---
title: "Stress concentration and its effect in brittle material"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:stress-concentration-brittle-effect"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/stress-concentration-brittle-effect
site: BCT Engineering
---

# Stress concentration and its effect in brittle material

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2074 Asoj, 4 marks
- Video: [Stress CONCENTRATION Factors and Factor of Safety in 11 Minutes!](https://www.youtube.com/watch?v=kZN0xdPMQzw) — Less Boring Lectures
- 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-concentration-brittle-effect
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

What is the stress concentration? What effect is produced in brittle material due to stress concentration?

## Short answer

Stress concentration is a local stress peak at a geometric discontinuity. Brittle materials cannot yield to redistribute stress, so when the maximum stress reaches ultimate strength at the notch, a crack suddenly spreads and the member fails at a nominal stress far below strength, with no warning; design must use the full stress concentration factor.

## Answer

**Stress concentration** is the sudden rise of local stress near a geometric discontinuity (hole, notch, keyway, fillet, sharp change of section, crack) in a loaded member. Away from the discontinuity the stress is uniform (nominal), but at the discontinuity the stress flow lines crowd together and the peak stress becomes much higher.

The severity is measured by the **stress concentration factor**:

$$
K_t = \frac{\sigma_{max}}{\sigma_{nominal}}
$$

$K_t$ depends only on the geometry (for example, for a small circular hole in a wide plate under tension $K_t \approx 3$). It is larger for sharper corners and smaller radii.

#### Effect in brittle material
- A brittle material (cast iron, glass, concrete, ceramics) has no yield region, so it cannot redistribute the high local stress by plastic flow.
- When $\sigma_{max}$ reaches the ultimate strength at the notch, a crack starts there and spreads suddenly across the section. The member fails at an average (nominal) stress much lower than its strength, with no warning and very little deformation.
- Hence the full theoretical $K_t$ must be used in the design of brittle members.
- In a ductile material (mild steel), the material at the notch yields locally, the peak stress is shared with neighbouring fibres, and the effect on static strength is small. For repeated (fatigue) loading, however, stress concentration is dangerous for both.

#### Reducing stress concentration
Provide generous fillet radii, avoid sudden changes of section, use gradual tapers, and drill relief holes at crack tips.

## Check yourself

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

1. What is stress concentration?
   A. A sudden local rise of stress near a hole, notch or abrupt section change
   B. Uniform stress over the whole section
   C. Stress caused by temperature
   D. The stress at yield
   Answer: A. Geometric discontinuities crowd the stress flow lines and raise the peak stress. (Key point: Definition)

2. How is K_t defined?
   A. sigma_nominal / sigma_max
   B. sigma_max / sigma_nominal
   C. sigma_yield / sigma_max
   D. sigma_ultimate / sigma_nominal
   Answer: B. K_t is the ratio of peak to nominal stress and depends on geometry. (Key point: Factor)

3. Why is stress concentration serious in brittle materials?
   A. No yielding allows redistribution, so a crack starts and spreads suddenly at low nominal stress
   B. Brittle materials yield too much
   C. They are too soft
   D. It only affects colour
   Answer: A. Without plastic flow the peak stress hits ultimate strength and fracture occurs without warning. (Key point: Brittle effect)

4. How can stress concentration be reduced?
   A. Sharp corners
   B. Smaller radii
   C. Generous fillet radii and gradual section changes
   D. Adding notches
   Answer: C. Smoother geometry lowers K_t. (Key point: Design)

## Related in Strength of Materials

- [Stress concentration and Saint-Venant's principle](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Astress-concentration-saint-venant) — Strength of Materials, chapter 3
- [Simply supported I-beam: stress at flange-web junction](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Ai-beam-flange-web-junction-stress) — Strength of Materials, chapter 7
- [Resultant stress on planes EF and GE, principal stresses](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aresultant-stress-plane-ef-ge) — Strength of Materials, chapter 4
- [Max shear for 150 MPa stress limit; principal stresses](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Adirect-stresses-100t-60c-shear-limit) — Strength of Materials, chapter 4

## Related in other subjects

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