Examples
Equivalent Thickness
• When a thermoplastics is specified as a
replacement for another material, the new
part often needs to have the same stiffness
as the old one
• Deflection is proportional to 1/E*I
– E is modulus
– I is moment of inertia
– I is proportional to thickness3
Equivalent Thickness
Equivalent Thickness
Equivalent Thickness
Equivalent Thickness
• Calculate the thickness
of a part that when
made of polycarbonate
will have the same
deflection as a
0.75mm thick
aluminum part at
73deg using moduli of
the two materials
Equivalent Thickness
• Calculate the thickness
of a part that when
made of polycarbonate
will have the same
deflection as a
0.75mm thick
aluminum part at
73deg using thickness
conversion factors
Thermal Stress
• Thermal expansion and contraction are important
considerations in plastic design
• Expansion-contraction problems often arise when
two parts made of different materials having
different coefficients of thermal expansion are
assembled at temperatures other than the end use
temperature
• When the assembled part goes into service in the
end use environment, the materials react
differently, resulting in thermal stress
Thermal Stress
• Thermal Stress can be calculated by:
Thermal Stress
Thermal Stress
Thermal Stress

E

• E = 300,000 psi for polycarbonate
• σ = 1000 psi
Beam Analysis
• Alternate designs for park bench seat members
• Example of the method a designer will use to
estimate bending stress, strain and deflections
• Material is recycled polyolefin
• Design for two people, 220lbs each, for 8 hours
per day
• 10 year service life
Beam Analysis
Beam Analysis
• Plastics have the advantage of durability, through
coloring and design flexibility
• Plastics have the disadvantage of relatively low
modulus values, particularly at elevated
temperatures
• Designer must estimate the maximum stress and
deflection for each of the proposed designs
– Failure could result in personal injury
• Creep must be consider in the long term
application
Beam Analysis
Beam Analysis
• Support
– The planks are beams resting on the bench
supports that have an unsupported length of 48
inches
– Support conditions at both ends exhibit
characteristics of both simple and fixed
supports
– A beam with simple supports represents the
worst case for maximum possible mid-span
stress and deflection
Beam Analysis
• Loading conditions
– Bench is loaded and unloaded periodically, not
continuous
– Loading is intermittent rather than fatigue
– Loads are static
– Weight of the beam is of concern, due to creep
– Assume 2 people, 220 lbs each, for 8 hour per
day distributed over the length of one beam
Beam Analysis
• Loading conditions
– Full recovery is assumed to occur overnight
– The size of the continuous, uniformly
distributed load, due to the weight of the beam
must be determined
– The deflection and stresses resulting from the
intermittent external load are superimposed on
the continuous uniformly distributed load
caused by the weight of the beam
Beam Analysis
Beam Analysis
Mm *c
m 
I
2
w* L
Mm 
8
4
 5* w * L
ym 
384* E * I
• Equations
– Generalized equations for a
beam with partially
distributed loads and simple
supports are
• At L/2
• L length in inches
• C distrance from the
neutral axis to surface
• W is load in lbs/in
• E is the materials modulus
• I moment of inertia, in4
• M the bending moment,
Beam Analysis
• Service Environment
–
–
–
–
Used outdoors throughout the year
Used in various climates
Contacts various cleaners
Maximum service temperature is assumed to be
100ºF
– Service life is ten years
Beam Analysis
• Material Properties
– In this application, the planks are loaded for
extended periods of time and creep effects must
be taken into account
– The appropriate creep modulus is used in the
maximum deflection equation
– The deflection and stress are due to both the
beam weight and the external load
Beam Analysis
• Material Properties
– Maximum deflection will occur at the end of
the service life, 10 years, due to internal loading
• E = 2.5 x 105 psi
– Maximum deflection will occur after 8 hours of
continuous loading due to the external load
• E = 3 x 105 psi
Beam Analysis
Beam Analysis
Beam Analysis
• The external loading, uniformly distributed due to
the weight of the two adults is the same for all
four cases
– we = 2*220lbs/48 inches = 9.17 lbs/in
• The internal load change in each case
– wi = density*volume/length
•
•
•
•
Solid
Hollow
Rib
Foam
=
=
=
=
0.46 lbs/in
0.22 lbs/in
0.28 lbs/in
0.37 lbs/in
Beam Analysis
Beam Analysis
Beam Analysis
Maximum Deflection Calculation
ym ,T  ym ,e  ym ,i
y m ,e
( 5)(9.2)(484 )

(384)(300,000)(1.69)
( 5)(0.46)(484 )
ym ,i 
(384)(250,000)(1.69)
ym ,T  ( 1.25in )  ( 0.075in )
ym ,T  1.325inches
Beam Analysis
MaximumStress Calculation
M *c
( w * L2 )
m  m
Mm 
I
8
 m,T   m,e   m ,i
( we * L2 ) c
*
 m ,e 
I
8
(9.2 * 482 ) 0.75
*
 m ,e 
1.69
8
( wi * L2 ) c
*
 m ,i 
I
8
(0.46* 482 ) 0.75
*
 m ,i 
1.69
8
lbs
lbs
lbs
 m,T  1170 2  58.6 2  1230 2
in
in
in
Beam Analysis
Beam Analysis
• Comparisons
– Solid is lowest in stress and deflection, but the material
and manufacturing costs are excessive and quality
problems with voids and sink marks
– Hollow offers a 50% material savings, but only a
26% increase in deflection and 28% increase in
stress
– Rib offers a 38% material savings and a 41% increase
in deflection and 59% increase in stresses
– Foam offers a 20% material savings and 28% increase
in deflection and 29% increase in stresses
Living Hinge
Living Hinge
• A living hinge is a thin flexible web of material
that joins two rigid bodies together.
• A properly designed hinge molded out of the
correct material will never fail.
• Long-life hinges are made from polypropylene or
polyethylene.
• If the hinge is not expected to last forever,
engineering resins like nylon and acetal can be
used.
Figure: This polypropylene package for baby wipes utilizes a
living hinge.
Living Hinge
• Before designing a living hinge, it is important to
understand how the physical properties relate to
the hinge design calculations.
• There are three types of hinges:
– a fully elastic hinge, capable of flexing several
thousand cycles
– a fully plastic hinge, capable of flexing only a few
cycles
– and a combination of plastic elastic, capable of flexing
hundreds of times
Living Hinge
Stress / Strain Curve
Yield Stress
Stress
Elastic Limit
Initial Modulus
Ultimate (breaking) Strength
Secant Modulus at Yield
Elastic Region
Plastic Region
Plastic w ill recover its original shape.
Long life hinges are designed in this
region.
Plastic w ill not recover its original shape. A
living hinge designed in this region w ill not last
long.
Strain
Figure 1: Typical stress/strain curve for metals and some plastics.
Living Hinge
• When a living hinge is flexed, the hinge's plastic
fibers are stretched a certain amount, depending
on its design. The amount of stretch is the crucial
factor determining hinge life.
• To design a fully elastic hinge, the hinge's
maximum strain must be in the elastic region of
the curve; the plastic will fully recover its shape
after a flex, and should last for many flexes.
• A plastic hinge design that experiences strain in
the plastic region, will see permanent deformation,
and will last only a few flexes.
Living Hinge
Figure 3: Dimensions for a right angle hinge.
Figure 2: Dimensions for a 180 polypropylene and polyethylene
living hinge.
Living Hinge
• Hinges designed for polypropylene and
polyethylene should follow dimensional
guidelines to create a fully elastic hinge that
will last forever.
– Figure 2 shows some general dimensions for a
properly designed living hinge.
– Figure 3 shows dimensions for a right angle
hinge
Living Hinge
Figure 4: This is an example of a poorly
designed hinge with no recess. When bent, the
absence of a recess creates a notch.
Figure 5: The recess on top of the hinge
eliminates the notch when it is folded.
Living Hinge
• The two major features of a living hinge are the
recess on the top and the generous radius on the
bottom.
• Figures 4 and 5 show the purpose of the recess.
– Many hinges are designed without a recess; as a result,
when the hinge is bent 180, a notch is formed. This
hinge design creates greater stress in the web, and the
notch acts as a stress concentrator. Hinges designed
this way will not last long.
– Figure 5 shows that with a recess, the notch is
eliminated, and the web is able to fold over easier.
Living Hinge
• The large radius on the bottom of hinge helps
orient the polymer molecules as they pass through
the hinge.
• Molecular orientation gives the hinge its strength
and long life.
• Commonly, immediately after a hinge part is
molded, the operator or a machine will flex the
hinge a few quick times to orient the molecules
while the part is still warm.
Living Hinge
• The hinge dimensions for polyethylene and
polypropylene are based on the materials'
properties, including modulus, yield stress, yield
strain, ultimate stress, and ultimate strain.
• Because other resins' properties vary widely,
living hinge dimensions must be calculated for
each particular resin.
• Figure 6 shows the dimensions that will be used in
the calculations.
Living Hinge
• Basically, the calculations find the maximum
strain in the hinge and compare it to the material
properties.
• If the strain is below the elastic limit, the hinge
will survive.
• If the strain is in the plastic region, the hinge will
last a few cycles.
• If the strain is the past the breaking point, the
hinge will fail.
Living Hinge
• Several simplifying assumptions are made,
and tests have shown the assumptions are
sound.
– 1) The hinge bends in a circle and the neutral
axis coincides with the longitudinal hinge axis.
– 2) The outer fiber is under maximum tension;
the inner fiber is under maximum compression.
– 3) When the tension stress reaches the yield
point, the hinge will fail by the design criteria.
Living Hinge
Refer to Figure 6.
L1 = R (the perimeter
of semicircle).
L0 = (R + t)
Figure 6
L1:Length of the hinge's neutral axis
t:Half the hinge's thickness
l:Hinge recess
R:Hinge radius
L0:Length of the hinge's outer fibers
ε bending
L 0 - L1

L1
Living Hinge
L1 
Figure 6
L1:Length of the hinge's neutral axis
t:Half the hinge's thickness
l:Hinge recess
R:Hinge radius
L0:Length of the hinge's outer fibers
L1 
tπ
ε bending
tπ E secant,yield
σ bending
Living Hinge
• Elastic Hinge
– In a fully elastic hinge design,
• bending must be less than yield
• and bending must be less than yield.
– Failure occurs when
• bending = yield
• and when bending=yield.
– Either equation can be used, depending on
whether yield stress or strain is known.
Living Hinge
• To use the equations, find the yield strain (yield),
or the yield stress (yield) and secant modulus at
yield (Esecant, yield).
• Substituting these values into the equations will
result in the lowest value of L1 that will yield an
elastic hinge.
• Either the hinge thickness or its length must be
known as well.
• Generally, a minimum processing thickness is
selected, ranging from 0.008" to 0.015", and then
a length is calculated.
Living Hinge
Figure 6
L1:Length of the hinge's neutral axis
t:Half the hinge's thickness
l:Hinge recess
R:Hinge radius
L0:Length of the hinge's outer fibers
Figure 7: Hinge dimensions for
calculations
Living Hinge
• Plastic Hinge:
– A plastic hinge will only last a few cycles.
– Cracks will probably start on the first flex.
– Calculations for a plastic hinge are the same as those of
for an elastic hinge, except ultimate and ultimate are used.
L1 
tπ
ε ultimate
L1 
tπ Esecant,ultimate strength
σultimate
Living Hinge
• Processing Conditions
– The key to living hinge life is to have the polymer
chains oriented perpendicular to the hinge as they cross
it.
– As stated earlier, parts are generally flexed a few times
immediately after molding to draw and further orient
the hinge molecules.
– Another important factor in determining orientation is
gate location.
• It is crucial to maintain a flow front as parallel to the living
hinge as possible.
Living Hinge
Figure 9: An example of a poorly gated part.
Living Hinge
Figure 10: A properly gated hinged part.
• Example of a properly gated
part. A wide flash gate is
placed on one end to create a
flat flow front when the plastic
reaches the hinge.
• This results in even flow over
the hinge, and provides proper
orientation direction.
• Locating a gate at the center of
one end of the part would be
another suitable gate location.
Living Hinge
• Material: Hoechst Celanese
Acetal Copolymer, Grade TX90
Unfilled High Impact
• Tensile Strength at Yield: 45
MPa
• Elongation at Yield: 15%
• 2t (hinge thickness) = 0.012"
• l (hinge recess) = 0.010"
• This is a 180 hinge.
• Find the minimum hinge length
for a fully elastic hinge.
Living Hinge
• For a fully elastic
hinge, the minimum
hinge length is
calculated using
• L1 = (t) / yield
• L1 = (0.006"*3.14159)
/ 0.15
• L1 = 0.126" for a
fully elastic hinge
Living Hinge
•
•
•
•
•
•
•
•
Material: Dupont Zytel 101 NC010 Nylon 66, Unfilled
Tensile Strength at Yield: 83 MPa
Elongation at Yield: 5%
Elongation at Break: 60%
2t (hinge thickness) = 0.012"
l (hinge recess) = .010"
This hinge only has to bend 90.
Find the minimum hinge length for a fully elastic design.
Living Hinge
• Since the bend is 90,  can be substituted with
/2 (this can be found from the previous
derivation).
– L1 = (t/2) / yield
– L1 = (0.006"*3.14159*0.5) / 0.05
– L1 = 0.188"
• For a 180 bend, L1 would need to be 0.376".
– This is probably not moldable.
– Even 0.188" may be difficult to mold.
Snap Fits
Snap Fit
• Snap fits are the simplest, quickest and most cost
effective method of assembling two parts
• When designed properly, parts with snap-fits can
be assembled and disassembled numerous times
without any adverse effect on the assembly.
• Snap-fits are also the most environmentally
friendly form of assembly because of their ease of
disassembly, making components of different
materials easy to recycle.
Snap Fit
Snap Fit
• Most engineering material
applications with snap-fits
use the cantilever design
• Other types of snap-fits
which can be used are the
“U“ or “L“ shaped
cantilever snaps
• These are used when the
strain of the straight
cantilever snap cannot be
designed below the
allowable strain for the
given material
Snap Fit
• A typical snap-fit
assembly consists of a
cantilever beam with
an overhang at the end
of the beam
• The depth of the
overhang defines the
amount of deflection
during assembly.
Snap Fit
• The overhang typically has a
gentle ramp on the entrance
side and a sharper angle on the
retraction side.
• The small angle at the entrance
side (α) helps to reduce the
assembly effort, while the sharp
angle at the retraction side (α“)
makes disassembly very
difficult or impossible
depending on the intended
function.
• Both the assembly and
disassembly force can be
optimized by modifying the
angles mentioned above.
Snap Fit
• The main design consideration of a snap-fit is
integrity of the assembly and strength of the beam.
• The integrity of the assembly is controlled by the
stiffness (k) of the beam and the amount of
deflection required for assembly or disassembly.
• Rigidity can be increased either by using a higher
modulus material (E) or by increasing the cross
sectional moment of inertia (I) of the beam.
• The product of these two parameters (EI) will
determine the total rigidity of a given beam length.
Snap Fit
• The integrity of the assembly can also be
improved by increasing the overhang depth.
• As a result, the beam has to deflect further and,
therefore, requires a greater effort to clear the
overhang from the interlocking hook.
• However, as the beam deflection increases, the
beam stress also increases.
• This will result in a failure if the beam stress is
above the yield strength of the material.
Snap Fit
• Thus, the deflection must be optimized with
respect to the yield strength or strain of the
material.
• This is achieved by optimizing the beam
section geometry to ensure that the desired
deflection can be reached without exceeding
the strength or strain limit of the material.
Snap Fit
• The assembly and disassembly force will increase
with both stiffness (k) and maximum deflection of
the beam (Y).
• The force (P) required to deflect the beam is
proportional to the product of the two factors:
– P= kY
• The stiffness value (k) depends on beam geometry
Snap Fit
• Stress or strain is induced by the deflection
(Y)
• The calculated stress or strain value should
be less than the yield strength or the yield
strain of the material in order to prevent
failure
Snap Fit
• Cantilever beam:
deflection-strain
formulas
Snap Fit
• Cantilever beam:
deflection-strain
formulas
Snap Fit
• Cantilever beam:
deflection-strain
formulas
Snap Fit
• The cantilever beam formulas used in
conventional snap-fit design underestimate the
amount of strain at the beam/wall interface
because they do not include the deformation in the
wall itself.
• Instead, they assume the wall to be completely
rigid with the deflection occurring only in the
beam.
• This assumption may be valid when the ratio of
beam length to thickness is greater than about
10:1.
Snap Fit
• However, to obtain a more accurate
prediction of total allowable deflection and
strain for short beams, a magnification
factor should be applied to the conventional
formula.
• This will enable greater flexibility in the
design while taking full advantage of the
strain-carrying capability of the material.
Snap Fit
• A method for estimating these deflection
magnification factors for various snap-fit
beam/wall configurations has been developed
• The results of this technique, which have been
verified both by finite element analysis and actual
part testing, are shown graphically
• Also shown are similar results for beams of
tapered cross section (beam thickness decreasing
by 1/2 at the tip).
Snap Fit
• Determine:
– The maximum
deflection of snap
– The mating force
Snap Fit
• The maximum deflection of snap
Snap Fit
• The mating force
Snap Fit
• Is this type of snap fit
acceptable for nylon
6?
Snap Fit
• Solution