Overview
This lecture introduces Young's modulus, explaining its definition, measurement via tensile testing, atomic-level origins, and importance in engineering material selection.
Elastic Constants and Young's Modulus
- Young's modulus, shear modulus, and bulk modulus are main elastic constants that describe how materials deform under load.
- Young's modulus (E), or modulus of elasticity, measures material stiffness under uniaxial tension or compression.
Tensile Test and Stress-Strain Curve
- The tensile test stretches a sample in one direction to measure load and deformation.
- The main output is the stress-strain curve, showing deformation for different applied stresses.
- The curve has two regions: elastic (linear, reversible deformation) and plastic (permanent deformation).
- In the elastic region, stress is proportional to strain (linear relationship).
Hooke's Law and Young's Modulus Calculation
- Hooke’s law relates stress and strain in the elastic region: stress = E × strain.
- Young's modulus equals the slope of the stress-strain curve in the elastic region.
- Higher Young’s modulus means stiffer material and less elastic deformation for a given load.
Material Differences and Anisotropy
- Different materials have different Young's modulus values: ceramics > metals > polymers.
- In anisotropic materials (e.g., wood, composites), Young’s modulus depends on loading direction.
Atomic-Level Explanation
- Young’s modulus is determined by the strength of inter-atomic bonds, modeled as tiny springs.
- Elastic deformation is stretching these bonds; plastic deformation rearranges atoms.
- Polymers have lower modulus due to weaker intermolecular bonds.
Alloys and Young's Modulus
- Small changes in alloy composition (e.g., mild vs. high carbon steel) typically have little effect on Young’s modulus.
- Different mechanical properties (like yield strength) may vary even if Young’s modulus stays similar.
Engineering Significance
- Young’s modulus is essential for selecting materials to minimize elastic deformation in structures.
- Using materials with a high Young’s modulus prevents excessive deflection, e.g., in bridges.
Key Terms & Definitions
- Young's modulus (E) — The ratio of stress to strain in the elastic region; measures material stiffness.
- Tensile test — Mechanical test that stretches a sample to record load and deformation.
- Stress-strain curve — Graph showing how a material deforms (strain) for different stresses.
- Elastic region — Part of stress-strain curve where deformation is reversible.
- Plastic region — Part where deformation is permanent.
- Anisotropic — Having properties that depend on direction of measurement.
Action Items / Next Steps
- Review and understand the stress-strain curves for polymers, metals, and ceramics.
- Consider examples of structures where material stiffness is critical.