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An MD&DI January 1998 Column
TESTING
Calculating
Factors of Safety for Package Burst and Creep
Test Fixtures
A
method for inflation seal strength testing employs
flat restraining plates.
Stephen Franks
Testing
flexible packaging for burst seal strength and
creep resistance continues to be an important
aspect in ensuring overall device integrity. An
improved method of performing these tests involves
the use of restraining plates to restrict package
movement. Given the high pressures and forces
used in such testing, the safe and effective design
of these restraining fixtures is critical to protecting
operating personnel. When equipment designers
are determining appropriate construction of the
plates, a factor of safety-the ratio of the allowable
load on a structure to the actual load-must be
calculated and incorporated into the process.
UNRESTRAINED TESTING
This article explains an approach that can be
used to create safe and effective flat plate fixtures.
Because of risks inherent in pressure testing,
the author recommends that a knowledgeable engineering
group determine the proper design criteria, materials,
and processes for manufacture and maintenance
of these fixtures. Selection of adequate factors
of safety for fixture design must be based on
the understanding of the specific application.
Burst seal strength and creep resistance tests
are commonly used to minimize the time involved
in obtaining quantitative values of flexible package
quality parameters or to provide information about
process control or performance. A burst test value
is obtained by inflating the package at a uniform
rate to its maximum pressure, which is indicated
by rupture of one of the seals. A creep or creep-to-failure
test delivers a constant inflation pressure to
the package interior to measure the creep resistance
of seals during a specified time period. These
creep tests are considered analogs of differential
pressures experienced by the package during sterilization
or transport cycles.
Since the initial implementation of inflation-type
seal-strength tests, most manufacturers have used
them on packages that are not restrained in any
axis and that therefore are not prevented from
expanding. This technique, described in "ASTM
F 1140-96, Standard Method for Failure Resistance
of Unrestrained and Nonrigid Packages for Medical
Applications,"1is subject to variations in
package geometry and material properties. In its
essence, the method permits the package geometry
to attempt to move into a balloon or membrane
structure. While the inflation pressure is uniformly
distributed in the package, the seal stresses
generally are not, unless the package geometry
is spherical, which is not common for medical
device packages. As a result, packages with asymmetrical
geometry will have varying stresses and deflection
to rupture the seals. Most commonly, for example,
rectangular packages with one long axis will rupture
along this axis unless a manufacturing abnormality
weakens the adjacent short-axis seals. Such long-axis
rupturing is expected if each axis is considered
a beam whose deflection is a function of its length
and subsequent stress is highest at the point
of maximum deflection. The seal stress can also
be increased by the presence of geometry-related
hoop stresses, in which forces are applied to
the package's periphery. Furthermore, properties
of the packaging material may affect test results
when stretching or fracture of the films occur.
RESTRAINED
TESTING
While unrestrained testing produces a reliable
measure of flexible package strength and process
operation, some manufacturers have found that
restraining plate tests control the uniformity
of applied stress at the seal and provide more
consistent information about a package's minimum
seal strength area. Restrained testing is characterized
by the presence of a wall, force, or device that
prevents the package from full expansion. Information
on the precision and bias of the methodology is
being compiled by ASTM committee F2.6 on flexible
medical packaging.
Applying uniform stress to all three or four seals
of a rectangular open or closed package is one
aspect of evaluating seal strength. The uniformity
of stress arises from the uniform geometry of
the restrained seal around the perimeter of the
package. An approximation of this geometry is
shown in Figure 1. In an ideal model, the package
film material is supported by the restraining
plates that are rigid relative to the film. A
relatively uniform radius (R) is then created
at the seal with uniform force vectors being applied
by the internal pressure (P). If for simplicity's
sake we assume that only forces perpendicular
to the seal (Fy) are acting to peel open the seal
surfaces and the forces parallel to the seal (Fx)
have no effect, then we can understand how uniformity
of geometry and lack of hoop stress effects will
provide more consistent seal strength results
along the seal perimeter.
 |
Figure
1. An approximation of the stress created
by uniform seal geometry around the package
perimeter (P = internal pressure, R = radius,
Fy = forces perpendicular to the seal, and
Fx = forces parallel to the seal)
|
The
use of restraining plate tests as part of the
measuring process for burst seal strength and
creep resistance tests is expected to grow. In
anticipation of the method's increasing use, ASTM
committee F2.6 is drafting proposed standards
for restrained pouch and blister package configurations.
However, there are concerns about the safe use
of such restraining fixtures. The issues of fastener
strength and proper materials selection for the
plates must be addressed since significant forces
may be created by using pressure sources and large-area
bags.
The
forces placed on the restraining plates are caused
by the inflation pressure applied to the package
and the package's area of contact on the fixture
according to the following equation:
F
= P x A
where
F = force in pounds, P = applied pressure in pounds
per square inch, and A = the area of contact in
square inches. For example, a 5 x 5-in. bag at
3 psig at burst will apply 75 lb of equivalent
force to each plate in a restraining fixture.
For a 12 x 15-in. bag at 20 psig, there is an
equivalent force of 3600 lb applied to each plate.
These forces must be resisted by both the plates
and their restraining fasteners.
PLATE
FIXTURE DESIGN
When considering the construction of the restraining
plate fixture, the designer must anticipate the
largest loads expected, determine the fastening
configuration of the fixture, and take into account
the test operator's ease of use. Other aspects
to consider include factor of safety, bolt size
and material, effects of repeated loading (fatigue),
plate thickness, allowable deflection, and maximum
pressure. These are discussed below.
Factor of Safety. Before considering the
bolt size and load relationship, a factor of safety
should be chosen. Applying a factor of safety
of 3.0 to 5.0 will usually be adequate, based
on a well-designed fixture created by a knowledgeable
engineering staff.
Bolt Selection. To understand bolt size
requirements, consider a fixture with two plates
that are bolted at the four corners and in the
middle of the two longest sides. The shorter sides,
where the package will be inserted, are left open.
The minimum bolt size required to resist the applied
load can then be calculated. Using six bolts with
a 12 x 15-in. fixture with a 20-psig maximum working
load, the total load is 12 x 15 in. x 20 psi =
3600 lb. Dividing the force over six retaining
bolts yields 600 lb per bolt, and using the factor
of safety of 3.0, the design load is 1800 lb per
bolt.
For
a common steel bolt, the allowable yield stress
is defined by material properties and the stress
area of the bolt. This enables the allowable load
to be calculated by multiplying the allowable
stress by the specified stress area.
Using the calculated load and applied factor of
safety of 3.0, the bolt size with the minimum
tensile strength nearest to and greater than the
design load is 5/16-18 (Table I). This bolt has
a minimum tensile strength of 2850 lb, whereas
a bolt one size lower is below the design load
requirement. The actual factor of safety is 2850/600
= 4.75. Even though this figure is greater than
the original target, it is advisable to use it
when also considering the fatigue life of the
bolt under conditions of repeated loading.
 Fatigue. The engineering literature indicates that bolts
that are properly tightened (and therefore have
adequate preload) and subject to variable loads
that are less than the preloads will have virtually
infinite life. Consider a 5/16-18 bolt that, as
indicated in Table I, has a preload of 1710 lb
at 60% of its yield strength. If the bolt is subjected
to a repeated load of 600 lb, it will have a life
of 1 million to 10 million or more cycles with
a factor of safety of 2.85. This calculation is
also predicated on the selection of bolt materials.
If a higher-grade bolt such as a grade 5 or 8
is used, then an even greater factor of safety
is achieved. Since bolt quality can vary, the
selection of higher-grade bolts will provide greater
assurance of meeting the design criteria.
Table I indicates the torque required to achieve
a preload of 60% of the yield strength of the
bolt. Proper preloading assumes that the material
surfaces are smooth and uniform, that there are
no gaskets or compliant washers to prevent substantial
contact of the bolt with the plates, and that
the applied preload is maintained. If the preload
is lost, the factor of safety for repeated loading
is lost, and fatigue failure may become an issue.
Plate
Selection. The plate thickness is chosen based
on several factors, including safety, material,
size, and restraining conditions. From standard
engineering references such as Formulas for Stress
andStrain,3 formulas can be found to approximate
stress and deflection in the fixture plates for
given test pressures and pouch sizes. However,
these formulas consider only standard boundary
and loading conditions and should be used only
as a guide to and approximation of real-life designs.
For example, our model assumes that the plate
edges are held on two sides, not four. A change
in boundary conditions may affect the choice of
the factor of safety used in the following calculations.
A more sophisticated finite-element analysis of
specific design configurations can be conducted
with appropriate computer and engineering expertise.
The designer of the fixtures must use caution
in applying formulas based on idealized design
equations. Because most real-life designs do not
precisely fit the engineering model equations,
it is advisable to consult with a knowledgeable
engineering professional to confirm the safety
aspects of these mechanical designs.
 A
simplified approach to estimating the basic strength
and deflection of the fixture is to use the standard
plate deflection formula for simply supported
plates of thickness (t) and dimensions a (length)
and b (width) (Figure 2). The "simply supported"
assumption allows for rotating edges during deflection
and represents a maximum case compared to a "fixed
edge" assumption. The stress and deflection,
respectively, can be calculated as follows:
S
= ßwb2/t2 and Y = wb4/Et3
where
S = stress, Y = deflection, and both are maximum
at the center of the plate. and ß are empirically
derived constants that are a function of dimensions
a and b. The material factor for rigidity of the
plates is Young's modulus (E), and the load w
is in pounds per square inch. The load is assumed
to be uniform over the entire surface. Table II
shows the relationship of , ß, and dimensions
a and b.
The
designer must consider first of all the safety
of the design by choosing a plate thickness (t)
and its material through determination of its
stiffness factor E and its yield strength. Table
III lists the approximate modulus and yield strength
for four common materials: stainless steel, aluminum,
acrylic, and polycarbonate polymers. The most
rigid material is steel, the weakest are acrylic
and polycarbonate polymers. Generally, a high-quality
aluminum is a better choice for strength, deflection,
weight, and machinability. However, steel may
be required for larger plates or higher pressures.
Plastic should be avoided because of its inadequate
strength and stiffness properties, as well as
its relaxation properties under loads from the
restraining bolts.
 Figure
3, using an assumed value of w = 20 psi, shows
data on a 6-in.-wide plate fixture and demonstrates
the relationship of a, b, and t, related to deflection.
The same data are used in Figure 4 to show the
relationship of yield stress to a, b, and t. Again,
using a factor of safety in the design is prudent.
An indication of a stress factor of safety of
2.0 is shown in Figure 4. By decreasing the allowable
stress from the expected yield stress of 42,000
psi to 21,000 psi, the plate thickness is increased
for the factor of safety.
 In
this example with a 6 x 6-in. plate of 2024 -T4
aluminum with an assumed pressure contact area
over its entire surface, a minimum thickness of
0.125 in. would be suggested since its a/b = 1
and its calculated stress of 13,250 psi is below
the yield stress with a factor of safety.
Deflection
Allowance.
Another consideration for the designer is the
allowable deflection of the package and fixture.
Returning to Figure 3, the deflection of the plate
at 20 psi when the plate thickness is 0.125 in.
can be found from the chart as 0.06 in. For the
most consistent test results, the package and
fixture should deflect a minimal amount to maintain
the geometry of the seal forces. While this consideration
is in the hands of the designer, a maximum deflection
of 0.03 to 0.06 in. at the plate center is, in
practice, very noticeable. In this case, selection
of a thicker plate will lower the visible deflection
as well as provide a greater factor of safety
in the design. The deflection and related burst
seal strength pressure can be influenced by the
plate separation distance 2R seen in Figure 1.
Larger separations will yield lower average burst
seal strength pressures and thereby lower both
the stress and deflection values. Required bolt
sizes and loads are calculated and designed as
previously discussed.
Maximum
Pressure. Finally, the maximum pressure capability
of the test instrument should be evaluated for
the 0.125-in.-plate-thickness fixture in the same
way as the working pressure was evaluated. This
evaluation indicates that if a product package
were able to withstand this maximum instrument
pressure, or if accidental application of the
maximum instrument pressure were applied to the
fixture, then the fixture would be of adequate
strength.
For a test instrument with a maximum capability
of 50 psig, when w = 50 psi, b = 6 in., a = 6
in., a/b = 1.0, and t = 0.125 in., the stress
is calculated to be about 33,000 psi for the plate,
a figure that is below the maximum yield of 42,000
psi for this particular aluminum alloy and temper.
The bolt load is 450 lb per bolt for a four-bolt
pattern. Referring to Table I, the use of 1/4-20
steel bolts would provide adequate strength and
a factor of safety of 1750/450 = 3.9. This may
be a larger and more prudent bolt size selection
than previously calculated for the working pressure
design criteria.
CONCLUSION
As plate dimensions grow, so do the stress and
deflection. Careful planning must be used in the
design of the restrained plate fixture to ensure
the safety of its use in its maximum loading condition
as well as in its expected operating condition.
A prudent operating facility will also observe
safety precautions such as use of safety glasses
and protective shields for operating pressurized
equipment.
In practice, most porous packages made of paper
or Tyvek with peelable adhesives will burst in
the 1-3-psi range. In these cases, using metal
plates and properly designed bolts will provide
adequate protection against catastrophic failure
of the fixture. However, with nonporous materials,
more attention must be paid to expected seal-burst
pressures, since some heat-welded seals may yield
at burst pressures of 50 psi or more.
The practical designer, in conjunction with knowledgeable
engineering consultation, will use conservative
design criteria and will select materials with
known properties. By employing thicker plates
and larger fasteners when necessary, a fixture's
factors of safety can be increased.
REFERENCES
1. "ASTM F 1140-96, Standard Test Method
for Failure Resistance of Unrestrained and Nonrigid
Packages for Medical Applications," 1997
Annual Book of Standards, vol 15.09, West Conshohocken,
PA, American Society for Testing and Materials,
1997.
2. Daniels DB (ed), Society of Manufacturing Engineers,
Tool and Manufacturing Engineers Handbook, 3rd
ed, New York, McGraw-Hill, 1976.
3. Roark RJ, Formulas for Stress and Strain, New
York, McGraw-Hill, 1965.
4. Harper CA (ed), Handbook of Plastics and Elastomers,
New York, McGraw-Hill, 1975.
Stephen
Franks is executive vice president for T.M. Electronics,
Inc.
(Boylston, MA).
Copyright
©1998 Medical Device & Diagnostic Industry
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