Mechanical Properties of Solids
Easy Overview
Ever stretched a rubber band? It snaps back. But if you stretch too much, it breaks. This chapter is about what happens inside solid materials when you push, pull, or twist them. It's why bridges are built with steel, why your mattress springs work, and why bones can handle impact. Meet stress, strain, and Hooke's law.
Stress and Strain — What's Happening Inside?
Stress is the force per unit area inside a material (σ = F/A), measured in Pascal. Think of it as 'how hard are the atoms being pushed apart?' Strain is the deformation relative to the original size (ε = ΔL/L), a ratio with no units. Normal stress is perpendicular to the surface (pulling or pushing), shear stress is parallel (sliding layers).
Hooke's Law and Elastic Moduli
Within the elastic limit, stress ∝ strain. That's Hooke's law. The proportionality constant is the modulus of elasticity. Young's modulus (Y) for stretching = stress/strain = FL/AΔL. Bulk modulus (K) for volume change = −ΔP/(ΔV/V). Shear modulus (G) for shape change = shear stress/shear strain. Higher modulus = stiffer material.
Stress-Strain Curve — Reading a Material's Story
If you graph stress vs strain, you get a curve with distinct regions. First comes the elastic region (obeys Hooke's law, material returns to original shape). Then the yield point (permanent deformation starts). After that, plastic region (material deforms permanently). Finally, the breaking point. Ductile materials like copper have a long plastic region; brittle materials like glass break abruptly.
Elastic Limit and Plasticity
The elastic limit is the maximum stress a material can take and still spring back. Exceed it, and you've entered plastic deformation — the material won't fully recover. That's why a bent paperclip stays bent. Elastic aftereffect is when a material takes time to return to shape after a small load. Quartz and phosphor bronze have almost zero elastic aftereffect — that's why they're used in精密 instruments.
Key Points
- •Stress = F/A (Pascal), Strain = ΔL/L (no unit)
- •Hooke's law: stress ∝ strain within elastic limit
- •Young's modulus Y = FL / AΔL
- •Bulk modulus K = −ΔP / (ΔV/V)
- •Modulus of rigidity G = shear stress / shear strain
- •Ductile materials undergo plastic deformation before breaking; brittle materials don't
- •Elastic limit = max stress without permanent deformation
Practice Questions
- A wire of length 2 m and cross-sectional area 10⁻⁶ m² stretches by 1 mm under a 4 kg load. Find Young's modulus.
- Distinguish between stress and strain.
- Explain the stress-strain curve for a ductile material with a labeled diagram.
- Why does a brittle material break suddenly while a ductile one deforms first?