---
title: "Fracture mechanics from Griffith’s energy balance to branching cracks"
description: "Learn why cracks need energy, when they run away, how a phase-field model grows them and why fast cracks branch. Eight chapters with exercises and three Labs."
canonical_url: "https://sandboxphysics.com/stories/fracture-mechanics/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/fracture-mechanics/"
last_modified: "2026-10-29"
---

[Fracture mechanics · A course with experiments](https://sandboxphysics.com/stories/fracture-mechanics/)

FROM ONE NOTCH TO A BRANCHING CRACK

# Fracture mechanics from Griffith’s energy balance to branching cracks

A fine scratch can make a glass rod break far below the stress its atomic bonds could hold, because a crack grows whenever the energy it releases pays for the new surfaces. Start with that balance, then follow the crack as it grows stably, runs away, chooses a path and, at high speed, splits.

Sandbox Physics · 2026-10-29

Sharp cracks · Chapters 1–4

## When a crack can grow

Balance released elastic energy against the cost of new surface, measure it from a compliance curve, decide whether growth stays under control, then read the same criterion from the stress near the tip.

[Start with the energy balance →](https://sandboxphysics.com/stories/fracture-mechanics/why-cracks-need-energy/)

Cracks as fields · Chapters 5–8

## How a crack chooses its path

Replace the sharp crack by a damage band, predict when a notch starts to crack and test the prediction, then follow fast cracks into branching and disorder.

[Start with the damage band →](https://sandboxphysics.com/stories/fracture-mechanics/crack-as-a-damage-band/)

## Eight chapters, with examples and experiments

1. [01 L1 Why a crack needs energy to grow Why does a scratched glass rod break at a stress far below what its atomic bonds could hold? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/why-cracks-need-energy/)
2. [02 L2 Find the energy release rate from a compliance curve How can a record of load and displacement tell you how much energy a crack releases as it grows? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/energy-release-from-compliance/)
3. [03 L2 When a growing crack stays under control Why does the same crack creep forward in one test and run through the specimen in another? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/stable-and-unstable-cracks/)
4. [04 L2 Stress near a crack tip and the stress intensity factor If the stress at a sharp tip is infinite, what number tells you how close the crack is to growing? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/stress-near-the-crack-tip/)
5. [05 L3 Model a crack as a narrow band of damage How can a computer let a crack choose its own path, without a rule for where the tip should go? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/crack-as-a-damage-band/)
6. [06 L3 Predict when a notch starts to crack, then test the prediction Can a sharp-crack energy release rate, computed separately, predict when a phase-field notch begins to crack? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/predicting-notch-initiation/)
7. [07 L4 Fast cracks and branching in a dynamic phase-field model Why does a crack that runs fast enough stop travelling as a single straight line? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/fast-cracks-and-branching/)
8. [08 L4 How frozen disorder roughens a fast crack path If every piece of a material is a little different, how much does that move a fast crack off its straight line? Read and try →](https://sandboxphysics.com/stories/fracture-mechanics/disorder-and-rough-crack-paths/)

## Keep the experiments beside the chapters

The sharp-crack Lab, the phase-field Lab and the fast-crack Lab use three separate models. Compare a scene with its readouts through the record each Lab exports.

[Grow a crack and track where the work goes ↗](https://sandboxphysics.com/labs/griffith-crack-growth/) [Watch a damage band choose its path ↗](https://sandboxphysics.com/labs/phase-field-crack/) [Drive a fast crack until it wanders or splits ↗](https://sandboxphysics.com/labs/dynamic-crack-branching/)