Welcome to this session on fatigue and mechanical properties of metals. Most wind turbine components are made of metals with the exception of the blades. In this section, we will focus on basic mechanical properties of metals and with the special focus on fatigue since this is a major concern for wind turbine components. So let's start looking at the basic equations for stress and strain. Where we consider here a metallic rod which has the length, L_0, and the cross-section area, A_0. If you apply a force to this rod, if you pull it, then the rod will become longer and thinner. The engineering stress is calculated by dividing the force with the original cross-section area, while the engineering strain is calculated by dividing the increase in length with the original length. Now, let's look at the stress strain curve where we have a straight line here in the beginning. So there's a linear relationship between the stress and the strain. And this is known as Hookes law. Where E here, this is the modulus of elasticity also known as Young modulus. And this corresponds to the stiffness of the material. So the stiffness is basically the slope of this line here. The stiffness is related to how strong the atomic bonds are. And this is also related to the melting point. So all iron based alloys they will have roughly the same stiffness. While all aluminum based alloys they will have roughly the same stiffness. If you want to change the stiffness you need a major change in chemical composition. Metals that consist of metallic atoms, that are fixed in a crystal lattice, if we apply a low stress to this lattice, then we will stretch it and if we relax the stress then we will, the lattice will revert to it's original shape. And we call this elastic deformation, which is non-permanent. If we increase the stress, then we will reach a certain point called the yield stress. And here, we will actually break the atomic bonds. So this is called plastic deformation. And this is permanent. So if we relax our lattice here, then we will not go back to the original shape. We will have a new lattice shape. So we have permanently deformed our material. So looking at the stress-strain curve, again, we start it out with the stiffness, the slope with the curve here, then we get the yield stress point where we go plastic deformation, and on top of the curve, we have the tensile strength. And this is basically the ultimative strength of the material. And we can see here that the slope goes down again. And this is because for most metals, we can get some local deformation the metallic rod here. And since our engineering stress, it was based on the original cross sectional area, then the stress will drop. So finally here, we get a fracture, and here we can see what the ductility of our material is. So the three points here, the yield stress, the tensile strength and the ductility, they are dependent on the chemical composition of the metal and the thermal and mechanical treatment of the metal. When metallic components that are exposed to cyclic stress, they may fail from what is called fatigue. And these stresses they can be quite low, and the important factors for fatigue here, these are, the number of cycles, and the stress amplitude. And the stress amplitude is the difference between maximum and minimum stress. These curves here, they can be quite erratic. They don't need to be a perfect curve. So here we have S/N curves. These indicate when a material will fail as a function of the stress amplitude and the number of cycles. So for example, if we have a lower stress amplitude, it will take a larger number of cycles until the component fails. Different materials, they have different curves and also different steels, they also have different curves, but common for the steels is that they have a minimum threshold level. So that is, if the stress amplitude is below a certain point, then a steel component will not fail from fatigue. So this is in contrast with, for example, aluminum. Here, if aluminum is exposed to cyclic stresses, then it will fail from fatigue sooner or later. So when a component is exposed to cyclic stresses, then we will initiate a crack, or may initiate a crack. And this will typically happen at an unfortunate geometry or at a defect such as inclusions or a scratch in the surface. Wind turbine components the have many unfortunate geometries. And here are two examples where we have a gear, where we have an unfortunate geometry between the gear teeth. And here's also a bolt where the inside of the thread is quite unfortunate. When we have initiated, a crack, then it will start to grow. And it will grow with each cycle when the stress is at its maximum. So each time the crack it grows, it will leave a mark, like a ring here. And this will be visible in a microscope and it may also be visible with the naked eye. Eventually the component will fail, we will have a final fracture surface. This may be quite large or it can also be small. So the fatigue crack can sometimes grow almost all the way through the component before it fails. So this final fracture surface is usually quite rough compared to the surface of the fatigue crack, which is quite smooth. So here, we have an example of, this is a gear from a wind turbine gearbox. You can see it's quite large, this is the cross section of it. And if you look at the fracture surface here, we can see that there are some ring marks here and these are from fatigue, Where the crack has grown. And we can also see here where the crack is initiated we just follow the marks. We can see that it's in-between two gear teeths. And the final fracture area is also quite small. In this case, here, we can see that it is at angle with the fatigue crack. So in this example here we have a bolt, so this is from a wind turbine foundation, and again, here, we can see clear marks that indicate a fatigue mode failure. So in this case we can see that we have several cracks that have initiated down here at the bottom, and then they've grown into one large crack where we have the normal fatigue mode as the crack grows upwards. And the final fracture area is also here, quite small. In this case here, we can also see that we have a lot of corrosion down here. This also indicates where the crack has started, since the crack initiation point is the most exposed area to the elements. So this concludes our session. And you should here have learned about some basic mechanical properties of metals and fatigue.