Stress–Strain Curve: Quick Study Notes

Picture a metal wire that you pull harder and harder. The graph that tracks how much the wire stretches (strain) against the pulling force per area (stress) tells you a lot about the metal’s behavior and strength. Use this roadmap to master every stage of that curve.

Key Definitions

  • Hydraulic stress – When a fluid presses equally in every direction, the solid inside pushes back with an equal “internal” stress that matches the fluid pressure. :contentReference[oaicite:0]{index=0}
  • Volume strain – How much a solid’s volume changes, written as \( \displaystyle \frac{\Delta V}{V} \); it has no units. :contentReference[oaicite:1]{index=1}
  • Stress – Force per unit area acting on the object.
  • Strain – Fractional change in length, area, or volume.

Hooke’s Law – Region O → A (Purely Elastic)

For small stretches, the metal behaves like an ideal spring:

\[ \text{stress}=k\times\text{strain} \] where k is the modulus of elasticity. The graph looks like a straight line, and the wire snaps back perfectly when you let go. :contentReference[oaicite:2]{index=2}

Yield Point – Region A → B

Past O → A, stress stops rising in perfect lock-step with strain, yet the wire still returns to its original length once you unload it. Point B is the yield point (elastic limit); the stress there is the yield strength \( \sigma_y \). Pushing beyond \( \sigma_y \) means you leave the comfort zone of perfect elasticity. :contentReference[oaicite:3]{index=3}

Plastic Deformation – Region B → D

Cross \( \sigma_y \) and the wire stretches a lot more for a tiny extra load. If you stop anywhere between B and D, the wire stays permanently longer—this plastic deformation gives it a “set.” :contentReference[oaicite:4]{index=4}

Ultimate Tensile Strength & Fracture – Points D → E

The curve peaks at point D, the ultimate tensile strength \( \sigma_u \). After D you need less and less load to keep stretching until the metal finally breaks at E. :contentReference[oaicite:5]{index=5}

Brittle vs Ductile Breaks

  • Brittle – Points D and E sit almost together, so the metal snaps soon after the maximum stress.
  • Ductile – D and E lie far apart, so the metal necks and thins a long way before it breaks. :contentReference[oaicite:6]{index=6}

Handy Formulas to Memorize

  • \(\displaystyle \text{Volume strain} = \frac{\Delta V}{V}\) (unit-less).
  • \(\displaystyle \text{stress}=k\times\text{strain}\) (Hooke’s Law).

High-Yield NEET Points

  1. The linear O → A segment and Hooke’s Law with modulus \( k \).
  2. Yield point B and yield strength \( \sigma_y \).
  3. Ultimate tensile strength \( \sigma_u \) at point D.
  4. Plastic vs elastic behavior and the idea of permanent set.
  5. How the spacing of D and E tells you if a material is brittle or ductile.

You’ve got this! Sketch the curve a few times, label the key points, and these ideas will stick for good. 😊