9.1 Stress-strain behavior and mechanical models

Polymers exhibit diverse stress-strain behaviors, from elastic to plastic to viscoelastic deformation. These behaviors depend on factors like strain rate and loading duration, making polymers unique materials with time-dependent properties.

Mechanical models help predict polymer behavior, while stress-strain curves reveal key properties. Understanding these concepts is crucial for designing and selecting polymers for specific applications, from rubber bands to memory foam.

Stress-Strain Behavior of Polymers

Stress-strain behavior of polymers

Top images from around the web for Stress-strain behavior of polymers

• 

  newtonian mechanics - Why is the simple harmonic motion idealization inaccurate? - Physics Stack ... View original

  Is this image relevant?

• 

  Elasticity and Plasticity – University Physics Volume 1 View original

  Is this image relevant?

• 

  Stress–strain curve - Wikipedia View original

  Is this image relevant?

• 

  newtonian mechanics - Why is the simple harmonic motion idealization inaccurate? - Physics Stack ... View original

  Is this image relevant?

• 

  Elasticity and Plasticity – University Physics Volume 1 View original

  Is this image relevant?

1 of 3

Top images from around the web for Stress-strain behavior of polymers

• 

  newtonian mechanics - Why is the simple harmonic motion idealization inaccurate? - Physics Stack ... View original

  Is this image relevant?

• 

  Elasticity and Plasticity – University Physics Volume 1 View original

  Is this image relevant?

• 

  Stress–strain curve - Wikipedia View original

  Is this image relevant?

• 

  newtonian mechanics - Why is the simple harmonic motion idealization inaccurate? - Physics Stack ... View original

  Is this image relevant?

• 

  Elasticity and Plasticity – University Physics Volume 1 View original

  Is this image relevant?

1 of 3

• Elastic deformation involves reversible deformation where stress is proportional to strain (Hooke's law) and the polymer returns to its original shape upon removal of load (rubber band)
• Plastic deformation is irreversible deformation that occurs when stress exceeds the yield strength and the polymer does not return to its original shape upon removal of load (plastic grocery bag)
• Viscoelastic deformation exhibits time-dependent behavior with both elastic and viscous components, where strain depends on the rate of loading and the duration of the applied stress (memory foam)
• Strain rate sensitivity causes polymers to exhibit different stress-strain behavior at different strain rates, with higher strain rates leading to stiffer and more brittle behavior and lower strain rates resulting in more ductile and compliant behavior (impact testing vs. slow compression)

Types of polymer deformation

• Elastic deformation is reversible, has a linear relationship between stress and strain, and strain is independent of time (spring)
• Plastic deformation is irreversible, occurs when stress exceeds the yield strength, and results in a permanent change in shape (bent plastic ruler)
• Viscoelastic deformation is time-dependent, combines elastic and viscous behavior, and strain depends on the rate of loading and duration of the applied stress (silly putty)
  • Exhibits creep (increasing strain under constant stress) and stress relaxation (decreasing stress under constant strain)

Mechanical Models and Properties

Mechanical models for polymer prediction

• Maxwell model combines a spring (elastic element) and a dashpot (viscous element) in series to describe stress relaxation behavior
  • Total strain is the sum of elastic and viscous strains
  • Stress relaxation modulus: $E(t) = E_0 \exp(-t/\tau)$, where $E_0$ is the initial modulus and $\tau$ is the relaxation time
• Kelvin-Voigt model combines a spring and a dashpot in parallel to describe creep behavior
  • Stress is the same in both elements, while total strain is the sum of elastic and viscous strains
  • Creep compliance: $J(t) = \frac{1}{E}(1 - \exp(-t/\tau))$, where $E$ is the elastic modulus and $\tau$ is the retardation time

Interpretation of stress-strain curves

• Young's modulus (elastic modulus) is the slope of the linear portion of the stress-strain curve in the elastic region and measures the material's stiffness, calculated as $E = \frac{\sigma}{\varepsilon}$, where $\sigma$ is stress and $\varepsilon$ is strain (steel vs. rubber)
• Yield strength is the stress at which the material transitions from elastic to plastic deformation, determined by the point of departure from linearity in the stress-strain curve, and indicates the onset of permanent deformation (plastic vs. elastic deformation)
• Ultimate tensile strength is the maximum stress a material can withstand before failure and is the highest point on the stress-strain curve (breaking point)
• Elongation at break is the strain at which the material fractures and measures the material's ductility (brittle vs. ductile materials)