---
title: "Griffith Criterion for Crack Growth Interactive Lab | Sandbox Physics"
description: "When does a crack start to grow, and does it then stop or run away?"
canonical_url: "https://sandboxphysics.com/labs/griffith-crack-growth/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/griffith-crack-growth/"
last_modified: "2026-10-29"
---

Fracture mechanics · Energy release rate

# Griffith Criterion for Crack Growth

**When does a crack start to grow, and does it then stop or run away?** A crack grows when the elastic energy freed by a small advance at least pays for the new surface. Under a fixed stress the payment grows with crack length, so a plate crack runs away; between fixed grips the payment stays level or falls, so the crack tears steadily or stops.

Load a cracked plate, a gripped strip or an edge notch. The crack grows once released elastic energy pays for new surface. Export the energy record.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A two-dimensional linear elastic finite-element model with a straight crack on its symmetry plane. Crack-plane nodes are released one at a time once the energy release rate reaches the toughness. Units: Young modulus 1, toughness 1, specimen width 1. The model has no plasticity, process zone, inertia or crack turning.

Crack length over width

$0.3$

Load over predicted onset

$0.91$

Energy release rate over toughness

$0.828$

Excess release, share of work

$0\%$

Blue is the simulated energy release rate at this load; the red dashed line is the toughness. Bars split the work done by the load.

Save the run and read the model

The JSON lists the specimen, mesh, units, model version, predicted onset and every recorded load step with the four ledger terms.

The plate case is checked against the secant formula for a center crack quoted by Sargado and coworkers, and the gripped strip against its exact steady energy release rate. [Read the source](https://arxiv.org/abs/2210.06315)

[Read the fracture course: from Griffith energy to phase-field cracks and branching](https://sandboxphysics.com/stories/fracture-mechanics/)

Physics tutorial

## A crack grows when the energy bill is paid

**Background** Opening a crack creates two new surfaces, and surfaces cost energy. The loaded body can pay that cost only from its stored elastic energy and from the work its loads keep doing.

**Why it matters** Griffith turned fracture into an energy balance. The same balance also says whether a growing crack stops by itself or runs through the part.

Start with the essentials

- **Focus question**: When does a crack start to grow, and does it then stop or run away?
- **One-sentence intuition**: Growth starts when the energy release rate reaches the toughness. It stays stable only if a longer crack releases less energy at the same load.

### Core mathematical model

#### Griffith criterion

$$
G=-\frac{\partial\Pi}{\partial a}\ge G_c
$$

The potential energy of the loaded body falls by $G$ for each unit of crack advance per unit thickness. The crack can grow when that release reaches the toughness $G_c$, the energy needed per unit of new crack area.

#### The same rate from the compliance

$$
G=\frac{P^{2}}{2}\frac{dC}{da}
$$

For one crack tip and unit thickness, the energy release rate follows from how fast the compliance grows with crack length. It holds both at fixed load and at fixed grips. The Lab checks it against a crack-closure estimate that uses only nodal values at the tip.

#### Two reference cases

$$
G_{\text{plate}}=\frac{\pi\sigma^{2}a}{E}F\!\left(\frac{a}{w}\right)^{2},\qquad G_{\text{strip}}=\frac{(\lambda+2\mu)\Delta^{2}}{h}
$$

A center crack in a plate under remote stress releases more energy the longer it gets. A long crack between rigid grips, each moved by the displacement shown, releases a steady amount that no longer depends on its length.

#### Where the work goes

$$
W=U+\Gamma+D,\qquad D\ge 0
$$

Work done by the loads goes into stored elastic energy, new crack surface and an excess that a quasi-static model cannot track. That excess appears when a crack jumps ahead at a load above its onset.

### Common difficulties

#### Stress at the tip is not the criterion

**Typical misconception** The crack grows when the stress at its tip exceeds the strength.

**Better mental model** A sharp elastic crack has unbounded stress at its tip at any load. Griffith compares energies instead, which gives a finite onset load.

#### What this model leaves out

**Typical misconception** The predicted onset load is what a real specimen will show.

**Better mental model** A two-dimensional linear elastic finite-element model with a straight crack on its symmetry plane. Crack-plane nodes are released one at a time once the energy release rate reaches the toughness. Units: Young modulus 1, toughness 1, specimen width 1. The model has no plasticity, process zone, inertia or crack turning.

### Run the experiment

1. 01

   #### Watch a plate crack run away

   Choose Plate crack runs away and let the load rise. Watch the release curve in the data row as the crack starts to grow.

   **What to observe:** Once the white point reaches the toughness line, the curve keeps rising with length. The crack crosses the plate at the same load and the excess bar grows.

2. 02

   #### Compare a short crack

   Choose Short crack needs more stress, or drag the crack tip toward the centre.

   **What to observe:** A shorter crack needs a larger stress before it grows, because it releases less energy per step.

3. 03

   #### Hold the grips

   Choose Gripped strip tears steadily, then Edge notch grows under grips. Drag the grips to raise or lower the displacement.

   **What to observe:** Between fixed grips the crack grows over a narrow range of grip displacement and stops when the grips stop. The excess bar stays near zero, while the plate under fixed stress leaves about a third of the work as excess.

Physical conclusion

Ask how much energy a small advance would release and how that amount changes as the crack grows. The first answer gives the onset; the second tells you whether growth is stable.

## Related experiments and articles

Fracture mechanics · Reading path

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

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why a crack needs energy to grow**](https://sandboxphysics.com/stories/fracture-mechanics/why-cracks-need-energy/)
2. [Lab **Photoelastic Stress Viewer** See stress concentrate around a hole](https://sandboxphysics.com/labs/photoelastic-stress-viewer/)
3. [Lab **Stress–Strain Material Tester** Measure modulus and yield stress](https://sandboxphysics.com/labs/stress-strain-tester/)
4. [Article **Find the energy release rate from a compliance curve**](https://sandboxphysics.com/stories/fracture-mechanics/energy-release-from-compliance/)
5. [Article **When a growing crack stays under control**](https://sandboxphysics.com/stories/fracture-mechanics/stable-and-unstable-cracks/)
6. [Article **Stress near a crack tip and the stress intensity factor**](https://sandboxphysics.com/stories/fracture-mechanics/stress-near-the-crack-tip/)
7. [Article **Predict when a notch starts to crack, then test the prediction**](https://sandboxphysics.com/stories/fracture-mechanics/predicting-notch-initiation/)
8. [Lab **Phase-Field Fracture Model of a Growing Crack** Watch a damage band choose its path](https://sandboxphysics.com/labs/phase-field-crack/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)