Stress Swelling Soiree

Stress concentrations are locations in a material where applied stress is concentrated. This concentration makes it easier to pull apart the metal as the forces between the particles in the metal are already under stress. The stress about the point is maximum at the point and rapidly decreases to the average stress in the material as you move away. These points can be due to microscopic imperfections, such as cracks in the surface and flaws inside the material, or it could be due to larger cracks created across the material. For this module, the important concentrations we will be using are these 3 types of cracks.

For these cracks to get larger, they must first have a high enough stress to pull apart the forces holding the material together. This stress required is calculated using the Stress Intensity Factor. This is:

K_i = Yσ√(πa)

Where K_i is Stress Intensity Factor (the subscript i is 1, 2 or 3 depending on crack mode), Y is a given constant based on the geometry of the sample, σ is stress applied to the same and a is the length of the crack in the material. It has a unit of Pa*m^1/2.

Once the Stress Intensity Factor rises above the critical value, the crack will propagate through the material. This critical value is based on what the material is, and what mode of crack it is. A steel alloy will have a type 1 critical value of around 50 Mpa*m^1/2, but concrete will only have a value of around 1 Mpa*m^1/2, meaning a crack in concrete will propagate under smaller cracks or with less stress compared to steel alloys.

It is important to understand how stress concentration affects materials, as there are many examples where a point of concentrated stress can bring down something as big as a ship. Older models of aircrafts that used more square windows and other parts had stress concentrations that were unexpectedly large. This posed huge risks and maintenance problems with aircrafts, leading to rounded parts being used far more with newer models of planes.