---
title: "Stress-strain curve of ductile material"
subject: "Civil Engineering Materials"
chapter: 1
key: "semester_3/civil_engineering_materials:stress-strain-curve-ductile"
source: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/stress-strain-curve-ductile
site: BCT Engineering
---

# Stress-strain curve of ductile material

Civil Engineering Materials · Chapter 1: Introduction to Civil Engineering Material

- Asked in: 2059 Poush (old course), 3+4 marks
- Video: [STRESS STRAIN CURVE | DUCTILE | BRITTLE | MILD STEEL | CIVIL ENGINEERING](https://www.youtube.com/watch?v=FGvRv0sDrJI) — ACE CIVIL ENGINEER
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/stress-strain-curve-ductile
- Whole chapter: https://www.bctengineer.com/md/semester_3/civil_engineering_materials/chapter-1

## Question

Draw a neat stress-strain curve for a ductile material and explain the significant points in the curve.

## Short answer

A ductile stress-strain curve shows proportional limit, elastic limit, upper/lower yield, ultimate stress, necking and fracture. The area under the curve is toughness. Mild steel yields at about 250 MPa, then strain hardens to an ultimate stress before necking and fracture.

## Answer

A ductile material such as mild steel is tested in a universal testing machine and the stress $\sigma = P/A_0$ is plotted against the strain $\varepsilon = \Delta L/L_0$.

```text
 stress
   |            C
   |        B ,-'''-. D
   |   A  ,.'/        \
   | ,-'  / yield      \ E (fracture)
   |/ P  /              x
   +--------------------- strain
   O
 P proportional limit, A elastic limit,
 B upper yield, C ultimate, D necking, E fracture
```

#### Significant points
1. **Proportional limit (P):** up to this point stress is proportional to strain (Hooke's law). The slope is Young's modulus $E$.
2. **Elastic limit (A):** the maximum stress up to which the material returns to its original length on unloading. It is very close to the proportional limit.
3. **Upper and lower yield points (B):** the stress drops slightly and the material elongates at nearly constant stress. This is the start of plastic flow. The yield stress is used as the design strength.
4. **Strain hardening region:** after yielding, the stress rises again with strain because of work hardening.
5. **Ultimate stress (C):** the maximum stress on the curve, equal to the maximum load divided by original area.
6. **Necking (D):** the cross-section reduces locally, so the engineering stress falls although the true stress keeps rising.
7. **Fracture point (E):** the specimen breaks. The area under the curve to this point is the toughness.

Percentage elongation and reduction in area measure the ductility.

## Check yourself

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

1. Up to the proportional limit
   A. the material yields
   B. necking begins
   C. stress is proportional to strain and the slope is E
   D. fracture occurs
   Answer: C. Hooke's law. (Key point: Proportional limit)

2. At the yield point
   A. stress is maximum
   B. the specimen breaks
   C. stress is zero
   D. strain increases at nearly constant stress, marking plastic flow
   Answer: D. Yield stress is the design strength. (Key point: Yield)

3. Ultimate stress is
   A. maximum load divided by original area
   B. load at fracture over final area
   C. stress at proportional limit
   D. stress at necking onset only
   Answer: A. Highest engineering stress. (Key point: Ultimate stress)

4. After necking begins, the engineering stress falls because
   A. the material hardens
   B. the load decreases as the area locally reduces
   C. E decreases to zero
   D. the strain is reversed
   Answer: B. Engineering stress uses original area. (Key point: Necking)

## Related in Civil Engineering Materials

- [True stress; stress-strain curve of steel](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Atrue-stress-strain-curve-steel) — Civil Engineering Materials, chapter 1
- [Yield, strain hardening, stress-strain diagram](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Ayield-strain-hardening-stress-strain) — Civil Engineering Materials, chapter 1, asked 2×
- [Stress, strain, elongation of steel rod](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Anumerical-steel-rod-stress-strain) — Civil Engineering Materials, chapter 1

## Related in other subjects

- [Ductile and brittle stress-strain behaviour](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Aductile-vs-brittle-stress-strain) — Material Science, chapter 3
- [Stress-strain diagram of mild steel](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Astress-strain-diagram-mild-steel) — Strength of Materials, chapter 2
- [Tensile test and stress-strain diagram](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Atensile-test-engineering-stress-strain) — Material Science, chapter 3
- [True stress and true strain relations](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Atrue-stress-strain-relations) — Material Science, chapter 3