### ViscoLecture - Rose

```Design With Viscolelastic Materials
Dealing with Time and Temperature
Dependence
Design with Viscoelastic Materials
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How are Properties Defined?
Introduction to Viscoelasticity
Strain Rate and Temperature Effects
Simple Material Models
Empirical Methods
2
Learning Objectives
Upon completion of this session, participants will be able to:
mechanical properties.
2. Define creep and stress relaxation and describe design
situations for each.
3. Apply manufacturer’s data to design for applications in both
4. Relate data from creep curves and isochronous stress strain
curves.
5. Apply snap fit design guidelines.
3
Review
• Basic definitions: thermoplastic, thermoset,
elastomer.
• Let’s talk about the kind of mechanical
behavior seen in polymers.
1. Strength
2. Stiffness
3. Ductility
• Factors which can determine the strength of a
polymer.
4
Tensile Properties for Polymers
Polymer Yield Strength is
defined by the first peak
on the stress strain
diagram, not the 0.2%
offset used for metals.
5
Strength is:
• A measure of stress
units of ksi or MPa)
• Yield Strength (1st peak
in uniaxial tension test)
• Ultimate Tensile
Strength (Highest
stress in uniaxial
tension test)
6
Stiffness is:
• Young’s Modulus (Elastic
Modulus), E with units of
ksi or MPa
• The slope of the straight
line part of the stressstrain curve
• The ratio of stress to strain
(where strain is the change
in length with respect to
the original length, ΔL/L0)
E
7
Ductility is:
• % Elongation (with
units of in/in or
mm/mm)
• The permanent
percentage change on
length after fracture
(from a uniaxial
tension test)
ΔL/L
8
Mechanical Properties
Stress-strain
behavior of
polymers
brittle polymer
FS of polymer ca. 10% that of metals
plastic
elastomer
elastic modulus
– less than metal
Strains – deformations > 1000% possible
(for metals, maximum strain ca. 10% or less)
Callister 7e.
9
Question
1. Two cantilevered beams of identical geometry have identical loads applied at their free ends.
A
P
B
P
While the load is applied Beam A deflects twice as much as Beam B. Thus:
i) The Strength of Beam A is
a) Higher than Beam B
b) Lower than Beam B
c) Can’t be determined with respect to Beam B from this information
ii) The Stiffness of Beam B is
a)
Higher than Beam B
b)
Lower than Beam B
c)
Can’t be determined with respect to Beam B from this information
iii) The Ductility of Beam B is
a)
Higher than Beam B
b)
Lower than Beam B
c)
Can’t be determined with respect to Beam B from this information
10
Introduction to Viscoelasticity
1. Mechanical properties depend on
Temperature
2. Mechanical properties depend on Strain Rate
3. Creep (progressive change in strain at
constant stress)
4. Stress Relaxation (progressive change in
strain at constant strain)
5. Hysteresis (significant difference in load and
11
Effect of Temperature on Strength
As Temperature Increases
• Strength Decreases
• Stiffness Decreases
• Ductility Increases
“Celanese Nylon 6/6
Processing and
Troubleshooting Guide” by
Ticona
12
Time Temp for Delrin (Strain Rate)
http://www2.dupont.com/Plasti
gn/230323c.pdf
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Effects of Strain Rate and Temperature
stress
Increasing
strain rate
Increasing temp
strain
14
Time Temp for Delrin (Strain Rate and Temp)
http://www2.dupont.com/Plasti
gn/230323c.pdf
15
Time Temp Dependence
• Plastic deformation of polymers involves chain
uncoiling and chain sliding
• Increasing temperature increases relative
space between chains and makes uncoiling
easier.
• Slowing the strain rate means there is more
time for chain reconfiguration.
16
Questions
1. As you increase the temperature of a polymer, you expect
i) The yield strength to (increase, decrease, stay the same)
ii) The Young’s Modulus (stiffness) to (increase, decrease, stay the same)
iii) The % Elongation (ductility) to (increase, decrease, stay the same)
2. As you increase the strain rate (faster loading) of a polymer, you expect
i) The yield strength to (increase, decrease, stay the same)
ii) The Young’s Modulus (stiffness) to (increase, decrease, stay the same)
iii) The % Elongation (ductility) to (increase, decrease, stay the same)
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Creep
• Take a tension specimen
apply a constant stress.
• We observe
Creep: Progressive strain (deformation) over time at
constant stress (load), usually at high temperatures
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Creep Test
• We instantly load with constant stress for
a certain time, and instantly unload.
Note that both linear
elastic and viscous fluid
behaviors are present.
 Note that there seems to
be some residual strain at
the end, i.e. the material
does not completely
recover. There is both
elasticity and plasticity.

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“Zytel/Minlon Design
Guide” DuPont
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Creep of PEEK
“PEEK Properties
Guide” Victrex
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Stress Relaxation

Think of a polymer
with a constant
strain.

Note that both linear elastic
and viscous fluid behaviors
are present.
Note that there seems to be
some residual stress at the
end, i.e. the material does
not completely recover.
There is both elasticity and
plasticity.
Stress Relaxation: Progressive loss of stress (load) over
time under constant strain (deformation), usually at high
temperatures
23
Stress Relaxation of Delrin
http://www2.dupont.com/Plasti
gn/230323c.pdf
24
Questions
1. A plastic bolt is used to hold two halves of a housing together. The loading in the bolt is best
described as
a) Creep
b) Stress Relaxation
2. A gasket is compressed between the two halves of the housing described in the previous
b) Creep
b) Stress Relaxation
3. A cantilevered snap fit arm does not completely straighten after installation. The lading on the
arm is best described as
a) Creep
b) Stress Relaxation
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Effect of Temperature-Glass Transition
Or why does Garden
Hose behave the
way it does?
Vinyl Garden hose
can go from flexible
to rigid as the
seasons change.
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Glass Transition Temperature
Many amorphous materials show a
change in behavior as the material
changes from viscous to rigid.
For polymers, the rigid behavior
below Tg results from the inability of
the chains to move easily (chains
have insufficient free volume to coil
and uncoil).
29
Melting Temperature
For polymers, Tmelt usually refers to the transition from
semicrystalline to fully amorphous rather than a solid to
liquid transformation.
Thus, a melting temperature may not be reported for an
amorphous polymer, and some polymers may be both
liquid and crystalline.
(Some companies report a crystalline temperature and a
melting temperature.)
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Melting vs. Glass Transition Temp.
What factors affect Tm and Tg?
•
•
•
Both Tm and Tg increase with
increasing chain stiffness
Chain stiffness increased by
1. Bulky sidegroups
2. Polar groups or sidegroups
3. Double bonds or aromatic
chain groups
Regularity – effects Tm only
Callister 7e.
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Tg and Tm
32
Questions
1. As we increase the temperature of a polymer from below the glass transition temperature to
above the glass transition temperature we expect the stiffness
a. To increase by orders of magnitude
b. To increase slightly
c. To decrease by orders of magnitude
d. To decrease slightly
e. To remain the same
2. Below the glass transition temperature, molecular chains
a. Can’t coil and uncoil
b. Can coil and uncoil but with significant difficulty
c. Can easily coil and uncoil
33
Hysteresis
same line on the stress-strain curve.
• The difference in areas under those curves
represents energy loss (often to heat).
• This means that polymers can have inherent
energy damping.
• This means plastic springs may not be as good
an idea as plastic dampers.
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Hysteresis in Delrin
“Delrin Design Guide” DuPont
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Time Dependent Response can be
Modeled
• Maxwell Model
• Kelvin-Voight Model
• 4 Element Model
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Maxwell Model
• Here is an alternative to the simple spring
model of linear elasticity. Add a damper. This
gives what is called as the Maxwell model.
In the limit, it’s
a fluid!
strain
stress
Creep not too
good!
time
Stress
relaxation is
time
38
Kelvin-Voigt Model
• Try putting the spring and damper in series
This gives the Kelvin-Voigt model.
In the limit, it’s a
solid!
strain
stress
time
Doesn’t really
show stress
relaxation!
time
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4 Element Model
Standard Linear Solid
• Further improvement is possible.
stress
Shows both creep
and stress
relaxation!
strain
time
40
Stress Strain Relationships
• We can get stress from strain history and
strain form stress history through the
following heriditary relationships.
K is creep modulus, and F is the relaxation modulus.
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Examples of These Time Dependent
Moduli
Material
Creep Modulus
Relaxation Modulus
Maxwell
Kelvin Voigt
Standard Linear Solid
 1 1
 
E 

t  H ( t )

 E 
   t
1 

1 e  
 


1  
1   1 
ER  


E e

 H (t )


t
 
e



 H (t )

E 
   t
 
H (t )
  (t )  E H (t )
 

E R 1   1  

 
t
  
e



 H (t )

H(t) is the unit step function. (t) is the Dirac delta function
42
More on the material models
• Testing needs to be done to fit the parameters of
the model to the behavior of an actual material.
• Note the fact that the history of the material
must be recorded to be able to complete the
calculations.
• Some additional complexity. The parameters in
the creep modulus and relaxation modulus are
1. Temperature Dependent
2. Strain Rate Dependent
43
Summary
Polymers exhibit:
• Great sensitivity to temperature.
• Great sensitivity to strain rate.
• Very complex behavior
Model parameters are difficult to determine –
Therefore we will use an empirical approach.
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Without Effective Math Models we will rely on
Manufacturers Data to make Design Decisions
• What are the limitations of Material Data
Sheets?
• What do the polymer companies recommend?
• How do companies report time and
temperature dependent properties?
• Designing using Creep information.
45
Empirical approach
• Use published information on behavior
 Suppliers data sheets
 Suppliers creep curves
46
What can we learn from
Supplier Data Sheets
Polymer parts in service will generally have
lower material property values Strength,
Stiffness, and Impact Energy than the ones listed
in the Supplier Data Sheet.
47
What are the problems for
Strength and Stiffness values?
• Tested at a single temperature (usually room
temp)
• Tested at a single strain rate.
• Effects of colorants and other additives
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Impact data may thickness sensitive.
Polycarbonate Resin – Product Brochure, Sabic
49
Impact Data may Depend on Notch
Delrin Design Guide, DuPont
50
Polymer Flow Affects Properties
http://www.ides.com/articles/design/2006/sepe_07.asp
51
What does the Designer Do?
From Lavengood and Silver in “Interpreting supplier
Data Sheets”, ASM Engineered Material Handbook,
Polymers:
Tensile and Flexural moduli “may be used
directly in design calculations for items that do
not carry sustained loads and are not
exposed to elevated temperatures or adverse
environmental factors.”
In other words, we can use the supplier data for a
clean, dry, indoor application of primarily
decorative function.
52
Company Recommendations
General Design Principles for DuPont Engineering Polymers
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Company Recommendations –
Preliminary Design
What safety
factors do
these numbers
represent?
Designing with Plastics, The Fundamentals - Ticona
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What do Plastics Companies
Recommend?
• Checklists
• Use of Creep Curves
• Confirm by Testing
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Checklist from Bayer
http://www.bayermaterialsciencenafta.com/checklist/
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From the DuPont Checklist
http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
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DuPont Checklist-Mechanical
http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
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DuPont Checklist-Environment
http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
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Other DuPont Checklists
Writing Meaningful Specifications
A specification is intended to satisfy functional, aesthetic and economic requirements
by controlling variations in the final product. The part must meet the
complete set of requirements as prescribed in the specifications.
The designers’ specifications should include:
• Material brand name and grade, and generic name (e.g., Zytel® 101, 66 nylon)
• Surface finish
• Parting line location desired
• Flash limitations
• Permissible gating and weld line areas (away from
critical stress points)
• Locations where voids are intolerable
• Allowable warpage
• Tolerances
• Color
• Decorating considerations
• Performance considerations
General Design Principles for DuPont Engineering Polymers
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DuPont Example
General Design Principles for
DuPont Engineering Polymers
61
Long Term Properties for Example
General Design Principles for DuPont Engineering Polymers
62
General Design Principles for DuPont Engineering Polymers
63
General Design
Principles for
DuPont
Engineering
Polymers
64
General Design
Principles for
DuPont
Engineering
Polymers
65
How Do Companies Report Time and
Temperature Dependent Properties?
•
•
•
•
Creep Curves (Strain vs. Time)
Isochronous Stress Strain Curves
Creep Modulus (Modulus vs. Time)
Stress Relaxation Curves (Stress vs. Time)
All curves must contain information on:
Stress, Strain, Time, Temperature
66
Data is usually taken
in a creep test and
replotted for the
other graphs.
Designing with Plastics, The Fundamentals - Ticona
67
Creep Curve
Creep curves
show the data
as it was most
likely measured,
as strain vs. time
for constant
stress.
“PEEK Properties Guide” Victrex
68
Isochronous Stress-Strain Curves
Creep data is plotted as
constant time
(isochronous) stress vs
strain curves at a given
temperature
http://bmsnafta-campusi.com/matdb/matdb.php
69
Creep Modulus vs. Time
Creep Stress is
divided by strain
at a given time to
determine a
“Creep” modulus.
http://bmsnafta-campusi.com/matdb/matdb.php
70
Exercise
Confirm that the Creep Modulus Curve is a
replotting of the Isochronous Stress-strain
Curve.
Use the data shown on the Isochronous curve
for Apec 1745 polycarbonate to create the 15
Mpa line on the Creep Modulus plot for Apec
1745.
71
Stress Relaxation Curve
Stress Relaxation
should be tested
under constant
strain, but most
reported results
and replotted
creep curves.
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Designing with Celcon - Ticona
Where do these ratios come from?
Talk to the supplier.
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Designing with Celcon - Ticona
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A BASF Approach to Design
A method described in BASF’s document,
“Review of mathematical design methods for
thermoplastic machine parts”, uses multiplied
“efficiency factors” to account for the effects of
These factors multiply together in a manner you
may have seen before in fatigue design.
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A BASF Approach to Design
The design stress is the published strength, K,
divided by the safety factor and the product of
all the “efficiency factors”.
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Suggested Safety factors
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Efficiency factors
As can be seen below, the efficiency factors can
add 50 to 300% each to the safety factor,
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Cumulative Effect of Factors
If we start with a factor of safety of 3 on bending
and buckling and have efficiency factors of 1.5
1.25 for temperature, we would have an
effective Safety Factor of about 8. This is
consistent with the preliminary design
guidelines we saw earlier.
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Snap Fits
• Types of Snap Fits
• Snap Fit Issues
• Snap Fit Calculators
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Types of Snap fit -Annular Snap Fit
http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
81
Types of Snap Fit - Cantilever Snap Fit
http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
82
Snap Fit Issues
• Integral Fastener
• Can be designed for disassembly
• Snap fits represent an undercut that
complicates molding
• Snap fits that remain under load will stress
relax
83
Eliminating Snap Fit Undercut
http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
84
Dealing with Snap Fit Undercut
http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
85
Snap Fit Calculators
• Manufacturers have design guidelines
• Type “Snap Fit Calculator” in to Google will get
plenty of hits
• Most are a modification of cantilever beam
analysis
86
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BASF Definition of Terms
Snap-Fit Design Manual, BASF Plastics
88
Classical Beam Theory
Snap-Fit Design Manual, BASF Plastics
89
“Improved” Method
Snap-Fit Design Manual, BASF Plastics
90
BASF’s “Improved Canitlever
Snap-Fit Design”.
The Q factor accounts for the
flexibility of the part. Note
that Example 1 has the least
flexibility, so the Q factor is
close to a value of one.
From: Snap-Fit Design
Manual, BASF Plastics
91
Snap Fit - BASF
Snap-Fit Design Manual, BASF Plastics
92
Snap-Fit Design Manual, BASF Plastics
93
Snap fit calculator from Engineer’s Edge
www.engineersedge.com/ snap_fit_tapered.htm
Snap fit Design excerpt from Paul E. Tres’ book
http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
Annular Snap Fit article in Machine Design
http://machinedesign.com/article/fundamentals-of-annularsnap-fit-joints-0106
94
Press Fit Issues
• Initial stress could cause boss to crack
• Boss may have weakening weld line
• Continuous deflection and resultant stress
could cause
 Cracking
 Stress Relaxation and reduced pull-out force
95
Boss with weld line support
General Design Principles for DuPont Engineering Polymers
96
Loss of force in press fit
When subjected to
constant strain, the
resulting stress in the
plastics diminishes over
time. Imagine a metal
insert pressed into a
boss. As time goes on,
the plastic boss material
grips the insert with less
and less force. Eventually
the insert may become
too loose, resulting in a
failed joint.
http://www.bayermaterialsciencenafta.com/checklist/
97
Questions
1. A snap fit in which the cantilever arm remains bent after installation
a. Will maintain the same end force over time
b. Will have an increasing end force over time
c. Will have a decreasing end force over tim
2. If a metal pin is press fit into a plastic boss (circle all that are true)
a. The pullout force ill decrease over time
b. The boss may experience creep rupture
c. When the pin is removed the hole will decrease in diameter over time, but probably not
back to original diameter.
98
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