Experimental Study of the Fatigue Performance of Overhead Pure Aluminium Cables

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Procedia Structural Integrity 19 (2019) 688–697

Fatigue Design 2019 Fatigue Design 2019

Experimental Study of the Fatigue Performance of Overhead Pure Experimental Study of the Fatigue Performance of Overhead Pure Aluminium Cables Aluminium Cables R.B. Kalomboa,a,*, G. Reinkeaa, T.B. Mirandaaa, J.L.A. Ferreiraaa, C.R.M. da Silvaaa, J.A. R.B. Kalombo *, G. Reinke , T.B. Miranda Ferreira , C.R.M. da Silva , J.A. Araújo ,a,J.L.A. * Araújo a,* a a

UnB, University of Brasilia, Campus Universitário Darcy Ribeiro, Asa Norte, Brasilia CEP 70910-900, Brazil UnB, University of Brasilia, Campus Universitário Darcy Ribeiro, Asa Norte, Brasilia CEP 70910-900, Brazil

Abstract Abstract This work presents an experimental comparative study to evaluate the fatigue performance of two overhead cables made of different This presents an experimental evaluate fatigue of two overhead cables made of1120 different typeswork of pure aluminium. A batterycomparative of eighteen study fatiguetotests was the carried outperformance on two cables, named Orchid and AAAC 823 types of pure aluminium. A battery of eighteen fatigue tests was carried out on two cables, named Orchid and AAAC 1120 823 MCM, made of pure aluminium, i.e. AA 1350 and AA 1120, respectively. Fatigue of cables is a main cause of failure resulting MCM, made vibration. of pure aluminium, i.e. AA AA 1120,torespectively. Fatigue of which cables are is athe main cause of failure from aeolian Through wind, the1350 cableand is subjected three types of loading clamping force, theresulting bending from Through wind, thestretching cable is subjected tostretching three types of loading which theofclamping force, which the bending stressaeolian and thevibration. mean stress due to the cable load. This load is expressed in are term H/w parameter is the stress and the mean stress due to the cable stretching load isw.expressed in term of H/w parameter whichthe is use the ratio between the horizontal stretching loadstretching H and theload. linearThis weight of the cable The CIGRÉ organization has suggested ratio between the horizontal stretching load H and the linear weight of the cable w. The CIGRÉ organization has suggested the use of the H/w as a parameter of power line cable design against fatigue due to aeolian vibration. Fatigue tests were conducted for of the H/w as a parameter of power cablecurves designwere against fatigueatdue aeolian Fatigue for cable/suspension clamp systems and line two S-N generated thetosame H/wvibration. value of 1820 m. tests One were curveconducted was obtained cable/suspension clamp systems and two S-N curves generated at thecould samesustain H/w value of 1820 m. One curvebefore was obtained for each cable. The generated S-N curves proved thatwere the AA 1120 cable a higher number of cycles fatigue for eachthan cable. generated S-N curves proved the AA 1120 cablea failure could sustain a higher of cycles before fatigue failure the The AA 1350 for the considered value that of H/w. Additionally, map was raised number to determine the morphology of failure than the AA 1350 for the considered value of H/w. Additionally, a failure map was raised to determine the morphology of wire break. The microscopic analysis showed that the cracks were nucleated in the fretted marks. Data presented in this study will wire break.for The analysis showedcables that the cracksaeolian were nucleated be helpful themicroscopic fatigue design of overhead against vibration.in the fretted marks. Data presented in this study will be helpful for the fatigue design of overhead cables against aeolian vibration. © 2019 The Authors. Published by Elsevier B.V. © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Authors. Published by Peer-review under responsibility of Elsevier the Fatigue Design 2019 Organizers. Peer-review under responsibility of the Fatigue Design 2019 Organizers. Peer-review under responsibility of the Fatigue Design 2019 Organizers. Keywords: Fatigue, Fretting fatigue, cable, aluminium, S-N graph. Keywords: Fatigue, Fretting fatigue, cable, aluminium, S-N graph.

* Corresponding author. Tel.: +55-61-991112426. * Corresponding Tel.: +55-61-991112426. E-mail address:author. [email protected] [email protected] E-mail address: [email protected] [email protected] 2452-3216 © 2019 The Authors. Published by Elsevier B.V. 2452-3216 2019responsibility The Authors. of Published by Elsevier B.V. Organizers. Peer-review©under the Fatigue Design 2019 Peer-review under responsibility of the Fatigue Design 2019 Organizers.

2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Fatigue Design 2019 Organizers. 10.1016/j.prostr.2019.12.075

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1. Introduction Power line cables are one of the most important elements in the transmission of electrical energy and its effect on the rate of total installation time of a transmission line is significant. Due to wind, the cable vibrates and accumulates a number of cycles which leads to fatigue failure, especially at the element which restrains its vibration, such as the suspension clamp (Chan 2006). In addition to the force due to the wind, which generates the bending displacement, this power line element is also suggested to create many loads. Among these are the stretching load and the pressure load, caused by the bolt tighten torque of the suspension clamp (IEEE 2007, Fadel et al. 2012). Aeolian vibration and the stretching load are the main causes of power line cable fatigue (Cardou 1992, Volker et al. 2014). One of the main concerns of the transmission power line project against aeolian fatigue is to control the stretching load of the cable, as this tension should not exceed the allowable tension during the severe climate period. In addition, the stretching tension must be respected in order to protect the cable against aeolian vibrations (vibrations increase with stretching), and also to restrict the violation of the line clearance. Therefore, some organisations related to power line cables, such as the International Council on Large Electric Systems (Conseil International de Grand Reseaux Électriques, or CIGRÉ) have fixed some limits and defined the stretching tension as the Every Day Stress (EDS). These limits were created by the EDS panel commissioned by CIGRÉ, which established the upper limit for cable stretching load that can prevail for a long period of time without fatigue of the overhead cable (CIGRÉ 1979, Barrett and Motlis 2001, IEEE 2006). The safe stretching load was established for different types of cables after an in situ investigation of some power line transmission cables around the world, in combination with experimental data. Thus, CIGRÉ refer to the safe tension as the EDS, which has been fixed according to the cable type and to the configuration of the transmission power line cable (Quad, triple, twice bundles, etc.). The value of EDS is expressed as a percentage of the Ultimate Tensile Strength (UTS) of the cable and defined as the maximum tension load to which the cable can be subjected, at the temperature which will occur for the longest period of time in one year, without any risk of fatigue damage caused by aeolian vibrations. Recently, after in situ observation of power line transmission based on a questionnaire prepared by CIGRÉ's working group, it was shown that power line cable failure by fatigue due to aeolian vibration exists, in spite of the use of the recommended EDS value. For instance, for a power transmission lines that have been in service for five to ten years stretched with an EDS value of less than 18% UTS, almost 20% of the cables showed failure by fatigue. Certainly, the need for another parameter for the safe design tension is evident. CIGRÉ suggested the use of the H/w parameter for the safe design tension of transmission power lines to provide protection against fatigue and to better understand the fatigue damage occurring on the overhead cable due to aeolian vibration. The H/w parameter can be defined as the ratio between the initial horizontal tensile load (H) and the cable weight (w) per unit length. The tensile load (H) would be the initial horizontal tension before any significant wind and ice loading and before creep at the average temperature of the coldest month at the site of the power line (CIGRÉ 2005). The tenets of the H/w parameter suggest that all overhead cables stretched with the same value of H/w will have a similar fatigue life, although no experimentals laboratory work on overhead cables were performed to corroborate this idea (Barrett and Motlis 2001, CIGRÉ 2005). After a thorough investigation of current literature, some studies have been identified regarding fatigue of power lines related to the EDS parameter (Chan 2006, Fadel et al. 2012, Volker et al. 2014). However, there is a limited number of studies investigating the effect of the H/w parameter on the fatigue life of a cable made of pure aluminium, especially 1120 aluminium, which was recently applied to power line transmission worldwide. This study investigates the fatigue performance of two types of cable, namely AAC Orchid and 823 MCM, made from two pure types of aluminium: 1350 and 1120, respectively. Eighteen fatigue tests were carried out on the two types of cable. Furthermore, a failure map was made to determine the morphology of wire breaks that occurred. Microscopic analysis showed that the cracks were nucleated in the fretted marks. Data presented in this study will be helpful for the fatigue design and investigation of overhead cables against aeolian vibration.

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2. Fatigue of overhead cables 2.1. Cable material The overhead cable is the only component of the power line transmission which carries electricity. It is designed in order to sustain some electrical, mechanical and environmental loads in order to achieve the projected life expectancy. The cables used for this publication are made of aluminium 1350 and 1120, both pure aluminium belonging to series 1xxxx. The usage of 1120 aluminium for cables was recently initiated and currently, increasing numbers of transmission power companies around the world are starting to upgrade or construct their lines using cables made of this type of pure aluminium. Aluminium1120 has an electrical conductivity equal to almost 60% of the conductivity mean, while aluminium1350 has almost 62%. Although the aluminium1120 has a conductivity slightly lower than that of the pure aluminium 1350, it presents good mechanical properties such as a low strength to weight ratio and high mechanical strength. Beside the mechanical properties, the cable made of aluminium 1120 presents low costs as one can use low structure (tower) and long span for the transmission power line. The chemical composition of both pure aluminium types is presented in Table 1 by considering the maximum value of the component. Table 1. Chemical composition of Aluminium 1350 and 1120. Al

B

Cr

Cu

Ga

Fe

Mn

Mg

Si

V+Ti

Zn

1350

Bal.

0.05

0.01

0.05

0.03

0.40

0.01

----

0.10

0.02

0.05

1120

Bal.

0.05

0.01

0.01

0.03

0.40

0.01

0.20

0.10

0.02

0.01

Aluminium

2.2. Bending stress of cable Overhead cables are exposed to nature’s dynamic forces which could originate from snow, wind, rain or earthquakes. These forces lead overhead cables to vibration and could lead to damage and failure after extensive periods of time. One of the main causes of damage or failure of cables is fatigue mainly due to aeolian vibration, especially at points where the cyclic motion of the cable is restrained, for example at support locations, dead-ends, suspension clamp and other clamp types (Chan 2006, Loredo-Souza and Davenport 1998, Kiessling et al. 2003). The cyclic bending of a cable causes fatigue of cable strands near the devices which restrain the cable motion. As part of the cyclic bending, this increases stress because the stretching load of the cable and the pressure load due to the suspension clamp contribute to the fatigue of the strand cable. In the case of usage of the system suspension clamp/cable, most of the strand fatigue occurs inside the suspension clamps. Accurate measurement of bending stress at the strand fatigue points is quite difficult, therefore the implementation of some assumptions is vital. The strain gauges and the Poffenberger-Swart (P-S) formula allow for the measurement of the strain of wire and the confirmation of this measurement using the P-S calculation. Poffenberger and Swart (1965) considered that the dynamic behaviour of the cable is similar to an Euler beam close to the suspension. Figure 1 illustrates the schematic montage of the system cable and suspension clamp and the point and specification used by P-S to established the formula.

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Distance from the measurement point of the bending displacement (Yb) to the LPC between the cable and the suspension clamp Every Day Stress EDS (H/w) 89 mm

Bending displacement, Yb

Cable Suspension clamp

The last point of contact (LPC) between the cable and the suspension clamp

Every Day Stress EDS (H/w)

Fig. 1. Schematic montage of the system cable and suspension clamp showing the measurement point of the bending amplitude and the last point of contact.

Poffenberger-Swart related the bending amplitude peak to peak of the cable measured at the reference distance from the clamp with the stress in the strands of the outer layer diametrically opposite to the last point of contact (LPC). More specifically, the P-S formula can be written as follows:

 = Yb K where

(1)

𝜎𝜎𝑎𝑎 is the dynamic bending stress amplitude (zero to peak), 𝑌𝑌𝑏𝑏 is the cable´s vertical displacement range (peak to peak), measured at 89 mm from the last point of contact (LPC) between cable and clamp, K represents Poffenberger parameter and is given by:

K=

Ea dp 2 4(e− px − 1 + px)

(2)

where 𝐸𝐸𝑎𝑎 (MPa) is the Aluminum Young´s modulus, 𝑑𝑑 (mm) is the diameter of the outer layer´s wire. 𝑥𝑥 stands for the distance on the cable between the LPC between cable and clamp and the vertical displacement measuring point (usually = 89 mm), and

p=

T EI

(3)

with 𝑇𝑇 denotes the static cable tension at average ambient temperature during the test period in N. 𝐸𝐸𝐸𝐸 is the flexural stiffness of the cable in N.mm2, whose minimum value is:

EI min na Ea =

 d a4 64

+ ns Es

 d s4 64

(4)

where 𝑛𝑛𝑎𝑎 , 𝐸𝐸𝑎𝑎 , 𝑑𝑑𝑎𝑎 are respectively the number, the individual diameter and Young´s modulus of the wires under investigation and 𝑛𝑛𝑠𝑠 , 𝐸𝐸𝑠𝑠 , 𝑑𝑑𝑠𝑠 represent the same values for steel wires. In this approach, the cable is considered as a bundle of individual wires free to move relatively to each other and the flexural stiffness exhibits its minimum value

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𝐸𝐸𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 . When the cable is vibrated at smaller bending amplitudes, wires would stick together and the cable would behave as a solid rod, increasing the flexural stiffness to its maximum. Some approaches to calculate the value of 𝐸𝐸𝐸𝐸 which take into account the stick-slip between wires and hence the dynamic bending stress can be found in literature (Papailiou 1995 and 1997). 3. Materials and experimental procedure Two cables were tested for this study, namely Orchid and 838 MCM, made of pure aluminium 1350 and 1120, respectively. The cables made of these kinds of aluminium are called All Aluminium Cable Orchid (AAC Orchid) and All Aluminium Alloy Cable 823 MCM, respectively. Each cable has 37 strands of aluminium, as shown in Table 2. Table 2. Geometrical and mechanical properties of the two cables Cable type

Cable diameter (mm)

Ultimate Tensile Strength, UTS (kgf)

Number and diameter of strand (mm)

Liner mass (kg/m)

AAC Orchid

23.30

5143

37x3.33

0.889

AAAC 823 MCM

26.53

9705

37x3.79

1.150

Experimental work was carried out at the resonance fatigue bench of the Fatigue and Structural Integrity Laboratory of the University of Brasília. A schematic representation of the three resonance benches can be seen in Figure 2. Each bench is divided into two parts: the active and the passive span with lengths of 40 m and 6.8 m respectively. The active span is limited by two support points which form the centre of the pulley on the fixed block 1 and the suspension clamp mounted on the adjustable block.

Fig. 2. Three fatigue test benches for overhead cables at the University of Brasília: (a) overall three-dimensional view, and (b) side view.

The passive span is used to stretch the cable at the desired tension by means of the hand traction winch. The stretching tension is also adjustable by adding weights at the fixed block 1 side and the measurement is made by the

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load cell which is in series with the cable. The vibration of the sample on the bench is made by using an electrodynamic shaker which is connected to the cable with the alignment device. To detect the strand break of the cable during the test, a device is mounted on the cable at a point with a low vibration, which is the first node from the LPC (Kalombo et al. 2015). The recommendations of CIGRÉ and the Institute of Electrical and Electronics Engineers (IEEE) on the fatigue test of cable were used during the experimental campaign. Therefore, the bending displacement (Yb) was controlled and kept constant. All fatigue tests were performed according to IEEE and CIGRÉ standards where the established criterion to stop the cable´s fatigue test is when the number of broken strands amounts to 10% of the total number of cable aluminium strands (Cham 2006, Kalombo et al. 2015). The bending strain of the cable was measured using three strain gauges glued onto the three top strands diametrically opposite to the LPC, as recommended by IEEE and CIGRÉ. The amount of cycles to failure was counted by pointing a laser on the cable and the bending displacement was measured and controlled during the fatigue test (Fig. 3). Three strain gauges glues on the cable at the diametrically opposite point of LPC Cable

Accelerometer at 89 mm from LPC Laser at 89 mm for counting the number of cycles

Fig. 3. The system cable/suspension clamp on the resonance fatigue test bench with different sensors.

Three different bending stress values were used and the test was repeated three times for each bending stress to generate the S-N graph for each cable with a H/w value of 1820 m. Thus, eighteen fatigue tests were performed, with nine fatigue tests for each cable to generate the S-N graph. The parameters used to conduct the fatigue test are presented in Table 3. Table 3. Parameters used during the fatigue test; the banding amplitude (Yb) at 89 mm, the Poffenberger-Swart constant (K) and the bending stress calculated using Eq. 2 and 1, respectively. Cable type

H/w (m)

EDS (%UTS)

Poffenberger-Swart constant, K (MPa/mm)

Bending stress, (MPa) 26.8

28.22

31.35

Bending displacement, Yb (mm) AAC Orchid

1820

31.4

30.91

0.87

0.91

1.01

AAAC 823 MCM

1820

21.6

32.66

0.82

0.86

0.96

694

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4. Experimental results and discusions This section presents the results of the fatigue tests performed on both cables under the conditions presented in Table 3. In addition, the macroscopic and microscopic failure analyses are also discussed. Eighteen fatigue tests were performed; nine for each cable using the same value of H/w = 1820 m. One should know that the H/w value is proportional to the mean stress in the strand and the calculated is 48.03 MPa (Kalombo et al. 2017). Three different levels of bending stress were applied and three tests were carried out at each bending stress level. For both cables, the criterion to stop the test was the fourth strands break, as suggested by CIGRÉ. Using the experimental procedure presented in section 3, the S-N curves obtained are shown in Fig. 4 along with the CIGRÉ Safe Border Line (CSBL). The CSBL is the S-N curve suggested by CIGRÉ as the fatigue limit resistance of cables for the project design of power line transmission against aeolian fatigue when the S-N curves of the projected cable are not available. It is also used to verify the acceptance of the fatigue performance of the specific cable as its fatigue curves must be above the CSBL in order to be accepted (Chan 2006, Fadel 2012). As illustrated in Fig. 4, one could conclude that both cables of pure aluminium present a good fatigue performance as both S-N curves are located above the CSBL. The AAAC 823 MCM presents a fatigue life of almost 10% higher than the AAC Orchid for the same value of the H/w. It should be noted that the AAAC 823 MCM was stretched with a higher value of EDS than the AAC Orchid (Table 2). For example, hypothetically thinking that there are two transmission line projects, one with the AAAC 823 MCM and the other with AAC Orchid. Which one will be more advantageous in the same aeolian vibration history? In this specific hypothesis, for the same value of H/w, the project of AAAC 823 MCM will need lower tower and longer span than the one for the AAC orchid cable. On the other hand, by using the same value of EDS, the line with AAAC 823 can be used with a higher value of EDS and the line will still be safe against fatigue.

Fig. 4. S-N curves of the cables for the same value of H/w = 1820 m.

The fatigue strength of the two cables in terms of the number of cycles (mega cycles) was plotted for the same value of H/w (Fig. 5). It was observed that in order to have the same fatigue life, the AAAC 823 MCM must be vibrated at a significantly higher bending stress amplitude than the AAC Orchid cable.

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Bending stress, sa (MPa)

39

695

N = 106 Cycles

38

37 36 35 34

33

AAC Orchid

AAAC 823 MCM Cable type

Fig. 5. Constant fatigue life diagram for the two cables at 10 6 cycles.

Macroscopic and microscopic analysis of broken strands were also carried out. This information is important as it provides valuable data to compare with a numerical model for the fatigue of the cable/suspension clamp system in order to understand this fatigue phenomenon more accurately. Three types of strand fractures were observed; the quasi planar (QP), 45°, and the V type. One could conclude that the two cables presented a similar behaviour in terms of the percentage of the strand fracture, despite small differences (Fig. 6). 70%

AAC Ochid_Aluminium 1350

AAAC 823 MCM_Aluminium 1120

Purcentage of

broken strands

60% 50%

50% 40%

44% 36%

38%

30% 20%

18%

14%

10% 0%

QP

45°

V

Type of broken strand

Fig. 6. Percentage of type of broken strands for the two cables.

It is clear that both cables presented a similarity in the crack propagation in the strands during its fatigue (Fig. 7). To understand the fatigue phenomena better, the microscopic analysis of the fracture area was performed. The results indicate that the crack always originated at the fretting mark caused by the small relative movement between cable

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strands or between the cable and the suspension clamp. Dimples were observed, showing that the failure progressed through the cable strand until the applied load caused the remaining section to fail by ductile fracture (Fig. 7). a

b

Fretting mark.

c

d

Fretting mark.

Fig. 7. Fracture surface of strands showing the crack initiation at the fretting mark and dimples for the two cables (a, b) AAC Orchid Aluminium 1350 and (c, d) AAAC 823 MCM Aluminium 1120.

5. Conclusions This experimental study presents the fatigue performance of two cables made of pure aluminium 1350 and 1120 named AAC Orchid and AAAC 1120. Fatigue tests were performed on the two cables stretched with the same value of the H/w parameter. Two S-N curves were generated and failure analyses were established on a macroscopic and a microscopic scale. Based on the results and discussions presented, the following conclusions can be drawn: ❖ The two cables present a good fatigue performance compared to the CSBL. ❖ For the limited number of data here produced cables made of aluminium 1120 showed a longer fatigue life than those made of aluminium1350 for the same stress amplitude level. ❖ Transmission lines using cables made of aluminium 1120 could, in principle, be stretched at a higher EDS values than the AAC ones and still be safe against aeolian vibration. ❖ Similar fracture behaviours were observed for both types of cable. Acknowledgements The authors would like to acknowledge the support of Taesa, Transmissora Brasileira de Energia (TBE), ATE II Transmissora de Energia, ATE III Transmissora de Energia, Brasnorte Transmissora de Energia, Empresa

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Amazonense de Transmissão de Energia, AETE Amazonia Eletronorte Transmissora de Energia (AETE), Transmissora Matogrossense de Energia (TME) and of Finatec. The support of CNPq is also acknowledged. References Chan, J., 2006. EPRI Transmission Line Reference Book: Wind-Induced conductor motion, Electric Power Research Institute, Palo Alto, California. Fadel, A.A., Rosa, D., Murça, L.B., Ferreira, J.L.A., Araújo, J.A., 2012. Effect of High Mean Tensile Stress on The Fretting Fatigue Life of an Ibis Steel Reinforced Aluminium Conductor, International Journal of Fatigue 42, 24-34. IEEE, 2007. Guide for Aeolian Vibration Field Measurements of Overhead Conductors. Cardou, A., Cloutier, L., St-Louis M., Leblond, A., 1992. ACSR Electrical Conductor Fretting Fatigue at Spacer Clamps, M. Helmi Attia, R.B. Waterhouse (Eds.), Standardisation of Fretting Fatigue Test Methods and Equipment, 231-242. Volker, F.S., Kalombo, R.B., Cosme, R.M.S., Nogueira, M.N., Araújo, J.A., 2014. Effect of Chromium Nitride Coatings and Cryogenic Treatments on Wear and Fretting Fatigue Resistance of Aluminium, Electric Power Systems Research 116, 322-329. CIGRÉ WG 04 SC 22 - 02, 1979. Recommendations for the Evaluation of The Lifetime of Transmission Line Conductors, Electra 63, 103-145. Barrett, J.S., Motlis, Y., 2001. Allowable Tension Levels for Overhead Line Conductors, IEE Proceedings – Generation, Transmission and Distribution 148, 54-59. IEEE, STD 1368, 2006. Guide for Aeolian Vibration Field Measurements of Overhead Conductors. CIGRÉ Report 273, 2005. Overhead Conductor Safe Design Tension With Respect to Aeolian Vibrations, Task Force B2.11.04, CIGRÉ. Norma ASTM B398/B398M – 02, Reapproved 2007.Aluminum-Alloy 6201-T81 Wire for Electrical Purposes, Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. Silva, B.L., Araújo, J.A., Ferreira, J.L.A., 2010. High-Cycle Notch Sensitivity of Alloy Steel ASTM A743 CA6NM Used in Hydrogenator Turbine Components, Frattura Ed Integrità Strutturale 14, 36-44. Loredo-Souza, A.M., Davenport, A.G., 1998. The Effects of High Winds on Transmission Lines, Journal of Wind Engineering and Industrial Aerodynamics 74-76, 987-994. Kiessling, F., Nefzger, P., Kaintzyk, U., Nolasco, J.F., 2003. Overhead Power Lines: Planning, Design, Construction, Spring. Poffenberger, J.C., Swart, R.L., 1965. Differential Displacement and Dynamic Conductor Strain, IEEE Transactions 84, 281-289. Papailiou, K.O., 1997. On the Bending Stiffness of Transmission Line Conductors, IEEE Transactions on Power Delivery 12, 1576-1588. Papailiou, K.O., 1995. Improved Calculations of Dynamic Conductor Bending Stresses Using A Variable Bending Stiffness, CIGRÉ SC 22 WG11, Madrid. Kalombo, R.B., Martínez, J.M.G., Ferreira, J. L.A., Da Silva, C.R.M., Araújo, J.A., 2015. Comparative Fatigue Resistance of Overhead Conductors Made of Aluminium and Aluminium Alloy: Tests and Analysis, Fatigue Design 133, 223-232. Kalombo, R.B., Pestana, M.S., Ferreira, J.L.A, C.R.M. Da Silva, J.A. Araújo, 2017. Influence of the Catenary Parameter (H/w) On the Fatigue Life of Overhead Conductors, Tribology International 108, 141-149.