Windenergie 3 - Fatigue

13 May 2026, Po Wen Cheng

Questions at the beginning

• Which forces contribute to the lead-lag (edgewise) motion of the blade?
  • coriolis forces
  • inertial forces
  • stiffness forces
  • drag (not a lot)
• The first natural frequency of the larger offshore wind turbine (and rotor diameter)
  • will decrease
• Where do you see an excitation problem for the system, mark it on the Campbell diagramm
  • Where the natural frequencies cross the excitation frequencies
• How many degrees of freedom a OpenFast model contains approximately?
  • 25
• If the maximum stress is 2 times the minimum stress and both of them are tension stresses (pulling stresses), the stress ratio will be
  • 2
  • stress ratio is defined as $R = \frac{\sigma_{\text{lower}}}{\sigma_{\text{upper}}}$
• For materials such as fibre reinforced plastic
  • higher fatigue life can be achieved with tensions stresses
• during a storn the wind turbine suffers large amplitude loads, which materials will suffer more damage relative to the normal loading conditions
  • blade (m=10)
• At which site the wind turbine blades will have a longer lifetime
  • blade damage equivalent load DEL = 150 (Less means less damage)
  • Given the same number of cycles, same site, same materials, ... Which load will produce the same damage

Basics of Fatigue

If you are below a certain stress intensity, there is no crack growth. Above, the crack will grow linearly
(See Paris-Erdogan Crack Growth Law on Slide 9)

$$ \int_{a_i}^{a_f}\frac{da}{\left( F(a) \cdot \sqrt{a} \right)^m} = C \cdot \Delta \sigma ^m \cdot \pi^{\frac{m}{2}} \cdot N $$

$N$ is the number of cycles for the crack to grow from an initial size $a_i$ to a final size $a_f$

Stress Ratio R

• S-N curve depends on the stress ratio (mean stress level)
• The dependency of the mean stress varies from material to material, steel material is less sensitive than fibre reinforced composite material or concrete material
• Compression stress more favourable than tension stress

Experimental S-N Curve

• S-N curves are determined from experimental tests from samples
• Test is carried out for a statistical significant number to determine the probability destribution and characterisitc values (median, P95, etc.)
• Test is carried out for different mean stresses
• Fatigue characterization of materials is very time consuming and expensive

Linear Damage Accumulation Hypothesis

• Partial damage from different stress ranges can be added linearly
• Sequence of the load cycles has no influence on the fatigue damage (in reality the micromechanical changes of the material depends on the loading sequence)

$$ D = \sum _i \frac{n_i(\Delta \sigma _i)}{N_i(\Delta \sigma _i)} $$

• $n_i$: actual number of stress cycles
• $N_i$: number of allowable stress cycles