Stress Intensity Factor

What is this formula?

The Stress Intensity Factor quantifies the stress concentration at the tip of a crack. It is the fundamental parameter of Linear Elastic Fracture Mechanics (LEFM) and is used to predict crack propagation and structural failure.

When to use it

Use this formula when evaluating cracked components, pressure vessels, pipelines, aircraft structures, welded joints, or any engineering component where fracture risk must be assessed.

Example

A steel plate contains a crack of length:

a = 0.005 m

The applied stress is:

sigma = 150 MPa

The geometry factor is:

Y = 1.12

Formula:

KI = Y*sigma*√(π*a)

Substitution:

KI = 1.12 × 150000000 × √(π × 0.005)

Result:

KI = 2.11×10^7 Pa·√m

The crack tip experiences a stress intensity factor of approximately 21.1 MPa·√m.

Applications

- Fracture mechanics

- Structural integrity assessment

- Pressure vessel design

- Pipeline inspection

- Aircraft maintenance

- Failure analysis

Note

The geometry factor Y depends on crack shape, crack location, specimen geometry, and loading conditions. Numerous handbooks provide Y values for common engineering configurations. This equation is valid within the assumptions of Linear Elastic Fracture Mechanics.