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- Composite Fatigue Analysis
Q: Do composites have a fatigue limit? If not, how do you approach fatigue analysis in composite components?
In theory, composites do not have a fatigue limit as steels do so a fatigue limit approach cannot be applied to the analysis of composite components.
However, due to the extremely high fatigue performance compared to steels, in some industries, many standards do take a pragmatic approach to fatigue requirements. The image below compares typical S-N curves for glass and carbon composites and for steel.
In the marine industry, for example, it can be easily shown that a vessel would have to undergo unrealistically severe day-to-day loading and be in continuous operation in order for the design to be fatigue critical compared to the ultimate strength of the material.
Fatigue, of course, is a major consideration in other industries such as wind and ocean energy, particularly for cross-flow devices such as vertical axis wind turbines where the load reverses with each cycle and a fatigue analysis must typically be performed in these industries. The basic wind energy approach is shown in the images below.
Firstly, a fatigue loading spectrum needs to be computed. This is typically done with an aero-elastic analysis in a program such as Garrad Hassans Bladed or WMCs Focus software based on the load cases defined in IEC61400-1.
As this type of analysis needs a structural model of the blade to determine its responses to gusts and turbulence, this makes blade design an iterative process between the structural engineer and aerodynamicist.
Typically, a process such as Rain flow counting may then be applied, simplifying the blade loading spectra into a 2d table of mean and range of loading cycle and the number of cycles of each combination. This is known as a Markov Matrix. (Unlike Steel, the mean load does have an effect on composite fatigue). In the image below we can see that there are Ni loading cycles for that given mean and range load.
With the loading in-hand, we then need to characterise the fatigue performance of the materials. For a full materials characterisation of the type shown below, coupon fatigue testing would need to be performed at a range of different R-values (Ratio of min/max peak stresses) up to 10^7 cycles. A Goodman / Constant life diagram of the type shown below can then be plotted.
Testing is required by some standards but is very time-consuming and expensive. Luckily, Germanisher Lloyd provide some default values and a simplified method in GL2010.
Having characterised the materials, a structural analysis is performed (typically with Finite Element Analysis) to determine the strains which those loads impart to the structure.
These strains can then be plotted on our Goodman Diagram and an allowable number of cycles for that mean and amplitude strain combination calculated. In the image above, we can see it is just below 10^6 cycles.
Hopefully we find that the number of cycles in the Markov Matrix is below this number (otherwise the component would fail on just this one bin alone) but those cycles have done some fatigue damage to the structure. We sum up the damage from all the bins of the Markov matrix using Miners rule and find if the structure passes (damage<1).
Markov Matrices are typically produced for all six force and moment components at multiple sections along the blade. Combined with using different materials and the fact that a calculation has to be performed on every bin of every Markov Matrix (up to 50 x 50) means that fatigue analysis typically involves a lot of data processing! PlySim have developed some in-house tools for exactly that process.
- Matrix Cracking
Q: What is Matrix Cracking and when is it neccesary to analyse for this type of failure?
Answer coming soon...