Dynamic Mechanical Behaviors
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Questions and Answers

What happens to the shear modulus of atactic polystyrene as the testing temperature increases?

  • It remains constant.
  • It fluctuates without trend.
  • It increases steadily.
  • It decreases sharply at the glass transition. (correct)

    • At what temperature is the β-peak located in the tan δ curve for atactic polystyrene?

  • Approximately 150°C
  • Approximately 100°C
  • Approximately 50°C (correct)
  • Approximately 0°C

    • What is believed to cause the γ-peak in the tan δ curve for polymers?

  • Head-to-head repeat sequences. (correct)
  • Disruption in the polymer backbone.
  • Formation of side-chain entanglements.
  • Growth of crystallinity in the material.

    • What does the equation $E_1 = \frac{E \tau_0^2 \omega^2}{\tau_0 \omega + 1}$ represent?

    <p>The elastic modulus of the material.</p> Signup and view all the answers

    What is the significance of the peak (α) in the tan δ curve according to the content?

    <p>It corresponds to the glass transition.</p> Signup and view all the answers

    Which of the following statements is true regarding viscoelastic materials?

    <p>They exhibit both viscous and elastic characteristics.</p> Signup and view all the answers

    In the provided equations, what is represented by $\tau_0$?

    <p>The material's viscoelastic time constant.</p> Signup and view all the answers

    How does the frequency $\omega$ affect the β-peak in tan δ?

    <p>The β-peak merges with α-relaxation at high frequencies.</p> Signup and view all the answers

    What term describes the relative angular displacement of stress and strain in a viscoelastic material?

    <p>Phase angle</p> Signup and view all the answers

    What is the form of stress when expressed in relation to strain and the phase angle?

    <p>$\sigma = \sigma_0 sin(\omega t + \delta)$</p> Signup and view all the answers

    Which component of stress in a viscoelastic material is in phase with the strain?

    <p>$\sigma_0 cos \delta$</p> Signup and view all the answers

    How is dynamic modulus E1 defined in terms of stress and strain?

    <p>$E_1 = (\sigma_0 / e_0) cos \delta$</p> Signup and view all the answers

    Which of the following equations represents the relationship of complex modulus in a viscoelastic material?

    <p>$E^* = (E_1 + iE_2)$</p> Signup and view all the answers

    What is the relationship between E2 and E1 as described by tangent of the phase angle?

    <p>tan $\delta = \frac{E_2}{E_1}$</p> Signup and view all the answers

    In what way does strain behave in a viscoelastic material under sinusoidal stress?

    <p>Strain lags behind stress.</p> Signup and view all the answers

    What model can be used to demonstrate the frequency dependence of viscoelastic properties?

    <p>Maxwell Model</p> Signup and view all the answers

    Study Notes

    Dynamic Mechanical Behaviors

    • Dynamic mechanical testing is used to analyze materials when a sinusoidal load is applied at a specific frequency.
    • Applied stress (σ) varies as a function of time (σ = σ₀sinωt), where σ₀ is the stress amplitude and ω is the angular frequency.
    • Elastic materials exhibit strain (e) in a similar sinusoidal manner as stress (e = e₀sinωt).
    • Viscoelastic materials exhibit a phase lag (δ) between stress and strain, meaning strain doesn't occur simultaneously with stress. Strain lags behind the stress during creep.
    • The phase angle (δ), or phase lag, represents the relative angular displacement between stress and strain.
    • Stress can be represented as two components: one in phase with strain (σ₀cosδ) and another 90° out of phase with strain (σ₀sinδ).
    • Two dynamic moduli (E₁, E₂) can be defined: E₁ is in phase with strain, and E₂ is 90° out of phase with strain.
    • The stress and strain variation, given by e = e₀sin(ωt + δ) and σ = σ₀sin(ωt + δ), where δ reflects the phase shift.

    Frequency Dependence of Viscoelastic Behavior

    • The Maxwell model helps understand the frequency dependence of viscoelastic properties.
    • The relationship between stress (σ) and strain (e) with time (t) can be represented by complex equations if stress is sinusoidally varied as σ = σ₀ exp i(ωt + δ) and e = e₀ exp iωt where ω is the angular frequency.
    • Stress (σ) and strain (e) values vary with time (t) .

    Transitions and Polymer Structure

    • Shear modulus (G₁) and tan δ (the tangent of the phase angle) vary with temperature for amorphous polymers (e.g., atactic polystyrene).
    • A significant drop in shear modulus occurs at the glass transition temperature (Tg) in amorphous polymers.
    • Minor peaks in tan δ at lower temperatures correspond to secondary transitions.
    • The relaxation time (τ) significantly affects how stress and strain behave at different frequencies
    • Crystallinity influences α' and α relaxations decreasing in intensity in a reduction in crystallinity and implying that they are associated with motion within the crystalline regions.
    • Y-relaxation increases with a reduction in crystallinity and is related to amorphous material.

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    Description

    This quiz focuses on dynamic mechanical testing used to analyze materials under sinusoidal loads. It covers concepts such as stress, strain, phase lag, and dynamic moduli, providing insight into the behaviors of elastic and viscoelastic materials. Test your understanding of these fundamental principles in materials science.

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