Cracking Dams: Cracks Theory, a

How do cracks grow?

How a crack grows is called "crack propagation" and this takes into account when a crack can start to grow, how far it grows, and what direction it goes in.

So when can it grow? Well there are two ways to look at it. First, from the point of view of the stress intensity factor, K_I. The material resists cracking with everything it has, which is called its fracture toughness. (K_Ic, which was mentioned before, stands for fracture toughness. It's said "K one c".)

The crack can grow when its stress intensity factor (sif) reaches the fracture toughness of the material:

K_Ic=K_I

The other way to look at when a crack can grow is the energy way, which was also mentioned before. When a crack is formed, new surfaces are also formed, along the edges where the material has split apart. The material has to have enough energy to create these new surfaces or it will not crack. If G is the energy necessary for the crack to grow and R is the material's resistance to crack growth, the condition for a crack to grow is:

G = R

But once the crack has grown, will it keep growing? Things change once a crack has grown. The resistance of the material may have gone up or down; the energy necessary to grow the crack may also have gone up or down. In order for the crack to continue growing each time, the change in energy must equal the change in resistance. If the change in energy is less than the change in resistance, then the crack will not grow any more unless more force is applied. If the change in energy is greater than the change in resistance, there will be unstable crack growth. In this case the crack may grow until the structure fails.

Which way does the crack grow? Well, as long as the material is being loaded like this, a crack will always grow perpendicular to the load.

Check out this movie of a crack at the molecular level!
(ref: F.F.Abraham et al)

But if the material is being loaded in more than one mode, this isn't true. If the material is being pushed and pulled in more than one direction, the crack may have different choices on which direction to go in. There are a couple different theories on which way the crack will go.

One theory says the crack will try to imitate mode I: the crack looks for the greatest forces that would pull it apart, and then grows perpendicular to those forces.
Another theory says the crack will grow in the direction of the maximum energy release, the direction where it can get rid of the greatest amount of energy.

Once the crack doesn't have enough energy to grow any more, it stops, or arrests. Hopefully, the structure hasn't failed by then.

Cracking your model in a simulation

At this stage of the game, computer simulations for crack growth can figure out how the crack will grow, but not how or where it will start. So you have to tell the program where the crack starts and then it can do the rest.
Here is an image of a model with an initial cracks on both the left hand edge and the right hand edge (cracks are green lines). The program which will analyzed this model can only handle cracks which start from the outside of the structure.

This is what the model looks like after the program has grown the crack. The tips of the cracks have moved to where you see the blue patches.
So what is this computer program that does cracking simulations?