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POLYMERSIntroductionMicrostructureMechanical PropertiesViscoelastic BehaviorTime Temperature SuperpositionDynamic Mechanical AnalysisPolymer Failure

MEL 844 Designing with New Materials

Department of Mechanical Engineering, IIT Delhi

Dynamic Mechanical Analysis (DMA)

MEL844 2

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Dynamic Mechanical Analysis (DMA)

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𝐸′is Storage Modulus𝐸′′ is Loss Modulus

Kelvin model

𝐸∗ = 𝐸 + 𝑖𝜇𝑡

Dynamic Mechanical Analysis (DMA)

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𝜖 𝑡 = 𝑅𝑒 𝜖𝑜𝑒𝑖𝜔𝑡 = 𝜖𝑜 cos 𝜔𝑡

𝜎 𝑡 = 𝑅𝑒 𝜖𝑜𝐸∗𝑒𝑖𝜔𝑡

𝜎 𝑡 = 𝜖𝑜 𝐸′ 𝜔 cos 𝜔𝑡 − 𝐸′′ 𝜔 sin 𝜔𝑡

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Dynamic Mechanical Analysis (DMA)

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Dynamic Mechanical Analysis (DMA)

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Strength of Polymers

Strength-limiting processes know in polymers

1. Brittle fracture

2. Cold drawing

3. Shear banding

4. Crazing

5. Viscous flow

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1. Brittle fracture 2. Cold drawing

• < 0.75 TG polymers are brittle• Low toughness• Stress concentration like cracks,

notches, sharp section changes are dangerous

• About 50°C below TG, thermoplastics become plastic

• Yields at about 0.1 strain, then draws

• Chains unfold (crystal) or untangle (amorphous)

• Starts to neck, then spreads throughout

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3. Crazing 4. Shear banding• Visible white streaks on cheap plastics• High TG polymers (PS) craze• Small crack shaped regions with

drawn polymer (ligaments) that link craze surfaces

• Crack usually start from a craze and propagates

• Large plastic strains• Finite strain occurs in each shear

band• Occurs due to deviatoric stresses,

unlike crazing that occurs due to dilatational stresses

Strength Diagram for Polymers

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PMMA

Strength is less understood than stiffness

At low temperature, there is brittle failure, estimated using fracture mechanics

Depends on strain rateand temperature

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Stress–Strain Behavior of Polymers

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Variation in stress strain behaviour in different polymers

Temperature Dependent

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Brittle epoxy

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Strain Rate Dependent

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Brittle epoxy

Fatigue Failure

May or may not have endurance limitHigh frequency can lead to excessive heat build up

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Creep Failure

Larson-Miller Theory

𝐿𝑀𝑃 = 𝑇 𝐶𝑙𝑚 + log10 𝑡𝑟 = 𝑓 𝜎

LMP - Larson-Miller parameterT - TemperatureC – constanttr - time to rupture

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Cumulative Creep Damage

𝑡1 − 𝑡0𝑡𝑐1+𝑡2 − 𝑡0𝑡𝑐2+⋯ =

𝑖=1

𝑘𝑡𝑛 − 𝑡𝑛−1𝑡𝑐𝑛

= 1

𝑡𝑖−𝑡𝑖−1

𝑡𝑐𝑖is the increment of creep damage

𝑡𝑐𝑖 is critical time at respective load levels

Miner’s Rule