The Stress Intensity Factor

How Stresses can be Accurately Predicted around Cracks


The stress intensity factor uses geometric and load distribution properties to determine stress levels and predict crack growth.


The study of fracture mechanics helps engineers understand how mechanical system behave and eventually fail due to the initiation and progression of cracks. One of the parameters that are used to understand crack growth is the stress intensity factor. The stress intensity factor shows how stresses in the region near the tip of the crack, where the crack growth is actively progressing, are affected by the applied load and the crack geometry.
Stress Intensity Factor Development

The stress intensity factor was developed by engineers at the U.S. Naval Research Laboratory in the 1940s. The team, led by G.R. Irwin, was attempting to calculate the amount of energy in a material that was available for fracture progression. They developed an equation for the stress field at the tip of a crack. One of the terms in this equation was the stress intensity factor, which is based on the size and location of the crack, as well as the geometry of the component that contains the crack.
Stress Intensity Factor Notation

The stress intensity factor is represented in equations as “K”. The stress intensity factor often contains a subscript of I, II, or III to define the loading mode. Because Mode I scenarios (a part loaded axially with the crack progressing perpendicular to the load application) are more common than the other loading modes, and contribute more to crack initiation and growth, this mode is the most commonly studied of the three.
Influences of the Stress Intensity Factor

The value and rate of change of the stress intensity factor directly influences the rate of crack growth in a component. A common reference graph for many materials plots the rate of crack growth (change in crack length per load cycle) versus the change in the stress intensity factor.

The stress intensity factor does help to provide an accurate understanding of stress levels in the crack tip region, but assumes a purely elastic situation. The accuracy is reduced as the location approaches the actual crack tip where local plastic deformation is occurring. The stress intensity factor is also more accurate when evaluating brittle materials as opposed to ductile materials that deform significantly prior to failure.




Values for stress intensity factor for a wide variety of materials and geometries have been empirically and experimentally determined, and are available in existing literature.
Sources

Irwin, G., Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate, Journal of Applied Mechanics, Vol. 24, pp 361-364, 1957.

Shukla, A., Practical Fracture Mechanics in Design, CRC Press, 2004