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[Hiroyuki Oguma](https://orcid.org/0000-0003-1104-7317), [Kimiyoshi Naito](https://orcid.org/0000-0002-3334-4876)

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[Effects of mean stress on the fatigue properties of core‐in‐sheath‐type carbon/glass hybrid thermoplastic composite rods: Experimental investigation and practical predictive method](https://mdr.nims.go.jp/datasets/608a8ef6-ba91-4bc4-bd4e-fe10c5d0f6ab)

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Effects of mean stress on the fatigue properties of core‐in‐sheath‐type carbon/glass hybrid thermoplastic composite rods: Experimental investigation and practical predictive methodOR I G I N A L AR T I C L EEffects of mean stress on the fatigue properties ofcore-in-sheath-type carbon/glass hybrid thermoplasticcomposite rods: Experimental investigation and practicalpredictive methodHiroyuki Oguma1 | Kimiyoshi Naito1,21Research Center for Structural Materials,National Institute for Materials Science,Tsukuba, Japan2Department of Aerospace Engineering,Tohoku University, Sendai, JapanCorrespondenceHiroyuki Oguma, Research Center forStructural Materials, National Institute forMaterials Science, Sengen 1-2-1, Tsukuba305-0047, Ibaraki, Japan.Email: oguma.hiroyuki@nims.go.jpFunding informationMinistry of Education, Culture, Sports,Science and Technology; Japan Scienceand Technology AgencyAbstractA systematic acquisition of fatigue test data was conducted under differentstress ratio conditions to investigate the effect of mean stress on the fatigueproperties of carbon/glass hybrid thermoplastic composite rods. Our findingsrevealed that as the stress ratio increased with a higher mean stress, the stressdependency of the fatigue life also increased, and the slope of the S-N curvebecame gentler. Under identical stress ratio conditions, hybrid rods with agreater volume fraction of carbon fiber exhibited the highest strength and amore gradual slope of the S-N curve. To account for mean stress effects, anequivalent stress amplitude was introduced, resulting in data collapse ataround 107 cycles, rendering this approach an industrially useful method topredict fatigue behavior when working with limited experimental datasets.This study presents a practical technique for estimating fatigue strength undermean stress through a weighted average efficiency and equivalent stressamplitude.KEYWORD Scarbon/glass hybrid, composite, fatigue properties, mean stress, strength estimationHighlights• This study empirically explores how mean stress influences carbon/glasshybrid rods.• Our findings unveil the correlation between material structure and fatigueperformance.• A practical method for estimating fatigue strength, which considers meanstress, is proposed.Received: 23 November 2023 Revised: 17 April 2024 Accepted: 4 May 2024DOI: 10.1111/ffe.14332This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in anymedium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.© 2024 The Authors. Fatigue & Fracture of Engineering Materials & Structures published by John Wiley & Sons Ltd.2922 Fatigue Fract Eng Mater Struct. 2024;47:2922–2933.wileyonlinelibrary.com/journal/ffehttps://orcid.org/0000-0003-1104-7317https://orcid.org/0000-0002-3334-4876mailto:oguma.hiroyuki@nims.go.jphttps://doi.org/10.1111/ffe.14332http://creativecommons.org/licenses/by-nc-nd/4.0/http://wileyonlinelibrary.com/journal/ffehttp://crossmark.crossref.org/dialog/?doi=10.1111%2Fffe.14332&domain=pdf&date_stamp=2024-05-251 | INTRODUCTIONOver the past few years, the application of continuousfiber-reinforced polymers (FRPs) in various fields,including aerospace, automotive industry, and civiland architectural engineering, has been expanding dueto their advantageous properties, such as high strength,light weight, corrosion resistance, and non-magneticproperties.1 A very efficient way to maximize theadvantages of FRPs is to apply them as a tensionedmaterials in ground anchors, prestressed concretemembers, cable-stayed bridges, suspension bridges,and so on.2–6 Their specific fatigue life depends ontheir design, layup, and manufacturing process, as wellas load conditions and environmental factors. Basicresearch on the mechanical properties of FRPs, includ-ing their application to various structures, is beingactively conducted. Consequently, data on fatigue,7,8creep, and relaxation9 are continuously gathered andevaluated to ensure their long-term safety andreliability.Recently, novel core-in-sheath carbon/glass hybridthermoplastic composite rods have been developed totake advantage of their excellent hybridization perfor-mance.10 The high strength-to-weight ratio, excellentstiffness, and high temperature resistance of carbonfibers are well known. In contrast, glass fibers offergood impact resistance, cost-effectiveness, and rela-tively easy handling during the manufacturing process.When these two types of fibers are combined in ahybrid material, their distinct properties complementeach other, resulting in the development of a compos-ite with balanced strength, stiffness, impact resistance,and cost efficiency.11 Furthermore, this hybrid materialcan be tailored to achieve a desired balance betweencarbon and glass fibers characteristics, rendering itsuitable for various industries where specific perfor-mance requirements need to be met. For example,hybrid thermoplastic composite rods have been intro-duced in Japan for use in the anti-seismic reinforce-ment of architectural structures.12In previous studies, the physical and static proper-ties of the carbon/glass hybrid thermoplastic compositerods have been investigated.13–16 In addition, the keyfactors influencing the fatigue properties of thesehybrid rods were identified through a fatigue testingcampaign.17 Based on the structure and degree of dis-persion of hybrid rods, a simple parallel model wasemployed to predict fatigue behavior. The results sug-gest that a stress-based approach could accurately esti-mate the fatigue strength of hybrid rods. Although,cyclic loading conditions under various average stres-ses are conceivable,18–20 especially when consideringthe actual use environment of these rods, the actualeffect of mean stress on their fatigue properties has notyet been the subject of detailed analysis. Consequently,the present study conducted fatigue tests on carbonfiber/glass fiber hybrid rods under various stress ratiosR (=σmin/σmax). The effects of mean stress on fatiguestrength properties were investigated. Furthermore, wediscuss various methods for predicting the criteria offailure, including the effect of mean stress using anequivalent stress amplitude.2 | EXPERIMENTAL PROCEDURES2.1 | MaterialsThe materials tested in this study were core-in-sheathcarbon/glass hybrid thermoplastic rods as shown inFigure 1, namely, CABKOMA, developed by KOMATSUMATERE Co., Ltd.12 Three types of hybrid rods with dif-ferent carbon fiber contents and carbon/glass fiber ratioswere used. Each rod was designated as 24K1P (one 24Ktow), 24K2P, or 24K3P. Details of the physical andmechanical properties are given in the literature17 and inAppendix A.2.2 | Testing conditionsUni-axial fatigue tests were performed under sinusoi-dal loading using electro-servo hydraulic testingmachines (SERVOPULSER EHF-E, Shimadzu Corpora-tion and 858 Mini Biomix, MTS System Corporation).The gripping parts of the samples were fabricated usingthe wet hand layup process,21,22 and the gauge lengthof the fatigue specimen was 50 mm.17 The stress ratio,that is, the ratio of minimum stress to maximum stressin one cycle of loading cycle, R = σmin/σmax, was set as0.1, 0.5, 0.7, or 0.9. The test frequency was 10 Hz, andthe tests were terminated at 107 cycles. All tests wereperformed under laboratory conditions at room tem-perature (RT = 23�C ± 3�C, RH = 50% ± 5%). Fractureparts were observed using a scanning electron micro-scope (SEM) (Quanta 200, FEI).3 | TEST RESULTS ANDFRACTURE PART OBSERVATIONS3.1 | Fatigue test resultsThe results of fatigue tests under various stress ratios areshown in Figure 2 as a double logarithmic plot. TheOGUMA and NAITO 2923 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensevertical axis shows the maximum stress, σmax, with thenumber of cycles to failure, Nf, on the horizontal axis.The regression lines in Figure 2 were obtained by theleast squares method using the failed sample data asfollows:σmax ¼ a Nf� �b ð1ÞThe coefficients obtained from this process are alsosummarized in Figure 2. Overall, the exponentb became larger (gentler slope of the S-N curve) withincreasing the stress ratio, suggesting that stress depen-dency of the fatigue life became larger under highermean stress conditions. Typical of carbon fiber andCFRP (Carbon-fiber reinforced polymer) fatigue testresults is the gentle slope observed in the S-Ncurve.23–25 Under the same stress ratio conditions,24K3P with higher volume fraction of carbon fiber hadthe greatest strength and the gentle slope of the S-Ncurve, indicating that the carbon fiber core part domi-nates the fatigue properties of the hybrid rod. The dif-ference in the stress dependency of the fatigue life wasmore clearly observed under R = 0.1, and the S-Ncurve of 24K1P with higher volume fraction of voidexhibited a steep slope. This, in turn, confirmed thatvoids in the hybrid rod had a greater effect under smal-ler σmin in cyclic loading.The fatigue strength at 107 cycles was obtained from theregression line according to Equation (1) and summarizedin Figure 3. The stress amplitude σa and mean stress σmeanare represented on the vertical and horizontal axes, respec-tively. The fatigue strength in stress amplitude decreasedwith increasing mean stress. Several models have been pro-posed to estimate the effect of mean stress on fatiguestrength.26 In this study, the data plots can be approximatedby a straight line, which connects the tensile strength, σL.ult(24K1P: 1423 MPa, 24K2P: 1804 MPa, 24K3P: 1837 MPa),17on the abscissa and the fatigue strength under R = 0.1;however, some of the data were plotted on the lower side ofthe line. This result indicates that the use of a linear rela-tionship to estimate the effect of mean stress on fatiguestrength may be on the dangerous side. Applying a down-ward convex curve was expected to more accurately explainthe trend of the experimental data.The equivalent stress amplitude, defined byEquation (2), was introduced to rearrange the fatigue testdata with consideration of the mean stress correction.27σeq ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiσmaxσap ð2ÞThe rearranged data were subsequently organized inthe log–log plot of the equivalent stress amplitude againstfatigue life, as shown in Figure 4, and the regression lineswere obtained with the least squares method. All datapoints with different stress ratios almost collapsed into asingle line, particular at around 107 cycles. This resultindicated that the fatigue strength in the long-life regimeunder different mean stress values could be estimated byusing single fatigue data set obtained under a single stressratio condition.FIGURE 1 Appearance of a hybridrod (θ: braid angle).17 [Colour figure canbe viewed at wileyonlinelibrary.com]2924 OGUMA and NAITO 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://wileyonlinelibrary.com3.2 | Fracture part observationsFatigue fracture occurred in the gauge part of thespecimen, which were observed by SEM. The frac-tured parts of 24K1P are shown in Figure 5A–D. Arapid catastrophic fiber breakage phase occurredunder higher stress conditions predominantly, andthe matrix polymer clung to the carbon fiber, asshown in Figure 5A,B. In contrast, splitting of thecarbon fiber bundles and pull-out of the carbon fiberswere observed in the parts fractured at low-stresslevels. In addition, carbon fiber fragments were fre-quently observed, as indicated by the arrows inFigure 5C. Under high stress ratio with high meanstress, pull-out and breakage of carbon fibers mainlyoccurred; however, fragments were not observed, asshown in Figure 5D. The fractured parts of 24K3Pare shown in Figure 6. Also, polymers clinging tocarbon fibers were more frequently observed. Thistendency was probably due to a lower volume frac-tion of void17 and related to the higher fatiguestrength and gentler slope of the S-N curve of 24K3Pthan that of 24K1P and 2P.In a prior investigation, X-ray computed tomogra-phy demonstrated that elongated and needle-likevoids were randomly dispersed throughout the bun-dles of carbon fibers.17 These voids had an impacton force transmission between the fibers and couldpotentially initiate a fatigue crack. Additionally, fiberwaviness decreased the fatigue life. Bending or(B) 24K2P(C) 24K3P(A) 24K1PFIGURE 2 Fatigue test results for (A) 24K1P, (B) 24K2P, and(C) 24K3P; the arrow indicates cut-off data. [Colour figure can beviewed at wileyonlinelibrary.com]FIGURE 3 Constant life diagram for 107 loading cycles.[Colour figure can be viewed at wileyonlinelibrary.com]OGUMA and NAITO 2925 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://wileyonlinelibrary.comhttp://wileyonlinelibrary.combuckling of carbon fibers under minimal cyclic stressin small stress ratio conditions might have resultedin localized failure. Under higher mean stress condi-tions, fibers were held in a tensioned state, and theeffect of waviness became smaller, changing the loaddistribution and stress dependency of fatigue life.4 | DISCUSSION4.1 | Fatigue strength estimation usingtest data under one stress ratio conditionIn Section 3.1, it was expected that the fatigue strengthunder different mean stress conditions could be esti-mated using only one fatigue test dataset, that is, one S-Ncurve. The fatigue test data obtained under R = 0.1 wererearranged using the equivalent stress amplitude andsummarized in Figure 7. The regression line expressed byEquation (3) was obtained with the least squares method,and the fatigue strength at 107 cycles was estimated byEquation (4), as shown in Figure 8. The lines obtainedfrom this equation were found to be in good agreementwith the test results, and therefore, the effect of meanstress on the fatigue strength was well expressed. This, inturn, indicates that the fatigue strength under differentmean stress conditions can be estimated by using onlyone S-N curve of the fatigue test, while the introductionof equivalent stress amplitude is an industrially usefulmethod to predict fatigue behavior when working withlimited experimental data sets.σeq ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiσmaxσap ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσaþσmð Þσap¼ a Nf� �b ð3Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσaþσmð Þσap¼ a 107� �b ð4Þ4.2 | Estimation of the fatigue strengthusing CFRP and GFRP test dataA previous study estimated the fatigue properties of ahybrid rod using test data of unidirectional CFRP andGFRP (Glass-fiber reinforced polymer) based on the vol-ume fraction of fibers and the weighted average efficiencyas follows17:σHybrid ¼VFCFσCF_CFRPþΦVFGFσGF_GFRP2ð5Þwhere the coefficient Φ¼ cosθ was introduced to con-sider the effect of the braid angle in the hybrid rod. VFCFand VFGF represent the volume fraction of carbon fiberFIGURE 4 Relationship between equivalent stress amplitudeand cycles to failure for (A) 24K1P, (B) 24K2P, and (C) 24K3P.[Colour figure can be viewed at wileyonlinelibrary.com]2926 OGUMA and NAITO 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://wileyonlinelibrary.comand glass fiber in the hybrid material. σCF_CFRP andσGF_GFRP are the fiber-dominant strength of CFRP andGFRP calculated as follows:σCF_CFRP ¼ σCFRPVFCF_CFRPð6aÞσGF_GFRP ¼ σGFRPVFGF_GFRPð6bÞThe fiber-dominant strength was introduced based onthe assumption that the fatigue strength of FRP is solelydue to the fibers in the FRP. A detailed explanation ofthe fiber-dominant strength can be found in Appendix B.σCFRP and σGFRP are the strength of CFRP and GFRP.VFCF_CFRP and VFGF_GFRP represent the volume fractionof carbon fibers in CFRP and glass fibers in GFRP,respectively.(A) R = 0.1, max = 1000 MPa, Nf = 170 (B) R = 0.1, max = 1000 MPa, Nf = 170(C) R = 0.1, max = 350 MPa, Nf = 1280322 (D) R = 0.9, max = 850 MPa, Nf = 1174220FIGURE 5 Images of 24K1Pfracture parts fractured during thefatigue tests (R: stress ratio; σmax:maximum stress; and Nf: number ofcycles to failure).(A) R = 0.1, max = 1000 MPa, Nf = 1046 (B) R = 0.9, max = 1800 MPa, Nf = 2034035FIGURE 6 Images of 24K3Pfracture parts fractured during thefatigue tests (R: stress ratio; σmax:maximum stress; and Nf: number ofcycles to failure).OGUMA and NAITO 2927 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseThat case was validated under specific stress ratiocondition; that is, the fatigue behavior of the hybrid rodunder R = 0.1 was predicted using CFRP and GFRPfatigue test data under the same stress ratio. In this study,fatigue test data were obtained under several stress ratioconditions, and the fatigue strength prediction methodwas validated, including the effect of mean stress.Here, the fatigue strength of 24K3P (VFCF: 46.2%,VFGF: 23.2%, θ = 35.2�) at 107 cycles is estimated. Thefatigue test data obtained by unidirectional CFRP(T700SC/#2592, VFCF_CFRP: 57.9%, Toray Industries,Inc.) and GFRP (E-glass/180�C-cured-type epoxy,VFGF_GFRP: 48.7%, Arisawa Mfg. Co., Ltd) under R = 0.1are summarized in Figure 9A. The estimated line of thehybrid rod from Equations (5) and (6), which is indi-cated by a green line in the figure, illustrates the testdata. In addition, the equivalent stress amplitude wascalculated by Equation (3); as shown in Figure 9B, thefatigue strength at 107 cycles was calculated by usingEquation (4), and the relation between mean stress andstress amplitude was estimated. The line obtained fromthis process and the fatigue strength at 107 cycles fromthe test data are shown in Figure 10. This figure clearlyshows that the estimated line could describe the testresults very well.The fatigue strength of the hybrid rod, including theinfluence of mean stress, can be predicted based onthe constituents of the rod with a weighted average effi-ciency and equivalent stress amplitude. This is probablydue to the simple core-in-sheath structure of the hybridrod; that is, the CFRP and GFRP parts exist inside andoutside the rod separately, while cross-interactions areexpected to be relatively smaller. This method is expectedto support the prediction of fatigue strength propertiesand design of hybrid materials.FIGURE 7 Fatigue test resultsunder R = 0.1. [Colour figure can beviewed at wileyonlinelibrary.com]FIGURE 8 Constant life diagram for 107 loading cycles (line:Equation 4; dashed line: connected fatigue strength at 107 cyclesunder R = 0.1 and tensile strength). [Colour figure can be viewed atwileyonlinelibrary.com]2928 OGUMA and NAITO 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://wileyonlinelibrary.comhttp://wileyonlinelibrary.com(A) Maximum stress(B) Equivalent stress amplitudeFIGURE 9 Prediction of the fatiguebehavior 24K3P hybrid rods. [Colour figurecan be viewed at wileyonlinelibrary.com]OGUMA and NAITO 2929 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://wileyonlinelibrary.com5 | CONCLUSIONSThe effect of mean stress on the fatigue properties ofcarbon/glass hybrid thermoplastic rods with differentvolume fraction of fibers was investigated, andfatigue strength at different stress ratio conditionswas predicted using one fatigue data set or fatiguetest data of pure CFRP and GFRP. The major conclu-sions of the present study can be summarized asfollows.• The difference in stress dependency of the fatiguelife was more clearly observed under small stressratio conditions. The hybrid rod with a higher vol-ume fraction of void demonstrated a steep slope ofthe S-N curve. This indicated that voids in thehybrid rod strongly affected fatigue propertiesunder smaller minimum stress conditions in cyclicloading.• The equivalent stress amplitude was introduced to con-sider a mean stress correction. All data points with dif-ferent stress ratios almost collapse into a single line,particular at around 107 cycles.• Under higher mean stress conditions, fibers were heldin a tensioned state, and the effect of waviness becamesmaller, consequently changing the load distributionand stress dependency of the fatigue life.• Fatigue strength under different mean stress condi-tions can be estimated with one S-N curve of thefatigue test, and the introduction of equivalent stressamplitude is an industrially useful method to predictfatigue behavior when working with limited experi-mental data sets.• The fatigue strength of hybrid rods, including theinfluence of mean stress, can be predicted based ontheir constituents by using a weighted average effi-ciency and equivalent stress amplitude.AUTHOR CONTRIBUTIONSHO designed and conducted the experiments, analyzedthe data, and wrote the manuscript. KN acquired fundingand edited the manuscript.ACKNOWLEDGMENTSThis research was supported by the Ministry of Educa-tion, Culture, Sports, Science and Technology (MEXT)and the Japan Science and Technology Agency (JST)through the Center of Innovation Program “Constructionof next-generation infrastructure using innovative mate-rials”—Realization of a safe and secure society that cancoexist with the Earth for centuries.CONFLICT OF INTEREST STATEMENTThe authors declare that they have no conflict of interest.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are avail-able from the corresponding author upon reasonablerequest.ORCIDHiroyuki Oguma https://orcid.org/0000-0003-1104-7317Kimiyoshi Naito https://orcid.org/0000-0002-3334-4876REFERENCES1. Sparks C, Zivanovic I, Luyckx J, Hudson W. Carbon fiber com-posite tendons for deepwater tension leg platforms. In: OffshoreTechnology Conference; 2003:OTC 15164.2. Meier U. 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J Mater. 1970;5:767-778.How to cite this article: Oguma H, Naito K.Effects of mean stress on the fatigue properties ofcore-in-sheath-type carbon/glass hybridthermoplastic composite rods: Experimentalinvestigation and practical predictive method.Fatigue Fract Eng Mater Struct. 2024;47(8):2922‐2933. doi:10.1111/ffe.14332OGUMA and NAITO 2931 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttps://www.komatsumatere.co.jp/cabkoma/en/fabo.htmlhttps://www.komatsumatere.co.jp/cabkoma/en/fabo.htmlinfo:doi/10.1111/ffe.14332TABLE A1 Physical properties ofthe hybrid rods.Diameter d [mm] Braid angle θ [�] Density ρh [g/cm3]Ave. SD Ave. SD24K1P 2.30 0.03 22.3 1.6 1.75924K2P 2.73 0.04 30.2 1.5 1.73724K3P 3.09 0.03 35.2 1.8 1.698TABLE A2 Volume fractions of the hybrid rod constituents.Carbon fiber VFCF [%] Glass fiber VFGF [%] Matrix VFM [%] Void VFV [%]Ave. SD Ave. SD Ave. SD Ave. SD24K1P 24.58 1.20 39.75 0.79 25.49 0.37 10.18 0.7624K2P 38.34 0.68 29.63 0.41 24.54 0.32 7.49 0.6024K3P 46.18 2.79 23.15 1.93 23.39 0.67 7.28 1.33TABLE A3 Mechanical properties of the hybrid rods.Tensile modulus EL [GPa] Poisson's ratio νLT Tensile strength σL.ult [MPa] Failure strain εL.ult [%]Ave. SD Ave. SD Ave. SD Ave. SD24K1P 65 3 0.39 0.08 1423 55 2.18 0.0724K2P 87 7 0.41 0.10 1804 64 2.13 0.1524K3P 91 7 0.45 0.07 1837 54 2.08 0.14APPENDIX A: MATERIAL CHARACTERISTICSThe materials tested involved carbon/glass hybrid ther-moplastic rods. Each rod had a core-in-sheath structureconsisting of carbon fiber bundle(s) covered with outerbraided glass fibers. The core carbon fiber bundle issurrounded by a braid of glass fibers in a sheath-corestructure and gently twisted to improve abrasionresistance and bending strength. Three types of hybridrods with different carbon fiber contents and carbon/glass fiber ratios were used. The physical and mechan-ical properties of the hybrid rods are summarized inTables A1 and A2, respectively. The braid angle (θ)was defined as the orientation angle of the interlacingyarns with respect to the longitudinal axis of the rod(see Figure 1). The volume fraction of each constitu-ent is listed in Table A3.2932 OGUMA and NAITO 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseAPPENDIX B: THE CONCEPT OF FIBER-DOMINANT STRENGTHThe concept of the fiber-dominant strength is describedin Figure B1. The figure shows the stress–strain relation.It is assumed that the strength of FRP is dominated bythe strength of fibers in FRP and proportional to theamount of fibers, and the contribution of the polymermatrix is considered negligible compared to that of thefibers.For example, if a high level of CFRP strength can beachieved with a small amount of carbon fibers (lowVFCF_CFRP), this can be interpreted as a high level ofstrength with 100% carbon fibers.FIGURE B1 The concept of fiber-dominant strength.OGUMA and NAITO 2933 14602695, 2024, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.14332 by National Institute For, Wiley Online Library on [02/09/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Effects of mean stress on the fatigue properties of core-in-sheath-type carbon/glass hybrid thermoplastic composite rods: E... 1  INTRODUCTION 2  EXPERIMENTAL PROCEDURES 2.1  Materials 2.2  Testing conditions 3  TEST RESULTS AND FRACTURE PART OBSERVATIONS 3.1  Fatigue test results 3.2  Fracture part observations 4  DISCUSSION 4.1  Fatigue strength estimation using test data under one stress ratio condition 4.2  Estimation of the fatigue strength using CFRP and GFRP test data 5  CONCLUSIONS AUTHOR CONTRIBUTIONS ACKNOWLEDGMENTS CONFLICT OF INTEREST STATEMENT DATA AVAILABILITY STATEMENT REFERENCES Appendix A MATERIAL CHARACTERISTICS Appendix B THE CONCEPT OF FIBER-DOMINANT STRENGTH