# Fileset

[wang_stam2020.pdf](https://mdr.nims.go.jp/filesets/8d7bc450-ad94-4380-a753-9d89253aead1/download)

## Creator

[Hongxin Wang](https://orcid.org/0000-0002-8984-0764), [Han Zhang](https://orcid.org/0000-0003-0298-8502), [Kenta Goto](https://orcid.org/0000-0002-0102-0658), [Ikumu Watanabe](https://orcid.org/0000-0002-7693-1675), [Hideaki Kitazawa](https://orcid.org/0000-0002-9756-2311), Masamichi Kawai, [Hiroaki Mamiya](https://orcid.org/0000-0002-7840-3008), [Daisuke Fujita](https://orcid.org/0000-0001-7025-0265)

## Rights

Creative Commons BY Attribution 4.0 International[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Stress mapping reveals extrinsic toughening of brittle carbon fiber in polymer matrix](https://mdr.nims.go.jp/datasets/67a0061a-742d-49a9-8502-e9c06eae5613)

## Fulltext

Stress mapping reveals extrinsic toughening of brittle carbon fiber in polymer matrixFull Terms & Conditions of access and use can be found athttps://www.tandfonline.com/action/journalInformation?journalCode=tsta20Science and Technology of Advanced MaterialsISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tsta20Stress mapping reveals extrinsic toughening ofbrittle carbon fiber in polymer matrixHongxin Wang, Han Zhang, Kenta Goto, Ikumu Watanabe, Hideaki Kitazawa,Masamichi Kawai, Hiroaki Mamiya & Daisuke FujitaTo cite this article: Hongxin Wang, Han Zhang, Kenta Goto, Ikumu Watanabe, HideakiKitazawa, Masamichi Kawai, Hiroaki Mamiya & Daisuke Fujita (2020) Stress mapping revealsextrinsic toughening of brittle carbon fiber in polymer matrix, Science and Technology ofAdvanced Materials, 21:1, 267-277, DOI: 10.1080/14686996.2020.1752114To link to this article:  https://doi.org/10.1080/14686996.2020.1752114© 2020 The Author(s). Published by NationalInstitute for Materials Science in partnershipwith Taylor & Francis Group.View supplementary material Published online: 12 May 2020. Submit your article to this journal Article views: 1493 View related articles View Crossmark data Citing articles: 4 View citing articles https://www.tandfonline.com/action/journalInformation?journalCode=tsta20https://www.tandfonline.com/loi/tsta20https://www.tandfonline.com/action/showCitFormats?doi=10.1080/14686996.2020.1752114https://doi.org/10.1080/14686996.2020.1752114https://www.tandfonline.com/doi/suppl/10.1080/14686996.2020.1752114https://www.tandfonline.com/doi/suppl/10.1080/14686996.2020.1752114https://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/doi/mlt/10.1080/14686996.2020.1752114https://www.tandfonline.com/doi/mlt/10.1080/14686996.2020.1752114http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2020.1752114&domain=pdf&date_stamp=2020-05-12http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2020.1752114&domain=pdf&date_stamp=2020-05-12https://www.tandfonline.com/doi/citedby/10.1080/14686996.2020.1752114#tabModulehttps://www.tandfonline.com/doi/citedby/10.1080/14686996.2020.1752114#tabModuleStress mapping reveals extrinsic toughening of brittle carbon fiber in polymermatrixHongxin Wanga, Han Zhanga, Kenta Goto b, Ikumu Watanabe c, Hideaki Kitazawaa, Masamichi Kawaid,Hiroaki Mamiyaa and Daisuke FujitaaaResearch Center for Advanced Measurement and Characterization, National Institute for Materials Science, Tsukuba, Ibaraki, Japan;bInternational Center for Young Scientists, National Institute for Materials Science, Tsukuba, Ibaraki, Japan;cResearch Center for Structural Materials, National Institute for Materials Science, Tsukuba, Ibaraki, Japan;dSystems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, JapanABSTRACTWe conducted an in situ study on CFRP fracturing process using atomic-force-microscopy-based stress-sensitive indentation. Tensile stress distribution during fracture initiation andpropagation was directly observed quantitatively. It led to a discovery that previously believedcatastrophic fracture of individual carbon fiber develops in a controllable manner in thepolymer matrix, exhibiting 10 times increase of fracture toughness. Plastic deformation incrack-bridging polymer matrix was accounted for the toughening mechanism. The modelwas applied to explain low temperature strength weakening of CFRP bulk material whenmatrix plasticity was intentionally ‘shut down’ by cryogenic cooling.ARTICLE HISTORYReceived 8 December 2019Revised 31 March 2020Accepted 2 April 2020KEYWORDSStress; AFM; indentation;CFRPCLASSIFICATIONAtomic force microscopy;104 Carbon and relatedmaterials1. IntroductionThe high stiffness and high strength per body weightoffered by carbon fiber reinforced polymer (CFRP) hasgained ever increasing applications for this structuralcomposite in areas of astronautics, aviation, automobiles,ships, infrastructure constructions, sports goods, etc.More than 50wt.% of large passenger aircraft are nowmade by CFRP [1]. While a simple law of mixture canexplain the high stiffness of CFRP coming from the highstiffness of carbon fiber with analogy to springs in paral-lel, the mechanism for the composite high strength is nottrivial [2]. Though individual carbon fiber has a highstrength, Griffith discovered 100 years ago that smallfiber of brittle material is stronger than its bulk counter-part only because of the lower chance to develop a criticalfracture-initiating defect [3]. It would then be deducedthat such statistical advantage of small fibers should van-ish due to averaging effect when large amount of them isused to form a bulk material. Fracture mechanics follow-ing Griffith’s study also established that the strength ofbrittle materials, including CFRP, is determined by theproperty of fracture toughness, which is the materialability to resist fracture propagation [4]. CFRP exhibitsfracture toughness almost twice that of both constituents:the strong but brittle carbonfiber (CF) and the ductile butweak polymer (P) matrix, thus breaking the law of mix-ture [5–7].Further increasing the toughness, thus the strength,of CFRP, especially under various environmental con-ditions, remained as one of the biggest effort-CONTACT Han Zhang ZHANG.han@nims.go.jp National Institute for Materials Science, Sengen 1-2-1, Tsukuba, Ibaraki 3050047, JapanSupplemental data for this article can be accessed here.SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS2020, VOL. 21, NO. 1, 267–277https://doi.org/10.1080/14686996.2020.1752114© 2020 The Author(s). Published by National Institute for Materials Science in partnership with Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.http://orcid.org/0000-0002-0102-0658http://orcid.org/0000-0002-7693-1675https://doi.org/10.1080/14686996.2020.1752114http://www.tandfonline.comhttps://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2020.1752114&domain=pdf&date_stamp=2020-05-08concentrating fields in material research. Despiteresearch efforts for over 40 years, the microscopicmechanism of CFRP toughening remains unclear. Atunidirectional ply level, models widely used by scholarsall assumed CFRP failure process starting with cata-strophic fracture of individual CFs at positions andstress levels of statistical nature [8–10]. The tougheningof composite was believed to be a result of reducedstress concentration on intact CFs adjacent toa fractured CF through a complex interaction betweenboth P matrix and CF/P interface [11]. The fact thatmechanical properties of CF/P interface being notdirectly measurable leads to inconsistent CFRP strengthpredictions throughout literature. For example, whenCFRP-constructed large passenger aircraft are at theircruising altitude, environmental temperature drops to−60°C. The phenomenon of low temperature weaken-ing of CFRP material demands a fundamental mechan-ism understanding to guide improvement. Existingmodel suggests that CF/P interface weakening was thecause, while other studies showed clear strengthincrease for both P matrix and CF/P interface as tem-perature decreases [12–14]. Therefore, it is of priority toscrutinize the microscopic process of CFRP fracturing/toughening using in situ direct stress characterizationwith spatial resolution adequate to resolve a singlenanoscale fracture-initiating defect. Current methodol-ogies, such as Raman spectroscopy, X-ray diffractome-try, and electron/optical microscopy, lack eithernanoscale resolution or stress sensitivity for CFRPbulk material [15–21]. The characterization challengeis exacerbated by the distinctively different physicalproperties of CF and P, which excludes methods suita-ble for only one constituent. For example, the fact of CFbeing conductive, semicrystalline, and opaque whileP being insulating, amorphous, and transparent, hin-ders both electron and photon beam-based stress-sensing techniques [22].In this work, we used atomic force microscopy(AFM) indentation to point-by-point characterizethe CFRP local tensile stress, which is defined as thestress value averaged over the specimen area coveredby an indentation point. The new technique revealedthat nanoscale fracture in brittle CF develops ina stable manner with increasing load, which wasconsidered only possible with ductile materials cap-able of plastic deformation. Energy dissipationthrough yielding of the adjacent P matrix isaccounted for the observation. It acts through anextrinsic toughening mechanism similar to biologicalsystems [23,24]. To prove this mechanism, we inten-tionally ‘shut down’ such extrinsic-toughening bycooling the specimen to cryogenic temperatures. CFfracture returned to brittle catastrophic manner. Bulkstrength of CFRP also significantly decreased. Ourobservation countered the previously believed signif-icance of stress concentration reduction in CFRPtoughening. It provides hope for further improvingCFRP toughness/strength by controlling fracturepropagation at subfiber level through matrix plasti-city engineering.2. MaterialsPolyacrylonitrile (PAN)-based high strength standardmodulus carbon fiber (T700s) provided by Toray com-pany was used for this study. The CFRP material usedin this study is a unidirectional composite T700S/2592. It consists of the high strength carbon fiberT700S and an epoxy resin 2592 with the cure tempera-ture of 130°C. The unidirectional carbon/epoxy lami-nates were fabricated from the prepreg tape of P3252-20 (Toray, Japan). They were laid up by hand andcured in an autoclave. The glass transition tempera-ture of the epoxy resin in the laminates was about 100°C. CFRP samples with size of 30 × 3 × 1.5 mmwere cutfrom bulk using diamond coated disk saw. Samplesurface was then sanded which is followed by multi-staged polishing with final finishing using SiO2 abra-sive with 50 nm particle size.Figure 1. (a) Photograph showing the three-point bending stage. Area marked by the white arrow is subjected to AFM pinpointindentation; (b) Illustration showing the mechanism of pinpoint indentation. Inset showing recorded Fl-d curve where x-interceptis used to construct height map.Sci. Technol. Adv. Mater. 21 (2020) 268 H. WANG et al.3. MethodsThe CFRP sample was mounted on a three-pointbending stage, as shown in Figure 1a. The actuator inthe middle pushes the bar-shaped sample to generatetensile stress in the area marked by a white arrow. Thisarea is characterized by AFM. (Pinpoint mode byNX10, Park System, Korea) The principle of AFMpinpoint indentation is illustrated in Figure 1b.A sharp diamond probe with a tip radius R of 10 nmwas used to perform nanoscale indentation point-by-point on the CFRP surface [25]. With indentationforce Fl (1000 nN in this case), local specimen defor-mation d could be recorded for each scanned position.One example of such a recorded Fl-d curve is shown asthe figure inset. Hertz model of contact mechanics wasused to convert the local deformation into reducedindentation modulus E [26,27]:E ¼ 3Fl4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiR� d3p (1)Topographic height map (z map) is simultaneouslycreated for each indented spot using the stage heightvalue upon probe-specimen contact (x-intercept inFigure 1b inset).Stress calibration on CF was performed by placingthe same CFRP sample-bending stage under the objec-tive of a confocal Raman microscope (RAMANPlus,Nanophoton, Japan). Same area as that characterizedby AFM was analyzed by Raman spectroscopy. Stressvalue in the CF was obtained by Raman spectroscopy.In the same time, actuator force and displacementwere also recorded to calculate an average stress atposition of Raman characterization.4. Results and discussion4.1 Stress mapping of CFIt was reported in several AFM indentation studiesthat the measured value of E is affected by the presenceof in-plane tensile stress [28–30]. Therefore, it is pos-sible to extract the stress value from the change inapparent E values when specimen is measured beforeand after tensile load. Figure 2a displays a series ofapparent indentation E maps created about the samespecimen area with and without the tensile stress of 1.2GPa, which is generated by the three-point bendingmethod. The up-left panel shows an unstressed CFRPwith CF modulus averaged around 44 GPa andP modulus averaged around 8 GPa. The indentationmodulus value obtained on the CF longitudinal inter-section in a previous report is ~33 GPa for experimentand ~25 GPa for FEM simulation. The CF used in thatstudy (T300) and ours (T700) are both PAN-derivedFigure 2. (a) Indentation reduced modulus maps created for the same CFRP sample region during load/unload cycles with tensilestress of 1.2GPa; (b) modulus line profiles created along the white arrows marked in (a); (c) a typical height map of the same regionin (a) with a black arrow marked in the same position as the white arrows in (a); (d) height line profiles created along the blackarrow in (c).Sci. Technol. Adv. Mater. 21 (2020) 269 H. WANG et al.type with similar tensile moduli (~230 GPa vs.~250GPa) [31]. The 33% higher indentation moduluscan be explained by the much smaller indentationdeformation used in our case (<10 nm) comparedwith theirs (~150 nm). It is known that CF indentationmodulus decreases dramatically with increasing defor-mation due to buckling of graphitic layers [32]. Uponbending, the average E as measured for CF became 77GPa. The E for CF could return to low value afterremoving the external load and this cycle could repeatwith good consistency, as shown in Figure 2a. Figure2b is composed of line scan profiles created along thewhite arrows marked in the E maps of Figure 2a. Theline scans start from a smaller region of P towardsinside of CF. It is clearly shown that the E values forboth CF and P increase with increasing stress. It isknown that specimen topography, such as tiltingangle, influences indentation modulus [33]. Thesimultaneously recorded four height maps were care-fully compared and confirmed that they are identicalwithout external load dependence. One such heightmap is displayed in Figure 2c. Line scan profiles on thesame region are displayed in Figure 2d. Black arrowindicates the line scan region. The possibility of topo-graphic dependence on tensile load is therebyexcluded.For stress calibration, we collected Raman spectraon CF for each bending conditions and the averagedspectra are displayed in Figure 3a. The red-shift of1590 cm−1 peak in response to tensile stress has beenextensively studied in literature for PAN-based CF[34]. We adopted the shift rate of 1.8 cm−1/GPa tocalibrate stress used in our experiments. E maps werecreated for the same CF region with conditions of nostress and four increasing stresses. Typical force-deformation (Fl-d) curves representing five modulusmaps are displayed in Figure 3b. The indentationmodulus E obtained from curve fitting with equation(1) increases with increasing tensile stress. The stress-response of E could be explained by a model based onstressed surface [28–30]:ΔEE0¼ E� E0E0¼ 1FlβΔσ � 1(2)Where E0 denotes unstressed indentation modulus; σdenotes stress in the surface; β is a coefficient related toindentation deformation. When β � σ is much smallerthan Fl, the relative modulus change ΔE/E0 forms linearrelationship with membrane stress σ. We plotted ΔE/E0against the Raman calibrated applied stress values inFigure 3c. ΔE/E0 was found roughly with a linear rela-tion with tensile stress forming a gradient of 26GPa−1.This linear response was then used as basis for follow-ing quantitative analysis of CFRP fracture propagation.4.2 In situ stress characterization of CFfracturingFigure 4a–c are three stress distribution maps con-verted from the corresponding CF modulus mapsFigure 3. (a) Raman spectra recorded on the same carbon fiber under five different tensile stresses; (b) force-deformation curvesrecorded by using AFM on the same carbon fiber under the same tensile stress in (a); and (c) correlation between the relativechange of indentation moduli and the tensile stresses as calibrated by Raman spectroscopy.Sci. Technol. Adv. Mater. 21 (2020) 270 H. WANG et al.using the conversion relation of Figure 3c. In P region,indentation modulus is used as it is without conversion.CF region and P region are displayed with separatescales with left stress scale for CF and right modulusscale for P. Figure 4d–f are the corresponding heightmaps for 4a–4 c respectively. Figure 4a displays theoriginal state for the double CF region before bending.Several shallow surface defects with ~10 nm in depthare visible on both CFs which are bridged by a hill-and-valley region in the connecting polymer matrix. Thoseare likely caused by the sanding/polishing treatmentduring sample preparation. Figure 4b and e presentthe stage where the initial defect in the upper CFdeveloped into a crack. It is interesting to notice thata line of higher stress formed in the P matrix below theupper CF crack, as marked by the lower white rectanglein Figure 4b. Figure 4c and f present the state where thestress transferred from the upper CF crack induceda new crack in the lower CF. The higher stress linemarked by the bigger rectangle in Figure 4b has devel-oped into a region where stress is lower than surround-ings, as marked by the bigger rectangle in Figure 4c. Itsuggests matrix yielding where local tensile stressstopped increasing with increasing strain and elasticenergy is consumed by plastic deformation [35].4.3 FEM simulation on CFRP stress distributionFinite element simulation was used to verify thishypothesis with a model shown in Figure 5a. Themodeled contains two CFs and the interconnectingP matrix. The upper CF is fixed at all surfaces whilethe lower CF is fixed at all surfaces except its topsurface, which is displaced towards tensile load direc-tion (z direction) by 125 nm. (see supplementarymaterials for more details) Maximum principle stressdistribution on the model top surface is displayed forboth CF and P. Two areas marked by white rectanglesare highlighted as Figure 5d and e to compare withexperimental result of Figure 5b and c. Figure 5b ismagnified rescaled Emap of the region marked by theupper rectangle in Figure 4b. Contour lines showingthe broken edges of the CF parts are also displayed inthe same graph. It is apparent, especially on the leftside of the broken edge, that stress magnitude startedto drop before the drop of height due to scanningprobe tip shape. The gradient zone before the edgecould be as long as 500 nm, which is more than 20times the diameter of the probe tip. It is known ina fiber reinforced composite that stress ona completely broken fiber is rebuilt to form a stressgradient over a distance called ineffective length [36].The minimum ineffective length assuming a perfectlybonded interface is larger than 8 times the diameter ofthe fiber, which would be longer than 60 μm in ourcase [37]. As can be seen in Figure 4b, the stress on thebroken fiber is almost the same as the lower intactfiber, except for the 500 nm gradient zone shown inFigure 5b. A partially broken fiber with a stabilizedcrack growth is therefore suggested. Figure 5c isa magnified view of E map on P area marked by thelower rectangle in Figure 4b. Figure 5d is a stress mapon the surface outside of the crack and mirrored forbetter visualization. It shows that the created surfacecrack does generate a localized stress gradient within800 nm away from the crack edge. There is also a goodFigure 4. (a–c) Local tensile stress maps created for a CFRP specimen under tensile stresses of 0, 2.4, and 4.8 GPa, respectively; (d–f) height maps recorded simultaneously with modulus/stress maps shown in (a–c).Sci. Technol. Adv. Mater. 21 (2020) 271 H. WANG et al.match between the simulated stress map of Figure 5eand the measured stress map of Figure 5c about theP area adjacent to the crack. Besides the central highstress area just below the crack, there are also twohorizontal strips of high stress region along thez direction at the CF-P interfaces, with the lowerstrip wider than the upper strip. The double stripfeature is a good match with those observed inFigure 5c.4.4 CF toughening mechanismEstimation of fracture energy could be carried out byconsidering modified Griffith’s criteria [3]:σfffiffiffiap ¼ffiffiffiffiffiffiEGπr(3)Where σf is fracture stress; a is fracture depth; E isYoung’s modulus of carbon fiber and G is total energyincreased during fracture growth. σf equals applied stressand a can be measured from height maps in Figure 4.We then could obtain the total energy G of the cases inFigure 4a and c respectively. With a crack depth of13 nm, G becomes 0.13 J/m2 for Figure 4a, where noplastic deformation in P is observed. Assuming a purebrittle fracture, the surface energy for CF is then half ofG, as 0.065 J/m2. It agrees quite well with ~0.04 J/m2 forsimilar CF in literature [38]. The case in Figure 4c givesG value of 19 J/m2, which cannot be explained by surfaceenergy alone in the case of brittle fracture. Therefore,energy dissipation through plastic deformation must beconsidered. However, slit tests were used to study indi-vidual CF fracturing process in literature and they allreached the same conclusion of typical brittle fracturewithout plastic deformation. Only epoxy matrix could bethe source for the elastic energy dissipation induced byplastic deformation. G obtained from Figure 4c is how-ever 1 order of magnitude smaller than typical fractureenergy reported for epoxy blends [39]. It indicates thatthe toughening mechanism observed here might not beconventional intrinsic toughening where plastic defor-mation zone is ahead of the crack opening. It suggests anextrinsic type where plastic deformation functionsbehind the crack opening as crack bridging [40].A recent study indicated that even brittle epoxy matrixcould undergo equivalent plastic strain as large as 50%without losing stiffness under appropriate load condi-tion [41].An explanation of the observed toughness is thusproposed. The increased stress enlarged the opening ofthe fracture as shown in Figure 6. The release of CFelastic energy is in competition with thermal energyconversion of the bridging P plastic deformation, asevidenced by the observed P yielding zone in Figure 6,which is a magnified view of Figure 4c. The fracture isstabilized and its propagation is stopped when thesetwo energies reached balance.Next, crack growth resistance curve (R-curve) isused to differentiate intrinsic and extrinsic tougheningmechanism by observing the trend of fracture tough-ness change against balanced crack extension size.Mode I fracture toughness KIC is defined as criticalstress intensity factor, σBffiffiffiap, where σB is the appliedtensile stress on CF in balance with the crack depthand a is the depth of crack. Since the crack depthmeasurement by AFM is heavily influenced by thetip size and shape, a is therefore taken as crack widthwhich can be accurately measured from AFM heightFigure 5. (a) Finite element model created to simulate a polymer matrix containing two carbon fibers with one intact and onecracked only on its surface; (b) magnified and rescaled stress map for the region marked by the upper rectangle in Figure 4b. Whitesolid lines marked crack edges as measured in height map of Figure 4e; (c) magnified modulus map for the region marked by thelower rectangle in Figure 4b; (d) a mirrored maximum principal stress map simulated from the region marked by the rightrectangle in (a); and (e) a mirrored maximum principal stress map simulated from the region marked by the left rectangle in (a).Sci. Technol. Adv. Mater. 21 (2020) 272 H. WANG et al.maps. If a fixed ratio between a crack depth and widthis assumed, such approximation will not change thetrend in an R-curve even though the absolute KICvalues could be underestimated. Altogether sevenrandomly located fracture sites were analyzed fora CFRP specimen and their calculated KIC wereplotted against crack width in Figure 7a. A clear risingR-curve is evident to support an extrinsic tougheningFigure 6. Illustration of the extrinsic toughening mechanism accounted for the stable fracture growth inside of a carbon fiber withupper, middle, and lower black arrows pointing at CF crack opening, P plastic deformation zone, and P elastic deformation zonerespectively; Stress map on the left with one-to-one correspondence with zones labeled in the model.Figure 7. (a) Plot of fracture toughness against crack width measured at seven random fracture locations on CFRP specimensstressed at room temperature and −200°C respectively. (b) A typical stress map of a CFRP specimen stressed at three-pointbending stress of 1.2 GPa and at −200°C. The left scale bar for CF indicates tensile stress and the right scale bar for P indicates localmodulus; (c) stress-strain curves obtained by three-point bending tests for CFRP specimen at 25°C, −15°C and −30°C respectively;inset shows plot of ultimate strength for three specimens at each temperature.Sci. Technol. Adv. Mater. 21 (2020) 273 H. WANG et al.mechanism. The situation is similar to biologicalmaterial toughening in natural nacre or bones, whichare also composites of brittle calcium carbonate andductile proteins [40]. To further verify the proposedmechanism, the effect of the P matrix plasticity wasintentionally ‘shut down’ by cooling the CFRP speci-men to low temperature. After applying bending loadto specimens at −200°C, they were naturally warmedto room temperature before characterization by AFMindentation. A typical stress map for a CFRP deformedat −200°C is shown in Figure 7b. The upper CF witha crack is found with a much lower stress value com-pared with the intact adjacent CFs in the same image,showing that the crack is completely fractured throughits thickness so that no stress could be carried on theCF near the fracture site. The existence of only onePoisson strip near the intact CF side in the P matrixalso supports the complete loss of load carry ability ofthe upper fractured CF. This contrasts with the twostrips observed in Figure 4b. Unlike the case whereCFRP was deformed at room temperature, the crackwidth of the −200°C deformed specimen was muchnarrower. Plot with KIC, as previously defined, wasmade by seven random fracture locations and theresults are added to Figure 7a for comparison. Itclearly showed a flat R-curve with low values of KIC,which is typical for brittle CF fracture. It must benoted that the crack width measured at completefiber fracture is larger than the critical crack widthfrom which CF failure developed. However, it givesan upper boundary for the true critical crack size. NineCFRP specimens were subjected to bending force tillcomplete failure with 3 specimens per testing tempera-ture at −15°C, −30°C, and −200°C, respectively. Samestrain rate was used so that the composite strength willonly be affected by testing temperature. Typical stress-strain curves were compared in Figure 7c and thereduction of both ultimate strength and strain withdecreasing temperature was evident, agreeing withprevious reports by others [12,42]. Our characteriza-tion and analysis are all based on surface phenom-enon. Both AFM and Raman spectroscopy detectsonly stress on the surface. We also based our discus-sion on surface crack and polymer yielding zone onthe surface. These surface observables are adjacent toeach other and showed clear correlations. So, we pro-posed the mechanism revealing the interplay by thesesurface observables. However, it should also apply inbulk form, because the mechanism itself does notinvolve surface-only phenomenon. Moreover, it islikely that, even in the CFRP body, CF crack andP yielding occur first on their surface/interface.T9To test our proposed model on fracture propa-gation in a CFRP bulk, we compared morphology offractured surface of specimens fractured at −200°Cand room temperature. It is also intended to examinethe validity of the previously believed mechanismwhere reduction of stress concentration is the causefor CFRP toughening. During room temperaturefracturing, the surface crack observed in Figure 4bclearly propagate into the adjacent intact CF throughstress concentration in the P matrix. On the contrary,for −200°C fracturing, a through crack observed inFigure 7b did not propagate or cause high degree ofstress concentration. These observations intuitivelycountered the previously believed model. Moreover,we also conducted scanning electron microscopy(SEM) characterization over the fractured surfacefor both the specimens failed at −200°C and those atroom temperature, as shown in Figure 8a and b. Thedirect effect of stress concentration is to allow frac-ture propagation to stay in the same direction. Itimplies that at the fracture surface, one shouldobserve broken CFs out of the P matrix with similarprotrusion length. Relatively flat area of about0.01 mm2 which contain about 80 broken CFs wasimaged for both samples. The number of CFs isplotted against the difference between individual pro-trusion length and the average value for the entirearea, as shown in the histograms of Figure 8c and d. Itis quite clear that room temperature fracture is witha more uniform ‘cut’ at the fracture surface, whereCFs broke at similar positions. On the contrary,−200°C sample showed a rather random distributionof protrusion length, indicating breakage of CFsoccurred rather independently based on their ownstatistical distribution of defects with critical size.Our observation suggested that stress concentrationis less in the case of low temperature fracture, oppo-site to what was believed in the past. This is becausein the low temperature case, defected CF did notdevelop high strain yet before complete fracture.Therefore, the amount of elastic energy releasedupon such catastrophic fracture is less than the casefor stable fracture where the larger crack width gen-erated much higher elastic deformation in the adja-cent P matrix and consequently adjacent intact CFs.However, the significantly reduced toughness in theindividual CF fracture caused premature failure ofthe whole CFRP at the lower temperatures, eventhough stress concentration is also reduced. SEMhead-on shots of the fractured CFRP surface werepresented in Figure 8e and f. In the case of −200°C fracture, the CF surface can be clearly divided intotwo zones. According to fractography of brittle mate-rials, the upper zone, as marked by the red rectanglein Figure 8e, is with smooth surface and termed as‘mirror zone’. The lower part of the fracture surfacewith higher degree of roughness is the zone of ‘mist’and ‘hackle’ [43]. The transition from the smoothzone to the rough zone indicates that crack tip pro-pagation velocity dropped due to a reduced drivingenergy. The roughness is due to formation of manysmall cracks along the direction of the original majorSci. Technol. Adv. Mater. 21 (2020) 274 H. WANG et al.crack front [44]. The appearance of the −200°C fractured CF surface is quite similar to focusedion beam (FIB)-notched fracture surface of thesame type of CF (T700), though the latter fracturingwas performed at room temperature [7]. It is quiteinteresting to notice in Figure 8f that the room tem-perature fractured CF surface, inside of CFRP, canalso be divided into two zones with the upper zoneoccupying about 1/3 of the total cross-section.However, though the lower zone is with similardegree of roughness as that in Figure 8e, the upperzone is much rougher, as marked by the red rectanglein Figure 8f. The CF fractured at room temperatureinside of CFRP is observed lack of a mirror zone withhigh crack propagating velocity. It is thereforededuced that when crack started inside of a CF inCFRP at room temperature, additional energy con-sumption occurred, which resulted in less crack-driving energy and consequently lower propagationspeed. This observation agrees well with our pro-posed model where CF crack elastic energy is con-sumed by plastic deformation of the P matrix duringfracture propagation.5. ConclusionsCalibrated using Raman spectroscopy, AFM pinpointindentation provides a quantitative in situ approach tocharacterize CFRP stress distribution. The tensilestress distribution was characterized during propaga-tion of a CF fracture to neighboring CFs. An extrinsictoughening mechanism by bridging polymer matrixwas accounted for the observed stable growth of frac-ture inside of a carbon fiber. Carbon fiber was believedto fracture only in brittle manner. The proposedmechanism was verified by comparing single CF frac-turing behavior and bulk CFRP strength at low tem-peratures. The high-resolution stress characterizationFigure 8. (a, b) SEM images taken for specimens fractured at −200°C and 25°C, respectively; Two broken CFs were outlined in redcolor to assist image comprehension; (c, d).Histograms of protrusion length of broken CFs in SEM images of (a) and (b); (e, f) SEMhead-on shots of CF surface fractured at −200°C and 25°C, respectively.Sci. Technol. Adv. Mater. 21 (2020) 275 H. WANG et al.capability of the new technique will offer a powerfultool in assisting macroscale component virtual test. Itwill also help optimize matrix mechanical propertiestowards new CFRP materials with both high stiffnessand high toughness.AcknowledgmentsThis work was supported by Cross-ministerial StrategicInnovation Promotion Program—Unit D66—InnovativeMeasurement and Analysis for Structural Materials(SIPIMASM).Author contributions statementHongxin Wang designed and conducted the experimentalmeasurements. Kenta Goto and Ikumu Watanabe con-ducted the finite element method simulations. HongxinWang and Han Zhang analyzed data and wrote the manu-script. M. Kawai prepared CFRP samples. Hideaki Kitazawa,Hiroaski Mamiya, and Daisuke Fujita contributed in projectorganization and data analysis.Disclosure statementThe author(s) declare no competing interests.FundingThis work was supported by SIP-IMASM program fromJapan Science and Technology Agency.ORCIDKenta Goto http://orcid.org/0000-0002-0102-0658Ikumu Watanabe http://orcid.org/0000-0002-7693-1675Data availabilityAll data generated or analyzed during this study areincluded in this published article (and its SupplementaryInformation files).References[1] Breuer UP. Commercial aircraft composite technol-ogy. Switzerland: Springer Nature; 2018. p. 19–20.[2] Chawla KK. Composite materials science and engi-neering. 3rd ed. New York: Springer; 2012.[3] Griffith AA. The phenomena of rupture and flow insolids. Philos Trans R Soc A. 1921;221:582–593.[4] Courtney TH. Mechanical behavior of materials.Long grove, IL: Waveland Press Inc.; 2005.[5] Kim J, Baillie C, Poh J, et al. Fracture toughness ofCFRP with modified epoxy resin. Matrices ComposSci Technol. 1992;43:283–297.[6] Araki W, Nemoto K, Adachi T, et al. Fracture tough-ness for mixed mode I/II of epoxy resin. Acta Mater.2005;53:869–875.[7] Kant M, Penumadu D. Fracture behavior of indivi-dual carbon fibers in tension using nano-fabricatednotches. Compos Sci Technol. 2013;89:83–88.[8] Hitchon JW, Phillips DC. The dependence of thestrength of carbon fibres on length. Fiber SciTechnol. 1979;12:217–233.[9] Cox B, Yang QD. In quest of virtual tests for struc-tural composites. Science. 2006;314:1102–1107.[10] LLorca J, Gonzalez C, Molina-Aldareguia JM, et al.Multiscale modeling of composite materials:a roadmap towards virtual testing. Adv Mater.2011;23:5130–5147.[11] Harlow DG, Phoenix SL. The chain-bundles prob-ability model for the strength of fibrous materials I:analysis and conjectures. J Compos Mater.1978;12:195–214.[12] Sanchez SS, Barbero E, Navarro C. Analysis of thedynamic flexural behavior of composite beams at lowtemperature. Compos Sci Technol.2007;67:2616–2632.[13] Behzadi S, Jones FR. The effect of temperature onstress transfer between a broken fibre and the adja-cent fibres in unidirectional fibre composites.Compos Sci Technol. 2008;68:2690–2696.[14] Detassis M, Pegoretti A, Migliaresi C. Effect of tem-perature and strain rate on interfacial shear stresstransfer in carbon/epoxy model composites.Compos Sci Technol. 1995;53:39–46.[15] Miyagawa H, Sato C, Ikegami K. Experimental deter-mination of fracture toughness of cfrp in model II byRaman spectroscopy. Appl Compos Mater.2001;8:25–41.[16] Montes-Moran MA, Young RJ. Raman spectroscopystudy of high-modulus carbon fibres: effect ofplasma-treatment on the interfacial properties ofsingle-fibre-epoxy composites part II: characterizationof the fibre-matrix interface. Carbon. 2002;40:857–875.[17] Kobayashi T, Sumiya K, Kukuba Y, et al. Structuralheterogeneity and stress distribution in carbon fibermonofilament as revealed by synchrotronmicro-beam X-ray scattering and micro-Raman spec-tral measurements. Carbon. 2011;49:1646–1652.[18] Okuda H, Young RJ, Tanaka F, et al. Tensile failurephenomena in carbonfibres. Carbon. 2016;107:474–481.[19] Schemmel P, Moore AJ. Monitoring stress changes incarbon fiber reinforced polymer composites withGHz radiation. Appl Opt. 2017;56:6405–6409.[20] Canal LP, Gonzalez C, Molina AJ, et al. Application ofdigital image correlation at the micro scale in fiberreinforced composites. Compos Part A Appl SciManuf. 2011;43:1630–1638.[21] Lecomte GP, Paluch B, Brieu M, et al. Interlaminarshear strain measurement on angle-ply laminate freeedge using digital image correlation. Compos PartA Appl Sci Manuf. 2009;40:1911–1920.[22] Wachi Y, Koyanagi J, Arikawa S, et al. In situ semdeformation behavior observation at CFRPfiber-matrix interface. Composite Hybrid MultifunMater. 2015;4: 67–73. In: Tandon G. (eds).[23] Ritchie RO. The conflicts between strength andtoughness. Nat Mater. 2011;10:817–822.[24] Koyama M, Zhang Z, Wang M, et al. Bone-like crackresistance in hierarchical metastable nanolaminatesteels. Science. 2017;355:1055–1057.[25] Dokukin ME, Sokolov I. Quantitative mapping of theelastic modulus of soft materials with harmonix andSci. Technol. Adv. Mater. 21 (2020) 276 H. WANG et al.peak force QNM AFM modes. Langmuir.2012;28:16060–16071.[26] Braga PC, Ricci D. Atomic force microscopy biome-dical methods and applications. Totowa, NJ: HumanaPress; 2004.[27] HardimanM, Vaughan TJ, McCarthy CT. A review ofkey developments and pertinent issues in nanoinden-tation testing of fibre reinforced plasticmicrostructures.Compos Struct. 2017;180:782–798.[28] Polop C, Vasco E, Perrino AP, et al. Mapping stress inpolycrystals with sub-10nm spatial resolution.Nanoscale. 2017;9:13938–13946.[29] Vasco E, Polop C. Intrinsic compressive stress inpolycrystalline films is localized at edges of the grainboundaries. Phys Rev Lett. 2017;119:256102.[30] Wang H, Zhang H, Tang D, et al. Stress dependenceof indentation modulus for carbon fiber in polymercomposite. Sci Technol Adv Mater. 2019;20:412–420.[31] Csanadi T, Nemeth D, Zhang C, et al.Nanoindentation derived elastic constants of carbonfibres and their nanostructural based predictions.Carbon. 2017;119:314–325.[32] Diss P, Lamon J, Carpentier L, et al. Sharp indenta-tion behavior of carbon/carbon composites and vari-eties of carbon. Carbon. 2002;40:2567–2579.[33] Malave V, Killgore JP, Garboczi EJ, et al. Decouplingthe effects of surface topography and material hetero-geneity on indentation modulus: a simple numericallinear-elastic model. Int J Solids Struct.2017;124:235–243.[34] Kobayashi T, Sumiya K, Fujii Y, et al. Stress concentra-tion in carbon fiber revealed by the quantitative analy-sis of X-ray crystallite modulus and Raman peak shiftevaluated for the variously-treated monofilamentsunder constant tensile forces. Carbon. 2013;53:29–37.[35] Behzadi S, Curtis PT, Jones FR. Improving the pre-diction of tensile failure in unidirectional fibre com-posites by introducing matrix shear yielding. ComposSci Technol. 2009;69:2421–2427.[36] Rich MJ, Drzal LJ. Interfacial properties of some highstrain carbon fibers in an epoxy matrix. J Reinf PlastCompos. 1998;7:145–154.[37] Xia Z, Okabe T, Curtin WA. Shear-lag versus finiteelement models for stress transfer in fiber reinforcedcomposites. Compos Sci Technol. 2002;62:1141–1149.[38] Tsutsumi K, Ishida S, Shibata K. Determination of thesurface free energy of modified carbon fibers and itsrelation to the work of adhesion. Colloid Polym Sci.1990;268:31–37.[39] Kinloch AJ, Lee SH, Taylor AC. Improving the frac-ture toughness and the cyclic-fatigue resistance ofepoxy-polymer blends. Polymer. 2014;55:6325–6334.[40] Launey ME, Ritchie RO. On the fracture toughness ofadvanced materials. Adv Mater. 2009;21:2103–2110.[41] Turk M, Hamerton I, Ivanov D. Ductility potential ofbrittle epoxies: thermomechanical behaviour ofplastically-deformed fully-cured composite resins.Polymer. 2017;120:43–51.[42] Reed RP, Golda M. Cryogenic properties of unidirec-tional composites. Cryogenics. 1994;34:909–928.[43] Honjo K. Fracture toughness of PAN-based carbonfibers estimated from strength–mirror size relation.Carbon. 2003;41:979–984.[44] Mecholsky JJ, Rice RW, Freiman SW. Prediction offracture energy and flaw size in glasses from measure-ments ofmirror size. J AmCeram Soc. 1974;57:440–443.Sci. Technol. Adv. Mater. 21 (2020) 277 H. WANG et al. Abstract 1. Introduction 2. Materials 3. Methods 4. Results and discussion 4.1 Stress mapping of CF 4.2 In situ <italic>stress characterization of CF fracturing</italic> 4.3 FEM simulation on CFRP stress distribution 4.4 CF toughening mechanism 5. Conclusions Acknowledgments Author contributions statement Disclosure statement Funding ORCID Data availability References