Designing adhesively bonded joints for wind turbines

4 Designing adhesively bonded joints for wind turbines C. N AG E L, A. S O N DAG and M. B R E D E, Fraunhofer Institute for Manufacturing Technology and Advanced Materials, Germany

Abstract: This chapter examines the fatigue-resistant design of adhesively bonded joints for wind turbine rotor blades. The adequacy of the local stress-life approach for estimating crack initiation fatigue life in the adhesive layer is discussed. It is shown that in the case of adhesives, the treatment of mean stresses, the method of damage accumulation, and the treatment of environmental impact need careful attention before the result can be interpreted. Two application examples are presented where crack initiation fatigue life is considered: a bonded fibre reinforced composite beam loaded in cyclic bending and a bonded insert loaded in cyclic tension. Key words: adhesively bonded joints, wind, fatigue life, local stress-life approach.

4.1

Introduction

Rotor blades of wind turbines are subject to fatigue loads due to service loads and natural fluctuations in wind speed. This causes the risk of crack initiation in the adhesive layers which are used to bond the fibre composite parts of the rotor blade. Cracks may grow as the number of stress cycles increases, which can ultimately result in failure of the whole rotor blade. The need for higher efficiency of modern wind turbines leads to a persistent weight reduction, which in turn means that the rotor blades become longer and the slenderness ratio increases. This causes higher loads in the adhesive joints which increases the risk of crack formation. The main theme of this chapter is: how can cracks be avoided in adhesive joints used in rotor blades? In the first section, we will describe general requirements for adhesively bonded joints in rotor blades. Specific design and modelling methods will be addressed in Section 4.3. Two examples will be shown to illustrate the general method of design. In Section 4.5 we will summarise the results of our studies and address some future trends. 46 © Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

47

Spar cap

Shear web Spar cap

4.1 Cross-section of a rotor blade (schematic). Adhesive joints are shown as hatched areas. See text for further details.

4.2

Requirements for adhesively bonded joints for wind rotor blades

Rotor blades are usually designed for a service life of 20 years. Within this time span, materials and joints are subject to 108–109 load cycles due to wind and waves. In order to avoid fatigue cracks which may develop at such high cycle numbers, stresses need to be kept sufficiently low. This is usually referred to as high cycle fatigue (HCF). A rotor blade typically consists of a pair of semi-shells which are bonded together by adhesive joints. A premanufactured shear web is co-bonded with the semi-shells. The semi-shells serve for aerodynamics and typically contain the spar caps, which form a beam-like structure together with the shear web (Fig. 4.1). Semi-shells, spar caps and shear webs consist of laminated fibre reinforced plastic composites (FRP). A typical damage situation in HCF is the initiation of cracks in the adhesive layers connecting spar caps and shear web. These cracks may subsequently grow and propagate in the interface or in the laminate. This may finally cause a total failure of the structure. Consequently, fatigue crack initiation in the adhesive has to be considered in the design of a bonded rotor blade structure. Generally, the number of cycles until a crack appears in a part depends on the load history and on the material of which the part is made. For a given material, the number of cycles until cracking (termed fatigue life) can in principle be calculated if the load history and the material properties are known. For construction materials such as steel, aluminium or even fibre composites, the material behaviour is quite well known and – more or less – independent of the environment. Requirements for construction materials are covered by common standards (e.g. Guideline for the Certification of Wind Turbines, 2004; Guideline for the Certification of Wind Turbines, 2010; Guideline for the Certification of Offshore Wind Turbines, 2005; Offshore Standard Composite Components DNV-OS-C501, 2010). For adhesive joints, the situation is more complicated: first of all, fatigue life of adhesives shows a wide variation due to numerous types of polymers, fillers, and reinforcements used in the adhesive formulation. Secondly,

© Woodhead Publishing Limited, 2012

48

Adhesives in marine engineering

adhesives exhibit a pronounced temperature and moisture dependence of their elastic constants, strength, and fatigue life. Thirdly, the load is transferred by adhesion forces between adherends and the adhesive layer. The interphase is prone to ageing effects and thus adhesion may change over time. In ageing tests it is frequently observed that a cohesive fracture pattern changes over time into an adhesive fracture pattern accompanied by a loss in fatigue strength. From an engineering point of view, general requirements for rotor blade adhesive joints can be formulated as follows. First, the load–life relation needs to be known for a specific adhesive. Then, the influence of temperature and moisture on the material properties needs to be quantified. Finally, adhesion must be stable over time. These general requirements will be discussed in more detail in the next section.

4.3

Design and modelling methods

In the following, the procedure of calculating the number of cycles until the formation of a technical crack in the adhesive layer of a bonded structure will be outlined. It was stated before that fatigue of adhesive joints in rotor blades occurs typically in the HCF range. Here, it is appropriate to relate the number of cycles to failure to a local stress. This is commonly known as stress-life or S–N approach. The calculated number of cycles to failure will be termed theoretical fatigue life, while the measured value will be termed actual fatigue life in the following. The fatigue life calculation starts with a stress calculation in the bond line, Fig. 4.2. Since adhesives typically obey linear material behaviour under

Stress calculation

Load spectrum σ

S−N curve

Damage accumulation

σ

D=∑

ni N0

N0 Load history F

t

Mean stress correction Stress amplitude

Initial stress state

ni Nf,i

Nth = N0 /D

Fatigue life − number of cycles to failure

Mean stress

4.2 Flow diagram of a crack initiation life calculation procedure – cohesive fracture within the adhesive layer is assumed.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

49

the relatively low fatigue loads, it is often sufficient to perform a linear static calculation under a unit load. Besides the material properties of all bonded components in the structure, only the elastic constants of the adhesive are needed. The stresses are then scaled by the load spectrum, which is generated from load history data based on statistical methods (ASTM E 1049-85, 1997). It gives the frequency of occurrence, ni, of the specific load amplitudes in the spectrum. The total number of cycles is denoted by N0, also known as the extent of the load spectrum. At each specific stress level, the number of cycles until fracture Nf is calculated based on the S–N curve, which characterises the material behaviour based on experimental data. The frequency ni is then related to Nf to give the damage contribution Di, which is summed over all stress levels to give the total damage D. Under the assumption that a crack will be formed if D approaches one, the theoretical fatigue life Nth can be calculated by N0/D. The assumption of failure at D = 1 originates from single level fatigue and is not fulfilled under spectrum loading. Testing is needed to determine the exact value of D if desired. More detailed information on fatigue life assessment can be found in Radaj and Sonsino (1998). It is convenient to separate oscillating and constant parts of the load in order to assess the dependence of fatigue life on the mean stress. At a given stress amplitude, fatigue life will be reduced if the mean stress is not equal to zero, similar to a pre-stressed spring. This effect is usually corrected for by well-established empirical relations (Radaj and Sonsino, 1998). Based on this method, the number of cycles until crack initiation can be calculated up to a factor of two for conventional construction materials. For adhesive joints, the situation is different: due to the countless adhesives on the market, S–N data for specific adhesive systems are not available. Moreover, the whole concept may be drawn into doubt if viscoelasticity is considered. It can therefore be expected that the local stress-life approach can be applied only if the adhesive behaves predominantly elastic and timedependent effects like stress relaxation and creep can be neglected. This condition is fulfilled for many adhesives which form a tight network with a relatively high glass transition temperature Tg, like structural epoxies used in rotor blades for wind energy converters. The dependence of fatigue life on the superimposed mean stress can be corrected for by simple rules for conventional construction materials, but nothing is known about the validity of these relations for adhesive joints. Therefore, the mean stress correction rules need critical examination in order to avoid erroneous calculation results for adhesive joints. For conventional construction materials, it is common to handle variable load amplitudes by linear damage accumulation. However, no information is available on the validity of linear damage accumulation with adhesives.

© Woodhead Publishing Limited, 2012

50

Adhesives in marine engineering

Since it is known that the calculation result depends on the value of the damage sum, it is necessary to perform tests. The loss of time information caused by the extraction of the load spectrum from the load–time history is not severe in wind energy applications since the sequence of load amplitudes is not deterministic. It is, however, useful to check the extent of the load sequence effect in order to be confident of the degree of randomisation which is necessary to avoid this effect in block loading tests at variable amplitudes. Temperature and moisture effects on fatigue life are seldom considered for conventional construction materials since their material properties are nearly constant under normal operation conditions. This is not the case for adhesives, where the material properties can change considerably, depending on the location of Tg relative to the operational conditions. Operating conditions of rotor blades include temperatures between −40°C to +80°C and a relative humidity (r.h.) of up to 80%. However, numbers which describe how much the environmental conditions can change fatigue life of a specific joint are not available. Finally, the fact that adhesive joints may fail by loss of adhesion (interfacial failure) needs to be discussed. The local stress-life approach relies on the assumption that cracks develop in the bond line first. Interfacial failure cannot be treated by means of continuum mechanics. Therefore, the prediction by the stress-life concept will be wrong if the interface fails before the bond line. Therefore, it is not sufficient to know the properties of the adhesive and adherends. Adhesive joints need to be tested under relevant conditions to evaluate adhesion over time. It has become clear that in the application of the stress-life method to adhesive joints it is not enough to know the relation between fatigue life and load for a specific joint design. The assumption that mean-stress correction rules apply for fatigue life of adhesive joints needs critical examination. Furthermore, the applicability of linear damage accumulation has to be proved. The influence of load sequence effects needs to be checked. The impact of temperature and moisture needs to be quantified. Additional testing is needed to confirm adhesion. In the following, these statements will be illustrated using experimental results of studies on adhesive joints which were performed in our laboratory during the past seven years.

4.3.1 S–N curves under environmental conditions S–N curves can be measured by applying a harmonic load with constant amplitude and mean load to a sample of adhesive and counting the number of cycles until fracture. This is done for a set of samples where the load amplitude is varied and the mean stress fraction is kept constant. In order to evaluate the effect of temperature and humidity on material and joint properties, fatigue tests can be performed in a climate chamber. Typical S–N

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

51

Stress amplitude (N/mm2)

20 10 7 5 4 3 2 1 103

−40°C 23°C 40°C/80% r.h.

104 105 106 107 Cycles to failure

108

4.3 Effect of temperature and moisture on fatigue life of two-part methacrylate bulk adhesive material.

data of a two-part methacrylate adhesive tested at different environmental conditions are depicted in Fig. 4.3. The tests were performed at a mean stress fraction of ∼1.2 using un-notched bulk adhesive tensile bars. The nominal tensile stress is shown. At 40°C and 80% relative humidity, the S–N curve is located beneath the S–N curve measured at 23°C, whereas at −40°C, the S–N curve is located above the S–N curve measured at 23°C. This indicates that low temperatures increase fatigue resistance and high temperatures reduce fatigue resistance with respect to room temperature. S–N curves can be described by a power law of the form σ = σ0N−1/k

[4.1]

where σ denotes stress amplitude and N the number of cycles to failure; σ0 and k are material-dependent parameters which may depend on environmental conditions and on the mean stress fraction. Straight lines in Figure 4.3 were calculated by linear regression of equation [4.1] using log N as dependent variable and log σ as independent variable. Values of the fit parameters k and log σ0 are given in Table 4.1 along with their standard errors. Considering the standard errors of the S–N curve parameters, it can be seen that both k and log σ0 are sensitive to the test conditions. The statistical scatter of fatigue life is measured by the standard regression error on the logarithmic scale. Values of S are given in the last column of Table 4.1. Taking the inverse logarithm of S gives a factor of about two or three in the fatigue life, which is typically observed in stresslife data of adhesives. Figure 4.3 may suggest that low temperatures are generally less severe to the fatigue resistance than high temperatures. This is not true due to the

© Woodhead Publishing Limited, 2012

52

Adhesives in marine engineering

temperature-sensitivity of the elastic modulus of the adhesive. Consider a piece of adhesive which is loaded 1 × 106 times with a constant strain of ε = 0.1% in cyclic tension at three different temperatures as given in Table 4.2. The resistance σ1 000 000 of the adhesive is calculated from the S–N curve using parameters from Table 4.1. It is highest at low temperature but lowest at high temperature/moisture. Considering the elastic modulus E of the adhesive, it can be seen that the adhesive is stiff at low temperature but soft at high temperature. This leads to a high stress σ = εE at low temperature but to a low stress at high temperature. If the stress is calculated as percentage related to the fatigue resistance, a utilisation factor is obtained which describes how far the adhesive is from fracture. It can be seen in Table 4.2 that the utilisation at −40°C is about twice as high as compared to the other considered conditions. The current example shows that in strain-controlled loading, low temperatures increase the risk of cracking in adhesive joints. Strain-controlled loading typically occurs in cases where the stiffness of the bonded component is not affected by the bond line such that the deformation of the parts enforces always the same strain in the bond line, as in bonded beam structures. If the bond line in the current example would be loaded with the same stress at the different conditions, it is clear that 40°C/80% relative humidity would be the more critical case. This simple example shows that it is

Table 4.1 S–N curve parameters of bulk adhesive tensile bars tested at different conditions, stress ratio R = 0.1, test frequency f ∼ 7/s

−40°C 23°C 40°C/80% r.h.

k

logσ0

R2

S(logN)

5.13 ± 1.72 8.76 ± 0.77 11.95 ± 2.66

1.94 ± 0.30 1.24 ± 0.06 0.86 ± 0.09

0.56 0.91 0.67

0.33 0.51 0.42

Table 4.2 Resistance, elastic constants, and utilisation of an adhesive under a uniaxial, cyclic strain of 0.1% at different environmental conditions. The cycle number, N, is 1 000 000 N = 1 000 000 σ1 000 000 E ε σ Utilisation

(N/mm2) (N/mm2) (%) (N/mm2) (%)

−40°C

23°C

40°C/80% r.h.

5.87 2700 0.1 2.70 46.0

3.62 1000 0.1 1.00 27.6

2.27 650 0.1 0.65 28.6

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

53

Stress amplitude (N/mm2)

20 −40°C 23°C 40°C/80% r.h.

10 7 5 4 3 2 1 103

104 105 106 107 Cycles to failure

108

4.4 Effect of temperature and moisture on fatigue life of single lap shear joints made of steel and FRP using two-part methacrylate adhesive.

essential to identify the critical environmental conditions before a fatigue life calculation is started.

4.3.2 Adhesion Results obtained with plain adhesive material under tension indicate that high temperature combined with elevated humidity is more critical than low temperature. This situation can change quite rapidly if an adhesive joint is considered rather than bulk adhesive material. Typical S–N data of single lap shear joints using the same methacrylate adhesive as discussed above are depicted in Fig. 4.4 using nominal shear stress. Here, one adherend is made of glass fibre laminate and the other one consists of mild steel. The adhesive layer thickness is 1.5 mm, the overlap length is 5 mm and the joint width is 20 mm. The machined mild steel surfaces were carefully degreased and a primer was applied prior to bonding. At 23°C and 40°C/80% relative humidity, all joints failed cohesively within the adhesive layer. As we have seen in bulk adhesive tensile bar tests, fatigue life is reduced relative to normal climate if environmental conditions change to 40°C and 80% relative humidity. The same trend can be identified in lap joint S–N curves in Fig. 4.4 with a similar strength reduction effect. S–N data measured at −40°C do not follow the trend observed in bulk adhesive tests. Figure 4.4 shows that joint fatigue life at −40°C is between joint fatigue lives at 23°C and 40°C/80% relative humidity instead of showing longest fatigue life. By comparing Fig. 4.3 and Fig. 4.4 it becomes clear that joint fatigue life at −40°C is strongly reduced in relation to bulk adhesive fatigue life at −40°C. Fracture surface analysis of samples tested at −40°C indicated loss of adhesion between adhesive layer and mild steel

© Woodhead Publishing Limited, 2012

54

Adhesives in marine engineering

surface. This shows that fatigue life may be strongly reduced if adhesion is not stable. It is therefore recommended to perform adhesion tests at relevant conditions before the local stress-life approach is used.

4.3.3 Mean stress effects An oscillating stress can be decomposed into a time-dependent, alternating part with stress amplitude σa and mean stress σm which is independent of time. Fatigue life N depends on both σa and σm. In fatigue testing, the number of cycles to failure Nf is counted at controlled σa and constant stress ratio R = σl/σu. Here, σl and σu denote the minimum (lower) stress and the maximum (upper) stress of the load cycle. The mean stress can easily be calculated as σm = σa (1 + R)/(1 − R). Figure 4.5 shows typical S–N curves of a one-part epoxy adhesive under uniaxial tension (Hennemann et al., 2007). The influence of σm on fatigue life is commonly measured by evaluating a constant life diagram (CLD), where σa is plotted against σm for constant N (Sendeckyi, 2001). The data given in Fig. 4.5 was used to set up a CLD, which is shown in Fig. 4.6, left. It can be seen that σa depends linearly on σm for low values of R while there is non-linearity at high values of R. The straight lines in Fig. 4.6(b) correspond to Goodman’s rule (Farahmand et al., 1997), which is written as σa = σ−1(1 − σm/σT)

[4.2]

Stress amplitude (N/mm2)

where σT represents the tensile strength. It is shown as a point at 43 N/mm2 on the mean stress axis. Goodman’s rule states that all lines intersect at σT. It is obvious from Fig. 4.6 that the dependence of σa on σm is well

40 30

R = −1.0 R = −0.4 R = 0.1 R = 0.4 R = 0.6 R = 0.8

20 10 8 6 4 3 2 1 2

3 4 5 6 Log cycles to failure

7

4.5 S–N curves of epoxy bulk adhesive tensile bars showing influence of stress ratio.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

Stress amplitude (N/mm2)

30

R = −1.0

30

R = −0.4

25 20

N = 102 N = 103 N = 104 N = 105 N = 106 N = 107

(b)

R = 0.1

15

R = 0.4

10

R = 0.6 R = 0.8

5

Stress amplitude (N/mm2)

(a)

55

25 20

Goodman Gerber modified

15 10 5

R = 1.0 0

0 0

10

20

30

40 2

Mean stress (N/mm )

0

10

20

30

40 2

Mean stress (N/mm )

4.6 Constant life diagram constructed from the data in Fig. 4.5 with indicated R ratios (a); piecewise representation at low R ratio by Goodman’s rule and at high R ratio by modified Gerber rule (b).

reproduced at low values of R, but Goodman’s rule fails at high values of R. The non-linear part can be better described by using a quadratic form of equation [4.2]. σa = σ−1(1 − σm/σt)2

[4.3]

where σt represents stress-rupture test data which are shown on the mean stress axis. Equation [4.3] is equivalent to Gerber’s rule (Farahmand et al., 1997) except that σt is not constant. It is termed modified Gerber rule in the following. The consequence for practical applications with adhesives is that Goodman’s rule is only applicable if R is sufficiently low. It is therefore recommended to perform model calculations in order to identify the relevant values of R in the bond line at specific loads. A fatigue test of a simple adhesive joint should then be performed at relevant values R1 and R2. Equation [4.2] could then be used to transform the measured S–N curves. Equation [4.2] is valid if the data points measured at R1 fall into the prediction band of R2 after transformation. An example for this is shown in Fig. 4.7. S–N curves measured at R = 0.1 are shown using grey symbols and 95% prediction limits. Another data set was measured at R = 0.4, which is shown using open symbols. These data points were transformed to R = 0.1 by using equation [4.2]. The transformation result is indicated by black symbols. It can be seen that the transformed data points fall into the 95% prediction band of the data measured at R = 0.1. Hence it is clear that Goodman’s rule applies in this case. If such a test shows that Goodman’s rule is not valid, it is recommended to

© Woodhead Publishing Limited, 2012

56

Adhesives in marine engineering 8

Stress amplitude (N/mm2)

7 6 5

4

3 102

103

104

105

106

107

Cycles to failure

4.7 Stress-life data of single lap shear joints bonded with structural epoxy adhesive taken at R = 0.1 (triangles) and R = 0.4 (open circles). The transformation based on Goodman’s rule is indicated by black symbols. Lines refer to the 95% prediction limit of the R = 0.1 test result.

set up an appropriate mean stress correction rule based on measured data as shown in the example above.

4.3.4 Damage accumulation If a material is subject to cyclic loading, it is commonly assumed that a number of load cycles n causes the damage D = n/N

[4.4]

where N is the number of cycles the material can withstand until it breaks. It is given by the S–N curve of the material. If the material is loaded at a constant amplitude, it is evident that, since n → N, failure would occur if damage D approaches one. If loading occurs with varying amplitudes, each load level i contributes the damage increment Di and it is assumed that damage accumulates as D = ΣDi. This is called linear damage accumulation, or Miner’s rule. If it is assumed that, as in loading with constant amplitudes, failure would occur at D = 1, theoretical fatigue life can be estimated by N th = N 0

∑D

i

[4.5]

where N0 is the total number of fatigue cycles. In reality, failure does not occur at D = 1 but the value of D at which the material breaks depends on the material. It will be called actual damage sum in the following.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

57

Normalised load amplitude

1.0

0.8

0.6

0.4

0.2

0.0 103

104

105

106

Number of level crossings

4.8 Normalised test load spectra with mean value of 0.5 and total of 1 × 106 cycles. Standard deviations are 0.125 (black) and 0.5 (dashed).

The actual damage sum was determined for a two-part methacrylate adhesive system. Rectangular tensile bars consisting of adhesive were tested under varying cyclic loads, where amplitudes followed a Gaussian distribution. Two normalised load spectra with a mean value of 0.5 and a total of N0 = 1 000 000 cycles were tested. One load spectrum had a standard deviation of 0.125; the other one had a standard deviation of 0.5. They will be denoted as narrow and wide load spectra in the following. The load spectra are shown in Fig. 4.8. It can be seen in Fig. 4.8 that the fraction of high amplitudes is low in the narrow spectrum while it is high in the wide spectrum. If the highest relative amplitude level approaches the number of 1 000 000, the Gaussian distribution transforms into a rectangular one. This corresponds to a single level fatigue test. Tests were run as block loading sequences starting at the lowest amplitude level and ending at the highest amplitude level. After completion of 1/10 of the total number of cycles at a specific level, the sequence was continued at the next higher level. Hence, each test sequence ended at N0/10. After completion of one specific sequence, the same sequence was run again, and this was done as often as was necessary to break the sample. The subdivision of the load spectrum into blocks of 100 000 cycles is necessary to avoid load sequence effects. Load sequence effects will be discussed in a subsequent section. Experimental fatigue life values Ntest are given in Table 4.3 for the narrow and wide load spectra. In Table 4.3, the cycle number to failure is given as function of the maximum stress amplitude level σa,max from the load spectrum. The remaining levels are not shown in the table, but they can easily

© Woodhead Publishing Limited, 2012

58

Adhesives in marine engineering

Table 4.3 Fatigue test results of two-part methacrylate bulk adhesive tensile bars at loading with variable amplitudes, stress ratio R = 0.1, test frequency f ∼ 7/s, narrow load spectrum (left), wide load spectrum (right), sequences starting with low amplitudes s.d. = 0.125

s.d. = 0.5

σa,max (N/mm2)

Ntest

Nth

Dtest

σa,max (N/mm2)

4.50 5.00 5.50 5.50 6.00 6.00 6.50 6.50

10 595 246 3 895 820 2 495 579 1 199 182 1 910 344 1 596 073 989 029 696 293

3 146 651 1 249 849 542 147 542 147 252 907 252 907 125 408 125 408

3.37 3.12 4.60 2.21 7.55 6.31 7.89 5.55

4.50 4.50 5.00 5.00 5.20 5.50 5.50 5.50

5.08

Mean

Mean

Ntest

Nth

Dtest

1 743 665 3 016 163 1 650 553 1 555 772 819 738 452 044 1 283 162 453 822

1 100 928 1 100 928 437 288 437 288 310 097 189 682 189 682 189 682

1.58 2.74 3.77 3.56 2.64 2.38 6.76 2.39 3.23

be calculated as σa,i = i·σa,max/8|i = 1, ... ,7. Similarly to a common S–N test, the value of σa,max and the values of the remaining levels σa,i were varied by multiplying with a constant. A graphical representation of actual fatigue life is given in Fig. 4.9 using filled symbols. The left plot (a) refers to the narrow load spectrum and the right plot (b) refers to the wide load spectrum. The confidence limits of the S–N curve are plotted using dashed lines. It can be seen that actual fatigue life for varying amplitudes appears right from the S–N curve, which is a consequence of using the maximum amplitude of the load spectrum as ordinate. Comparison of the experimental data points in Fig. 4.9(a) and (b) shows that fatigue life tends to be shorter (i.e. shifted towards the S–N curve) if samples are loaded with the wide load spectrum. This clearly shows the dependence of fatigue life on the shape of the load spectrum. Wide load spectra, which contain a large fraction of relatively high amplitudes, tend to produce a relatively short fatigue life. Values of theoretical fatigue life Nth were calculated following equation [4.5] assuming failure at D = 1. They are given in Table 4.3 along with actual fatigue life Ntest at each level. It can be seen that theoretical fatigue life tends to be shorter than actual fatigue life. Theoretical fatigue life is represented by solid lines in Fig. 4.9. It can be seen in the figure that actual fatigue life is longer than theoretical fatigue life for the narrow as well as for the wide load spectra. For the adhesive system considered here, actual fatigue life is underestimated by applying Miner’s rule. As a consequence, using Miner’s rule would result in a higher degree of safety in component design.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

7 Stress amplitude (N/mm2)

(b) 8

7 Stress amplitude (N/mm2)

(a) 8 6 5 4 3

2 103

104

105 106 107 Cycles to failure

108

59

6 5 4 3

2 103

104

105 106 107 Cycles to failure

108

4.9 Fatigue life of methacrylate bulk adhesive tensile bars subject to cyclic loading with variable amplitudes. Narrow load spectrum, s.d. 0.125 (a), wide load spectrum, s.d. 0.5 (b). Solid lines refer to theoretical fatigue life based on Miner’s rule.

The actual damage sum was calculated from actual and theoretical fatigue life using Dtest = Ntest/Nth. Values of Dtest are given along with Nth and Ntest at each maximum stress level in Table 4.3. It can be seen that the actual damage sum is not a constant but it depends on the shape of the load spectrum. Since actual fatigue life in the test was always larger than theoretical fatigue life, we find that the actual damage sum is larger than one for the specific adhesive system. Consequently, using the assumption D = 1 in the fatigue life estimation of a component bonded with this specific adhesive would be very conservative. It should be noted that the interesting observation of Dtest > 1 for the current adhesive system is not expected to be valid for adhesives in general. Depending on the material, Dtest may be expected to be more or less than one, as is suggested by experimental data on welded joints. If, for design purposes, it is desired to make use of some specific value of Dtest, it is necessary to run tests at variable amplitudes to derive the correct value of Dtest. It should also be considered that Dtest depends on the shape of the specific load spectrum.

4.3.5 Load sequence effect In order to explore the load sequence effect, i.e. the dependence of the fatigue life on whether low amplitudes or high amplitudes occur first in the load history, the direction of running through the load spectra in Fig. 4.8 was changed. While in the tests presented in Section 4.3.4, blocks started

© Woodhead Publishing Limited, 2012

60

Adhesives in marine engineering

Table 4.4 Fatigue test results of two-part methacrylate bulk adhesive tensile bars at loading with variable amplitudes, stress ratio R = 0.1, test frequency f ∼ 7/s, narrow load spectrum (left), wide load spectrum (right), sequences starting with high amplitudes s.d. = 0.125

s.d. = 0.5 σa,max (N/mm2)

σa,max (N/mm2)

Ntest

Nth

Dtest

4.50 7.00

20 000 000 610 474

3 146 651 65 506

6.36 9.32

3.93 4.00 4.50 4.60 4.70 5.00 5.00 5.30 5.50

7.84

Mean

Mean

Ntest

Nth

Dtest

3 583 869 2 391 384 1 752 613 747 416 553 002 1 021 477 280 851 186 592 189 177

3 607 630 3 090 503 1 100 928 908 050 752 072 437 288 437 288 262 423 189 682

0.99 0.77 1.59 0.82 0.74 2.34 0.64 0.71 1.00 1.08

with the lowest amplitude and ended with the highest amplitude, in the current tests this direction was reversed. Experimental fatigue life values Ntest are given in Table 4.4 for the narrow and wide load spectra. In Table 4.4, the number of cycles to failure is given as function of the maximum stress amplitude level σa,max in the spectrum. The remaining levels are given as σa,i = i·σa,max/8|i = 1, ... ,7. The value of σa,max and all other values of the remaining levels σa,i were varied by multiplying with a constant, as in a typical S–N test. For technical reasons, only two experimental results were available for the narrow load spectrum. A graphical representation of the measured fatigue life Ntest from Table 4.4 is shown Fig. 4.10 using filled symbols. The left plot (a) refers to the narrow load spectrum and the right plot (b) refers to the wide load spectrum. The experimental results for the same load spectra but with the original, non-reversed sequence are plotted using open symbols (data from Table 4.3). By comparing the results obtained at original and reversed sequences, it can be seen that fatigue life depends on the load sequence if the load spectrum is wide while the dependence on the load sequence is less obvious if the load spectrum is small. Values of theoretical fatigue life Nth were calculated following equation [4.5] assuming failure at D = 1. They are given in Table 4.4 along with actual fatigue life Ntest at each level. Theoretical fatigue life is represented by solid lines in Fig. 4.10. It can be seen that, independently of the load sequence, actual fatigue life is longer than theoretical fatigue life, if the load spectrum

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

7 Stress amplitude (N/mm2)

(b) 8

7 Stress amplitude (N/mm2)

(a) 8 6 5 4 3

2 103

104

105 106 107 Cycles to failure

108

61

6 5 4 3

2 103

104

105 106 107 Cycles to failure

108

4.10 Fatigue life of methacrylate bulk adhesive tensile bars subject to cyclic loading with variable amplitudes – load sequence effect. Narrow load spectrum, s.d. 0.125 (a), wide load spectrum, s.d. 0.5 (b).

is small. In the case of the wide load spectrum, test results are well resembled by theoretical fatigue life if the load sequence is reversed. The actual damage sum Dtest at reversed load sequence is larger than one if the load spectrum is small, as with non-reversed load sequence (Table 4.4). However, if the load spectrum is wide, we find that Dtest is close to one, as is assumed in damage calculations if D is not known exactly. We can see that in the current example the application of Miner’s rule would have given a reasonable estimate of fatigue life even in the case of reversed load sequence. It can however be assumed that this will not generally be the case.

4.4

Applications of adhesively bonded joints

In the remainder of this chapter, we will present two application cases out of our studies on wind turbine rotor blades. The first application is a beamlike structure which contains adhesive joints between shear webs and flanges made out of fibre composites (Fig. 4.11). A beam-like structure was chosen since rotor blades are predominantly loaded in bending. Shear webs and spar caps of the test structure were separately manufactured using vacuum infusion and were subsequently bonded together. Adhesives and curing methods matched conditions in the rotor blade production industry. The fibre composite beam was loaded in four-point bending giving constant bending momentum between the inner load transmission points and linear decreasing momentum from the outer load transmission points to the beam ends. This enforces failure in the undisturbed area between the inner load transmission points and thus helps to overcome a major difficulty which is

© Woodhead Publishing Limited, 2012

(a)

Adhesives in marine engineering (b)

Normalised load amplitude

62

1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 10 10 10 10 10 10 10 Number of level crossings

1000 mm X

Z

150 mm

4.11 Bond line stress in a four-point bending test of a composite beam at an applied load of 22.8 kN (a). The model is clipped at the X–Z symmetry plane. Only one half of the beam is shown. Dark areas indicate highly stressed regions. (b) Schematic of the loading conditions of the fatigue test.

encountered in fatigue tests, i.e. failure at the clamping devices/load transmission points. The objective of this study was to show the feasibility of fatigue life estimation of adhesive joints between fibre reinforced composite parts, to design the beam such that a certain number of cycles will be reached at a given probability of survival and to approve this in a test at variable load amplitude. The second application is an adhesive joint which was designed to overcome a common disadvantage of conventional bolted joints, where the point-like load transfer is closely connected with high local stresses in the fibre laminate. In order to avoid bearing failure due to high local stresses, a cross section increase is required in the vicinity of the joints. This in turn enhances the weight of the structure. In contrast to bolted joints, a gradual stress distribution is inherent to adhesive joints. Hence, local thickening is not required and the weight of the structure is not affected. Bolted joints are currently used to connect rotor blades to the hub of wind energy converters. In the rotor blade, threaded bolts are currently fixed by T-bolts which are set into drill holes in the fibre laminate. This application requires the joint to be detachable and fail safe. This means that if one joint fails, the other joints must take over the function of the failed joint. Therefore, solutions based on a continuous adhesive layer were not acceptable. Instead, a number of thread sleeves which take up the fixing bolts was bonded into drill holes in the fibre composite. This solution combines the principles of fail safety and detachability.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

63

The objective of this study was to show feasibility of such a joint and to test the joint at a load spectrum which represents real service conditions.

4.4.1 Bonded fibre reinforced composite beam The fatigue life of adhesive joints in a bonded glass fibre reinforced composite beam with dimensions of 1080 mm × 60 mm × 60 mm is considered at room temperature. The beam structure consists of uni-directionally reinforced spar caps which are bonded to a bi-directionally reinforced, laminated shear web. The spar caps contain 13 layers of unidirectional glass fabric oriented along the beam axis and have a cured thickness of 8 mm. The shear web consists of two C-shaped profiles which contain four layers of bi-directional fabric with a cured thickness of 3 mm. The fibres are oriented at 45° to the beam axis. All laminates are made of E-glass and epoxy resin. Spar caps and shear web were separately manufactured and subsequently bonded using short-fibre filled, two-part epoxy adhesive. The bond line thickness is ∼3 mm. The beam is loaded in a cyclic 4-point bend test with a load ratio of Fl/Fu = 0.1, leading to cyclic tensile stresses in the adhesive layer on the tension side of the beam, which cause fatigue and eventually lead to cracks in the adhesive layer. The fibre laminates were modelled as homogeneous individual layers with transversal isotropy, which is characterised by absence of shear coupling, an orientation-dependent elastic modulus, and invariance against rotation around the fibre axis. The individual layers were oriented along the beam axis according to their fibre directions and they were coupled to each other such that interfacial strains were equal. The elastic constants used were E11 = 40 338 MPa, E22 = 10 160 MPa, ν12 = 0.29, Gij = 3622 MPa. The adhesive layer was modelled with a rectangular cross-section and isotropic material properties using elastic constants of E = 4500 MPa and Poisson’s ratio of ν = 0.3. Numerical stress calculations were carried out with ABAQUS. Laminated spar caps and shear web were modelled with 8-node, reduced integration shell elements S8R in connection with a layered cross-section and each layer was considered as a homogeneous, transversally isotropic material. The adhesive layers were modelled with 20-node, reduced integration solid elements C3D20R in connection with homogeneous, isotropic material properties. The coupling between shells and solids was achieved by congruent meshing and shared nodes. Thereby, the reference surfaces of the spar cap and shear web shell meshes were shifted to the surface adjacent to the adhesive layer. The width between the supports was L = 1000 mm and the load transmission points were in a distance of 150 mm from the supports. The applied load was 22.8 kN.

© Woodhead Publishing Limited, 2012

64

Adhesives in marine engineering

Figure 4.11 shows the distribution of the maximum principal stress in the bond lines at an applied load of 22.8 kN. It can be seen that the stress maximum is in the adhesive layer at the tension side of the beam between the load transmission points. Excessive stresses away from the centre region of the beam are due to the split web geometry and due to load transmission and support effects. The second and third principal stress components are low compared to the first one and do not significantly contribute to the stress state. It can hence be stated that the stress state is close to uniaxial as can be expected for beam bending. Fatigue life was estimated from the maximum principal stress shown in Fig. 4.11. Since the stress is proportional to the load due to adhesive material linearity, the stress at 22.8 kN can be interpreted as stress amplitude and the corresponding stress ratio R is equal to the load ratio Fmin/Fmax = 0.1. The stress amplitudes at load amplitude levels other than 22.8 kN are simply held by scaling the stress in Fig. 4.11 by the ratio of the related load amplitude levels. The S–N curve parameters of the adhesive are k = 13 and σa,0 = 29 MPa. Since the S–N curve was measured using adhesive tensile bars under tensile fatigue load, the stress state in the bonded composite beam relates directly to the stress state at which the S–N parameters are valid. It is hence sufficient to use the calculated maximum principal stress for the fatigue life calculation. The S–N curve was measured at a stress ratio of R = 0.1 which is identical to the stress ratio in the bonded composite beam. Hence no mean stress correction is necessary and the maximum principal stress can be used in the fatigue life calculation without transformation. A standard error of S = 0.4 was determined for logNf in the adhesive tensile bar S–N test. In order to account for the scatter inherent to the adhesive material properties when calculating fatigue life of the bonded composite beam, the mean value of logNf was reduced based on S. Here, it was assumed that logNf follows a normal distribution with standard deviation S = 0.4. The cumulated distribution function of logNf can be interpreted as the probability of failure Pfail. The probability of finding fatigue life values logNf greater than some value logNf,0 is then given by taking the value of 1 − Pfail at logNf,0. This can be interpreted as the probability of survival, Psurv. This is schematically depicted in Fig. 4.12 for a mean value of logNf = 6, a standard deviation of S = 0.4, and Psurv = {50, 90, 99.9}%. It can be seen that higher values of survival probability involve a larger reduction of logNf. The reduced fatigue life logNf,0 is also designated as the lower tolerance limit. Bond line fatigue life of the composite beam was calculated based on the described assumptions and a chosen survival probability of Psurv = 99% using linear damage accumulation, equations [4.4], [4.5]. The calculation is summarised in Table 4.5. The columns give the load level, i, the load

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

65

99.9% 1.0

Probability of survival

90% 0.8

0.6 50% 0.4

0.2

0.0 4

5

6

7

8

Log cycles to failure

4.12 Tolerance limits using a normal distribution.

Table 4.5 Theoretical fatigue life of the adhesive layer in a bonded composite beam (standard normal distribution, procedure outlined in ISO 12107 was followed) i

Fa (kN)

ni (cyc.)

1 2 3 4 5 6 7 8 9

42.9 37.1 32.0 27.6 23.9 22.8 20.6 19.3 15.4

7 1 573 73 755 680 433 1 234 873 1 000 000 440 860 171 135 428

σa,i (MPa)

Nf,0,i (cyc.)

8.47 7.32 6.32 5.45 4.72 4.50 4.07 3.81 3.04

1.05 6.92 4.73 3.24 2.10 3.88 1.45 3.39 6.37

× × × × × × × × ×

N0 = 3 603 064

106 106 107 108 109 109 1010 1010 1011

Di (–)

Nf,0,i (cyc.)

0.0000 0.0002 0.0016 0.0021 0.0006 0.0003 0.0000 0.0000 0.0000

5.91 2.60 1.11 4.52 1.72 2.65 6.65 1.19 8.85

× × × × × × × × ×

Di (–) 104 105 106 106 107 107 107 108 108

0.0001 0.0061 0.0666 0.1504 0.0718 0.0378 0.0066 0.0014 0.0000

D = 0.0048

D = 0.3408

Nth = 7.51 × 108

Nth = 1.06 × 107

k

σa0

S

n

Psurv

1−α

κ (P, 1 − α, n − 2)

(–)

(MPa)

(–)

(–)

(–)

(–)

(–)

13

29

0.4

9

99.0%

95.0%

4.353

© Woodhead Publishing Limited, 2012

66

Adhesives in marine engineering

amplitude, Fa, the number of cycles at load level, ni, the local value of the maximum principal stress amplitude in the bond line of the composite beam, σa,i, the lower tolerance limit of the fatigue life Nf,0,i at each level corresponding to the S–N curve, and the related damage contribution, Di. The damage sum is close to 0.005, which means that the test could be repeated about 210 times, giving a total of Nth = 7.51 × 108 cycles until crack initiation. The related S–N curve parameters, k, σa0, and the standard error S of log Nf are given in the lower part of Table 4.5. Here it was assumed that the parameters of the S–N curve are exactly known. In fact, k and σa0 represent statistical estimates which are based on a limited sample size of n = 9 individual tests. The degree of uncertainty which is added to the theoretical fatigue life by considering a limited sample size leads to a further reduction of the lower tolerance limit. Theoretical bond line fatigue life of the composite beam was calculated based on lower tolerance limits following the procedure outlined in ISO 12107 (2003): see Table 4.5. Lower tolerance limits were calculated for Psurv = 99% at a confidence level of 1 − α = 95% and ν = n − 2 degrees of freedom. The related coefficient for the one-sided tolerance limit of the normal distribution κ (Psurv, 1 − α, ν) = 4.353 was taken from the table in ISO 12107 (2003). The parameters Psurv, 1 − α, ν = n − 2, and κ(Psurv, 1 − α, ν) are given in the lower part of Table 4.5. The damage sum is about 0.34, which means that the test could be repeated about three times, giving a total of Nth = 1.06 × 107 cycles until crack initiation. It can be seen that the consideration of a limited sample size results in a lower tolerance limit and gives a much more conservative estimate of fatigue life. The bonded composite beam was tested in a servo-hydraulic machine under cyclic 4-point bending at room temperature. Load amplitudes and frequencies given in Table 4.5 were applied starting with the lowest amplitudes and ending with the highest amplitudes. Since nothing was known on the actual value of D but crack initiation should be avoided in order to derive at least a lower boundary for D from the test, it was decided to abort the test after a third of the predicted life, i.e. 3.60 × 106 cycles, for bond line inspection. The beam was cut in the x-z symmetry plane for inspection of the adhesive joints. The bond lines appeared to be fully intact without any cracks. This means that the actual value of D was at least 0.3.

4.4.2 Fatigue life of a bonded insert Fatigue life of bonded inserts under cyclic loading with variable amplitudes was considered based on the local stress-life approach. The geometry of the test structure is shown in Fig. 4.13. Threaded steel inserts with a diameter of 16 mm and a length of 50 mm were bonded into drill holes in blocks of multi-directional glass fibre laminate consisting of E-glass and epoxy resin.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

67

Hub Bolt Insert

Adhesive

Z Y X

Laminate

4.13 Sectional view of bonded insert.

The drill holes had a diameter of 20 mm, giving a bond line thickness of 2 mm. The adhesive used was cold-curing, two-part methacrylate. Threaded bolts were used to simulate the connection between the bonded inserts and the hub. The inserts were designed such that the loads which are generated by tightening the bolts were retained within the steel parts (Fig. 4.13). Thus it was achieved that the bond lines were predominantly loaded by the test load while they were nearly free from the tightening loads. The test structures were made symmetric as shown in Fig. 4.13 for ease of clamping in a testing machine. Unlike the composite beam, the behaviour of the bond line is controlled by the load rather than by the deformation. High temperatures are critical here since the bolt load produces similar stresses in the bond line but the strength of the adhesive is lower. Therefore, the joint was studied at 40°C and 80% relative humidity. Numerical stress calculations were carried out with ABAQUS. The bond line and the steel parts were modelled as homogeneous, isotropic material. The fibre laminate was modelled as homogeneous solid with transversal isotropy, the principal direction oriented along the bolt axis. The model was meshed using 8-node, reduced integration solid elements C3D8R. The coupling between different parts was achieved by congruent meshing and shared nodes. The element dimensions in the bond line were 0.5 mm in radial direction and 1.0 mm in axial direction. The elastic constants used were E = 195 000 MPa, ν = 0.3 for steel, and E = 749 MPa, ν = 0.41 for the adhesive. The elastic constants were chosen as E11 = 30 000 MPa, E22 = 10 140 MPa, ν12 = 0.38, Gij = 3500 MPa for the laminate. Boundary conditions were applied such that the symmetry shown in Fig. 4.13 was achieved. The model was pre-tensioned in order to simulate

© Woodhead Publishing Limited, 2012

68

Adhesives in marine engineering

tightening of the screw connections in a first loading step. In a second step, the test load was applied. The stress distribution in the adhesive is shown in Fig. 4.14 for an applied load of 7.2 kN. The stress amplitude was calculated from upper and lower stresses since the stress ratio was different from the load ratio due to bolttightening. The calculated stress amplitude was mean stress corrected for by using Gerber’s rule. Based on experimental testing it was found that this rule gave better results than Goodman’s rule. The damage calculation was performed using linear damage accumulation based on a load spectrum which was derived from field tests. The S–N curve parameters of the adhesive were k = 11.95 and σa,0 = 7.24 MPa. The standard error of log life was S = 0.42. A mean value of Nth = 2 × 107 cycles was calculated (Rudnik et al., 2010, Nagel and Brede, 2011).

S, Max. Principal (Avg: 75%) +1.208e+01 +1.065e+01 +9.223e+00 +7.795e+00 +6.368e+00 +4.940e+00 +3.512e+00 +2.085e+00 +6.571e−01 −7.705e−01 −2.198e+00

4.14 Bonded insert – distribution of the maximum principal stress in the adhesive at an applied load of 7.2 kN.

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

69

VA fatigue tests of the bonded inserts were carried out in a climate chamber at 40°C/80% relative humidity based on the same load spectrum which was used in the model calculations. The test was terminated after exceeding 1 × 108 cycles without failure. The average calculated fatigue life based on linear elastic stress analysis, the adhesive material S–N curve, and linear damage accumulation, had a value of 2 × 107 cycles under the same conditions. It can be seen that the cycle number achieved in the test without failure was much larger than the average calculated fatigue life. The probability of failure at 1 × 108 cycles, which was estimated assuming a normal distribution and standard error of log life of S = 0.42 has a value of Pfail ∼ 95%. The probability of failure would be even higher if the lower tolerance limit of fatigue life would have been calculated after ISO 12107 (2003). The fact that the part did not fail gave rise to check the assumption of linear damage accumulation. In Section 4.3.4 it was shown that the actual value of the damage sum of the considered adhesive was larger than one. Depending on the shape of the load spectrum, values of D = 3 and D = 5 were measured. This means that the actual fatigue life could be up to five times higher than the theoretical value which was calculated based on the assumption of D = 1. It is even possible that the bolts fail before the adhesive, as some of the experiments indicated.

4.5

Future trends and conclusions

This chapter reviewed the fatigue-resistant design of adhesively bonded joints for wind turbine rotor blades. The adequacy of the local stress-life approach for estimating crack initiation fatigue life in the adhesive layer was discussed. It was stated that the method can be applied if the material behaviour of the adhesive can be treated elastic and time-independent, which is the case for many structural adhesives below Tg. However, there is only little experience on the validity of the assumptions which are known to apply to conventional construction materials. It was shown that in the case of adhesives, the treatment of mean stresses, the method of damage accumulation, the load sequence effect, and the treatment of environmental impact need careful attention before the result can be interpreted. For a hot-curing, structural epoxy adhesive it was shown that Goodman’s rule for mean stress correction applies only if the mean stress fraction is low. In the case of a cold-curing, two-part structural methacrylate adhesive, it was shown that the actual damage sum D can take values far from one, whereas D = 1 is often assumed in calculations. For the same adhesive it was found that there can be a significant influence of the load sequence on fatigue life, depending on the shape of the load spectrum. In contrast to conventional construction materials, temperature and moisture can

© Woodhead Publishing Limited, 2012

70

Adhesives in marine engineering

significantly change stiffness and fatigue strength of the adhesive. Depending on whether the bond line is actuated under load-control or deformationcontrol, either low temperatures or high temperatures can be critical. Two application examples were presented where crack initiation fatigue life was considered: a bonded fibre reinforced composite beam loaded in cyclic bending and a bonded insert loaded in cyclic tension. Fatigue life of the adhesive joint in the composite beam was estimated under block loading with variable amplitudes at room temperature including tolerance limits for a small sample size. Doubts about the assumption of D = 1 led to abortion of the test after one third of the expected lifetime. No bond line cracks were visible. This led to the conclusion that D > 0.3. Fatigue life of the adhesive joint in the bonded insert was estimated under block loading with variable amplitudes at elevated temperature and moisture. It was found that fatigue life was widely underestimated. For the specific adhesive system, the deviation could be explained by D > 1, which was proved by testing. As a concluding remark, it can be stated that present fatigue life estimations for adhesive joints based on the local stress-life approach are less accurate than those for conventional construction materials. The reason is that exact numbers are rarely available for the numerous adhesives on the market. It has, however, been shown that common rules for conventional construction materials apply in approximation also for adhesives. Therefore, conservative calculations can be made if the numbers are measured for the specific adhesive or if reasonable assumptions are made. The accuracy of the predictions can be expected to increase with the growing experience in the application of adhesive bonding. It was shown that the local stress-life approach can be used to estimate crack initiation fatigue life of bonded joints if specific assumptions are fulfilled. There are, however, a number of problems which should be investigated in more detail in the future. In the applications considered here, the degree of stress multiaxiality was not considered. While in the composite beam the stress state was uniaxial and could therefore be directly compared with tensile fatigue tests, the stress state in the bonded insert was multi-axial. The absence of unexpectedly low fatigue life indicated that the influence of stress multiaxiality on fatigue life was low. However, it is known that quasi-static strength is highly influenced by hydrostatic stresses and knowledge on this topic is therefore desirable for fatigue loading. It was shown that the assumption of linear damage accumulation was conservative in the applications considered. There is, however, less confidence about the general validity of linear damage accumulation. Since detailed information on non-linear damage accumulation is not available

© Woodhead Publishing Limited, 2012

Designing adhesively bonded joints for wind turbines

71

for adhesive joints, using linear damage accumulation with an adjusted damage sum is seen to be a pragmatic solution. The determination of adjusted damage sums requires testing in the near future. Environmental conditions were shown to have a strong influence on fatigue life. It seems to be straightforward to apply the stress-life approach at constant temperature as shown in the bonded insert example, but it is unlikely that a bonded component would spend its life under constant environmental conditions. Therefore, an approach is needed which allows variable temperatures and/or moisture to be taken into account. It was argued that fatigue crack initiation is critical for bond lines in rotor blades but there are indications that cracks cannot be avoided in some cases. It is then useful to know whether existing cracks will grow or will rather be stable throughout life; hence there is a need for knowledge on fatigue crack propagation in adhesive joints. It can be concluded that future work should focus on stress multiaxiality, damage accumulation, impact of temperature/ moisture, and fatigue crack propagation.

4.6

References

ASTM E 1049-85 (1997), Standard practices for cycle counting in fatigue analysis. Farahmand B, Bockrath G, Glassco J (1997), Fatigue and Fracture Mechanics of High Risk Parts, New York, Chapman & Hall. Guideline for the Certification of Wind Turbines (2004), Edition 2003 with Supplement 2004, Hamburg, Germanischer Lloyd. Guideline for the Certification of Offshore Wind Turbines (2005), Hamburg, Germanischer Lloyd. Guideline for Certification of Wind Turbines (2010), Hamburg, Germanischer Lloyd. Hennemann O-D, Brede M, Nagel C, Hahn O, Jendrny J, Teutenberg D, Schlimmer M, Mihm K-M (2007), Methodenentwicklung zur Berechnung und Auslegung geklebter Stahlbauteile im Fahrzeugbau bei schwingender Beanspruchung, final report IGF141ZN, P653, Düsseldorf, FOSTA Forschungsvereinigung Stahlanwendung eV. ISO 12107 (2003), Metallic materials – fatigue testing – statistical planning and analysis of data, International Standard, ISO 12107:2003(E), 1st Ed, 2003. Nagel C, Brede M (2011), Bonded inserts as blade to hub connections for wind energy converters, Proc 34th Ann Meeting of the Adhesion Society, Savannah. Offshore Standard Composite Components DNV-OS-C501 (2010), Det Norske Veritas. Radaj D, Sonsino C M (1998), Fatigue assessment of welded joints by local approaches, (ISBN 1 85573 403 6), Woodhead Publishing Limited. Rudnik Y, Schneider B, Nagel C, Brede M (2010), Auslegung struktureller Klebverbindungen von faserverstärktem Kunststoff mit Metall für Windenergieanlagen, Joining Plastics, 2, 92–95. Sendeckyi G P (2001), Constant life diagrams – a historical review, Int J of Fatigue, 23, 347–353.

© Woodhead Publishing Limited, 2012