---
title: "Short note: Griffith theory"
subject: "Civil Engineering Materials"
chapter: 1
key: "semester_3/civil_engineering_materials:griffith-theory"
source: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/griffith-theory
site: BCT Engineering
---

# Short note: Griffith theory

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

- Asked in: 2057 Chaitra (old course), 4 marks
- Video: [Griffiths theory for brittle material Material CEM BE first semester. #materials #civilengineering](https://www.youtube.com/watch?v=4jAbLWC6yMo) — Civil Engineering Solution Channel
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/civil_engineering_materials/griffith-theory
- Whole chapter: https://www.bctengineer.com/md/semester_3/civil_engineering_materials/chapter-1

## Question

Write a short note on Griffith theory.

## Short answer

Griffith theory states that microscopic cracks concentrate stress, making the actual fracture strength of brittle materials much lower than theoretical. The critical stress for crack extension is σc = √(2Eγ/πa). Larger flaws reduce strength. The theory underpins fracture mechanics.

## Answer

**Griffith theory** (A. A. Griffith, 1920) explains why the actual fracture strength of brittle materials is far below the theoretical strength. It states that every real material contains microscopic cracks or flaws, which magnify the local stress at their tips.

#### Principle
A crack extends only if the elastic strain energy released by its growth is at least equal to the surface energy needed to create the new crack surfaces. For a thin plate with an internal crack of length $2a$, the critical (fracture) stress is

$$
\sigma_c = \sqrt{\frac{2E\gamma}{\pi a}}
$$

where $E$ is the modulus of elasticity, $\gamma$ is the surface energy per unit area and $a$ is half crack length.

#### Conclusions
- Larger flaws give lower fracture strength.
- Brittle materials (glass, ceramics, concrete) fail by crack propagation under tension, and are much stronger in compression, where cracks close.
- For ductile materials, plastic work at the crack tip also adds to the energy needed (Irwin-Orowan modification).

The theory is the base of fracture mechanics.

## Check yourself

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

1. Griffith theory explains why
   A. steel is ductile
   B. concrete shrinks
   C. timber rots
   D. actual strength of brittle materials is far below theoretical strength
   Answer: D. Due to microscopic flaws. (Key point: Purpose)

2. A crack extends if
   A. released strain energy is at least the surface energy for the new surfaces
   B. the load is zero
   C. surface energy is infinite
   D. the crack is closed
   Answer: A. Energy balance. (Key point: Principle)

3. Critical stress is
   A. 2 E gamma / (pi a)
   B. sqrt(2 E gamma / (pi a))
   C. sqrt(pi a / 2 E gamma)
   D. E gamma a
   Answer: B. Given. (Key point: Formula)

4. Larger flaws give
   A. higher fracture strength
   B. no change
   C. lower fracture strength
   D. infinite strength
   Answer: C. sigma_c falls as a increases. (Key point: Conclusion)