thermomechanicalfatigueofunidirectionalcarbonfiber/epoxy

Research ArticleThermomechanical FatigueofUnidirectionalCarbonFiberEpoxyComposite in Space

Ali Anvari

Department of Mechanical and Aerospace Engineering University of Missouri-Columbia Columbia Missouri USA

Correspondence should be addressed to Ali Anvari aabm9mailmissouriedu

Received 24 April 2020 Revised 9 June 2020 Accepted 16 June 2020 Published 29 June 2020

Academic Editor Yuanxin Zhou

Copyright copy 2020 Ali Anvari is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

ermomechanical fatigue is one of the challenges for spacecrafts during space missions As a result of the extreme temperaturevariation in space thermal cycles are created and due to the imposed mechanical loads to spacecrafts such as engine loads whilethey turn on and off mechanical cycles are created e worst structural fatigue for spacecrafts occurs when both thermal andmechanical cycles happen simultaneouslye reason is that both thermal andmechanical cycles could cause stress concentrationin the spacecraft structureerefore the probability of crack initiation or propagation in the spacecraft structure increases In thisstudy for the first time novel thermomechanical fatigue relations are introduced to evaluate the safety of unidirectional carbonfiberepoxy composite in the space environment is composite material has been used in the spacecraft structure due to itslightweight and high strength Furthermore with applying thermal fatigue relations thermally-safe planets moons and asteroidsin the solar system for unidirectional carbon fiberepoxy composite are identified

1 Introduction

Unidirectional Carbon Fiber-Reinforced Epoxy (UD CFRE)has been used in many applications such as aerospaceautomotive sporting goods and ships In the space industryUD CFRE can be used to fabricate the spacecraft structures[1] UD CFRE composites have been used in space appli-cation due to their best mechanical properties such as lowweight and high strength Nevertheless one of the failuremodes of UD CFRE is due to the thermomechanical fatiguein the space environment erefore the effect of thermo-mechanical fatigue on the mechanical behavior of thismaterial is under extensive study [2]

e application of UD CFRE is very broad in manyindustries It could be applied in automobiles tidal turbineblades jet-engine fan blades wind turbine blades andstructural members of an aircraft Experiments have shownthat the failure mechanism in UDCFRE could be in the formof interlaminar and intralaminar matrix cracks fiber-matrixdebonding and fiber breakage [3] Mechanical properties ofCFRE include corrosion resistance high strength to weightratio nonmagnetic properties and fatigue resistance Epoxy

is a thermosetting resinerefore its mechanical propertiesdegrade intensely when it is exposed to elevated tempera-tures in the space environment e epoxy deterioration canbe severe in cases where the extreme heat in space is higherthan the glass transition temperature (Tg) and the decom-position temperature (Td) [4 5]

Design processes have shown that fatigue properties areimportant characteristics of engineering materials ereason is the statistics which has indicated that fatiguefailures are over 90 of all the failurese experiments haveshown that at temperatures higher than 100degC fatiguestrength of CFRE decreases significantly e reduction inthe fatigue strength of CFRE is due to the induced defectswhich causes high stress concentration [6]

Since the birth of CFRE many studies have been providedto evaluate the mechanical properties failure and fatigue ofthis composite [7ndash13] Among these studies ldquosignificance ofdefects in the fatigue failure of carbon fiber-reinforcedplasticsrdquo is submitted by Prakash [7] Furthermore ldquomicro-mechanisms of interlaminar fracture in carbon-epoxy com-posites at multidirectional ply interfacesrdquo is published bySingh and Greenhalgh [8] Additionally ldquoprediction of tensile

HindawiJournal of EngineeringVolume 2020 Article ID 9702957 5 pageshttpsdoiorg10115520209702957

fatigue life for unidirectional CFRE in progress in durabilityanalysis of composite systemrdquo is studied by Miyano et al [9]

A few studies have been provided to predict the thermalfatigue of UD CFRE [14 15] in space Nevertheless there isno research to predict the thermomechanical fatigue of UDCFREerefore in this study for the first time relations areintroduced to predict the thermomechanical fatigue of UDCFRE is space ermomechanical fatigue occurs when aspacecraft is exposed to thermal and mechanical cyclessimultaneously Each time the spacecraft engine turns onand off it is both a mechanical cycle and a thermal cyclebecause it imposes mechanical stress on the spacecraft andthe engine heats up and cools down simultaneously Fur-thermore each time the spacecraft passes through a shadowof a planet moon or an asteroid its temperature decreasesand while it passes through the sun illumination its tem-perature increases erefore a thermal cycle can be createdas a result of cooling down and heating up

Stress concentration and possible crack initiation andorpropagation can develop in a spacecraft structure as a result ofthermal and mechanical cycles Hence while thermal andmechanical cycles happen at the same time the stress con-centration which is induced in the structure and the prob-ability of crack initiation andor propagation in the structurecould be higher than when only thermal or mechanical cycleoccurs erefore an exact analysis to evaluate the thermo-mechanical fatigue in space missions is required us in thisstudy thermomechanical fatigue of UD CFRE is evaluated

2 Problem Formulation

In 2018 [15] it has been proved that the degradation ofInterlaminar Shear Strength (ILSS) of UD CFRE is the maincause of failure in a thermal fatigue condition e reason isdue to the Interlaminar Shear stress (ILSs) within theCarbon Fiber (CF) and epoxy interface while UD CFRE isexposed to thermal cycles e main cause of developingILSs within the CF and epoxy interface is the difference ofthe Coefficient of ermal Expansions (CTE) between thesetwo materials in axial direction erefore ILSs equation[15] has been defined as follows

ILSs GCF|(23 minus T)| middot αepoxyA minus αCFA

11138681113868111386811138681113868

11138681113868111386811138681113868 (1)

In equation (1) GCF is the shear modulus of CF in theaxial direction 23 is the crack-free or stress-free temperaturein Celsius T is the space temperature αepoxyA is the CTE ofepoxy in the axial direction and αCFA is the CTE of CF in theaxial direction

In a thermal cycling environment ILSs must be less thanILSS As a result relation (2) for thermal fatigue is developedIn relation (2) FST is the thermal fatigue factor of safety

ILSsILSS

FST lt 1 (2)

For deriving a relation for thermomechanical fatiguemechanical fatigue expression must be added to relation (2)erefore the first thermomechanical fatigue relation isindicated as follows

ILSsILSS

FST +σM

σf

FSM lt 1 (3)

In relation (3) FSM is the factor of safety for mechanicalfatigue σM is the amplitude of appliedmechanical stress and σfis the failure mechanical stress σM and σf must be both eithercompression or tension For the highest safety both com-pression and tension stresses must be evaluated in relation (3)e next thermomechanical relation which must be evaluatedin order to have a safe design for UD CFRE is as follows

ΔTspace1113872 1113873NT

ΔTexp1113872 1113873NTf

FST +σM

σf

FSM lt 1 (4)

In the relation (4) ΔTexp is the temperature variation ateach thermal cycle in the experiment which has beenconducted on UD CFRE NTf is the number of thermalcycles to failure in the thermal cyclic experiment ΔTspace isthe temperature variation at each thermal cycle in space NTis the number of thermal cycles in space If there are two ormultiple space environments with different thermal cycleswith different temperature variations at each thermal cyclethen the following relation must be used

1113936ni0 ΔTiNTi

ΔTexp 1113872 1113873NTf

FST +σM

σf

FSM lt 1 (5)

ILSS FST FSM and NTf must be obtained by con-ducting experiments on UD CFRE According to this ther-momechanical fatigue evaluation method relations (2)ndash(4)must hold to make sure that UD CFRE is fail-safe or in otherwords it does not fail under thermomechanical fatigue

Based on the latest experiments at temperatures lessthan 0degC epoxy shows a brittle behavior erefore attemperatures less than 0degC mechanical fatigue tensile stressamplitude must be less than 600MPa (σMlt 600MPa) [6]Furthermore the number of mechanical fatigue cycles mustbe less than 105 (NMlt 105) [2] to prevent brittle fractureAdditionally experiments have shown that after epoxy hadbeen exposed to thermal cycles its glass transition tem-perature (Tg) has been reduced by 9 [5] erefore inthermal cycling environments the epoxy temperature mustbe always less than 091Tg to make sure it can carry load anddoes not fail It seems necessary to mention that for differentapplications such as aerospace and automotive the valueswhich can be chosen for mechanical and thermal fatiguefactors of safety can be different Nevertheless based on theresults of research studies and experiments which have beenconducted [2 5 6 14 15] for the thermal and mechanicalfatigue factors of safety in relations (2) (3) (4) and (5) theminimum value of 15 is recommended

3 Safe Planets Moons and Asteroids in theSolar System for UD CFRE

In this section of the manuscript thermal analysis is pro-vided to identify which planets moons and asteroids aresafe for UD CFRE in the spacecraft structure For thispurpose the following relation is employed

2 Journal of Engineering

ILSS ILSs (6)

Relation (6) indicates that when ILSs reaches the ILSS itis the end of the thermal life for UD CFRE For solvingrelation (6) it should be extended and written in the form ofrelation (7) All the parameters in the relation (7) are thesame as in equation (1) and the only difference is thatinstead of ILSs at the left-hand side of the equation ILSS issubstituted


11138681113868111386811138681113868

11138681113868111386811138681113868 (7)

Since all the values of ILSS GCF αepoxyA and αCFA areavailable [15]erefore with substituting these values in therelation (7) the following relation is obtained

809e + 6 (759e + 9)|(23 minus T)||(4392e minus 6) minus (minus 083e minus 6)|

(8)

By solving equation (8) T is derived and it has twovalues Tmin minus 215degC and Tmax 261degC It means that thetemperature of UD CFRE should be between minus 215 and261degC e reason is that if the temperature of UD CFREreaches minus 215 or 261degC the ILSs reache the ILSS and thecomposite material could fail at these temperatures due tothe stress concentration in the CF and epoxy interfaceHence UD CFRE is safe in temperatures between minus 215 and261degC However if a mechanical load applies to UD CFRE atthis temperature range the safety must be evaluated basedon the thermomechanical fatigue relations which have beenintroduced in the previous section Please note that inequation (8) ILSS and GCF are in Nm2 T is in Celsius andCTEs are in 1degC units

Based on this safe temperature range(minus 215degCltTlt 261degC) in this part it can be evaluated whichplanets moons and asteroids are safe for UD CFREAccording to the data in Tables 1 and 2 which are provided byChown in 2011 [16] temperature range of planets moonsand asteroids in the inner (Table 1) and outer (Table 2) solarsystem are indicated If the temperature range is between theminus 215 and 261degC they are thermally-safe for UD CFRE

4 Future Work

Due to the excellent properties of Carbon Nanotubes (CNT)nowadays its application is broad in many industries such asaerospace and automotive industries Carbon nanotubeshave great mechanical properties such as high tensilestrength high Youngrsquos modulus and high aspect ratio whichmakes CNT one of the best materials for different appli-cations Furthermore the electrical conductivity of CNT ishigh [17 18] Hence recently for enhancing the knowledgeregarding the CNTs a few studies to further analyze themechanics and forest synthesis of CNT have been published[19ndash22] Since CNTs have superior mechanical propertieswhen they are compared with carbon fibers such as highertensile strength they are expected to be applied widely infuture space structures erefore for the future work re-search regarding to the ldquothermomechanical fatigue of CNT-reinforced epoxyrdquo is recommended

5 Discussion

As it has been discussed in Section 2 at temperatures lessthan 0degC epoxy is brittle and it can crack when applying asmaller load with a much higher crack growth rateerefore at temperatures less than 0degC the factor ofsafeties which must be used in relations (2)ndash(5) needs to beadjusted according to epoxy brittleness Hence FST andFSM must have higher values However the amount of thefactor of safeties must be determined by conducting ther-momechanical fatigue experiments

Furthermore after several hundred thermal cycles theepoxy glass transition temperature will drop by 9erefore epoxy will soften at lower temperatures and is notcapable to carry load and withstand mechanical cyclesHence this drop in Tg must be considered in design pro-cesses and determining the appropriate values of safetyfactors

All the thermomechanical fatigue relations which havebeen introduced in this work can be applied for carbonnanotube-reinforced epoxy as well Nevertheless theamounts of safety factors maximum allowed number ofthermal and mechanical cycles and maximum ILSs and

Table 1 Safe planets moons and asteroids for UD CFRE in the inner solar system [16]

Star planets moons and asteroids in the inner solar systemStar Planet Moon Asteroid Temperature range (degC) Safety

Sun

5507 Not safeMercury minus 173 to 427 Not safeVenus 464 Not safeEarth minus 69 to 58 Safe

Earthrsquos moon minus 233 to 123 Not safeMars minus 140 to 20 Safe

Marsrsquos moon Phobos minus 40 SafeMarsrsquos moon Deimos minus 40 Safe

Ceres minus 106 to minus 34 SafeEros minus 46 Safe

Gaspra minus 92 SafeIda minus 73 Safe

Itokawa minus 67 Safe

Journal of Engineering 3

mechanical stress must be adjusted to the mechanical andthermal properties of CNTepoxy

For determining the thermally-safe planets moons andasteroids for UD CFRE in Section 3 it has been assumedthat the UD CFRE does not have a coating against the spacetemperature us if an appropriate coating can be appliedto cover the UDCFRE it can enhance the safety temperaturerange

6 Conclusions

In this research by applying physical equations [15] and ex-perimental data [14] novel relations are developed to predictthe fatigue life of UDCFRE For the fatigue safety of UDCFREone thermal fatigue and three thermomechanical fatigue re-lations are provided All these relations must be satisfied if asafe fatigue design is required For deriving all the unknownparameters in these thermal and thermomechanical relationsfatigue experiments must be conducted According to theserelations space temperature ILSs mechanical stress ampli-tude and the number of thermal and mechanical cycles canaffect the thermomechanical fatigue life of UD CFRE How-ever these relations can be applied to predict the thermal andthermomechanical fatigue life of CNTepoxy if the parametersin these relations are adjusted to the CNTepoxy properties

As it is discussed in Section 3 thermally safe planetsmoons and asteroids can be identified with applying thethermal fatigue relation Finally according to the recentstudies CNT has a superior mechanical property when it iscompared to CF erefore it is expected to be applied inspace composites such as CNTepoxy in the futurespacecrafts

Data Availability

e data which have been used to write this manuscript areavailable in the following references [2] [4] [5] [6] [14][15] and [16]

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

Part of the funding of this research was provided by Pro-fessor Sanjeev Khanna a faculty member of the Mechanicaland Aerospace Engineering Department in the University ofMissouri Columbia erefore the author would like tothank him for his support

References

[1] B Surowska J Bienias and H Debski ldquoFatigue of unidi-rectional carbon fiber reinforced epoxy compositesrdquo inProceedings of the ECCM15-15th European Conference onComposite Materials pp 24ndash28 Venice Italy June 2012

[2] P Coronado A Arguelles J Vintildea V Mollon and I VintildealdquoInfluence of temperature on a carbon-fibre epoxy compositesubjected to static and fatigue loading under mode-I de-laminationrdquo International Journal of Solids and Structuresvol 49 no 21 pp 2934ndash2940 2012

[3] A Hosoi and H Kawada ldquoFatigue life prediction for trans-verse crack initiation of CFRP cross-ply and quasi-isotropiclaminatesrdquo Materials vol 11 no 7 p 1182 2018

[4] F Zhou J Zhang S Song D Yang and C Wang ldquoEffect oftemperature on material properties of carbon fiber reinforcedpolymer (CFRP) Tendons experiments and model assess-mentrdquo Materials vol 12 no 7 p 1025 2019

[5] M Mohamed M Johnson and F Taheri ldquoOn the thermalfatigue of a room-cured Neat epoxy and its compositerdquo OpenJournal of Composite Materials vol 9 no 2 pp 145ndash1632019

[6] M Okayasu and Y Tsuchiya ldquoMechanical and fatigueproperties of long carbon fiber reinforced plastics at lowtemperaturerdquo Journal of Science Advanced Materials andDevices vol 4 no 4 pp 577ndash583 2019

[7] R Prakash ldquoSignificance of defects in the fatigue failure ofcarbon fibre reinforced plasticsrdquo Fibre Science and Technol-ogy vol 14 no 3 pp 171ndash181 1981

Table 2 Safe planets moons and asteroids for UD CFRE in the outer solar system [16]

Planet Moon Asteroid Temperature range (degC) SafetyJupiter minus 163 to minus 121 Safe

Jupiterrsquos moon Io minus 183 to minus 143 SafeJupiterrsquos moon Europa minus 223 to minus 148 Not safe

Jupiterrsquos moon Ganymede minus 203 to minus 121 SafeJupiterrsquos moon Callisto minus 193 to minus 108 Safe

Saturn minus 191 to minus 130 SafeSaturnrsquos moon Titan minus 179 Safe

Saturnrsquos moon Enceladus minus 240 to minus 128 Not safeSaturnrsquos moon Lapetus minus 173 to minus 143 SafeSaturnrsquos moon Mimas minus 209 Safe

Saturnrsquos moon Hyperion minus 180 SafeUranus minus 214 to minus 205 Safe

Uranusrsquos moon Miranda minus 223 to minus 187 Not safeNeptune minus 223 to minus 220 Not safe

Neptunersquos moon Triton minus 235 Not safePluto minus 240 to minus 218 Not safeEris minus 246 to minus 230 Not safeMakemake minus 243 to minus 238 Not safe


[8] S Singh and E S Greenhalgh ldquoMicromechanisms of inter-laminar fracture in carbon-epoxy composites at multidirec-tional ply interfacesrdquo in Proceedings of the 4th InternationalConference on Deformation and Fracture of Compositespp 201ndash210 Manchester UK March 1997

[9] Y Miyano M Nakada and H Kudoh ldquoPrediction of tensilefatigue life for unidirectional CFRPrdquo in Progress in DurabilityAnalysis of Composite Systems pp 303ndash308 CRC Press BocaRaton FL USA 1998

[10] A Sjogren and L E Asp ldquoEffects of temperature on de-lamination growth in a carbonepoxy composite under fatigueloadingrdquo International Journal of Fatigue vol 24 no 2ndash4pp 179ndash184 2002

[11] A Arguelles J Vintildea A F Canteli M A Castrillo andJ Bonhomme ldquoInterlaminar crack initiation and growth ratein a carbon-fibre epoxy composite under mode-I fatigueloadingrdquo Composites Science and Technology vol 68 no 12pp 2325ndash2331 2008

[12] V Mollon J Bonhomme J Vintildea A Arguelles andA Fernandez-Canteli ldquoInfluence of the principal tensilestresses on delamination fracture mechanisms and their as-sociated morphology for different loading modes in carbonepoxy compositesrdquo Composites Part B Engineering vol 43no 3 pp 1676ndash1680 2012

[13] M Okayasu T Yamazaki K Ota K Ogi and T ShiraishildquoMechanical properties and failure characteristics of a recy-cled CFRP under tensile and cyclic loadingrdquo InternationalJournal of Fatigue vol 55 pp 257ndash267 2013

[14] S Y Park H S Choi W J Choi and H Kwon ldquoEffect ofvacuum thermal cyclic exposures on unidirectional carbonfiberepoxy composites for low earth orbit space applica-tionsrdquo Composites Part B Engineering vol 43 no 2pp 726ndash738 2012

[15] A Anvari ldquoermal life of carbon structures from the earthto after the titanrdquo International Journal of Aerospace Engi-neering vol 2018 Article ID 7628614 6 pages 2018

[16] M Chown Solar System Black Dog amp Leventhal PublishersInc New York NY USA 2011

[17] S Lijima ldquoHelical microtubules of graphic carbonrdquo Naturevol 354 no 6348 pp 56ndash58 1991

[18] T R Fromy F K Hanson and T Olsen ldquoe optimumdispersion of carbon nanotubes for epoxy nanocompositesevolution of the particle size distribution by ultrasonictreatmentrdquo Journal of Nanotechnology vol 2012 Article ID545930 14 pages 2012

[19] J Brown T Hajilounezhad N T Dee S Kim A J Hart andM R Maschmann ldquoDelamination mechanics of carbonnanotube micropillarsrdquo ACS Applied Materials amp Interfacesvol 11 no 38 pp 35221ndash35227 2019

[20] T Hajilounezhad D M Ajiboye and M R MaschmannldquoEvaluating the forces generated during carbon nanotubeforest growth and self-assemblyrdquoMaterialia vol 7 p 1003712019

[21] T Hajilounezhad and M R Maschmann ldquoNumerical in-vestigation of internal forces during carbon nanotube forestself-assemblyrdquo in Proceedings of the International MechanicalEngineering Congress and Exposition Pittsburgh PA USANovember 2018

[22] Hajilounezhad T Oraibi Z A Surya R et al Exploration ofCarbon Nanotube Forest Synthesis-Structure RelationshipsUsing Physics-Based Simulation andMachine Learning 2019IEEE 1ndash8


fatigue life for unidirectional CFRE in progress in durabilityanalysis of composite systemrdquo is studied by Miyano et al [9]

A few studies have been provided to predict the thermalfatigue of UD CFRE [14 15] in space Nevertheless there isno research to predict the thermomechanical fatigue of UDCFREerefore in this study for the first time relations areintroduced to predict the thermomechanical fatigue of UDCFRE is space ermomechanical fatigue occurs when aspacecraft is exposed to thermal and mechanical cyclessimultaneously Each time the spacecraft engine turns onand off it is both a mechanical cycle and a thermal cyclebecause it imposes mechanical stress on the spacecraft andthe engine heats up and cools down simultaneously Fur-thermore each time the spacecraft passes through a shadowof a planet moon or an asteroid its temperature decreasesand while it passes through the sun illumination its tem-perature increases erefore a thermal cycle can be createdas a result of cooling down and heating up

Stress concentration and possible crack initiation andorpropagation can develop in a spacecraft structure as a result ofthermal and mechanical cycles Hence while thermal andmechanical cycles happen at the same time the stress con-centration which is induced in the structure and the prob-ability of crack initiation andor propagation in the structurecould be higher than when only thermal or mechanical cycleoccurs erefore an exact analysis to evaluate the thermo-mechanical fatigue in space missions is required us in thisstudy thermomechanical fatigue of UD CFRE is evaluated

2 Problem Formulation

In 2018 [15] it has been proved that the degradation ofInterlaminar Shear Strength (ILSS) of UD CFRE is the maincause of failure in a thermal fatigue condition e reason isdue to the Interlaminar Shear stress (ILSs) within theCarbon Fiber (CF) and epoxy interface while UD CFRE isexposed to thermal cycles e main cause of developingILSs within the CF and epoxy interface is the difference ofthe Coefficient of ermal Expansions (CTE) between thesetwo materials in axial direction erefore ILSs equation[15] has been defined as follows


11138681113868111386811138681113868

11138681113868111386811138681113868 (1)

In equation (1) GCF is the shear modulus of CF in theaxial direction 23 is the crack-free or stress-free temperaturein Celsius T is the space temperature αepoxyA is the CTE ofepoxy in the axial direction and αCFA is the CTE of CF in theaxial direction

In a thermal cycling environment ILSs must be less thanILSS As a result relation (2) for thermal fatigue is developedIn relation (2) FST is the thermal fatigue factor of safety

ILSsILSS

FST lt 1 (2)

For deriving a relation for thermomechanical fatiguemechanical fatigue expression must be added to relation (2)erefore the first thermomechanical fatigue relation isindicated as follows

ILSsILSS

FST +σM

σf

FSM lt 1 (3)

In relation (3) FSM is the factor of safety for mechanicalfatigue σM is the amplitude of appliedmechanical stress and σfis the failure mechanical stress σM and σf must be both eithercompression or tension For the highest safety both com-pression and tension stresses must be evaluated in relation (3)e next thermomechanical relation which must be evaluatedin order to have a safe design for UD CFRE is as follows

ΔTspace1113872 1113873NT

ΔTexp1113872 1113873NTf

FST +σM

σf

FSM lt 1 (4)

In the relation (4) ΔTexp is the temperature variation ateach thermal cycle in the experiment which has beenconducted on UD CFRE NTf is the number of thermalcycles to failure in the thermal cyclic experiment ΔTspace isthe temperature variation at each thermal cycle in space NTis the number of thermal cycles in space If there are two ormultiple space environments with different thermal cycleswith different temperature variations at each thermal cyclethen the following relation must be used

1113936ni0 ΔTiNTi

ΔTexp 1113872 1113873NTf

FST +σM

σf

FSM lt 1 (5)

ILSS FST FSM and NTf must be obtained by con-ducting experiments on UD CFRE According to this ther-momechanical fatigue evaluation method relations (2)ndash(4)must hold to make sure that UD CFRE is fail-safe or in otherwords it does not fail under thermomechanical fatigue

Based on the latest experiments at temperatures lessthan 0degC epoxy shows a brittle behavior erefore attemperatures less than 0degC mechanical fatigue tensile stressamplitude must be less than 600MPa (σMlt 600MPa) [6]Furthermore the number of mechanical fatigue cycles mustbe less than 105 (NMlt 105) [2] to prevent brittle fractureAdditionally experiments have shown that after epoxy hadbeen exposed to thermal cycles its glass transition tem-perature (Tg) has been reduced by 9 [5] erefore inthermal cycling environments the epoxy temperature mustbe always less than 091Tg to make sure it can carry load anddoes not fail It seems necessary to mention that for differentapplications such as aerospace and automotive the valueswhich can be chosen for mechanical and thermal fatiguefactors of safety can be different Nevertheless based on theresults of research studies and experiments which have beenconducted [2 5 6 14 15] for the thermal and mechanicalfatigue factors of safety in relations (2) (3) (4) and (5) theminimum value of 15 is recommended

3 Safe Planets Moons and Asteroids in theSolar System for UD CFRE

In this section of the manuscript thermal analysis is pro-vided to identify which planets moons and asteroids aresafe for UD CFRE in the spacecraft structure For thispurpose the following relation is employed


ILSS ILSs (6)



11138681113868111386811138681113868

11138681113868111386811138681113868 (7)



(8)



4 Future Work


5 Discussion






Sun










6 Conclusions



Data Availability




Acknowledgments


References


































ILSS ILSs (6)



11138681113868111386811138681113868

11138681113868111386811138681113868 (7)



(8)



4 Future Work


5 Discussion






Sun










6 Conclusions



Data Availability




Acknowledgments


References




































6 Conclusions



Data Availability




Acknowledgments


References


































thermomechanicalfatigueofunidirectionalcarbonfiber/epoxy

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