stress strain curve.

• Stress-strain curve


  Graphical representation of how a material responds to a force applied in a stretching or pulling manner (tensile stress)
• Stress (σ)


  Force (F) applied to the material divided by the original cross-sectional area (A) of the material
• Strain (ε)


  Relative deformation experienced by the material due to the applied stress, calculated as the change in length (ΔL) divided by the original length (L) of the material
• General shape of the stress-strain curve

  1. Linear Region (Hooke's Law Region)

  2. Yield Point

  3. Strain Hardening

  4. Ultimate Tensile Strength

  5. Fracture
• Linear Region (Hooke's Law Region)


  • Stress and strain are directly proportional, material behaves elastically and will return to original shape once stress is removed
• Yield Point


  • Point where curve deviates from linearity, material experiences plastic deformation and won't return to original shape entirely
• Strain Hardening


  • Stress required to cause further deformation increases after yield point
• Ultimate Tensile Strength


  • Maximum stress the material can withstand before failure (fracture)
• Fracture


  • Material breaks or ruptures beyond ultimate tensile strength
• Stress-strain curve


  • Indicates material's elasticity, strength, ductility, and brittleness
• By analyzing the stress-strain curve, engineers can select the most appropriate material for a specific application based on the required strength, ductility, and other mechanical properties
• Linear region of the stress-strain curve

  Represents the elastic behavior of the material
• Hooke's Law


  Stress (σ) = Young's Modulus (E) * Strain (ε)
• Stress (σ)


  Force per unit area
• Strain (ε)


  Relative deformation
• Young's Modulus (E)


  A constant that represents the material's stiffness
• Young's Modulus (E)


  • Quantifies how much a material deforms under a given applied stress
  • A higher Young's Modulus indicates a stiffer material, meaning it resists deformation more for a given force
  • A lower Young's Modulus signifies a more compliant material that deforms more readily
• Slope of the linear region in the stress-strain curve

  Equal to Young's Modulus
• By measuring the slope of the initial linear portion, we can directly determine the material's stiffness
• Young's Modulus only applies to the linear elastic region of the stress-strain curve
• Beyond the yield point, the relationship between stress and strain becomes non-linear, and Young's Modulus is no longer a valid measure of material behavior
• Poisson's ratio


  Another important concept related to the stress-strain curve and material behavior, denoted by the Greek letter ν (nu)
• Poisson's ratio


  Describes the relationship between the deformation in one direction (due to applied stress) and the resulting deformation in a perpendicular direction
• Stretching a rubber band

  • As you pull it longer in one direction (longitudinal strain), it also gets thinner in the perpendicular direction (transverse strain)
• Poisson's ratio


  The negative ratio of the transverse strain (ε_t) to the longitudinal strain (ε_l) within the elastic limit (linear region) of the stress-strain curve
• The negative sign is a convention to ensure the value is always positive
• Values of Poisson's ratio

  • Typically ranges between 0 and 0.5
  • A value of 0.5 indicates a material that deforms significantly in the transverse direction when stretched (e.g. rubber)
  • A value closer to 0 indicates minimal transverse deformation for a given longitudinal strain (e.g. cork)
• Applications of Poisson's ratio

  • Material characterization
  • Engineering design
  • Material selection
• Poisson's ratio and the stress-strain curve

  Poisson's ratio reflects the material's behavior within the elastic region, and a steeper slope in the linear region of the curve (higher Young's modulus) often corresponds to a lower Poisson's ratio (less transverse deformation)
• Understanding Poisson's ratio, along with Young's modulus, equips engineers and scientists with a more comprehensive picture of how a material responds to stress