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[Kimiyoshi Naito](https://orcid.org/0000-0002-3334-4876), Chiemi Nagai, [Shota Kawasaki](https://orcid.org/0009-0003-8791-4824)

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[Tensile Properties and Weibull Modulus of Polymeric-Fiber-Reinforced Epoxy-Impregnated Bundle Composites](https://mdr.nims.go.jp/datasets/5123f79a-502d-422d-8e63-f598a51e3a56)

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Tensile Properties and Weibull Modulus of Polymeric-Fiber-Reinforced Epoxy-Impregnated Bundle CompositesCitation: Naito, K.; Nagai, C.;Kawasaki, S. Tensile Propertiesand Weibull Modulus ofPolymeric-Fiber-ReinforcedEpoxy-Impregnated BundleComposites. J. Compos. Sci. 2024, 8,390. https://doi.org/10.3390/jcs8100390Academic Editor: Pietro RussoReceived: 20 August 2024Revised: 24 September 2024Accepted: 28 September 2024Published: 30 September 2024Copyright: © 2024 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).ArticleTensile Properties and Weibull Modulus of Polymeric-Fiber-Reinforced Epoxy-Impregnated Bundle CompositesKimiyoshi Naito 1,2,* , Chiemi Nagai 1 and Shota Kawasaki 11 Polymer Matrix Composites Group, Research Center for Structural Materials, National Institute for MaterialsScience (NIMS), Tsukuba 305-0047, Japan; nagai.chiemi@nims.go.jp (C.N.); kawasaki.shota@nims.go.jp (S.K.)2 Department of Aerospace Engineering, Tohoku University, Sendai 980-8577, Japan* Correspondence: naito.kimiyoshi@nims.go.jp; Tel.: +81-29-859-2803Abstract: The tensile properties and the Weibull statistical distributions of the tensile strength ofpoly-(para-phenylene-2,6-benzobisoxazole) (PBO), poly-(para-phenylene terephthalamide) (PPTA),copoly-(para-phenylene-3,4′-oxydiphenylene terephthalamide (PPODTA), polyarylate (PAR), andpolyethylene (PE) polymeric fiber epoxy-impregnated bundle composites have been investigated.The results show that the Weibull modulus decreases as the tensile modulus, strength, and inverse ofthe failure strain increase. The interfacial shear properties were also examined using the microdropletcomposite. For the lower interfacial shear strength of polymeric fibers, the Weibull modulus de-creases as interfacial shear strength increases. Conversely, for the higher interfacial shear strength ofpolymeric fibers, the Weibull modulus increases as interfacial shear strength increases. Interestingly,these inflection points were also observed for the 20–30 MPa interfacial shear strength.Keywords: polymeric fibers; tensile properties; tensile modulus; tensile strength; failure strain;Weibull statistical distributions1. IntroductionCommercially available polymeric fibers, including Zylon, Kevlar, Twaron, Technora,Vectran, Dyneema, and Spectra, exhibit high tensile strength and modulus and low density(0.9–1.6 g/cm3). These fibers also demonstrate excellent strength-to-weight ratios, gooddimensional stability, and enhanced thermal and chemical resistance [1,2]. Extensive re-search has been conducted to study the properties of polymeric fibers and their composites.Marder et al. [3] characterized the adhesion properties between Zylon fiber with somesurface modifications (ultraviolet irradiation, plasma, and acidic treatments) and an epoxymatrix. Murthy et al. [4] examined the tensile behavior and fracture of Kevlar and Spec-tra fiber bundles at both quasi-static and high strain rates. Farris et al. [5] and Wu andBlackwell [6] evaluated the relationships between the structure parameters using the X-raydiffraction and mechanical properties of Technora and Kevlar fibers. Pegoretti et al. [7]examined the possibility of preparing polymer composites based on Vectran fibers. Xuand Farris [8] reported the physical, thermomechanical, and microstructural propertiesof Dyneema and Spectra fibers and their composites. In order to evaluate the mechanicalproperties of these polymeric fibers, it is necessary to have an understanding of their me-chanical characteristics. The morphology and tensile mechanical responses of single fibershave been investigated by Naito [9].Polymeric fibers are generally used in these fiber-reinforced polymer matrix compos-ites. Clarifying the mechanical properties of polymeric fibers and polymer compositesreinforced with polymer fibers is important. Bundle composites are basic fiber-reinforcedpolymer matrix composites [7,10]. One of the main possible advantages of this type ofcomposite is that many samples can be easily produced. Another important advantageis the ease of comparing the mechanical properties of the various fiber-reinforced poly-mer matrix composites that can be achieved using the same polymer matrix. This aspectJ. Compos. Sci. 2024, 8, 390. https://doi.org/10.3390/jcs8100390 https://www.mdpi.com/journal/jcshttps://doi.org/10.3390/jcs8100390https://doi.org/10.3390/jcs8100390https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://www.mdpi.com/journal/jcshttps://www.mdpi.comhttps://orcid.org/0000-0002-3334-4876https://doi.org/10.3390/jcs8100390https://www.mdpi.com/journal/jcshttps://www.mdpi.com/article/10.3390/jcs8100390?type=check_update&version=1J. Compos. Sci. 2024, 8, 390 2 of 12is particularly desirable for high-volume industries. In fact, in the field of traditionalfiber-reinforced polymer composites, bundle composites are widely used to evaluate themechanical properties of fiber-reinforced polymer matrix composites [11,12].The objective of the present study was to evaluate the tensile properties of commer-cially available polymeric fiber epoxy-impregnated bundle composites. Weibull statisticaldistributions on tensile strengths and interfacial shear properties between fiber and matrixwere also evaluated, with the objective of deriving a deeper understanding of the tensileproperties of polymeric-fiber-reinforced epoxy matrix composites. The novelty and advan-tage of this study are to reveal the modulus, strength (including Weibull modulus), failurestrain, and interfacial shear strength of polymeric fiber epoxy-impregnated composites withvarying modulus/strength of polymeric single fibers, and to comprehensively elucidatethe complex relationship between the Weibull modulus and the modulus, strength, failurestrain, and interfacial shear strength of polymeric fiber epoxy-impregnated composites.2. Materials and Methods2.1. MaterialsThe polymeric fibers used in this study [9] were PBO (poly-(para-phenylene-2,6-benzobisoxazole)) fibers (ZylonAS, ZylonHS), PPTA (poly-(para-phenylene terephthala-mide)) fibers (Kevlar29, Kevlar49, Kevlar119, Kevlar129, Twaron), PPODTA (co-poly-(para-phenylene-3,4′-oxydiphenylene terephthalamide)) fiber (Technora), PAR (liquid crystalpolymer polyarylate) fibers (VectranHT, VectranUM), and PE (polyethylene) fibers (SpectraS900, Spectra S1000, Spectra S2000, Dyneema SK60, Dyneema SK71). The Zylon/Dyneema,Kevlar, Twaron/Technora, Vectran, and Spectra fibers were supplied by Toyobo Co., Ltd.,Osaka, Japan, DuPond-Toray Co., Ltd., Teijin Techno Products, Ltd., Tokyo, Japan, KurarayCo., Ltd., Tokyo, Japan, and Honeywell International, Inc., North Carolina, USA, respec-tively. The physical and tensile properties of these polymeric fibers are listed in Table 1 [9].The density of the polymeric fibers was found to be lower than that of the carbon fibers.The tensile strength of the polymeric fibers was observed to be similar to that of the carbonfibers, while the failure strain of the polymeric fibers was determined to be higher than thatof the carbon fibers. Consequently, these polymeric fibers were selected for the preparationof the bundle composites.Table 1. Physical and tensile properties of polymeric fiber epoxy-impregnated bundle composites.PBO PPTA PPODTAZylonAS ZylonHM Kevlar29 Kevlar49 Kevlar119 Kevlar129 Twaron TechnoraFilaments (Count) *1 332 1992 956 968 956 956 1000 1000Tex (g/1000 m) *1 55.5 327 167 127 167 167 168 167Density ρf (g/cm3) *1 1.54 1.56 1.44 1.45 1.44 1.44 1.44 1.39Tensile modulus of fiberEf.ave (GPa) *2 184.5 235.8 85.3 149.1 61.4 99.0 77.9 85.7Tensile strength of fiberσf.ave (GPa) *2 5.49 5.35 3.30 3.85 2.97 3.27 3.28 3.45Failure strain of fiberεf.ave (%) *2 3.06 2.41 3.68 2.45 3.97 3.33 3.77 4.19Weibull modulus of fibermf *2 7.8 7.4 11.8 8.2 11.8 10.3 10.6 13.2Tensile modulusEb.ave (GPa)175(12)229(27)71(8)119(14)67(6)102(13)79(7)81(7)Tensile strengthσbf.ave (GPa)5.14(0.37)4.46(0.33)2.95(0.18)3.08(0.21)3.09(0.18)3.20(0.20)2.73(0.17)3.20(0.17)J. Compos. Sci. 2024, 8, 390 3 of 12Table 1. Cont.PBO PPTA PPODTAZylonAS ZylonHM Kevlar29 Kevlar49 Kevlar119 Kevlar129 Twaron TechnoraFailure strainεbf.ave (%)3.03(0.38)2.22(0.30)3.95(0.68)2.60(0.60)4.49(0.45)3.23(0.56)3.69(0.38)4.16(0.37)Weibull modulusmb15.14 13.90 18.29 16.04 18.69 17.66 17.17 20.69Fracture morphology(amount of resin in fibers) Small Small Small Small Small Small Small SmallInterfacial shear strengthτIFSS.ave (MPa)31.07(4.12)29.87(4.56)33.39(3.75)38.01(5.57)34.31(4.81)32.31(4.40)47.42(6.59)38.70(5.77)PAR PEVectranHT VectranUM SpectraS900SpectraS1000SpectraS2000DyneemaSK60DyneemaSK71600 200 120 120 60 192 192167 158 133.3 72.2 20 22 221.41 1.41 0.97 0.97 0.97 0.97 0.9782.1 104.7 54.0 85.4 128.5 71.6 107.94.23 4.12 2.18 2.71 3.26 2.60 3.223.43 3.06 7.61 6.89 4.60 3.90 3.6911.9 9.4 15.2 13.3 10.0 11.3 11.079(9)105(6)59(7)78(10)118(26)75(10)118(13)3.32(0.19)3.16(0.20)2.09(0.10)2.57(0.13)3.27(0.20)2.36(0.14)2.79(0.17)3.73(0.45)2.74(0.39)5.38(0.68)4.07(0.46)3.36(0.59)3.61(0.30)3.26(0.65)18.20 16.39 22.94 20.46 17.96 18.48 18.42No No No No No No No18.75(3.03)12.48(2.81)6.04(0.98)10.62(1.93)11.80(2.11)10.66(1.27)14.81(2.03)*1 Producer’s data sheet ZylonAS and HM: Catalog for PBO Fiber Zylon, Toyobo Co., Ltd., Osaka, Japan, 2005.Kevlar29, 49, 119, and 129: Catalog for DuPont Kevlar, DuPont-Toray Co., Ltd., Tokyo, Japan, 2008. Twaron:Catalog for Twaron, Teijin Techno Products, Ltd., Tokyo, Japan, 2009. Technora: Catalog for High Strength AramidFiber Technola, Teijin Techno Products, Ltd., Tokyo, Japan, 2009. VectranHT and UM: Catalog for Vectran, KurarayCo. Ltd., Osaka, Japan, 2006. Spectra900, 1000, and 2000: Catalog for high-strength, lightweight polyethylene fiber,Honeywell International, Inc., Charlotte, NC, USA, 2007. Dyneema SK60 and SK71: Catalog for Dyneema, ToyoboCo., Ltd., Osaka, Japan, 2009. *2 Single fiber tensile data (25 mm gage length, corrected for machine compliance)from previous investigation [9]. Tensile testing of the polymeric fibers was conducted based on ASTM C1557.( ) indicate standard deviations.The solution of thermoset epoxy consists of JER813 (diglycidyl ether of bisphenol A)epoxy and YH306 (acid anhydride grade hardener) at a ratio of JER813:YH306 = 100:124 byweight. The JER813/YH306 were supplied by Mitsubishi Chemical Corp., Tokyo, Japan.The bundles were impregnated with a liquid solution, and excess resin was removedwith a roller. The bundles were cured at a temperature rise rate of 3 ◦C/min at 150 ◦C for6 h (12 h at 120 ◦C for PE fiber bundle composite) with tension applied by hanging a weighton the bundle. The volume fractions of polymeric fibers were controlled to 50% ± 5%.J. Compos. Sci. 2024, 8, 390 4 of 122.2. Tensile TestTensile tests of the bundle composites (gage length, L of 25 mm) were performed usinga universal testing machine (Autograph AG-series, Shimadzu Corp., Kyoto, Japan) with a5 kN load cell and active gripping systems. Crosshead speeds of 5 mm/min were applied.The tensile test provides a load P as a function of extension U* curve. The tensile stress σand strain ε were calculated according to the following formulae:σb =PS=P ρ fTex, (1)εb =U∗L∗ , (2)The total cross-sectional area of filaments in a bundle, denoted by S, can be calculatedfrom the bundle tex, Tex, and density, ρf, of the fibers. From Equation (1), it can be seen thatthe fiber bundle bears all the load, with the effects of the resin being ignored. Consequently,the stress experienced by the fiber bundle is considered, but the impact of the polymericfiber volume fraction is not. L* is the distance between targets and is ≈ 15 mm. Theextension U* was measured using a non-contact video extensometer (DVE-201, ShimadzuCorp.). All tests were performed in a laboratory environment under ambient conditions(23 ◦C ± 3 ◦C and 50% ± 5% relative humidity). Thirty specimens were tested, includingstress–strain analysis.After testing, the fracture surfaces of the specimens were osmium coated (HPC-1SW,Vacuum Device, Ibaraki, Japan) and then examined using a high-resolution scanning elec-tron microscope (Quanta 200FEG, Thermo Fisher Scientific, Tokyo, Japan) at an operatingvoltage of 5 kV.The specimen preparation and test procedures were conducted in accordance with thestandards in JIS R7608 and ISO 10618.2.3. Interfacial Shear Strength TestThe interfacial shear properties were evaluated using microdroplet composites [13,14].A single filament of the polymeric fiber was fastened to a thin stainless steel holder withthe epoxy matrix (JER813/YH306). The microdroplet composites were cured under thesame conditions as the bundle composites.Interfacial shear tests were conducted using an interfacial micro-bond evaluationinstrument (HM410, Tohei Sangyo, Tokyo, Japan) with a 5 N load cell and a 0.12 mm/mincrosshead speed. All tests were conducted under laboratory conditions. A total of100 samples were tested for each instance.3. Results and Discussion3.1. Stress–Strain RelationshipFigure 1 shows typical tensile stress–strain (σ-ε) curves for the PBO, PPTA, PPODTA,PAR, and PE polymeric fiber epoxy-impregnated bundle composites.For the PBO, PPTA, PPODTA, and PAR fiber bundle composites, the stress–straincurves exhibit slight nonlinear behavior. The stress–strain curve for the PE fiber bundlecomposites also exhibits a significant degree of nonlinearity. The tensile strengths of allpolymeric fiber bundle composites exhibited high values (exceeding 2 GPa), which werecomparable to those of carbon fiber bundle composites. Furthermore, the failure strains ofthese polymeric fiber bundle composites demonstrated high values (exceeding 2%), whichwere higher than those of carbon fiber bundle composites (less than 2%). Additionally,the tensile responses of these fiber bundle composites exhibited linear behaviors duringthe initial stage of loading. The design of the strength criterion was straightforward, andthese composites are among the most robust load-bearing components in a polymericfiber-reinforced composite. However, it is crucial to assess the interfacial shear strength,J. Compos. Sci. 2024, 8, 390 5 of 12particularly in PBO and PE fiber bundle composites. Similar behaviors were observed forthe PBO, PPTA, PAR, and PE composites in previous studies [3,4,7].J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 5 of 14     (a) (b) Figure 1. Typical tensile stress–strain curves for the PBO, PPTA, PPODTA, PAR, and PE polymeric fiber epoxy-impregnated bundle composites: (a) PBO, PPTA, and PPODTA fiber bundle composites; (b) PAR and PE fiber bundle composites. For the PBO, PPTA, PPODTA, and PAR fiber bundle composites, the stress–strain curves exhibit slight nonlinear behavior. The stress–strain curve for the PE fiber bundle composites also exhibits a significant degree of nonlinearity. The tensile strengths of all polymeric fiber bundle composites exhibited high values (exceeding 2 GPa), which were comparable to those of carbon fiber bundle composites. Furthermore, the failure strains of these polymeric fiber bundle composites demonstrated high values (exceeding 2%), which were higher than those of carbon fiber bundle composites (less than 2%). Additionally, the tensile responses of these fiber bundle composites exhibited linear behaviors during the initial stage of loading. The design of the strength criterion was straightforward, and these composites are among the most robust load-bearing components in a polymeric fiber-reinforced composite. However, it is crucial to assess the interfacial shear strength, particularly in PBO and PE fiber bundle composites. Similar behaviors were observed for the PBO, PPTA, PAR, and PE composites in previous studies [3,4,7]. 3.2. Tensile Modulus, Strength, and Failure Strain The tensile modulus Eb was calculated using a least square method for the straight-line section of the stress–strain curve. The tensile strength of the polymer fiber bundle composites σbf was calculated as 𝜎 = =  , (3)where Pmax is the maximum fracture load of the specimen. The failure strain εbf was defined as the maximum strain. The average values Eb.ave, σbf.ave, and εbf.ave are summarized in Table 1. The Eb.ave, σbf.ave, and εbf.ave of these fiber bundle composites were almost equal to those given in the manufacturers’ product data. The PBO fiber bundle composites have σbf.ave values of 5.14 GPa (ZylonAS) and 4.46 GPa (ZylonHM), and εbf.ave values of 3.03% (ZylonAS) and 2.22% (ZylomHM). The PPTA, PPODTA, PAR, and PE fiber bundle composites have σbf.ave values ranging from 2.09 to 3.32 GPa and εbf.ave values ranging from 2.60 to 5.38%, respectively. 3.3. Weibull Modulus The Weibull statistical distribution of strength is attributed to the nature and distribution of the flaws, which are present in the fibers; while the strength is assumed to TechnolaZylonHMTensile strain, εb (%)Tensile stress,σb(GPa)01234560 1 2 3 4 5 6Kevlar49Kevlar29Kevlar119Kevlar129TwaronTensile strain, εb (%)Tensile stress,σb(GPa)01234560 1 2 3 4 5 6VectranHTVectranUMS900S1000S2000 SK60SK71Figure 1. Typical tensile stress–strain curves for the PBO, PPTA, PPODTA, PAR, and PE polymericfiber epoxy-impregnated bundle composites: (a) PBO, PPTA, and PPODTA fiber bundle composites;(b) PAR and PE fiber bundle composites.3.2. Tensile Modulus, Strength, and Failure StrainThe tensile modulus Eb was calculated using a least square method for the straight-line section of the stress–strain curve. The tensile strength of the polymer fiber bundlecomposites σbf was calculated asσb f =PmaxS=Pmax ρ fTex, (3)where Pmax is the maximum fracture load of the specimen. The failure strain εbf was definedas the maximum strain. The average values Eb.ave, σbf.ave, and εbf.ave are summarized inTable 1.The Eb.ave, σbf.ave, and εbf.ave of these fiber bundle composites were almost equal tothose given in the manufacturers’ product data. The PBO fiber bundle composites haveσbf.ave values of 5.14 GPa (ZylonAS) and 4.46 GPa (ZylonHM), and εbf.ave values of 3.03%(ZylonAS) and 2.22% (ZylomHM). The PPTA, PPODTA, PAR, and PE fiber bundle compos-ites have σbf.ave values ranging from 2.09 to 3.32 GPa and εbf.ave values ranging from 2.60 to5.38%, respectively.3.3. Weibull ModulusThe Weibull statistical distribution of strength is attributed to the nature and distri-bution of the flaws, which are present in the fibers; while the strength is assumed to becontrolled by defects, which are statistically distributed. The weakest link hypothesis istaken into account in the Weibull approach.The results presented in Table 1 demonstrate a notable dispersion in tensile strength.The statistical distribution is typically described by the Weibull equation [15,16]. Thetwo-parameter Weibull distribution is defined as follows:PF = 1 − e−(σb fσb0)mb(4)J. Compos. Sci. 2024, 8, 390 6 of 12where PF is the cumulative probability of failure at an applied tensile strength (σbf), mb isthe Weibull modulus, and σb0 is the Weibull scale parameter. The cumulative probability offailure PF under a particular stress is defined as follows:PF =in + 1, (5)where i is the number of fiber bundles that have broken at or below a stress level and nis the total number of fiber bundles tested. Rearrangement of the two-parameter Weibullstatistical distribution expression (Equation (4)) yields the following:ln{ln(11 − PF)}= mbln(σb f)− mbln(σb0), (6)Consequently, the mb can be derived through linear regression from a Weibull plot ofEquation (6).Figure 2 shows the Weibull plots of the ZylonHM, Kevlar49, Technora, VectranHT,and S900 fiber bundle composites.J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 6 of 14   be controlled by defects, which are statistically distributed. The weakest link hypothesis is taken into account in the Weibull approach. The results presented in Table 1 demonstrate a notable dispersion in tensile strength. The statistical distribution is typically described by the Weibull equation [15,16]. The two-parameter Weibull distribution is defined as follows: 𝑃 = 1 − e  (4)where PF is the cumulative probability of failure at an applied tensile strength (σbf), mb is the Weibull modulus, and σb0 is the Weibull scale parameter. The cumulative probability of failure PF under a particular stress is defined as follows: 𝑃 = , (5)where i is the number of fiber bundles that have broken at or below a stress level and n is the total number of fiber bundles tested. Rearrangement of the two-parameter Weibull statistical distribution expression (Equation (4)) yields the following: 𝑙𝑛 𝑙𝑛 = 𝑚 𝑙𝑛 𝜎 − 𝑚 𝑙𝑛 𝜎 , (6)Consequently, the mb can be derived through linear regression from a Weibull plot of Equation (6). Figure 2 shows the Weibull plots of the ZylonHM, Kevlar49, Technora, VectranHT, and S900 fiber bundle composites.  Figure 2. Weibull plots of ZylonHM, Kevlar49, Technora, VectranHT, and S900 fiber bundle composites. The mb for the ZylonHM, Kevlar49, Technora, VectranHT, and S900 fiber bundle composites were calculated to be 13.90, 16.04, 20.69, 18.20, and 22.94, respectively. The mb values are also summarized in Table 1. The results clearly show that the high modulus ZylonHM fiber bundle composite has the lowest mb and εbf, while the high ductility S900 fiber bundle composite has the highest mb and εbf. 3.4. Weibull Modulus vs. Tensile Modulus and Strength and Failure Stain In the previous investigation of single carbon [17] and polymeric fibers [9], it was observed that the Weibull modulus decreased as the tensile modulus and strength increased and the failure strain decreased. Additionally, a linear relationship between the tensile modulus, failure strain, and the Weibull modulus was identified on the log–log scale. -5-4-3-2-10123Tensile strength, σbf (GPa)1 2 3 4 5 6 7 8mb (S900) = 22.94mb (VectranHT) = 18.20mb (Technola) = 20.69mb (Kevlar49) = 16.04 mb (ZylonHM) = 13.90Figure 2. Weibull plots of ZylonHM, Kevlar49, Technora, VectranHT, and S900 fiber bundle composites.The mb for the ZylonHM, Kevlar49, Technora, VectranHT, and S900 fiber bundlecomposites were calculated to be 13.90, 16.04, 20.69, 18.20, and 22.94, respectively. The mbvalues are also summarized in Table 1. The results clearly show that the high modulusZylonHM fiber bundle composite has the lowest mb and εbf, while the high ductility S900fiber bundle composite has the highest mb and εbf.3.4. Weibull Modulus vs. Tensile Modulus and Strength and Failure StainIn the previous investigation of single carbon [17] and polymeric fibers [9], it wasobserved that the Weibull modulus decreased as the tensile modulus and strength increasedand the failure strain decreased. Additionally, a linear relationship between the tensilemodulus, failure strain, and the Weibull modulus was identified on the log–log scale.Figure 3 shows a representation of mb as a function of Eb.ave, σbf.ave, and εbf.ave for thePBO, PPTA, PPODTA, PAR, and PE fiber bundle composites. The results for the singlepolymeric [9], single carbon fibers of the same gage length (25 mm) [17], and unidirectionalcarbon fiber laminate composites [18] are also shown in this figure (Unidirectional carbonfiber laminate composites were produced using epoxy or cyanate-ester matrix-based unidi-rectional CFRP prepreg material P3060-15 (fiber: T300, matrix: #3601), P3212G-25 (fiber:T700SC, matrix: #3631), QC133-149A (fiber: IM600, matrix: 133), M60JB-WF150/EX-1515(fiber: M60JB, matrix: EX-1515), K13C-150grm/EX-1515 (fiber: K13C, matrix: EX-1515),HYEJ16M95DHX1 (fiber: K13D, matrix: HX1), and E0536A-10N (fiber: XN-05, matrix:J. Compos. Sci. 2024, 8, 390 7 of 12NM-.35). Fiber orientation of the laminate composites were set to [0]8 ([0]4 for P3212G-25)and the laminate composites were fabricated by an autoclave (Ashida Mfg. Co., Ltd., Osaka,Japan, ACA Series) in the laboratory. The rectangular straight-sided tensile test specimenswith length of 200 mm (gage length 100 mm) and width of 10 mm were used).J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 7 of 14   Figure 3 shows a representation of mb as a function of Eb.ave, σbf.ave, and εbf.ave for the PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites. The results for the single polymeric [9], single carbon fibers of the same gage length (25 mm) [17], and unidirectional carbon fiber laminate composites [18] are also shown in this figure (Unidirectional carbon fiber laminate composites were produced using epoxy or cyanate-ester matrix-based unidirectional CFRP prepreg material P3060-15 (fiber: T300, matrix: #3601), P3212G-25 (fiber: T700SC, matrix: #3631), QC133-149A (fiber: IM600, matrix: 133), M60JB-WF150/EX-1515 (fiber: M60JB, matrix: EX-1515), K13C-150grm/EX-1515 (fiber: K13C, matrix: EX-1515), HYEJ16M95DHX1 (fiber: K13D, matrix: HX1), and E0536A-10N (fiber: XN-05, matrix: NM-.35). Fiber orientation of the laminate composites were set to [0]8 ([0]4 for P3212G-25) and the laminate composites were fabricated by an autoclave (Ashida Mfg. Co., Ltd., Osaka, Japan, ACA Series) in the laboratory. The rectangular straight-sided tensile test specimens with length of 200 mm (gage length 100 mm) and width of 10 mm were used).    (a) (b)  (c) Figure 3. Relationship between the Weibull modulus and the tensile modulus and strength and failure strain of PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites: (a) tensile modulus; (b) tensile strength; (c) failure strain. From the viewpoints of the Weibull modulus distribution, it can be seen that for all polymeric fiber bundle composites, the mb tends to decrease with an increase in the Eb.ave and σbf.ave and a decrease in the εbf.ave. Additionally, there is an almost linear relation between the Eb.ave, σbf.ave, εbf.ave, and mb on a log–log scale. For the carbon fiber bundle composites, the mb also decreases with an increase in the Eb.ave and a decrease in the εbf.ave. There is also an almost linear relation between the Eb.ave, εbf.ave, and mb on the log–log scale. Tensile modulus, Eb.ave (Eave) (GPa)Weibull modulus, mb(mf)bundle composites45710203050PBOPPTAPPODTASingle fibers20 50 70 100 200 1000500PARPECFTensile strength, σbf.ave (σf.ave) (GPa)Weibull modulus, mb(mf)bundle composites45710203050Single fibers1 2 3 4 5 6 7 8PBOPPTAPPODTAPARPECFFailure strain, εbf.ave (εf.ave) (%)Weibull modulus, mb(mf)bundle composites45710203050Single fibers0.2 102 3 5 710.5PBOPPTAPPODTAPARPECFFigure 3. Relationship between the Weibull modulus and the tensile modulus and strength andfailure strain of PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites: (a) tensile modulus;(b) tensile strength; (c) failure strain.From the viewpoints of the Weibull modulus distribution, it can be seen that for allpolymeric fiber bundle composites, the mb tends to decrease with an increase in the Eb.aveand σbf.ave and a decrease in the εbf.ave. Additionally, there is an almost linear relationbetween the Eb.ave, σbf.ave, εbf.ave, and mb on a log–log scale. For the carbon fiber bundlecomposites, the mb also decreases with an increase in the Eb.ave and a decrease in the εbf.ave.There is also an almost linear relation between the Eb.ave, εbf.ave, and mb on the log–log scale.The mb also decreases with an increase in the σbf.ave. However, a clear linear relationship onthe log–log scale was not observed between the σbf.ave and the mb.The Weibull modulus is indicative of the strength distribution, while the tensilemodulus is indicative of flaw sensitivity [19,20]. These relationships indicate that the tensilestrength distribution of fibers is strongly dependent on the flaw sensitivity and strengthvalues, and are clearly observed in Figure 3a,b. Weibull modulus values highly dependon the failure strain, as illustrated in Figure 3c, due to the nonlinear tensile responsesof the polymeric fibers and the ductile nature of the fracture process. The εbf.ave is avaluable parameter for illustrating the differences in tensile properties, including the mb. ForJ. Compos. Sci. 2024, 8, 390 8 of 12example, the higher the Eb.ave, the broader the distribution of tensile strength. Consequently,higher σbf.ave and lower εbf.ave lead to a broader distribution of tensile strength.3.5. Fracture MorphologyScanning electron microscope (SEM) micrographs of longitudinal-sectional views forthe tensile fractured surfaces of the ZylonAS, Kevlar29, Technora, VectranHT, and DyneemaSK60 fiber bundle composites are shown in Figure 4.J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 9 of 14(a) (b)(c) (d)(e)Figure 4. SEM longitudinal views of the tensile fractured surfaces of the polymeric fiber bundle composites: (a) ZylonAS; (b) Kevlar29; (c) Technora; (d) VectranHT; (e) Dyneema SK60.A report indicated that a unidirectional carbon-fiber-reinforced polymer (CFRP) specimen exhibited axial tension failure, resulting in a fracture in the transverse direction at multiple points, which was associated with longitudinal splitting of the composite, resulting in a brush-like fracture surface [21]. This suggested that fiber-dominated fracture behavior was present [10]. The bundle composites exhibit smooth fiber surfaces with a Figure 4. SEM longitudinal views of the tensile fractured surfaces of the polymeric fiber bundlecomposites: (a) ZylonAS; (b) Kevlar29; (c) Technora; (d) VectranHT; (e) Dyneema SK60.J. Compos. Sci. 2024, 8, 390 9 of 12A report indicated that a unidirectional carbon-fiber-reinforced polymer (CFRP) spec-imen exhibited axial tension failure, resulting in a fracture in the transverse direction atmultiple points, which was associated with longitudinal splitting of the composite, re-sulting in a brush-like fracture surface [21]. This suggested that fiber-dominated fracturebehavior was present [10]. The bundle composites exhibit smooth fiber surfaces with asmall amount of resin. The fracture morphology (amount of resin in polymeric fibers)is roughly summarized in Table 1. It was difficult to establish the relationship betweenthe fracture morphology and tensile properties. The polymeric fibers may result in weakinterfacial properties (strength) between fiber and matrix. Similar fracture behaviors wereobserved for the PPTA and PE in a previous study [4].3.6. Interfacial PropertyThe load was found to be almost linearly proportional to the displacement, andinterfacial fracture was observed for all microdroplet composites.The interfacial shear strength τIFSS was calculated as follows:τIFSS =Pmaxπd f le, (7)where Pmax, df, and le are the maximum fracture load, diameter of fibers, and embeddedlength of the individual microdroplet, respectively. This equation is predicated on theassumption that the shear lag model is that of a cylindrical fiber embedded in a surroundingmatrix [14].Figure 5 shows the interfacial shear strength τIFSS vs. the embedded length le obtainedfrom the microdroplet test. The average value τIFSS.ave is summarized in Table 1.J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 10 of 14   small amount of resin. The fracture morphology (amount of resin in polymeric fibers) is roughly summarized in Table 1. It was difficult to establish the relationship between the fracture morphology and tensile properties. The polymeric fibers may result in weak interfacial properties (strength) between fiber and matrix. Similar fracture behaviors were observed for the PPTA and PE in a previous study [4]. 3.6. Interfacial Property The load was found to be almost linearly proportional to the displacement, and interfacial fracture was observed for all microdroplet composites. The interfacial shear strength τIFSS was calculated as follows: 𝜏 = , (7)where Pmax, df, and le are the maximum fracture load, diameter of fibers, and embedded length of the individual microdroplet, respectively. This equation is predicated on the assumption that the shear lag model is that of a cylindrical fiber embedded in a surrounding matrix [14]. Figure 5 shows the interfacial shear strength τIFSS vs. the embedded length le obtained from the microdroplet test. The average value τIFSS.ave is summarized in Table 1.   (a) (b) Figure 5. Interfacial shear strength-embedded length curves for the ZylonHM, Kevlar49, Technora, VectranHT, and S900 polymeric fiber microdroplet composites: (a) ZylonHM, Kevlar49, and Technora fibers; (b) VectranHT and S900 fibers. The τIFSS.ave values of the microdroplet composites of the PBO, PPTA, and PPODTA fibers are 35.64 ± 5.68 MPa, which are 193% higher than those of the PAR and PE fiber samples (12.17 ± 3.93 MPa), although the τIFSS.ave of all polymeric fiber microdroplet composites were lower than those of carbon fiber samples (47.75 ± 16.38 MPa). There is no difference in the fracture surface morphology of the microdroplet composites among all polymeric fibers. The microdroplet composites have smooth original fiber surfaces with a small amount of resin. Similar results were observed in Figure 4. A correlation was identified between the fracture morphology and interfacial shear strength. Bundle composites with smooth original fiber surfaces exhibited lower interfacial shear strength. The interfacial shear strengths using a single fiber pull-out test for the PBO fiber with several modifications were measured in ref. [3]. 3.7. Weibull Modulus vs. Interfacial Shear Strength Embedded length, le (μm)Interfacial shear strength, τIFSS(MPa)020406080ZylonHMKevlar49Technora30 40 50 60 70Embedded length, le (μm)Interfacial shear strength, τIFSS(MPa)010203040VectranHTS9000 100 200 300 400Figure 5. Interfacial shear strength-embedded length curves for the ZylonHM, Kevlar49, Technora,VectranHT, and S900 polymeric fiber microdroplet composites: (a) ZylonHM, Kevlar49, and Technorafibers; (b) VectranHT and S900 fibers.The τIFSS.ave values of the microdroplet composites of the PBO, PPTA, and PPODTAfibers are 35.64 ± 5.68 MPa, which are 193% higher than those of the PAR and PE fibersamples (12.17 ± 3.93 MPa), although the τIFSS.ave of all polymeric fiber microdropletcomposites were lower than those of carbon fiber samples (47.75 ± 16.38 MPa). There isno difference in the fracture surface morphology of the microdroplet composites amongall polymeric fibers. The microdroplet composites have smooth original fiber surfaceswith a small amount of resin. Similar results were observed in Figure 4. A correlationwas identified between the fracture morphology and interfacial shear strength. Bundlecomposites with smooth original fiber surfaces exhibited lower interfacial shear strength.J. Compos. Sci. 2024, 8, 390 10 of 12The interfacial shear strengths using a single fiber pull-out test for the PBO fiber withseveral modifications were measured in ref. [3].3.7. Weibull Modulus vs. Interfacial Shear StrengthFigure 6 is a representation of the mb as a function of the τIFSS.ave for the PBO, PPTA,PPODTA, PAR, and PE fiber bundle composites. The results for the unidirectional carbonfiber laminate composites [18] are also shown in this figure.J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 11 of 14   Figure 6 is a representation of the mb as a function of the τIFSS.ave for the PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites. The results for the unidirectional carbon fiber laminate composites [18] are also shown in this figure.  Figure 6. Weibull modulus of PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites as a function of the interfacial shear strength. For the lower τIFSS.ave of PAR and PE fibers, the mb decreases with an increase in the τIFSS.ave and there is an almost linear relation between the τIFSS.ave and the mb on a log–log scale. Conversely, for the higher τIFSS.ave of the PBO, PPTA, PPODTA fibers and carbon fibers, the mb increases with an increase in the τIFSS.ave and there is also an almost linear relation between the τIFSS.ave and the mb on a log–log scale. There seems to be an inflection point in the 20–30 MPa interfacial shear strength. The ratio of the tensile modulus (Eb/E) and strength (σbf/σf) in fiber bundle composites is less sensitive to the interfacial shear strength because the bundle composites are the basic tensile load-bearing component [10] and shows fiber-dominated behavior. Actually, Eb/E = 1.00 ± 0.09 and σbf/σf = 0.90 ± 0.08 for all bundle composites including carbon fibers. However, the ratio of the failure strain and the Weibull modulus in fiber bundle composites is related to the interfacial shear strength. Figure 7 shows the ratio of the failure strain (εbf/εf) and the Weibull modulus (mb/m) of the PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites as a function of the interfacial shear strength. The results for the single carbon fibers [17] and unidirectional carbon fiber laminate composites [18] are also shown in this figure.   Interfacial shear strength, τIFSS.ave (MPa)Weibull modulus, mb457102030504 10010 20 30 506 708PAR, PEPBO, PPTA, PPODTAPBOPPTAPPODTAPARPECFCFFigure 6. Weibull modulus of PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites as afunction of the interfacial shear strength.For the lower τIFSS.ave of PAR and PE fibers, the mb decreases with an increase in theτIFSS.ave and there is an almost linear relation between the τIFSS.ave and the mb on a log–logscale. Conversely, for the higher τIFSS.ave of the PBO, PPTA, PPODTA fibers and carbonfibers, the mb increases with an increase in the τIFSS.ave and there is also an almost linearrelation between the τIFSS.ave and the mb on a log–log scale. There seems to be an inflectionpoint in the 20–30 MPa interfacial shear strength.The ratio of the tensile modulus (Eb/E) and strength (σbf/σf) in fiber bundle compositesis less sensitive to the interfacial shear strength because the bundle composites are the basictensile load-bearing component [10] and shows fiber-dominated behavior. Actually, Eb/E= 1.00 ± 0.09 and σbf/σf = 0.90 ± 0.08 for all bundle composites including carbon fibers.However, the ratio of the failure strain and the Weibull modulus in fiber bundle compositesis related to the interfacial shear strength. Figure 7 shows the ratio of the failure strain(εbf/εf) and the Weibull modulus (mb/m) of the PBO, PPTA, PPODTA, PAR, and PE fiberbundle composites as a function of the interfacial shear strength. The results for the singlecarbon fibers [17] and unidirectional carbon fiber laminate composites [18] are also shownin this figure.The failure strain (εbf/εf) and the Weibull modulus (mb/m) ratios of the polymericfiber bundle composites increase with an increase in the interfacial shear strength, althoughthe εbf/εf of the carbon fiber composites showed almost equal values among the low-highinterfacial shear strength range because of lower failure strain compared with the polymericfibers. Interestingly, these inflection points were also observed for the 20–30 MPa interfacialshear strength.The Weibull modulus of tensile strengths for bundle composites (as well as thetensile modulus and strength and failure strain) is typically dependent on that of thefiber-reinforced composites (laminate composites) [10,18]. However, the interfacial shearstrengths are also dependent on the Weibull modulus of the fiber-reinforced compos-ites. These relationships, as illustrated in Figures 3 and 6, are considered useful formaterial selection.J. Compos. Sci. 2024, 8, 390 11 of 12J. Compos. Sci. 2024, 8, x FOR PEER REVIEW 12 of 14      (a) (b) Figure 7. Failure strain and Weibull modulus ratios of the PBO, PPTA, PPODTA, PAR, and PE polymeric fiber bundle composites as a function of the interfacial shear strength: (a) failure strain ratio; (b) Weibull modulus ratio. The failure strain (εbf/εf) and the Weibull modulus (mb/m) ratios of the polymeric fiber bundle composites increase with an increase in the interfacial shear strength, although the εbf/εf of the carbon fiber composites showed almost equal values among the low-high interfacial shear strength range because of lower failure strain compared with the polymeric fibers. Interestingly, these inflection points were also observed for the 20–30 MPa interfacial shear strength. The Weibull modulus of tensile strengths for bundle composites (as well as the tensile modulus and strength and failure strain) is typically dependent on that of the fiber-reinforced composites (laminate composites) [10,18]. However, the interfacial shear strengths are also dependent on the Weibull modulus of the fiber-reinforced composites. These relationships, as illustrated in Figures 3 and 6, are considered useful for material selection. The polymer fibers reinforcing the epoxy composites demonstrated enhanced axial tensile properties, although the interfacial shear properties of PAR and PE fibers exhibited low values. This is due to the fact that the bundle composites display fiber-dominated behavior. Polymeric-fiber-reinforced polymer composites are poised to become dominant materials in lightweight tension and reinforcing members for transportation and infrastructure applications. 4. Conclusions The tensile properties of PBO, PPTA, PPODTA, PAR, and PE polymeric fiber bundle composites have been investigated. Weibull modulus values of the tensile strength for the PBO, PPTA, PPODTA, PAR, and PE fiber bundle composites were also characterized. In addition, the interfacial shear properties were evaluated using microdroplet composites. The results can be briefly summarized as follows: 1. The Weibull modulus decreases as the tensile modulus and strength increase and the failure strain decreases. In addition, there is a nearly linear relationship between the tensile modulus and strength and failure strain and the Weibull modulus on a log–log scale. 2. For the lower interfacial shear strength polymeric fibers, the Weibull modulus decreases as the interfacial shear strength increases. Conversely, for the higher Interfacial shear strength, τIFSS.ave (MPa)Failure strain ratio, εbf/ε f00.51.01.52.04 10010 20 30 506 708PBOPPTAPPODTAPARPECFInterfacial shear strength, τIFSS.ave (MPa)Weibull modulus ratio, mb/m0123454 10010 20 30 506 708PBOPPTAPPODTAPARPECFFigure 7. Failure strain and Weibull modulus ratios of the PBO, PPTA, PPODTA, PAR, and PEpolymeric fiber bundle composites as a function of the interfacial shear strength: (a) failure strainratio; (b) Weibull modulus ratio.The polymer fibers reinforcing the epoxy composites demonstrated enhanced axialtensile properties, although the interfacial shear properties of PAR and PE fibers exhibitedlow values. This is due to the fact that the bundle composites display fiber-dominatedbehavior. Polymeric-fiber-reinforced polymer composites are poised to become domi-nant materials in lightweight tension and reinforcing members for transportation andinfrastructure applications.4. ConclusionsThe tensile properties of PBO, PPTA, PPODTA, PAR, and PE polymeric fiber bundlecomposites have been investigated. Weibull modulus values of the tensile strength for thePBO, PPTA, PPODTA, PAR, and PE fiber bundle composites were also characterized. Inaddition, the interfacial shear properties were evaluated using microdroplet composites.The results can be briefly summarized as follows:1. The Weibull modulus decreases as the tensile modulus and strength increase andthe failure strain decreases. In addition, there is a nearly linear relationship betweenthe tensile modulus and strength and failure strain and the Weibull modulus on alog–log scale.2. For the lower interfacial shear strength polymeric fibers, the Weibull modulus de-creases as the interfacial shear strength increases. Conversely, for the higher interfacialshear strength polymeric fibers, the Weibull modulus increases as the interfacial shearstrength increases. There is also an almost linear relation between the interfacial shearstrength and the Weibull modulus on a log–log scale.Author Contributions: K.N.: Conceptualization, Methodology, Software, Validation, Formal analysis,Investigation, Resources, Data curation, Writing–original draft, Writing–review and editing, Visual-ization, Supervision. C.N.: Validation, Investigation, Writing–review and editing. S.K.: Validation,Investigation, Writing–review and editing. All authors have read and agreed to the published versionof the manuscript.Funding: This paper is based on results obtained from a future pioneering project commissioned bythe New Energy and Industrial Technology Development Organization (NEDO) and the InnovativeScience and Technology Initiative for Security Projects (JPJ004596) commissioned by the Acquisition,Technology & Logistics Agency (ATLA).Data Availability Statement: The datasets supporting the conclusions of this article are includedwithin the article.J. Compos. Sci. 2024, 8, 390 12 of 12Conflicts of Interest: The authors declared no potential conflicts of interest with respect to theresearch, authorship, and/or publication of this article.References1. Kumar, S.; Wang, Y. Fibers, fabrics, and fillers. In Composite Engineering Handbook; Mallick, P.K., Ed.; Marcel Dekker: New York,NY, USA, 1997; pp. 51–100.2. Hersh, S.P. Polyblend fibers. 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Technol. 1994, 52, 449–466. [CrossRef]Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.https://doi.org/10.1007/s10853-006-1311-1https://doi.org/10.1016/j.msea.2008.09.075https://doi.org/10.1016/S0032-3861(00)00905-8https://doi.org/10.1021/ma951426ehttps://doi.org/10.1016/j.compscitech.2006.01.012https://doi.org/10.1002/pen.20876https://doi.org/10.1002/app.38420https://doi.org/10.1016/j.compositesa.2019.03.009https://doi.org/10.1016/j.jmrt.2022.05.077https://doi.org/10.1016/0266-3538(91)90018-Khttps://doi.org/10.1016/j.ijsolstr.2008.02.021https://doi.org/10.1115/1.4010337https://doi.org/10.1038/s41598-023-47159-9https://www.ncbi.nlm.nih.gov/pubmed/37963947https://doi.org/10.1016/j.carbon.2007.11.001https://doi.org/10.1007/s10853-011-6101-8https://doi.org/10.1023/B:JMSC.0000013913.84004.cdhttps://doi.org/10.1023/A:1004561023528https://doi.org/10.1016/0266-3538(94)90180-5 Introduction  Materials and Methods  Materials  Tensile Test  Interfacial Shear Strength Test  Results and Discussion  Stress–Strain Relationship  Tensile Modulus, Strength, and Failure Strain  Weibull Modulus  Weibull Modulus vs. Tensile Modulus and Strength and Failure Stain  Fracture Morphology  Interfacial Property  Weibull Modulus vs. Interfacial Shear Strength  Conclusions  References