Physics · Ch 9 — Mechanical Properties of Solids

Summary

Stress is the internal restoring force per unit area: $\sigma = \frac{F}{A}$ . Strain is the fractional change in dimension: $\varepsilon = \frac{\Delta L}{L}$ (longitudinal), $\frac{\Delta V}{V}$ (volumetric), or $\theta$ (shear).
Hooke’s law: Within the elastic limit, stress $\propto$ strain. The proportionality constant is the modulus of elasticity.
Young’s modulus $Y = \frac{\text{Longitudinal stress}}{\text{Longitudinal strain}} = \frac{F/A}{\Delta L/L}$ . It measures a material’s resistance to stretching/compression.
Bulk modulus $B = -\frac{\Delta P}{\Delta V/V}$ (the negative sign means volume decreases when pressure increases). Compressibility is $1/B$ .
Shear modulus (modulus of rigidity) $G = \frac{\text{Shear stress}}{\text{Shear strain}} = \frac{F/A}{\theta}$ (where $\theta$ is the shear angle in radians).
Poisson’s ratio $\sigma = -\frac{\text{Lateral strain}}{\text{Longitudinal strain}}$ . For most materials, $0 < \sigma < 0.5$ .
Stress-strain curve: The linear region obeys Hooke’s law up to the proportionality limit. Beyond that, the material may still be elastic up to the elastic limit. The yield point marks the onset of plastic deformation. The breaking point is where fracture occurs. …