Concepts of Stress and Strain - Module 4.1

Module 4.1: Concepts of Stress and Strain

• Learning Outcomes: Identify different types of loading, define stress and strain, differentiate engineering and true stress-strain, and review mechanical properties.

Types of Loading/Force

• Tensile Load: A force pulling apart or stretching a material.
• Compressive Load: A force causing a material to deform and occupy a smaller volume.
• Shear Load: A force tending to cause deformation by slippage along planes parallel to it.

Stress

• Definition: The internal distribution of forces within a body that balances and reacts to applied loads.
• Formula: Stress (σ) = Force (F) / Area (A)
• Units: Pascals (Pa) or N/m².
• Types:
  • Tensile Stress: Stress in a material experiencing a tensile load.
  • Compressive Stress: Stress in a material experiencing a compressive load.
  • Shear Stress: Stress in a material experiencing a shear load.

Strain

• Definition: The response of a system to an applied stress.
• Unitless: Often expressed as unsimplified values like in/in.
• Formula: Strain (ε) = Elongation / Original Length = ΔL / L₀

Stress-Strain Curve

• Definition: A diagram representing the relationship between stress and strain in a material.
• Types:
  • Engineering stress-strain diagram
  • True stress-strain diagram
• Mechanical properties obtained: Properties such as Young's Modulus are obtained from the curve.
• Elastic region: Temporary deformation.
• Plastic region: Permanent deformation.

Engineering Stress vs. True Stress

• Engineering Stress: Instantaneous force divided by the original cross-sectional area.
• True Stress: Instantaneous force divided by the instantaneous area. -Formula: σₜ = Fₜ/Aᵢ

Engineering Strain vs. True Strain

• Engineering Strain: Change in length divided by the original length.
• True Strain: Natural logarithm of the instantaneous gauge length of a specimen.
  • Formula: εₜ = ln(l₁/l₀)

Mathematical Relationships of Engineering and True σ – ε

• Relationship: σₜ = σ(1 + ε) and εₜ = ln(1 + ε).
• Validity: These relationships are only valid up to the onset of necking.

Mechanical Properties

• Those obtained from engineering σ-ε curve: This is typically used in place of true values.

Important Values (obtained from σ-ε curve)

• Proportional Limit: The point of departure from the linearity of the stress-strain curve.
• Yielding: The phenomenon where the transition from the elastic to plastic deformation occurs. This is typically measured by 0.2% proof stress on the curve.
• Yield Strength (σᵧ): Measure of the material's resistance to permanent deformation
• Ultimate Tensile Strength (UTS/TS): The stress at the maximum point of the engineering stress-strain curve
• Fracture Stress (σf): The stress at the point of breaking or fracture.
• Ductility: Degree of plastic deformation sustained at fracture, measured as percent elongation or area reduction.
• Modulus of Resilience (Uᵣ): Strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding (σᵧ).
• Toughness: Ability of a Material to absorb energy up to fracture.
• Poisson's Ratio (v): Ratio of the lateral and axial strains.

Moduli of Elasticity and Rigidity

• Modulus of Elasticity (E): Governed by Hooke's Law.
• Modulus of Rigidity (G): Also governed by Hooke's Law.

Explore the fundamental concepts of stress and strain in this quiz module. Learn about different types of loading, the definitions of stress and strain, and the distinction between engineering and true stress-strain. This quiz is essential for understanding mechanical properties and the behavior of materials under various forces.