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[Hongxin Wang](https://orcid.org/0000-0002-8984-0764), [Han Zhang](https://orcid.org/0000-0003-0298-8502), [Daiming Tang](https://orcid.org/0000-0001-7136-7481), [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)

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[Stress dependence of indentation modulus for carbon fiber in polymer composite](https://mdr.nims.go.jp/datasets/970c793f-91a2-4fd6-ba29-2ce860594997)

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Stress dependence of indentation modulus for carbon fiber in polymer compositeFull 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 dependence of indentation modulus forcarbon fiber in polymer compositeHongxin Wang, Han Zhang, Daiming Tang, Kenta Goto, Ikumu Watanabe,Hideaki Kitazawa, Masamichi Kawai, Hiroaki Mamiya & Daisuke FujitaTo cite this article: Hongxin Wang, Han Zhang, Daiming Tang, Kenta Goto, Ikumu Watanabe,Hideaki Kitazawa, Masamichi Kawai, Hiroaki Mamiya & Daisuke Fujita (2019) Stressdependence of indentation modulus for carbon fiber in polymer composite, Science andTechnology of Advanced Materials, 20:1, 412-420, DOI: 10.1080/14686996.2019.1600202To link to this article:  https://doi.org/10.1080/14686996.2019.1600202© 2019 The Author(s). Published by NationalInstitute for Materials Science in partnershipwith Taylor & Francis Group.View supplementary material Published online: 26 Apr 2019. Submit your article to this journal Article views: 3068 View related articles View Crossmark data Citing articles: 6 View citing articles https://www.tandfonline.com/action/journalInformation?journalCode=tsta20https://www.tandfonline.com/loi/tsta20https://www.tandfonline.com/action/showCitFormats?doi=10.1080/14686996.2019.1600202https://doi.org/10.1080/14686996.2019.1600202https://www.tandfonline.com/doi/suppl/10.1080/14686996.2019.1600202https://www.tandfonline.com/doi/suppl/10.1080/14686996.2019.1600202https://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/action/authorSubmission?journalCode=tsta20&show=instructionshttps://www.tandfonline.com/doi/mlt/10.1080/14686996.2019.1600202https://www.tandfonline.com/doi/mlt/10.1080/14686996.2019.1600202http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1600202&domain=pdf&date_stamp=2019-04-26http://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1600202&domain=pdf&date_stamp=2019-04-26https://www.tandfonline.com/doi/citedby/10.1080/14686996.2019.1600202#tabModulehttps://www.tandfonline.com/doi/citedby/10.1080/14686996.2019.1600202#tabModuleStress dependence of indentation modulus for carbon fiber in polymercompositeHongxin Wanga, Han Zhanga, Daiming Tangb, Kenta Goto c, Ikumu Watanabe c, Hideaki Kitazawaa,Masamichi Kawaid, Hiroaki Mamiyaa and Daisuke FujitaaaResearch Center for Advanced Measurement and Characterization, National Institute for Materials Science, Tsukuba, Japan;bInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan;cResearch Center for Structural Material, National Institute for Materials Science, Tsukuba, Japan;dSystems and Information Engineering, University of Tsukuba, Tsukuba, JapanABSTRACTElastic modulus measured through atomic force microscopy (AFM)-based indentation onsingle carbon fiber (CF) is found with dependence on lateral applied stress. An in situindentation experiment inside a high-resolution transmission electron microscope was per-formed to quantitatively understand this phenomenon by observing microstructure changein the indented area. Change of graphitic basal plane misalignment angle during indentationwas linked to a continuous change of modulus with the help of finite element simulation. Theestablished relationship between modulus and indentation force was further used to calcu-late residual stress distribution in CF imbedded in a CF reinforced polymer composite usingthe AFM indentation technique. The stress-induced formation of nanoscale defects in the CFand their transformation into fracture were directly characterized.ARTICLE HISTORYReceived 22 January 2019Revised 24 March 2019Accepted 24 March 2019KEYWORDSAtomic force microscopy;indentationCLASSIFICATION10 Engineering andStructural materials; 104Carbon and relatedmaterials; 500Characterization1. IntroductionModulus characterization by atomic force micro-scopy (AFM) provides a new method of mappingresidual stress in a material with nanometric resolu-tion [1,2]. The operating principle can be describedas: the lateral tensile/compressive stress preexistingin the specimen produces a partial force componentthat counters/enhances the vertically applied AFMprobe force; such reduced/increased vertical forceactually applied on the specimen would make theapparent Young’s modulus sensed by the AFMprobe smaller/bigger than when no residual stressis presented; the distribution of such apparentYoung’s modulus over a preassumed uniform mate-rial would thus reflect local stress distribution. Thisphenomenon of modulus hardening is similar to thesuperlattice modulus effect observed in metal filmsand modulus softening effect observed in nucleargraphite, but out of very different mechanism [3,4].This technique is very attractive as nondestructivestress sensing for carbon fiber (CF)-based compositematerials. Though widely used as filler materials forCF reinforced plastic (CFRP), the brittle nature ofCF often causes catastrophic fatigue failure of theCFRP structural component [5,6]. It imposes dangerfor structural applications especially forCONTACT Han Zhang ZHANG.han@nims.go.jp; Daisuke Fujita FUJITA.daisuke@nims.go.jpSupplemental data for this article can be accessed here.SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS2019, VOL. 20, NO. 1, 412–420https://doi.org/10.1080/14686996.2019.1600202© 2019 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/10.1080/14686996.2019.1600202http://www.tandfonline.comhttps://crossmark.crossref.org/dialog/?doi=10.1080/14686996.2019.1600202&domain=pdf&date_stamp=2020-02-02transportation safety, because large passenger air-planes are now manufactured with more than halfweight percent of CFRP based on polyacrylonitrile(PAN). The nanometric resolution provided by thenew modulus mapping method thus could poten-tially resolve a single defect presented in the CF thatmay later develop into a fatal fracture [7]. Existingnondestructive stress characterization methods forCF, including surface roughness optical sensing [8],acoustic emission [9], infrared thermography [10],electric resistance [11], digital image correlation[12], Raman spectroscopy [13] and X-ray diffraction[14], do not offer a spatial resolution that is highenough for single defect detection.Though the operation principle of the modulusmapping method is quite straight forward, one musthave the preknowledge of CF Young’s modulusdependence on applied probe force in order to accu-rately correlate the modulus measurement results toresidual stress values. This is because in the AFM-based modulus mapping, the force actually applied onthe specimen is different with and without residualstress. The intrinsic influence from modulus changedue to probe force difference, out of effect such aslattice anharmonicity, must be considered beforeextrinsic influence from residual stress can be suc-cessfully decomposed [15]. However, due to the highanisotropy of graphite atomic structure and the poly-granular nature of most graphite-based material, theintrinsic dependence of elastic modulus on appliedload force is quite complex. Large discrepancy existsin literature about both the elastic modulus valuesand their dependence on applied force. For example,Gauster and Fritz applied hydrostatic compressivepressure on a densified pyrolytic graphite andreported modulus values between 30 GPa and 1 TPaand relative modulus increases between 21%/GPa and3%/GPa against stress increase [16]; Diss studiedcompressive modulus on pyrolytic graphite film andCF by applying stress through sharp tip indentation.The resulting moduli are all smaller than 100 GPaand could either increase or decrease with compres-sive force, which depends on the modulus of sub-strate underneath the measured location [17]. Yodaet al. applied Instron-type compressive force on iso-tropic graphite and found modulus value of 10 GPawith decreasing relative modulus with the rate of642%/GPa [18]; Marrow et al. studied compressivesurface of similar isotropic graphite with coarsergrains under four-point bending load and found nochange of elastic modulus with compressive force[19]. It is evident that the differences in the graphite-based material under study and the particular way ofapplying load force are the main causes for the scat-tered elastic modulus data in literatures. Reliableelastic modulus data must be investigated individu-ally for a specific experimental setup.In this study, we applied a pinpoint indentationmethod based on AFM to acquire modulus values onthe surface of PAN-derived CF imbedded ina commercial CFRP. The modulus measurement issimilar to those widely used in micro and nanoinden-tation methods, except that the maximum penetra-tion depth in the pinpoint mode is only a fewnanometers instead of the over-hundredsof nanometers depth used in nanoindentation andover-micrometer depth used in microindentation[17,20]. The pinpoint mode thus has much less influ-ence from underneath substrate and could reflectonly the mechanical property of the targeted location.It is therefore understandable that the pinpointindentation modulus is much higher than those mea-sured by uniaxial tensile test and deep indentationtest, which are influenced by large-sized defects suchas voids [21].The main objective of this article is on the intrinsicmodulus dependence on load force for PAN-derivedCF, measured using the pinpoint indentationmethod. Intrinsic modulus changing mechanismwas studied using an in situ AFM holder insidea transmission electron microscope (TEM), whereatomic structure change in CF could be directlyobserved [22]. Focus was put on the buckling of CFgraphitic layers, which phenomena were speculatedmany times in literature but have not been quantita-tively investigated [23–27]. This microstructuralinformation combined with numerical simulationgives a quantitative prediction of the indentationmodulus response to externally applied stress.Finally, the established modulus–stress relationshipwas used to obtain local stress map on a CF subjectedto tensile stress applied by an AFM in situ three-pointbending holder. Stress concentration, defect forma-tion, fracture and stress redistribution were directlycharacterized. The pinpoint indentation techniquethus proves to be a highly sensitive and nondestruc-tive method to monitor stress distribution and defectformation in CFRP components in operationalconditions.2. Experimental detailsPAN-based high strength standard modulus CF(T700s) provided by Toray company was chosen forthis study. The CFRP material used in this study isa unidirectional composite T700S/2592. It consists ofthe high strength CF T700S and an epoxy resin 2592with the cure temperature of 130 °C. The unidirec-tional carbon/epoxy laminates were fabricated fromthe prepreg tape of P3252-20 (TORAY). They werelaid up by hand and cured in an autoclave. The glasstransition temperature of the epoxy resin in the lami-nates was about 100 °C. The CF is with nominaltensile modulus of 280 GPa and tensile strength ofSci. Technol. Adv. Mater. 20 (2019) 413 H. WANG et al.2 GPa. A bar-shaped specimen with the dimensionsof 30 mm × 1.5 mm × 1 mm was cut along the fiberdirection and has its surfaces polished with aluminapaste. This specimen was mounted onto a three-pointbending holder, which could be mounted on the stageof an AFM (NX10, Park System) for pinpoint inden-tation experiment.During pinpoint indentation, a sharp diamond tipwith approximated cone geometry is scanned overthe top surface of the CFRP specimen. At each pixellocations, the tip is pressed into the specimen surfaceuntil a preset indenting force is reached. Piezo stagerecords each indentation depth into the specimen,which was used to calculate the apparent elastic mod-ulus at each pixel locations. What also been recordedis the stage height at each tip–specimen contact pointand these height values could be used to generatea topological height map of the specimen. Three-point bending holder is used to apply a series ofbending forces to the specimen during the pinpointindentation experiment.A thin slice of sample (3 × 3 × 0.1 μm) was dugout from the CF surface using focused ion beamprocessing. The slice was attached onto the tip ofa tungsten needle which could be mounted onto anindentation holder for TEM (NanofactoryInstruments AB). The indenter tip of the holder canpress into the CF slice with known force values, whilemicrostructure of the CF could be observed by TEM.The TEM used in this study is a JEM-3100F operatedat 300 kV.The deformation of a CF during indentation wassimulated using finite element method (FEM) imple-mented in a commercial software ABAQUS 6.14 [28].The CF was assumed as a continuous body havingdifferent elastic properties in the in-plane directionand the stacking direction of graphene. The modelconsists of the fiber part and an indenter part asshown in Figure 3(b). The graphene layers are stackedin parallel with tilting θ° to the yz-plane in the fiber.Therefore, the xy-plane symmetrical model was gener-ated, and its size was 58.6 × 24.3 × 24.3 nm. It has 15,358nodes and 14,138 elements of 8-node hexahedron ele-ment with reduced integration (C3D8R). The mesh sizewas decreased in the region underneath the indenter,where the smallest mesh size was 0.3 nm. The elasticconstants of graphite are cited from literature [29]. Thesphere indenter of 10 nm in radius was generated asa rigid body assuming the stiffness of the diamond ishigher enough than that of the carbon to ignore itsdeformation. The indentation was achieved by displa-cing the indenter by 0.2 nm in the y-direction.3. Results and discussionFigure 1(a) shows a schematic of AFM-based pinpointindentation technique to characterize the local stress ofthe CF material. When a CF subjected to bending force,tensile and compressive stress is generated at outer andinner arch positions, which are represented by red andgreen color, respectively, an external stress was applied toCFRP bulk specimen by a three-point bending holder asshown in Figure 1(b). Each stress condition is named bythe average stress applied on the observed region. Theregion near upper edge of CFRP under tensile stress ischaracterized by AFM. We used a diamond probe forstress measurement of CF. The helium ion microscopyimage in Figure 1(c) shows that the radius of the dia-mond probe stayed around 15 nm even after 90 h ofcontinuous measurement. Modulus values of each pixelwere calculated automatically by AFM software usingHertz equation (Equation 2) by inputting maximumloaded force and tip indentation depth. The measure-ment of modulus could be affected by three factors: theinherent material property, surface morphology andexternal stress. Figure 1(d) shows the large change inthe modulus of CF measured before and after the appli-cation of 3.85 GPa tensile stress. The modulus value istwice higher for the stressed CF than for stress-free CF.Modulus profiles before and after applying the externalstress are created along the white arrows in Figure 1(d).Themodulus profiles in Figure 1(e) showed that appreci-able modulus change only occurs on CF, while that ofP remains unchanged.We also took height profiles of theCFRP along the same region with modulus, as shown inFigure 1(f). The height profiles for CFRP before and afterapplying external stress exhibit the same value. An insetin Figure 1(f) shows such a height. It shows that tensilestress has no noticeable effect on the morphology ofCFRP. Therefore, the changes observed in the modulusof CF before and after applying external stress are notcaused by surface morphology of CFRP. Measured mod-ulus response to four cyclic load–unload repetitions isplotted in Figure 1(g). The modulus values are obtainedby averaging all pixels on CF region. Unstressed CFproduces almost the same modulus except for thosestressed to a high average value of 3.85 GPa. This is likelydue to the viscoelastic nature of the epoxy matrix, whichneeds longer relaxation time after being stretched to highstrain values or load cycled for many times. Since wecompare only the relative change inmodulus valueΔE/E,the abnormal increase in unstressed modulus valuewould not introduce errors. In comparison, we alsoincluded stress values measured by Raman spectroscopymapping. The red shift of 1590 cm−1 peak is averagedfrom 2D maps on about the same CF region duringforce–load cycles. We adopted the shift rate of1.8 cm−1/GPa to calibrate the average stress values usedin our experiments [30]. It is noted that Raman responsedeviated from expectation after the second cycle. Thisclearly suggests the sample heating effect due to thestrong absorption of laser power for CF, even thoughwe have chosen the lowest laser power that is still capableof detecting stress-related band shift.Sci. Technol. Adv. Mater. 20 (2019) 414 H. WANG et al.An estimation was performed to understandwhether the observed CF modulus increase is onlythe effect of surface membrane as observed in thecase of Au film [1]. CF modulus is first assumed tobe constant as probe loading force (Fl) increased to1000 nN full value. When the probe indents on theCF surface, the elastically deformed CF producesan elastic force Fc that counters the probe to pro-gress downwards. In the same time, the externallyapplied stress produced a vertical partial compo-nent force, Fs, through surface membrane effect.The total loading force of the probe is equal tothe sum of Fs and Fc, which follows the definitionsof Refs. [1,31]:Fs ¼ 4π � R � d � σ � cos tan�1 2ffiffiffiffiffiffiffiffiR=dp� �h i(1)Fc ¼ 43 1� γ2ð ÞE �ffiffiffiRpd1:5 (2)where R is the radius of diamond probe taken as15 nm; d is the displacement of probe with respectto sample surface; γ is Poisson’s ratio taken to be 0.3.Taking the example presented in Figure 1(d): undera stressed condition with σ being 3.8 GPa, and theassumed constant modulus E0 being 200 GPa, Fs+Fc= Fl = 1000 nN. We can calculate the correspondingd to be 0.75 nm by solving Equations (1) and (2).Figure 1. (a) Experimental principle showing the diamond tip indenting in the in-plane direction of graphene layers of a CFimbedded in polymer matrix; (b) schematics showing the three-point bending holder used to apply tensile stress to the CFRPspecimen; (c) scanning helium ion microscopy image of the diamond tip after the experiment; (d) compressive modulus map ofthe same CF region with and without applied external tensile stress; (e) modulus line profiles created along the white arrows in(d) showing large modulus hardening of the stressed CF; (f) height line profiles created at the same positions as (e). Insetshowing one height map of the same CF region; (g) indentation moduli obtained from a CF during cyclic tensile loading of fourdifferent average stresses with comparison to Raman spectroscopy measurements.Sci. Technol. Adv. Mater. 20 (2019) 415 H. WANG et al.Since the apparent modulus E is determined by theAFM software assuming Fc = Fl = 1000 nN, Equation(2) is used again to obtain an apparent E value of207 GPa. Therefore, there will be only 3.5% increasein E if surface membrane effect was the only cause. Itis 30 times lower than the ~100% increase in E fromthe experimental observation as shown in the lowermap in Figure 1(d).To understand the large indentation modulus hard-ening observed for CF with tensile stress, we haveconducted an in situ study inside a TEM where anAFM probe indents a thin slice specimen cut froma CF. Low-magnification TEM showing the specimenand the AFM probe is presented in Figure 2(a) [22].The AFM probe position is fixed, and the specimenmoves in the dark arrow direction to perform indenta-tion. The thickness of CF specimen is 100 nm. Theinset in Figure 2(a) is a high-magnification imageabout a region marked by a dark rectangle near theedge of CF, where graphene layers are shown withmisalignment to the in-graphene-plane axis. We per-formed fast Fourier transform (FFT) analysis on thehigh-resolution TEM images acquired from the samearea as the AFM probe was pushed deeper into the CFspecimen. FFT results of images taken before probecontact and on the deepest indentation are shown inFigure 2(b) and (c), respectively. FFT pattern presentsan elliptical shape with long axis parallel to the in-graphene-plane axis. Perfectly aligned graphene layerswould produce two spots symmetric about the patterncenter. In the case of misaligned graphene layers, thesetwo spots elongated into two arches with arch exten-sion angles, which are used to define misalignmentangles in this case. Such misalignment angle is plottedagainst the indentation force sensed by the AFMprobe, as presented in Figure 2(d). The misalignmentangle was found to increase with indentation forcewith roughly a linear dependence. The TEM observa-tion is consistent with previous reports about com-pressive softening of graphite due to graphene layerbuckling.Figure 3(a) shows two typical force–displacementcurves collected at the same location on CF with andwithout tensile stress during the modulus mappingshown in Figure 1(d). After subtracting deformationof the calibrated AFM cantilever, d was obtained foreach Fl. Using the Hertz Equation (2), we thenobtained CF moduli E of 170 and 350 GPa with andwithout stress, respectively. This result is consistentwith the 100% increase in E as calculated by software.To elucidate the effect of graphene layer misalignmenton the measured indentation modulus, we have con-structed a FEM model to simulate the modulus mea-surement using AFM probe. Graphene layermisalignment angle was simulated by tilting a perfectsingle crystalline graphite at an angle θ with respect toindentation axis, as shown in the illustration in Figure3(b). Modulus was calculated following the definitionin Equation (2) while d was simulated by FEM usingmodel parameters as probe diameter being 15 nm andload force being 1000 nN. The simulation results ofFigure 3(c) show that as the CF misalignment angleincreases, the apparent modulus of CF decreases by asmuch as one order of magnitude [32]. The modulusdrop is especially quick when misalignment angle iswithin the range between 0° and 45°, whichcorresponds to situation encountered during in-planeindentation in our setup. To verify the simulationresult, we studied AFM indentation modulus obtainedat planes of selected orientations from a block of highlyFigure 2. (a) Low magnification TEM image showing the AFM tip indenting on a specimen sliced from a CF. Inset shows high-resolution image about the indented region; (b,c) fast Fourier transform patterns of the same region as marked by the darksquare in (a), where misalignment angle of graphene layers changed before and after the application of indenting force of220 nN; (d) plot of misalignment angle with the applied indenting force to the CF specimen.Sci. Technol. Adv. Mater. 20 (2019) 416 H. WANG et al.oriented pyrolytic graphite (HOPG). HOPG was cho-sen as a model system for CF because its modulusvalue is similar to that of CF and both materials exhibitgood elasticity even at small loading force, which is thescenario of this nanoindentation experiment. BulkHOPG could be easily made into samples of definedgraphene layer orientation (see supplementary infor-mation). Average HOPG moduli obtained at θ of 0°,10°, 20° from HOPG indentation were also plotted inFigure 3(c). While the agreement was fair, it shows aneven quicker drop of modulus with increasedmisalignment angle compared to simulation. It isbecause the experiment was carried out with sameload force other than same indentation depth. Highermisalignment angle thus produces larger depth andresults in a further reduction of apparent modulus.From Figures 2(d) and 3(c), the relationship betweenmodulus E and loading force Fl can be establishedthrough the misalignment angle after the correctionof difference between AFM probe and TEM–AFMprobe. Figure 3(d) is a comparison among such calcu-lated E–Fl curve for CF and experimentally measureddata from CF and P. The loading force ranges for CFare chosen from 0 to 1000 nN while that for P is from 0to 50 nN, because of their very different modulusvalues. It is shown that while measured modulus forCF shows a clear drop with increasing indentationforce, agreeing quite well with calculation, that forP presents an almost constant modulus value. It provesour point that the modulus drop for CF is due to thestrong heterogeneity of graphite structure while P iswith an isotropic structure. According to the HertzFigure 3. (a) Force–displacement curves obtained from the same position on a CF with and without external stress; (b) finiteelement method (FEM) model for indentation modulus simulation of carbon fiber; (c) simulation result of compressive moduliagainst misalignment angle for in-graphene-plane indentation; (d) calculated modulus of CF versus loading force compared withthat of experimentally measured values and measured modulus response to loading force for polymer matrix; (e) plot of elasticforce against deformation depth; dark line shows elastic force calculated from misalignment angle–force relationship obtainedin the TEM experiment; colored lines show elastic forces expected by subtracting each stress forces from total load force; (f) plotof calculated modulus relative change against external tensile stress.Sci. Technol. Adv. Mater. 20 (2019) 417 H. WANG et al.equation, we can thereby derive the relationshipbetween the elastic force, Fc, and the deformationdepth, d, of CF, which is presented by a black curvein Figure 3(e). Under each deformation depth, thepartial force component, Fs, from externally appliedstress can then be determined through Equation (1). InFigure 3(e), the cross points between the black line Fcand the color lines (1000 nN-Fs) give the deformations,dn, of CF under each external stress, σn, during thesame indentation load force of 1000 nN. The ratio ofthe deformation depth under stress, dn, over that with-out stress, d0, thus gives the relative increase of theapparent modulus, ΔEn/E0, through Equation (3) asΔEnE0¼ EnE0� 1 ¼ ðd0dnÞ1:5 � 1 (3)Finally, we arrive at the dependence of ΔEn/E0 on exter-nal stress, σn, which result is plotted in Figure 3(f). Theconsistency between the calculation and the experimen-tal observation proved that indentation modulus soft-ening must be considered to explain the large stress CFmodulus response to orthogonal stress. In summary,externally applied stress caused only small change inAFM probe deformation depth; however, through theunique modulus softening of CF material, this smallchange in deformation causes much larger change inresistance force sensed by the indentation probe.The above described modulus hardening of CFwas utilized in the following example where stressdistribution on CF was mapped by measuring localindentation moduli during an in situ fracturingexperiment on a bulk CFRP material. As shown inFigure 4(a), upon applying a small tensile stress, theaverage stress of the lower intact CF is 2.0 GPa whichis about 66% higher than 1.2 GPa of the upper brokenCF. When specimen bending amount was increased,the lower CF average stress became 2.8 GPa. It is 86%higher than that of the upper CF, which onlyincreased a little to 1.5 GPa. It is consistent withliteratures that an ineffective length exists in brokenCF over the range of which stress is no longer carried[33]. Two defect lines were also observed in the lowerintact CF as marked by the two white arrows inFigure 4(b). Such defects were not presented inFigure 4(a) under a smaller stress. No difference inheight maps between these two stress states could benoticed if one compares Figure 4(d) with (e). Thedefect lines exhibited lower modulus values com-pared to surrounding area. It suggests that localyield of material might have occurred, where localstress stopped increasing with increasing local strain.A line profile created crossing the defect is shown inFigure 4(g) as profile 1. The full width at half max-imum (FWHM) of the first defect line is 150 nm,which is consistent with previous observation aboutfracture-initiating defect size in CF [7]. Three otherline profiles in area outside of the highlight were alsocreated in Figure 4(b) to show that the defect contrastobserved in profile 1 was not due to AFM noise.Next, the external stress was further increased tillthe lower CF fractured at the location of the pre-viously observed defects. In Figure 4(c), the averagestress on lower CF dropped to 1.1 GPa by 60%. Thestress of the upper CF became 1.3 GPa, which iswithin 10% deviation of its initial state. This deviationshould be experimental uncertainty. Figure 4(h) isa stress line profile of CFRP created along the whitearrows in Figure 4(a–c). It is clearly seen that thestress in the upper CF did not change appreciablywhile that in the lower CF changed much moredramatically with the applied bending force to theCFRP specimen. Figure 4(i) is height line profilestaken along the black arrows in the height maps ofFigure 4(d–f). The height profiles of the unstressedand 3.5 GPa stressed are identical, which agrees withour previous observation that the local moduluschange did not come from the effect of the surfacetopography. The 4.3 GPa stressed CF showed a differ-ent height profile from the other cases, which mightindicate CF–P debonding at the interface during thelower CF fracture [34].4. ConclusionsIt has been found that pinpoint indentation modulusof CF increased with external tensile tress in theorthogonal direction. The phenomenon was investi-gated in a quantitative way using TEM in situ inden-tation experiment and FEM modeling. Themechanism was applied as a method of sensing stressdistribution in a CFRP bulk material during an AFMin situ fracturing experiment. Tensile stress wasobserved developing in the CF when external loadincreased. Nanometer-sized defects were found form-ing in the CF. As stress keeps increasing, the defectswere found developing into a complete fracture andstress disappeared in the broken CF. The introducedtechnique thus provides a nondestructive way tomonitor stress status of CFRP material to evaluateits load-carrying ability and to prevent catastrophicfracture. It would be interesting as one future plan toapply the technique on new CF–polymer compositewhere CF was pre-grafted with functionalgroups [35].The phenomenon of stress-sensitive indentationmodulus has been observed on CFRP in this studyand reported on Au films through a similar AFM-based technique. In our recent experiment withindentation pre-stressed Si wafer, the modulus pat-tern mapped around the indentation pit also showsgood agreement with stress field distribution con-firmed by Raman microscopy (see supplementarymaterials). A general mechanism may exist for theseobservations on different material systems, whichSci. Technol. Adv. Mater. 20 (2019) 418 H. WANG et al.however first needs further investigation on eachdifferent case.Disclosure statementNo potential conflict of interest was reported by theauthors.FundingThis work was supported by Cross-ministerial StrategicInnovation Promotion Program—Unit D66—InnovativeMeasurement and Analysis for Structural Materials.ORCIDKenta Goto http://orcid.org/0000-0002-0102-0658Ikumu Watanabe http://orcid.org/0000-0002-7693-1675References[1] Polop C, Vasco E, Perrino AP, et al. Mapping stressin polycrystals with sub-10 nm spatial resolution.Nanoscale. 2017;9:13938.[2] Vasco E, Polop C. Intrinsic compressive stress inpolycrystalline films is localized at edges of thegrain boundaries. Phys Rev Lett. 2017;119:256102.[3] Cammarata RC, Sieradzki K. Eff‘ects of surface stresson the elastic moduli of thin films and superlattices.Phys Rev Lett. 1989;62(17):2005–2008.[4] Oku T, Eto M. The effect of compressive prestressingon the mechanical properties of some nucleargraphites. 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Fiber/matrixdebond growth from fiber break in unidirectionalcomposite with local hexagonal fiber clustering.Compos Part B-Eng. 2016;101:124–131.[35] Deng HM, Xu JY, Li XY, et al. The synergistic actionbetween anhydride grafted carbon fiber and intu-mescent flame retardant enhances flame retardancyand mechanical properties of polypropylenecomposites. Sci Technol Adv Mater.2018;19:718–731.Sci. Technol. Adv. Mater. 20 (2019) 420 H. WANG et al.http://www.torayca.com/en/download/pdf/torayca.pdfhttp://www.torayca.com/en/download/pdf/torayca.pdf Abstract 1. Introduction 2. Experimental details 3. Results and discussion 4. Conclusions Disclosure statement Funding ORCID References