---
title: "Stress-strain diagram for mild steel"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:stress-strain-diagram-mild-steel"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/stress-strain-diagram-mild-steel
site: BCT Engineering
---

# Stress-strain diagram for mild steel

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2067 Asar (old course), 4 marks
- Video: [STRESS-STRAIN CURVE FOR MILD STEEL(Engineering Stress And True Stress)](https://www.youtube.com/watch?v=uO-p274-RyA) — Kudratnama
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/stress-strain-diagram-mild-steel
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

Neatly sketch stress-strain diagram for mild-steel showing salient points.

## Short answer

The diagram shows a linear elastic region (Hooke’s law) up to proportional limit, a distinct yield plateau with upper and lower yield points around 250 N/mm², strain hardening to ultimate stress, then necking and fracture at the breaking point.

## Answer

The diagram is obtained from a tension test on a mild steel specimen (nominal stress $= P/A_0$ against strain $= \Delta L/L_0$).

```text
 stress
   |            D (ultimate)
   |           ,-'''-.
   |       B C/       '.  E (fracture)
   |      ,-'''           x
   |     /  yield
   |    /  plateau
   |   /
   |  /  elastic
   | /A  (Hooke's law)
   |/__________________________ strain
   O
 A=proportional limit, B=upper yield, C=lower yield
 D=ultimate stress, E=breaking point
```

#### Salient points
1. **O to A, proportional limit:** stress is proportional to strain (Hooke's law); the slope is $E$.
2. **Elastic limit:** just beyond A; material returns to its original length on unloading.
3. **Upper yield point (B) and lower yield point (C):** the stress drops slightly and the specimen elongates considerably at nearly constant stress (yield plateau). Mild steel has $\sigma_y \approx 250\ \text{N/mm}^2$.
4. **Strain hardening (C to D):** the material regains strength and the curve rises to the maximum.
5. **Ultimate stress (D):** the maximum nominal stress; after this, necking starts.
6. **Breaking (fracture) point (E):** the nominal stress falls as the section necks, and the specimen breaks. The true stress, based on the reduced area, actually keeps rising to fracture.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is true between O and A (proportional limit) on the mild steel curve?
   A. Stress stays constant while strain increases
   B. The material starts necking
   C. Stress is proportional to strain and the slope equals E
   D. Stress falls while strain increases
   Answer: C. Up to A, Hooke's law holds, and the slope of the straight line is Young's modulus. (Key point: Proportional limit)

2. What happens at the yield points B and C?
   A. Specimen elongates considerably at nearly constant stress, with a slight drop from upper to lower yield
   B. Stress rises steeply with very little strain
   C. The specimen fractures immediately
   D. The material returns to its original length on unloading
   Answer: A. At yielding the stress drops slightly and the specimen stretches a lot at nearly constant stress. (Key point: Yield plateau)

3. Why does the nominal stress fall between the ultimate point D and the breaking point E?
   A. The material becomes elastic again
   B. True stress also falls to zero
   C. The specimen necks, and nominal stress uses the original area
   D. The load is increased beyond the ultimate load
   Answer: C. After D necking reduces the area, so the load and the nominal stress (P/A0) fall, though true stress keeps rising. (Key point: Ultimate and fracture)

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