Presentation Transcript

1. Design With ViscolelasticMaterials 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 ksior MPa) Yield Strength (1st peak in uniaxial tension test) Ultimate Tensile Strength (Highest stress in uniaxial tension test)
7. Stiffness is: E 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)
8. Ductility is: ΔL/L % Elongation (with units of in/in or mm/mm) The permanent percentage change on length after fracture (from a uniaxial tension test)
9. Mechanical Properties brittle polymer 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 strainca. 10% or less) Stress-strain behavior of polymers
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) http://www2.dupont.com/Plastics/en_US/assets/downloads/design/230323c.pdf
14. Effects of Strain Rate and Temperature stress Increasing strain rate Increasing temp strain
15. Time Temp for Delrin (Strain Rate and Temp) http://www2.dupont.com/Plastics/en_US/assets/downloads/design/230323c.pdf
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 Creep: Progressive strain (deformation) over time at constant stress (load), usually at high temperatures Take a tension specimen made from a polymer and apply a constant stress. We observe
19. Creep Test 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. We instantly load with constant stress for a certain time, and instantly unload.
20. Load-Unload Cycle in Nylon “Zytel/Minlon Design Guide” DuPont
21. Creep of PEEK “PEEK Properties Guide” Victrex
22. 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. Stress Relaxation: Progressive loss of stress (load) over time under constant strain (deformation), usually at high temperatures Think of a polymer specimen loaded with a constant strain.
23. Stress Relaxation of Delrin http://www2.dupont.com/Plastics/en_US/assets/downloads/design/230323c.pdf
24. Questions
25. 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.
26. 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 Tgresults from the inability of the chains to move easily (chains have insufficient free volume to coil and uncoil).
27. 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.)
28. Melting vs. Glass Transition Temp. Adapted from Fig. 15.18, Callister 7e. 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
29. Tg and Tm
30. Questions
31. 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.
32. Hysteresis in Delrin “Delrin Design Guide” DuPont
33. Time Dependent Response can be Modeled Maxwell Model Kelvin-Voight Model 4 Element Model
34. Maxwell Model In the limit, it’s a fluid! strain stress Stress relaxation is not bad Creep not too good! time time Here is an alternative to the simple spring model of linear elasticity. Add a damper. This gives what is called as the Maxwell model.
35. Kelvin-Voigt Model In the limit, it’s a solid! strain stress Doesn’t really show stress relaxation! time time Try putting the spring and damper in series This gives the Kelvin-Voigt model.
36. 4 Element Model Standard Linear Solid Shows both creep and stress relaxation! stress strain time Further improvement is possible.
37. Stress Strain Relationships K is creep modulus, and F is the relaxation modulus. We can get stress from strain history and strain form stress history through the following heriditary relationships.
38. Examples of These Time Dependent Moduli H(t) is the unit step function. d(t) is the Dirac delta function
39. 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
40. 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.
41. 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.
42. Empirical approach Use published information on behavior Suppliers data sheets Suppliers creep curves
43. 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.
44. 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
45. Impact data may thickness sensitive. Polycarbonate Resin – Product Brochure, Sabic
46. Impact Data may Depend on Notch Radius Delrin Design Guide, DuPont
47. Polymer Flow Affects Properties http://www.ides.com/articles/design/2006/sepe_07.asp
48. From Lavengood and Silver in “Interpreting supplier Data Sheets”, ASM Engineered Material Handbook, Polymers: What does the Designer Do? In other words, we can use the supplier data for a clean, dry, indoor application of primarily decorative function. 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.”
49. Company Recommendations General Design Principles for DuPont Engineering Polymers
50. Company Recommendations – Preliminary Design What safety factors do these numbers represent? Designing with Plastics, The Fundamentals - Ticona
51. What do Plastics Companies Recommend? Checklists Use of Creep Curves Confirm by Testing
52. Checklist from Bayer http://www.bayermaterialsciencenafta.com/checklist/
53. From the DuPont Checklist http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
54. DuPont Checklist-Mechanical http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
55. DuPont Checklist-Environment http://plastics.dupont.com/plastics/pdflit/americas/markets/H81079.pdf
56. Other DuPont Checklists Writing Meaningful Specifications A specification is intended to satisfy functional, aesthetic and economicrequirements 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
57. DuPont Example General Design Principles for DuPont Engineering Polymers
58. Long Term Properties for Example General Design Principles for DuPont Engineering Polymers
59. General Design Principles for DuPont Engineering Polymers
60. General Design Principles for DuPont Engineering Polymers
61. General Design Principles for DuPont Engineering Polymers
62. How Do Companies Report Time and Temperature Dependent Properties? All curves must contain information on: Stress, Strain, Time, Temperature Creep Curves (Strain vs. Time) Isochronous Stress Strain Curves Creep Modulus (Modulus vs. Time) Stress Relaxation Curves (Stress vs. Time)
63. Data is usually taken in a creep test and replotted for the other graphs. Designing with Plastics, The Fundamentals - Ticona
64. Creep Curve “PEEK Properties Guide” Victrex Creep curves show the data as it was most likely measured, as strain vs. time for constant stress.
65. Isochronous Stress-Strain Curves http://bmsnafta-campusi.com/matdb/matdb.php Creep data is plotted as constant time (isochronous) stress vs strain curves at a given temperature
66. Creep Modulus vs. Time http://bmsnafta-campusi.com/matdb/matdb.php Creep Stress is divided by strain at a given time to determine a “Creep” modulus.
67. 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.
68. Stress Relaxation Curve http://www2.dupont.com/Plastics/en_US/assets/downloads/design/230323c.pdf Stress Relaxation should be tested under constant strain, but most reported results and replotted creep curves.
69. Designing with Celcon - Ticona Where do these ratios come from? Talk to the supplier.
70. Designing with Celcon - Ticona
71. 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.
72. 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”.
73. Suggested Safety factors
74. Efficiency factors As can be seen below, the efficiency factors can add 50 to 300% each to the safety factor,
75. 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.
76. Snap Fits Types of Snap Fits Snap Fit Issues Snap Fit Calculators
77. Types of Snap fit -Annular Snap Fit http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
78. Types of Snap Fit - Cantilever Snap Fit http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
79. 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
80. Eliminating Snap Fit Undercut http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
81. Dealing with Snap Fit Undercut http://engr.bd.psu.edu/pkoch/plasticdesign/snap_design.htm
82. 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
83. http://www.basf.com/businesses/plasticportal/pp_techRes_tools_snapfit_en.html http://www.basf.com/businesses/plasticportal/pp_techRes_tools_snapfit_en.html
84. BASF Definition of Terms Snap-Fit Design Manual, BASF Plastics
85. Classical Beam Theory Snap-Fit Design Manual, BASF Plastics
86. “Improved” Method Snap-Fit Design Manual, BASF Plastics
87. 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
88. Snap Fit - BASF Snap-Fit Design Manual, BASF Plastics
89. Snap-Fit Design Manual, BASF Plastics
90. Additional Sources 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-annular-snap-fit-joints-0106
91. 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
92. Boss with weld line support General Design Principles for DuPont Engineering Polymers
93. 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/
94. Questions