# Assessing the fatigue of fibre-reinforced plastic composites using the example of rotor blades

Fibre-reinforced plastic composites have established themselves as lightweight construction materials for wind turbine rotor blades. However, understanding of their fatigue behaviour is still limited. EUROS performs research into this fatigue behaviour and hence into the thresholds of operationally reliable construction.

## High Material Efficiency as Goal

Fibre-reinforced plastic composites (FRCs) have been used for manufacturing wind turbine rotors since 1957 and have established themselves as lightweight construction materials in this field. A virtually unlimited range of design possibilities, a high elastic modulus, high stability and low densities qualify these materials for the application in question. Fibre-reinforced plastic composites are also being deployed in a number of other areas, in particular in the field of mobility. Increasing use across a wide range of applications results in cost pressure pushing material utilisation to its physical limits. The efficiency of the FRCs in the relevant application increases where scientifically plausible descriptions of these limits exist. However, the understanding of the fatigue behaviour and hence the possibility of assessing the operational fatigue resistance or durability behaviour of FRCs is still very restricted today. The thresholds of structural design with regard to operational stability are, quite naturally, reached in products that are exposed to high fatigue load. For this reason, the problem is discussed here in relation to wind turbines.

Optimisation of today’s wind turbines is primarily focused on improving yield in relation to the quantity of material employed rather than on improving performance. Wind turbines are consequently designed for lower nominal wind speeds, while the maximum tip-speed remains unchanged. This results in a continuous increase in the tip-speed ratio of modern wind turbines. The tip-speed ratio is the primary measure for wind turbines. It describes the ratio between the blade tip velocity and the wind speed in front of the rotor. Increasing the tip-speed ratio results in wind turbine rotor blades becoming increasingly slender and, at the same time, longer.

## Scaling Effects

*L*

_{1}as shown in Figure 1. If the size of the cube is now increased in such a way that the edge length doubles to

*L*

_{2}, the area

*A*

_{1}in the figure will increase by a factor of 4 in relationship to the area of the enlarged cube

*A*

_{2}. At the same time, the volume of

*V*

_{1}grows to the eightfold value

*V*

_{2}. This relationship is known as the square-cube law. It was first published by Galileo Galilei in 1638 and is valid for every solid body. This means that when the length of a rotor blade is increased by a factor of 2, its mass will increase by a factor of 8.

Rotor blades are primarily exposed to two types of load: first, loads originating from their own mass; second, loads caused by aerodynamic stresses. The loads caused by the mass of the rotor blade are directly dependent on its volume, whereas aerodynamic loads are determined by the surface area of the blade. Consequently, the structural mass of rotor blades does not actually grow proportionally to the power of 3 but approximately proportionally to the power of 2.5 of the length of the rotor blade.

In the design of rotor blade structures, a distinction is made fundamentally between quasi-static loads and fatigue loads. Here, again, the relationship between the surface area of the rotor blade and the aerodynamic and quasi-static loads, and the relationship between the mass of the rotor blade and fatigue loads, are significant. This can be explained by the fact that the leeward aerodynamic load of a rotor blade, i.e. in the direction away from, tends to result in quasi-static deformation, while the rotation of the rotor results in a cyclically changing bending load on the rotor blade due to its own mass on each revolution. It thus becomes clear that increasing the size of the rotor blades causes in particular a disproportionate growth in fatigue loads.

## Verification

The Puck [1] criterion is widely applied for verfication for FRC structures. Here, a distinction is made between failure in the form of fibre failure due to loading in the direction of the fibres and failures between the fibres resulting from loads that do not cause an effect in the direction of the fibres — so-called inter-fibre failures. The criterion regarding inter-fibre failure (IFF) in particular is currently used to dimension rotor blades. Various methods are used to demonstrate the operational fatigue resistance or durability of rotor blades. These are, however, not limiting, due to their lack of significance for rotor blade structures.

The disproportionate increase in fatigue loads on the one hand and the lack of significance in the demonstration of operational stability on the other suggest a discrepancy. This impression is reinforced when the quasi-static dimensioning loads are compared with the fatigue loads. For the sake of clarity, only root bending moments are considered below. These are the sectional loads that are determined for the blade flange. The blade flange is the end of the blade at its root where it is connected to the hub of the wind turbine rotor.

The disproportionate increase in fatigue loads on the one hand and the lack of significance in the demonstration of operational fatigue resistance or durability on the other suggest a discrepancy. This impression is reinforced when the quasi-static dimensioning loads are compared with the fatigue loads. For the sake of clarity, only root bending moments are considered below. These are the sectional loads that are determined for the blade flange. The blade flange is the end of the blade at its root where it is connected to the hub of the wind turbine rotor.

## Load Comparison

In this formula, *M*_{ Ai } is the amplitude of moment of the i-th load spectrum with the relevant load cycle *n*_{ i } and *m* is the negative inverse S/N slope for the material having the greatest effect on the fatigue of the rotor blade structure. It is assumed that the S/N-slope is a characteristic of the material. The fatigue loads are now converted in such a way that exactly one load cycle represents the fatigue life of the structure. This means that *n*_{ ref } = 1 is assumed to be the reference load cycle. m = 10 is assumed for the exponent of the S/N-slope, which is a well-founded assumption for epoxy resin matrices.

*M*

_{DELf}in the direction of impact and

*M*

_{DELe}in the direction of rotation for the reference load cycle

*n*

_{ref}= 1 canow be considered in relation to the quasi-static root bending moments

*M*

_{SLSLf}in flapwise direction and in the direction of impact and

*M*

_{SLSLe}in edgewise direction. The following fatigue load relationships then result.

_{ f }of the flapwise impact loads are shown in Figure 2 as hatched bars while the fatigue load relationships of edgewise rotation loads ζ

_{ e }are shown as black bars. The axis labels indicate rotor diameter, nominal output, spar cap material, design lifetime and area of application.

The blades show a development in the diagram from left to right towards current construction de-signs. It can be clearly seen that fatigue loads are up to four times as high, particularly with regard to edgewise loading, as quasi-static design loads. It is therefore incomprehensible that the dimensions of rotor blade structures are currently not determined by fatigue loads. Lower rotation fatigue loads for new generations are always used in combination with CFRP as spar cap material, as this results in a lowering of the load from its own mass.

**Today’s fatigue criteria do not have dimensioning effect.**

## Fatigue Assessment

As engineers, we learned as a general principle to identify the highest stressed point when assessing a structure. In metal engineering, this can be a groove or a flange. In a similar manner, the most highly stressed layer is sought in a multi-layered fibre composite structure. This is then subjected to load capacity analysis, for example in accordance with Puck.

Closer inspection accordingly reveals that the most highly stressed point is not simply in a layer but, instead, between two adjacent fibres within that layer. This point is usually situated in the matrix, as the fibres introduce excessive tension to the matrix. The consequence of this approach is the attempt to understand the physical behaviour of the individual layer of fibre- reinforced plastic composite as the result of the physical behaviour of the fibre and matrix together with the interaction between them.

This results in a shift from a phenomenological approach aand its physical interpretation towards a physically-based approach, leading to the realisation that the fatigue failure of a fibre-reinforced composite structure cannot be directly predicted. Instead, the load series together with the damage and degradation of the composite structure must be analysed. The process of damage and degradation is therefore divided into three phases.

## Phase 1: Load on the Undamaged Individual Layer

This phase is characterised by the undamaged individual layer being subjected to an oscillating load in such a way that no cracks arise and the density of cracks can therefore not increase. This phase ends with the onset of damage.

## Phase 2: Load during Degradation

In this phase the oscillating load is further applied resulting in an increase of crack density. The phase ends with the onset of phase 3.

## Phase 3: Failure

Phase 3 is rather a singular event characterised by the loss of load carrying capacity. It is defined by the load that contributes strain-energy that the laminate is not able to withstand.

## In-situ Effect

On closer consideration, the question arises as to hy, for example, the fibre-volume-fraction has no impact on the lateral contraction contraint due to the fibre. This would mean that, with the relevant mixing rules for elasticity of the individual layer, for example in accordance with Puck, the matrix would see lateral contraction constraint even when it contains no fibres.

*E*̄

_{F∥}is the in-situ Young’s modulus of the fibres in the direction of fibre taking into consideration the influence of undulation,

*E*

_{⊥ (ϕ)}is the lateral Young’s modulus of the individual layer as a function of the fibre volume content ϕ and

*E*

_{M}is the Young’s modulus of the matrix.

Using the in-situ Young’s modulus of the matrix, it is possible to calculate excessive tension in the matrix due to the embedded fibres. This then forms the basis for the assessment of the strenght or integrity, stability is a different failure mode of the matrix, taking into account, for example, hygrothermal strain effects.

## Simplified Assessment

The main advantage of this approach is the fact that the epoxy resin matrix used is an isotropic material. As a consequence, it is possible to work with conventional equivalent stress hypotheses. For example, with Beltrami [4]. This allows complex, 3-dimensional states of stress in the laminate to be transferred into states of stress for individual layers and their matrices. The 3-dimensional state of stress in a matrix can continue to be converted into an equivalent, uni-axial state of stress, with consideration of the fatigue of an individual element — taking into account the mean tension — being made possible with the assistance of a simple, symmetric Goodman diagram for the matrix. It is currently possible to calculate the onset of damage initiation under fatigue loading. In the simplest case, no damage is to occur in the laminate; the design threshold can then be determined. This would make the structures too heavy for wind turbine rotor blades. It is therefore necessary to choose a kind of fail-safe design. In this case, such states of damage may occur in the laminate that do not adversely affect the load carrying capacity or servicability of the structure. EUROS has been applying a corresponding method of dimensioning the fatigue resistance of rotor blades successfully since 2014.

**Degradation functions depending on defined depending on matrix stress have already been applied in small models in coupon tests.**

The UD scrim composite, which is reinforced extremely unidirectionally, fails laterally to the fibre in a matrix-dominated direction — as indicated by the circles near to the predicted matrix damage threshold. In comparison, the UD scrim composites can withstand considerably more load cycles when stressed in the 0° direction, represented by squares, together with the 3AX scrim composites, represented by triangles, before the specimens fail completely. Even the 2AX composites, reinforced at ±45°, can withstand considerably more load cycles than the UD composites stressed at 90° even though these are primarily matrix-dominated.

All specimens were subjected to tensile fatigue R = 0.1. A simple, symmetric Goodman diagram provided the basis for calculating the damage threshold. Stability of *R* _{M} ^{(+)} = 73 MPa and a negative inverse S/N-curve exponent of *m*_{M} = 10 were assumed for the matrix.

## Degradation

Investigations are currently being conducted into how elasticity and stability under fatigue loads behave after damage onset. Degradation behaviour is to a very large degree dependent on the element being considered. Approaches are generally based on classical laminate theory and are valid for infinitesimal continua. Applying them to finitely large elements such as those in finite element software always involves compromise. For example, in an infinitesimally small element, a crack corresponds to total failure, whereas in a finitely large element, a crack must be taken with the surrounding intact material.

As relatively large elements are to be used in the design of rotor blades in order to keep computing time to a minimum, it is necessary to introduce degradation functions to be able to describe the deterioration of the Young’s modulus of the material depending on the state of damage. The more precise the analytic description of degradation behaviour is, the fewer elements that need to be used in a finite element model. However, degradation functions may in some circumstances not be necessary if a big number of elements is selected. This will increase the computing time. Functions defined depending on matrix stress have already been applied in small models in coupon tests.

## Concluding Remarks

The description of the behaviour of fibre-reinforced composite structures is still associated with various compromises. However, an improvement in structural-mechanical modelling seems to be significantly affected by an understanding of the interaction between all the materials used. This applies to behaviour under fatigue load as well as for behaviour under quasi-static load. Although many problems can today be solved using finite element software, its basis is always an analytical model. The better the model can describe the behaviour of the material, the more efficiently structure modelling will ultimately work. This insight leads to the necessity for renewed and greater engagement with analytical modelling and how it reflects reality. |

## References

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- [3]SNL/MSU/DOE Composite Material Fatigue Data base: Mechanical Properties of Composite Materials for Wind Turbine Blades, Version 25.0; April 7, 2016, Montana State University — Bozeman, Online: www.montana.edu/composites or http://energy.sandia.gov/energy/renewable-energy/water-power/technology-development/advanced-materials/mhk-materials-database/, last call: 12 June 2017
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