these equations shows a deceleration
force of 6.7 x 106 (29.8 E + 6 N), a deceleration of 139.6
g's, and a displacement o 6.49 inches (0.1~ m). Since the
available material at the crushed corner calculates to be
8.49 inches ~0.~2 m), the percent displacement of the
material is 76.4%.
Corresponding significant values for the side
drop and the flat end drop for the example can be calculat-
20 ed from equations 8-12 and 16~
The volume of each impact skirt can readily be
calculated and then converted to the weight of the skirt,
which for the example calculates to 1823 lbs. (828 kg) for
each o~ t~e two skirts.
~5 Through the use of the solid, soft, light metal
impact skirts according to the invention and the dynamic
flow pressure principal, the impact skirt can ~e configured
to optimize the weight relative to deceleration forces to
specifi~d values required to protect the cask. This cannot
readily be done, if at all, with foam or honeycomb materi-
als since they do nct lend themselves to be shaped to
remain free standing. With the foam and honeycomb materi-
als, daceleratio~ forces and energy absorption vary with
the amount o~ compression, and complex computer programs
would be required to analyze such structures under impact
conditions.
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Figure 9 shows one example of how an impact skirt
could be configured to reduce weight and still provide
adequate impact protection. The extreme outside corner of
the impact skirt designated 28 in Figure 9 has been removed
since the amount of material displaced in crushing a corner
is small until significant displacement has occurred. The
cross hatched area is representative of the depth of the
crushed volume in a section with a corner drop.
For purposes of calculation, it is assumed that 5
inches of material is removed in each direction from the
extreme outside corner on an impact skirt identical to the
impact skirt of the first example. The calculated weight
removed from each skirt would be 373 lbs. (1~ kg).
Through calculations similar to those done in
connection with the first example, it is determined that
the area, deceleration force, and deceleration all increase
in the carner drop by about 9.8%. The displacement in-
creases about 6.6% so that the increase in displacement is
about 6%. The important result of such reconfiguring is
that while the deceleration is only increased by 9.8%, the
weight is decreased by 20.5%.
Other reconfiguring is also possible such as the
addition of material represented by the dash line triangle
30 which would decrease the deceleration force in a side
drop, although it would add some weight to the skirt. The
concept here is that the area of the displaced material
during displacement is held more constant since while it is
increasing in a circumferential direction, it is decreasing
in the axial direction.
