1. Dealing with Time and Temperature Dependence
Design With Viscolelastic Materials
Dealing with Time and Temperature Dependence

2. Design with Viscoelastic Materials
How are Properties Defined?
Introduction to Viscoelasticity
Strain Rate and Temperature Effects
Simple Material Models
Empirical Methods

3. Learning Objectives
Upon completion of this session, participants will be able to:
Describe how temperature and loading rate affect mechanical properties.
Define creep and stress relaxation and describe design situations for each.
Apply manufacturer’s data to design for applications in both short term and long term loading.
Relate data from creep curves and isochronous stress strain curves.
Apply snap fit design guidelines.

4. Review Basic definitions: thermoplastic, thermoset, elastomer.
Let’s talk about the kind of mechanical behavior seen in polymers.
Strength
Stiffness
Ductility
Factors which can determine the strength of a polymer.

5. 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.

6. Strength is:
A measure of stress (load per unit area with units of ksi or MPa)
Yield Strength (1st peak in uniaxial tension test)
Ultimate Tensile Strength (Highest stress in uniaxial tension test)

7. Stiffness is:
Young’s Modulus (Elastic Modulus), E with units of ksi or MPa
The slope of the straight line part of the stress-strain curve
The ratio of stress to strain (where strain is the change in length with respect to the original length, ΔL/L0) E

8. 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

9. Mechanical Properties
brittle polymer
Stress-strain behavior of polymers
FS of polymer ca. 10% that of metals
plastic
elastomer
elastic modulus – less than metal
Adapted from Fig. 15.1, Callister 7e.
Strains – deformations > 1000% possible (for metals, maximum strain ca. 10% or less)

10. Question

11. Introduction to Viscoelasticity
Mechanical properties depend on Temperature
Mechanical properties depend on Strain Rate
Creep (progressive change in strain at constant stress)
Stress Relaxation (progressive change in strain at constant strain)
Hysteresis (significant difference in load and unload stress-strain curves)

12. Effect of Temperature on Strength
As Temperature Increases
Strength Decreases
Stiffness Decreases
Ductility Increases
“Celanese Nylon 6/6 Processing and Troubleshooting Guide” by Ticona

13. Time Temp for Delrin (Strain Rate)

14. Effects of Strain Rate and Temperature
stress
Increasing strain rate
Increasing temp
strain

15. Time Temp for Delrin (Strain Rate and Temp)

16. 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.

17. Questions

18. Creep
Take a tension specimen made from a polymer and apply a constant stress.
We observe
Creep: Progressive strain (deformation) over time at constant stress (load), usually at high temperatures

19. 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.

20. Load-Unload Cycle in Nylon
“Zytel/Minlon Design Guide” DuPont

21. Creep of PEEK
“PEEK Properties Guide” Victrex

22. Write down two examples of parts that see constant tensile or bending load.

23. Stress Relaxation
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.
Think of a polymer specimen loaded with a constant strain.
Stress Relaxation: Progressive loss of stress (load) over time under constant strain (deformation), usually at high temperatures

24. Stress Relaxation of Delrin

25. Write down two examples of parts that see constant strain.

26. Questions

27. Time Dependent Deformation
• Stress relaxation test:
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
Adapted from Fig. 15.7, Callister 7e. (Fig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) 10 3 1 -1 -3 5 60
100
140
180
rigid solid
(small relax)
transition
region
T(°C) Tg
Er (10s)
in MPa
viscous liquid
(large relax)
-- strain to eo and hold.
-- observe decrease in
stress with time.
time
strain
tensile test eo
s(t)
• Relaxation modulus:
• Sample Tg(C) values:
PE (low density)
PE (high density)
PVC PS PC
- 110
- 90
+ 87
+100
+150
Selected values from Table 15.2, Callister 7e.

28. 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.

29. 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).

30. 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.)

31. Melting vs. Glass Transition Temp.
What factors affect Tm and Tg?
Both Tm and Tg increase with increasing chain stiffness
Chain stiffness increased by
Bulky sidegroups
Polar groups or sidegroups
Double bonds or aromatic chain groups
Regularity – effects Tm only
Adapted from Fig , Callister 7e.

32. Tg and Tm

33. Questions

34. Hysteresis
Polymers often don’t load and unload on the 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.

35. Sinusoidal Response Tests
We have a polymer specimen experiencing a sinusoidal loading.
Note that there is a phase shift, and that there is also hysteresis indicating that energy is being dissipated cyclically. This all suggests some simple material models.

36. Hysteresis in Delrin
“Delrin Design Guide” DuPont

37. Time Dependent Response can be Modeled
Maxwell Model
Kelvin-Voight Model
4 Element Model

38. 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
Stress relaxation is not bad
Creep not too good!
time
time

39. 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
Doesn’t really show stress relaxation!
time
time

40. 4 Element Model Standard Linear Solid
Further improvement is possible.
Shows both creep and stress relaxation!
stress
strain
time

41. 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.

42. Examples of These Time Dependent Moduli
Material
Creep Modulus
Relaxation Modulus
Maxwell
Kelvin Voigt
Standard Linear Solid
H(t) is the unit step function. d(t) is the Dirac delta function

43. 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
Temperature Dependent
Strain Rate Dependent

44. 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.

45. 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.

46. Empirical approach Use published information on behavior
Suppliers data sheets
Suppliers creep curves

47. 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.

48. What are the problems for Strength and Stiffness values?
Tested at a single temperature (usually room temp)
Tested at a single strain rate.
Polymer flow is in the direction of loading (advantage of molecular alignment)
Effects of colorants and other additives

49. Impact data may thickness sensitive.
Polycarbonate Resin – Product Brochure, Sabic

50. Impact Data may Depend on Notch Radius
Delrin Design Guide, DuPont

51. Polymer Flow Affects Properties

52. 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.

53. Company Recommendations
General Design Principles for DuPont Engineering Polymers

54. Company Recommendations – Preliminary Design
What safety factors do these numbers represent?
Designing with Plastics, The Fundamentals - Ticona

55. What do Plastics Companies Recommend?
Checklists
Use of Creep Curves
Confirm by Testing

56. Checklist from Bayer

57. From the DuPont Checklist

58. DuPont Checklist-Mechanical

59. DuPont Checklist-Environment

60. 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

61. DuPont Example
General Design Principles for DuPont Engineering Polymers

62. Long Term Properties for Example
General Design Principles for DuPont Engineering Polymers

63. General Design Principles for DuPont Engineering Polymers

64. General Design Principles for DuPont Engineering Polymers

65. General Design Principles for DuPont Engineering Polymers

66. 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

67. Data is usually taken in a creep test and replotted for the other graphs.
Designing with Plastics, The Fundamentals - Ticona

68. Creep Curve
Creep curves show the data as it was most likely measured, as strain vs. time for constant stress.
“PEEK Properties Guide” Victrex

69. Isochronous Stress-Strain Curves
Creep data is plotted as constant time (isochronous) stress vs strain curves at a given temperature

70. Creep Modulus vs. Time
Creep Stress is divided by strain at a given time to determine a “Creep” modulus.

71. 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.

72. Stress Relaxation Curve
Stress Relaxation should be tested under constant strain, but most reported results and replotted creep curves.

73. Designing with Celcon - Ticona
Where do these ratios come from?
Talk to the supplier.

74. Designing with Celcon - Ticona

75. 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 long-term loading, temperature, or strain rate. These factors multiply together in a manner you may have seen before in fatigue design.

76. 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”.

77. Suggested Safety factors

78. Efficiency factors
As can be seen below, the efficiency factors can add 50 to 300% each to the safety factor,

79. 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 for sustained loading, 1.5 for dynamic loads, and 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.

80. Snap Fits
Types of Snap Fits
Snap Fit Issues
Snap Fit Calculators

81. Types of Snap fit -Annular Snap Fit

82. Types of Snap Fit - Cantilever Snap Fit

83. 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

84. Eliminating Snap Fit Undercut

85. Dealing with Snap Fit Undercut

86. 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

88. BASF Definition of Terms
Snap-Fit Design Manual, BASF Plastics

89. Classical Beam Theory
Snap-Fit Design Manual, BASF Plastics

90. “Improved” Method
Snap-Fit Design Manual, BASF Plastics

91. 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

92. Snap Fit - BASF
Snap-Fit Design Manual, BASF Plastics

93. Snap-Fit Design Manual, BASF Plastics

94. Additional Sources Snap fit calculator from Engineer’s Edge
snap_fit_tapered.htm
Snap fit Design excerpt from Paul E. Tres’ book
Annular Snap Fit article in Machine Design

95. 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

96. Boss with weld line support
General Design Principles for DuPont Engineering Polymers

97. 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.

98. Questions