6 - Viscoelastic Response

Introduction to Viscoelastic Response of Polymers

  • Comparison with Metals:
    • Metals exhibit perfect elastic behavior; strains are instantly recoverable below yield stress.
    • Described by a linear relationship: \sigma = K \epsilon where \sigma is stress, \epsilon is strain, and K is a constant (Young's or shear modulus).

Characteristics of Polymers

  • Polymers exhibit viscoelastic behavior, incorporating:
    • Instantaneous elastic response: Immediate strain upon loading.
    • Viscous response:
    • Recovery time is not instantaneous; involves the rate of strain rather than the amount of strain.
    • Described by the viscosity component, related linearly to the rate of strain.

Strain vs. Time Plot

  • Initial Response: Instantaneous elastic strain occurs when load is applied.
  • Continued Strain: Additional strain accumulates over time due to viscous properties.
  • Recovery Process:
    • Instantaneous return upon load removal followed by a time-dependent viscous recovery.
    • Permanent strain may remain even after full viscous recovery.

Distinction Between Viscous and Viscoelastic Behavior

  • Purely Viscous Deformations:
    • Non-recoverable strain (e.g., creep, stress relaxation).
  • Viscoelastic Strains:
    • Recoverable but time-dependent (may take seconds to months) depending on load duration and size.
    • Example: Carpet's resilience shows quick recovery from brief loading but prolonged indentation from heavy furniture can take weeks.

Temperature Dependence

  • Thermal Softening: Polymers soften over a smaller temperature range than metals.
    • E.g., PMMA (Plexiglass): Transitions from brittle to ductile between 4°C and 60°C.
  • Strain Rate Dependency:
    • Higher deformation rates mimic low temperatures concerning thermally activated processes in polymers.

Dynamic Mechanical Analysis (DMA)

  • DMA measures viscoelastic properties, involving the complex modulus E^*:
    • Comprises:
    • Storage modulus E' (elastic response).
    • Loss modulus E'' (viscous response).
  • Oscillatory load tests: Measure displacement response of the sample to analyze viscoelastic behavior.

Phase Lag in Materials

  • Purely Elastic Material: No phase lag; stress peaks align with strain peaks.
  • Purely Viscous Material: 90-degree phase lag; stress peaks when strain rate is highest.
  • Viscoelastic Material: Phase lag \delta indicates the relative proportion of elastic and viscous characters.
    • Characterization:
    • \tan(\delta) = \frac{E''}{E'}
  • All polymers are viscoelastic, revealing distinctive phase lags and material behavior.

Tan Delta Curves

  • Provides insights into polymer characteristics, commonly featuring:
    • Peak in tan delta curve marks the glass transition temperature (e.g., epoxy example at 146°C).
  • Other definitions exist based on modulus curves but tan delta is most common for assessing glass transition temperature.

Conclusion

  • Viscoelastic response is critical for understanding polymer behavior under varying loads, temperatures, and strain rates, laying the foundation for further study in polymer characteristics, especially focusing on glass transition temperature in subsequent lectures.