This presentation is about composite materials for wind turbine blades. After this lecture, you'll be able to describe the use of uniaxial composites in wind turbine blades, calculate the stiffness and strength of a composite material, estimate the fatigue limit of a composite. Composites consist of two material phases, a brittle and a ductile material. The brittle is stiff, strong but also a brittle behavior, what we can see in example on the tensile curve here. Here you can see that the stresses is actually rather unpredictable and actually given by the biggest flaw in the material. On the other hand the soft phase which is a matrix material is weak and ductile as illustrated on the green curve. Mixing these two materials together then we get a, stiffness, and strength, which are in between the two phases. But the strengths is now predictable, and we can use this, in a design, of a structure. We would never imagine designing something of pure glass. If you look into a cross section of a wind turbine blade, then this is an illustration of this. We can see that the load carrying part is shown as green materials here, at three or four spots. The requirement for the material is high stiffness in order to avoid bending of the blade and high fatigue resistance of the material. If you take a close look into the material, inside the blade, then we can see that the uniaxial composits is built up of fiber bundes consisting of thousand to ten thousand fibers. The fibers have normally a diameter between 10 to 20 microns if we look at glass fiber or between 5 and 10 microns if we look at carbon fiber. The stiffness of composite can be predicted using a law called rule of mixture. If you look into a composite, a uni-axial composite, then as shown here as a x-ray scan of the fibers. This composite can be considered as perfectly aligned fibers in a matrix material. The fiber material has a stiffness called EF and a matrix called EM. The volume function of the fiber and the matrix is a value between zero and one, where zero is no material and one is full content of this material. The sum of the two is therefore equal to one. When we are straining the material in the fiber direction, then the straining of the fiber and the matrix will be equal to each other, and therefore, we can consider the material as two independent phases. While we have a strain of the matrix and a strain of the fiber equal to each other. Now we can calculate the stiffness of the composite as the volume fraction of the fiber multiplied with the stiffness of the fiber plus the volume fraction of the matrix multiplied with the stiffness of the matrix. And by this we get the rule of mixture shown here. If you are plotting the stiffness of the composite as a function of the volume fraction, then we can see that the stiffness is a linear relation going from the matrix stiffness without any fibers up to fiber stiffness for only fibers. If instead of the knowledge of the volume fraction of fiber, have the knowledge of the stiffness of composite, for example by doing some measurement. Then we can calculate the volume fraction of the fiber based on the equation here derived from the rules of mixture. Here we have the stiffness of the composite, stiffness of matrix and the stiffness of the fiber. Conventional composites is not covering the whole range of volume fractions. Normally we are only considering composites in between 50% to 60% fibers. If you look at the stiffness in the transverse direction of the fiber, then we cannot anymore use, you cannot use that straining of the two phases equal to each other. Instead we get the inverse rules of mixture shown here. This we solved in a stiffness variation shown at the curve here, we can see that the stiffness is much lower. Therefore we have anisotropic material behavior which will have a big difference in stiffness and fiber direction and in transverse direction. The rules of mixture can also be used for determining the density of the composite. Regarding tensile strength of the composite then we can still look at the material as consisting of the two phases of the fiber and the matrix, and we can use the knowledge that the straining of the two phases will be equal to each other. Therefore, loading up the composite which is the red curve up to the failure, then we will reach the failure when one of the phases is failing and the other phase cannot carry the load. This would normally be the case for the fiber which is a more brittle material than the matrix material. The straining can be calculated a the strength of the fiber divided by the stiffness of the fiber. When we would like to predict the strength of the composite then we need to take into account the stresses in the matrix at the failing point. So not the strength of the matrix but the stresses in the matrix at the failing point for the fiber. Which can be calculated as the straining of the fiber at failure multiplied with the stiffness of the matrix. This can be summed, again using rules of mixture, here we have volume function of fiber multiplied by strength of the fiber, plus the volume function of matrix, multiplied with the stresses in the matrix at the failing point. Finally, we can look at the fatigue behavior of a composite material. The fatigue behavior cannot be predicted in the same way as the stiffness and the strength of the composite. Instead, we must rely on experimental measurement, here shown such as set up, where we have a test sample, in between the grips for tensile machine setup. We will now load the material with the oscillating load given by a sine-variation between a max load and a minimum load. And when we talk about fatigue properties then we are talking about R ratio which was describing a ratio between the min and max value of the loading. If you do this at different load levels then we can count the number of cycles until failure and you can plot that on a diagram, here, shown six samples tested at different stress levels and then the reported number of cycles for failure for individual test. We have one extra test here which is something we call a run-out test. We have tested it at a stress level, but we didn't get failure until the point where we stopped the test. For those test points, we can do a fitting of a curve. And we normally get a relation looking like this, where we have the number to failure, given by a constant multiplied with the stress, we are putting on, the max stress we're putting on the sample in a potent here. Where we are measuring the maximum stress in Megapascal(MPa). This relation which is experimental, to determine for this specific composite material can now be used predicting the number of cycles for given stress level. In this lecture, you have learn how to describe the use of uniaxial composites in wind turbine blades, calculate the stiffness and strength of a composite material, estimate the fatigue limit of a composite.
