---
title: "Yield, strain hardening, stress-strain diagram"
subject: "Civil Engineering Materials"
chapter: 1
key: "semester_3/civil_engineering_materials:yield-strain-hardening-stress-strain"
source: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/yield-strain-hardening-stress-strain
site: BCT Engineering
---

# Yield, strain hardening, stress-strain diagram

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

- Asked in: 2070 Chaitra (old course), 3+2+3 marks; 2066 Shrawan (old course), 3+2+3 marks (asked 2 times)
- Video: [Mechanics of Materials: Lesson 10 - .2% Offset Rule Explained, Yield Point](https://www.youtube.com/watch?v=yxve9ZzpPrg) — Jeff Hanson
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/yield-strain-hardening-stress-strain
- Whole chapter: https://www.bctengineer.com/md/semester_3/civil_engineering_materials/chapter-1

## Question

Define 'yield' and 'strain hardening' related to the tensile strength test for steel. How is the yield point of a brittle material found out from the stress/strain diagram? Draw the stress/strain diagram for ductile and brittle materials.

## Short answer

Yield is the onset of plastic deformation without load increase; strain hardening is the subsequent rise in stress due to dislocation entanglement. For brittle materials, the yield point is determined by the 0.2% offset method: a line parallel to the elastic region from 0.2% strain intersects the curve at the proof stress.

## Answer

#### Yield
**Yield** is the stage in a tensile test of steel at which the specimen begins to deform plastically without any noticeable increase in load. The stress at this point is the **yield stress**. Mild steel shows an upper and a lower yield point; after the upper yield point the stress drops slightly, and the strain then increases rapidly at nearly constant stress (the lower yield point).

#### Strain hardening
After yielding, the dislocations in the metal multiply and become tangled, so more stress is needed to produce further strain. The curve rises again until the ultimate stress is reached. This region is called **strain hardening** (work hardening). Cold working of steel bars (TOR steel) uses this effect to raise the yield strength.

#### Yield point of a brittle material
A brittle material has no clear yield point on its stress-strain diagram. The yield point is found by the **offset (proof stress) method**: from a strain of 0.2% on the strain axis, draw a line parallel to the initial straight portion of the curve. The stress at which this line cuts the curve is taken as the 0.2% proof stress (yield strength).

#### Stress-strain diagrams
```text
 Ductile (mild steel)               Brittle (cast iron)
 stress                             stress
   |               U                  |
   |            .-'''-.               |           x F
   |   Yu      /       \              |         .'
   |   /\_Yl__/         \             |       .'
   |  /                  x F          |     .'
   | / E                              |   .'
   |/                                 | .'
   +------------------------- strain  +-------------- strain
 E: elastic limit, Yu/Yl: upper/lower yield point,
 U: ultimate stress, F: fracture
```
The ductile curve shows a long plastic region and necking before fracture, whereas the brittle curve is almost linear and ends suddenly at a small strain.

## Check yourself

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

1. At yield, steel
   A. deforms plastically without noticeable increase in load
   B. fractures suddenly
   C. returns fully to shape
   D. starts necking
   Answer: A. Yield is the start of plastic flow at nearly constant stress. (Key point: Yield)

2. In the strain hardening region
   A. stress drops to zero
   B. stress rises again with strain until ultimate stress
   C. strain stays constant
   D. the specimen is elastic
   Answer: B. Dislocations interlock so more stress is needed. (Key point: Strain hardening)

3. The yield point of a brittle material is found by
   A. the Charpy test
   B. reading the upper yield point
   C. the 0.2% offset (proof stress) method
   D. the Le Chatelier test
   Answer: C. A line parallel to the elastic slope from 0.2% strain cuts the curve at the proof stress. (Key point: Brittle yield)

4. Compared with a ductile curve, the brittle curve is
   A. long with necking
   B. flat with a long plateau
   C. rising after fracture
   D. almost linear and ends suddenly at small strain
   Answer: D. Ductile shows long plastic region and necking. (Key point: Diagram)

## Related in Civil Engineering Materials

- [Stress-strain curve of ductile material](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Astress-strain-curve-ductile) — Civil Engineering Materials, chapter 1
- [Ductile versus brittle failure](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aductile-brittle-failure) — Civil Engineering Materials, chapter 1
- [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
- [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
- [Tensile test numerical, 40 mm specimen](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Anumerical-tensile-test-40mm) — Civil Engineering Materials, chapter 1
- [Ferrite and pearlite in high strength steel](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aferrite-pearlite-high-strength-steel) — Civil Engineering Materials, chapter 8

## 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
- [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
- [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
- [Stress-strain diagram for mild steel](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Astress-strain-diagram-mild-steel) — Strength of Materials, chapter 3