1. Elasticity

  • Definition: The ability of a material to regain its original shape and size after the removal of external forces.
  • Stress: The force applied per unit area within a material. It’s a measure of how the internal forces are distributed over the cross-sectional area of the material.
    • Types of stress: Tensile stress (stretching), compressive stress (squeezing), shear stress (tangential force).
  • Strain: The fractional change in dimension caused by stress. It’s a measure of the deformation of the material.
    • Types of strain: Tensile strain (elongation), compressive strain (contraction), shear strain (change in shape).
  • Hooke’s Law: For small deformations, stress is directly proportional to strain. The proportionality constant is called the modulus of elasticity.
  • Elastic Limit: The maximum stress a material can withstand without permanent deformation.

2. Moduli of Elasticity

  • Young’s Modulus (Y): Measures the resistance of a solid to a change in length. Y = (Tensile stress)/(Tensile strain)
  • Bulk Modulus (B): Measures the resistance of a solid to a change in volume. B = (Volume stress)/(Volume strain)
  • Shear Modulus (G): Measures the resistance of a solid to a change in shape. G = (Shear stress)/(Shear strain)
  • Poisson’s Ratio (σ): The ratio of lateral strain to longitudinal strain. It describes how a material deforms in one direction when stressed in another direction.

3. Stress-Strain Curve

  • Graphical representation: A plot of stress against strain for a material under tensile stress.
  • Key points on the curve:
    • Proportional Limit: The region where Hooke’s law is valid.
    • Elastic Limit: The point beyond which the material undergoes permanent deformation.
    • Yield Point: The point where the material starts to deform plastically with a small increase in stress.
    • Ultimate Tensile Strength: The maximum stress the material can withstand before breaking.
    • Fracture Point: The point where the material breaks.

4. Plasticity

  • Definition: The ability of a material to undergo permanent deformation without breaking.
  • Ductile materials: Materials that can be drawn into wires (e.g., copper, gold).
  • Malleable materials: Materials that can be hammered into thin sheets (e.g., aluminum, gold).

5. Other Mechanical Properties

  • Hardness: The resistance of a material to scratching or indentation.
  • Toughness: The ability of a material to absorb energy before fracturing.
  • Brittleness: The tendency of a material to break without significant plastic deformation.

Formula Sheet