Presentation on theme: "Dealing with Time and Temperature Dependence"— Presentation transcript:
1 Dealing with Time and Temperature Dependence Design With Viscolelastic MaterialsDealing with Time and Temperature Dependence
2 Design with Viscoelastic Materials How are Properties Defined?Introduction to ViscoelasticityStrain Rate and Temperature EffectsSimple Material ModelsEmpirical Methods
3 Learning ObjectivesUpon 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.StrengthStiffnessDuctilityFactors 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 MPaThe slope of the straight line part of the stress-strain curveThe 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 polymerStress-strain behavior of polymersFS of polymer ca. 10% that of metalsplasticelastomerelastic modulus – less than metalAdapted from Fig. 15.1, Callister 7e.Strains – deformations > 1000% possible (for metals, maximum strain ca. 10% or less)
11 Introduction to Viscoelasticity Mechanical properties depend on TemperatureMechanical properties depend on Strain RateCreep (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 IncreasesStrength DecreasesStiffness DecreasesDuctility Increases“Celanese Nylon 6/6 Processing and Troubleshooting Guide” by Ticona
16 Time Temp DependencePlastic deformation of polymers involves chain uncoiling and chain slidingIncreasing temperature increases relative space between chains and makes uncoiling easier.Slowing the strain rate means there is more time for chain reconfiguration.
18 CreepTake a tension specimen made from a polymer and apply a constant stress.We observeCreep: Progressive strain (deformation) over time at constant stress (load), usually at high temperatures
19 Creep TestWe 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
22 Write down two examples of parts that see constant tensile or bending load.
23 Stress RelaxationNote 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
27 Time Dependent Deformation • Stress relaxation test:• Data: Large drop in Erfor T > Tg.(amorphouspolystyrene)Adapted from Fig. 15.7, Callister 7e. (Fig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)1031-1-3560100140180rigid solid(small relax)transitionregionT(°C)TgEr (10s)in MPaviscous liquid(large relax)-- strain to eo and hold.-- observe decrease instress with time.timestraintensile testeos(t)• Relaxation modulus:• Sample Tg(C) values:PE (low density)PE (high density)PVCPSPC- 110- 90+ 87+100+150Selected 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 TemperatureFor 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 stiffnessChain stiffness increased byBulky sidegroupsPolar groups or sidegroupsDouble bonds or aromatic chain groupsRegularity – effects Tm onlyAdapted from Fig , Callister 7e.
34 HysteresisPolymers 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 ModelKelvin-Voight Model4 Element Model
38 Maxwell ModelHere 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!strainstressStress relaxation is not badCreep not too good!timetime
39 Kelvin-Voigt ModelTry putting the spring and damper in series This gives the Kelvin-Voigt model.In the limit, it’s a solid!strainstressDoesn’t really show stress relaxation!timetime
40 4 Element Model Standard Linear Solid Further improvement is possible.Shows both creep and stress relaxation!stressstraintime
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 MaterialCreep ModulusRelaxation ModulusMaxwellKelvin VoigtStandard Linear SolidH(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 areTemperature DependentStrain Rate Dependent
44 Summary Polymers exhibit: Great sensitivity to temperature. Great sensitivity to strain rate.Very complex behaviorModel 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 sheetsSuppliers 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
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? ChecklistsUse of Creep CurvesConfirm by Testing
60 Other DuPont Checklists Writing Meaningful SpecificationsA specification is intended to satisfy functional, aesthetic and economic requirements by controlling variations in the final product. The part must meet thecomplete 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 fromcritical stress points)• Locations where voids are intolerable• Allowable warpage• Tolerances• Color• Decorating considerations• Performance considerationsGeneral Design Principles for DuPont Engineering Polymers
61 DuPont ExampleGeneral 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 CurvesCreep 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 CurveCreep 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. TimeCreep Stress is divided by strain at a given time to determine a “Creep” modulus.
71 ExerciseConfirm 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.
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”.
78 Efficiency factorsAs 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 FitsTypes of Snap FitsSnap Fit IssuesSnap Fit Calculators
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 - BASFSnap-Fit Design Manual, BASF Plastics
94 Additional Sources Snap fit calculator from Engineer’s Edge snap_fit_tapered.htmSnap fit Design excerpt from Paul E. Tres’ bookAnnular Snap Fit article in Machine Design
95 Press Fit Issues Initial stress could cause boss to crack Boss may have weakening weld lineContinuous deflection and resultant stress could causeCrackingStress 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.