Tiny yet tough: Maximizing the toughness of fiber-reinforced soft composites in the absence of a fiber-fracture mechanism

•Extremely high fracture toughness of soft composites at small specimen sizes•Fiber pullout-induced matrix rupture elucidated as the energy-dissipation source•Fiber bundle geometry is an important factor influencing composite toughness•A fiber pullout model can determine composite toughness from component parameters Developing methods to maximize toughness at small specimen sizes is extremely important for miniaturized applications, such as tiny robotics and medical devices. Herein, we demonstrate that soft fiber-reinforced polymers (FRPs) can achieve superior toughness, even at small size scales, without requiring fiber fracture as an energy-dissipation source. The key to the observed toughness amplification is a unique fiber pullout behavior, where a massive amount of energy is dissipated by the fracture of the extremely tough matrix surrounding the fiber bundles. Due to the strong interfacial interactions between the fibers and the matrix, the pullout process causes rupture of the tough matrix throughout the entire sample, even far away from the initial crack tip. A universal, semi-empirical equation is established from the consideration of a simple fiber-reinforced soft composite model that allows for the prediction of toughness of soft FRPs at limited size scales. The toughness of composite materials is size dependent below a critical load transfer length (lT). Fiber-reinforced viscoelastic polymers are uniquely suited to study the size-limited regime because the lT of these soft composites can be as high as several centimeters, in contrast to traditional composites where lT is extremely small, allowing a large window for macroscale characterization. In this work, we elucidate the parameters that influence the toughness of soft composites when failure is governed by a fiber pullout-induced matrix-fracture mechanism. We ultimately demonstrate three important points: (1) fiber-reinforced viscoelastic polymers can possess high toughness, even at dimensions well below lT, (2) significant toughness amplification occurs due to the presence of fibers, even when the fracture process consists solely of matrix rupture, and (3) the composite toughness in the fiber pullout region can be predicted from easily attainable component parameters. The toughness of composite materials is size dependent below a critical load transfer length (lT). Fiber-reinforced viscoelastic polymers are uniquely suited to study the size-limited regime because the lT of these soft composites can be as high as several centimeters, in contrast to traditional composites where lT is extremely small, allowing a large window for macroscale characterization. In this work, we elucidate the parameters that influence the toughness of soft composites when failure is governed by a fiber pullout-induced matrix-fracture mechanism. We ultimately demonstrate three important points: (1) fiber-reinforced viscoelastic polymers can possess high toughness, even at dimensions well below lT, (2) significant toughness amplification occurs due to the presence of fibers, even when the fracture process consists solely of matrix rupture, and (3) the composite toughness in the fiber pullout region can be predicted from easily attainable component parameters. IntroductionCutting-edge applications in the fields of soft robotics and advanced medical devices require materials with a combination of small size, high strength, low flexural stiffness, and high crack resistance. Molecular-scale composites, such as double-network materials, hybrid viscoelastic hydrogels, and nanocomposites have shown promise in achieving some of these requirements.1Gong J.P. Katsuyama Y. Kurokawa T. Osada Y. Double-network hydrogels with extremely high mechanical strength.Adv. Mater. 2003; 15: 1155-1158https://doi.org/10.1002/adma.200304907Crossref Scopus (2989) Google Scholar, 2Gong J.P. Why are double network hydrogels so tough?.Soft Matter. 2010; 6: 2583-2590https://doi.org/10.1039/B924290BCrossref Google Scholar, 3Sun J.-Y. Zhao X. Illeperuma W.R. Chaudhuri O. Oh K.H. Mooney D.J. Vlassak J.J. Suo Z. Highly stretchable and tough hydrogels.Nature. 2012; 489: 133-136https://doi.org/10.1038/nature11409Crossref PubMed Scopus (3273) Google Scholar, 4Sun T.L. Kurokawa T. Kuroda S. Ihsan A.B. Akasaki T. Sato K. Haque M.A. Nakajima T. Gong J.P. Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity.Nat. Mater. 2013; 12: 932-937https://doi.org/10.1038/nmat3713Crossref PubMed Scopus (1337) Google Scholar, 5Ducrot E. Chen Y. Bulters M. Sijbesma R.P. Creton C. Toughening elastomers with sacrificial bonds and watching them break.Science. 2014; 344: 186-189https://doi.org/10.1126/science.1248494Crossref PubMed Scopus (631) Google Scholar, 6Haraguchi K. Takehisa T. Nanocomposite hydrogels: a unique organic–inorganic network structure with extraordinary mechanical, optical, and swelling/de-swelling properties.Adv. Mater. 2002; 14: 1120-1124https://doi.org/10.1002/1521-4095(20020816)14:16<1120::AID-ADMA1120>3.0.CO;2-9Crossref Scopus (1785) Google Scholar However, integrating all of these required, yet often contradicting, properties into one material system is still a daunting challenge.Soft fiber-reinforced polymers (FRPs) are promising materials due to their unique mechanical and physical properties.7Wang Z. Xiang C. Yao X. Floch P.L. Mendez J. Suo Z. Stretchable materials of high toughness and low hysteresis.Proc. Natl. Acad. Sci. U S A. 2019; 116: 5967-5972https://doi.org/10.1073/pnas.1821420116Crossref PubMed Scopus (157) Google Scholar, 8Markvicka E.J. Bartlett M.D. Huang X. Majidi C. An autonomously electrically self-healing liquid metal–elastomer composite for robust soft-matter robotics and electronics.Nat. Mater. 2018; 17: 618-624https://doi.org/10.1038/s41563-018-0084-7Crossref PubMed Scopus (475) Google Scholar, 9Takahashi R. Sun T.L. Saruwatari Y. Kurokawa T. King D.R. Gong J.P. Creating stiff, tough, and functional hydrogel composites with low-melting-point alloys.Adv. Mater. 2018; 30: 1706885https://doi.org/10.1002/adma.201706885Crossref Scopus (60) Google Scholar, 10Hubbard A.M. Cui W. Huang Y. Takahashi R. Dickey M.D. Genzer J. King D.R. Gong J.P. Hydrogel/elastomer laminates bonded via fabric interphases for stimuli-responsive actuators.Matter. 2019; 1: 674-689https://doi.org/10.1016/j.matt.2019.04.008Abstract Full Text Full Text PDF Scopus (48) Google Scholar, 11Lin S. Cao C. Wang Q. Gonzalez M. Dolbow J.E. Zhao X. Design of stiff, tough and stretchy hydrogel composites via nanoscale hybrid crosslinking and macroscale fiber reinforcement.Soft Matter. 2014; 10: 7519-7527https://doi.org/10.1039/C4SM01039FCrossref PubMed Google Scholar, 12Agrawal A. Rahbar N. Calvert P.D. Strong fiber-reinforced hydrogel.Acta Biomater. 2013; 9: 5313-5318https://doi.org/10.1016/j.actbio.2012.10.011Crossref PubMed Scopus (122) Google Scholar, 13Zhalmuratova D. Chung H.J. Reinforced gels and elastomers for biomedical and soft robotics applications.ACS Appl. Polym. Mater. 2020; 2: 1073-1091https://doi.org/10.1021/acsapm.9b01078Crossref Scopus (38) Google Scholar, 14Liao I.C. Moutos F.T. Estes B.T. Zhao X. Guilak F. Composite three-dimensional woven scaffolds with interpenetrating network hydrogels to create functional synthetic articular cartilage.Adv. Funct. Mater. 2013; 23: 5833-5839https://doi.org/10.1002/adfm.201300483Crossref PubMed Scopus (188) Google Scholar Traditional soft FRPs are made by laminating or curing rubbery polymers with stiff fabrics, and have found use in large-size structural and load-bearing applications, such as flexible aircraft fuel tanks and pneumatic tires.14Liao I.C. Moutos F.T. Estes B.T. Zhao X. Guilak F. Composite three-dimensional woven scaffolds with interpenetrating network hydrogels to create functional synthetic articular cartilage.Adv. Funct. Mater. 2013; 23: 5833-5839https://doi.org/10.1002/adfm.201300483Crossref PubMed Scopus (188) Google Scholar,15Gent A.N. Walter J.D. The Pneumatic Tire. Mechanical Engineering Faculty Research, 2006Google Scholar16Yang X. Zhang Z. Yang J. Sun Y. Fluid-structure interation analysis of the drop impact test for helicopter fuel tank.SpringerPlus. 2016; 5: 1-21https://doi.org/10.1186/s40064-016-3040-5Crossref PubMed Scopus (14) Google Scholar These materials, however, are often plagued by poor crack resistance due to delamination and interfacial failure. Recently, extraordinarily crack-resistant soft FRPs have been developed by combining strong and stiff fibers with viscoelastic hydrogels or elastomers as matrices,17King D.R. Sun T.L. Huang Y. Kurokawa T. Nonoyama T. Crosby A.J. Gong J.P. Extremely tough composites from fabric reinforced polyampholyte hydrogels.Mater. Horiz. 2015; 2: 584-591https://doi.org/10.1039/C5MH00127GCrossref Google Scholar, 18Huang Y. King D.R. Sun T.L. Nonoyama T. Kurokawa T. Nakajima T. Gong J.P. Energy-dissipative matrices enable synergistic toughening in fiber reinforced soft composites.Adv. Funct. Mater. 2017; 27: 1605350https://doi.org/10.1002/adfm.201605350Crossref Scopus (90) Google Scholar, 19Huang Y. King D.R. Cui W. Sun T.L. Guo H. Kurokawa T. Brown H.R. Hui C.Y. Gong J.P. Superior fracture resistance of fiber reinforced polyampholyte hydrogels achieved by extraordinarily large energy-dissipative process zones.J. Mater. Chem. A. 2019; 7: 13431-13440https://doi.org/10.1039/C9TA02326GCrossref Google Scholar exhibiting fracture energy up to 2,500 kJ m−2.20Hofmann D.C. Suh J.Y. Wiest A. Duan G. Lind M.L. Demetriou M.D. Johnson W.L. Designing metallic glass matrix composites with high toughness and tensile ductility.Nature. 2008; 451: 1085-1089https://doi.org/10.1038/nature06598Crossref PubMed Scopus (1246) Google Scholar, 21Mao L.B. Gao H.L. Yao H.B. Liu L. Cölfen H. Liu G. Chen S.M. Li S.K. Yan Y.X. Liu Y.Y. Yu S.H. Synthetic nacre by predesigned matrix-directed mineralization.Science. 2016; 354: 107-110https://doi.org/10.1126/science.aaf8991Crossref PubMed Scopus (525) Google Scholar, 22Xu L. Zhao X. Xu C. Kotov N.A. Water-rich biomimetic composites with abiotic self-organizing nanofiber network.Adv. Mater. 2018; 30: 1703343https://doi.org/10.1002/adma.201703343Crossref Scopus (107) Google Scholar, 23Demetriou M.D. Launey M.E. Garrett G. Schramm J.P. Hofmann D.C. Johnson W.L. Ritchie R.O. A damage-tolerant glass.Nat. Mater. 2011; 10: 123-128https://doi.org/10.1038/nmat2930Crossref PubMed Scopus (488) Google Scholar, 24Smith B.L. Schäffer T.E. Viani M. Thompson J.B. Frederick N.A. Kindt J. Belcher A. Stucky G.D. Morse D.E. Hansma P.K. Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites.Nature. 1999; 399: 761-763https://doi.org/10.1038/21607Crossref Scopus (1032) Google Scholar, 25Munch E. Launey M.E. Alsem D.H. Saiz E. Tomsia A.P. Ritchie R.O. Tough, bio-inspired hybrid materials.Science. 2008; 322: 1516-1520https://doi.org/10.1126/science.1164865Crossref PubMed Scopus (1355) Google Scholar These soft composites show extremely high toughness due to the synergetic effect of three features of the soft matrix: strong bonding to fibers, low modulus (104Sun T.L. Kurokawa T. Kuroda S. Ihsan A.B. Akasaki T. Sato K. Haque M.A. Nakajima T. Gong J.P. Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity.Nat. Mater. 2013; 12: 932-937https://doi.org/10.1038/nmat3713Crossref PubMed Scopus (1337) Google Scholar–105 orders lower than the fibers), and high work needed for rupture (comparable with that of the fibers). As a result, these soft composites have a very large load transfer length (lT), on the centimeter scale, and high energy-dissipation density due to concurrent fracture of the fiber and matrix. We have shown that, for a sufficiently large specimen size, w > lT, the tearing energy (toughness) of the soft composites, Γ, is quantitatively related to the volume-weighted average of the work needed to rupture the two components, W, and the load transfer length, lT, as Γ = W·lT,26Cui W. King D.R. Huang Y. Chen L. Sun T.L. Guo Y. Saruwatari Y. Hui C.Y. Kurokawa T. Gong J.P. Fiber-reinforced viscoelastomers show extraordinary crack resistance that exceeds metals.Adv. Mater. 2020; 32: 1907180https://doi.org/10.1002/adma.201907180Crossref PubMed Scopus (43) Google Scholar,27Lake G. Thomas A. The strength of highly elastic materials.Proc. R. Soc. Lond. A. 1967; 300: 108-119https://doi.org/10.1098/rspa.1967.0160Crossref Google Scholar,28Volokh K. Trapper P. Fracture toughness from the standpoint of softening hyperelasticity.J. Mech. Phys. Solids. 2008; 56: 2459-2472https://doi.org/10.1016/j.jmps.2008.02.009Crossref Scopus (21) Google Scholar where lT scales with the square root of the fiber/matrix modulus ratio and can be explicitly calculated for a given component combination and geometry.29Hedgepeth J.M. Stress Concentrations in Filamentary Structures. National Aeronautics and Space Administration, 1961Google Scholar,30Cox H. The elasticity and strength of paper and other fibrous materials.Br. J. Appl. Phys. 1952; 3: 72https://doi.org/10.1088/0508-3443/3/3/302Crossref Scopus (2951) Google Scholar At large-size scales, these materials show extraordinary crack resistance, even exceeding metals, with significantly reduced weight and low cost.31Ashby M.F. Cebon D. Materials selection in mechanical design.J Phys IV. 1993; 3 (C7–1-C7-9)https://doi.org/10.1051/jp4:1993701Crossref Scopus (216) Google Scholar,32Gludovatz B. Hohenwarter A. Catoor D. Chang E.H. George E.P. Ritchie R.O. A fracture-resistant high-entropy alloy for cryogenic applications.Science. 2014; 345: 1153-1158https://doi.org/10.1126/science.1254581Crossref PubMed Scopus (3044) Google ScholarWhen the size, w, of these soft composites is decreased below lT, the toughness decreases from the plateau value and becomes size dependent due to a change in fracture mechanism (Figure 1A).19Huang Y. King D.R. Cui W. Sun T.L. Guo H. Kurokawa T. Brown H.R. Hui C.Y. Gong J.P. Superior fracture resistance of fiber reinforced polyampholyte hydrogels achieved by extraordinarily large energy-dissipative process zones.J. Mater. Chem. A. 2019; 7: 13431-13440https://doi.org/10.1039/C9TA02326GCrossref Google Scholar,26Cui W. King D.R. Huang Y. Chen L. Sun T.L. Guo Y. Saruwatari Y. Hui C.Y. Kurokawa T. Gong J.P. Fiber-reinforced viscoelastomers show extraordinary crack resistance that exceeds metals.Adv. Mater. 2020; 32: 1907180https://doi.org/10.1002/adma.201907180Crossref PubMed Scopus (43) Google Scholar The apparent size dependence in Figure 1A can be divided into three regions (Figure 1B) according to the failure process. A transition from fiber and matrix concurrent fracture at the saturated toughness (region III) to a mixed-mode fiber-fracture/pullout mechanism (region II) occurs at w ≈ lT. For sufficiently small composites, the failure mechanism consists of only fiber pullout with no fiber fracture (region I). The width at which this transition occurs is referred to as w1. Composites with specimen size below lT are not able to fully utilize the fiber-fracture energy-dissipation mechanism, resulting in reduced toughness. However, if we compare the toughness of the composites observed in region I with the neat matrix and fabric, we see that, within this region, they are still capable of exhibiting toughness much greater than either neat component (Figure 1C). The energy-dissipation mechanism that governs region I where only fiber pullout occurs is currently unknown, yet these composites fulfill many of the complex mechanical requirements for small-scale soft material devices, making them worthy of further study.The size-dependent behavior for composites at length scales smaller than lT has never before been the focus of investigation. For traditional rigid composites, the fracture behavior in the sub-lT region cannot be studied through macroscopic mechanical tests, because in these materials lT is extremely small (less than millimeter scale).33Chen C. Wang Z. Suo Z. Flaw sensitivity of highly stretchable materials.Extreme Mech. Lett. 2017; 10: 50-57https://doi.org/10.1016/j.eml.2016.10.002Crossref Scopus (110) Google Scholar, 34Hui C.Y. Liu Z. Phoenix S.L. Size effect on elastic stress concentrations in unidirectional fiber reinforced soft composites.Extreme Mech. Lett. 2019; 33: 100573https://doi.org/10.1016/j.eml.2019.100573Crossref Scopus (12) Google Scholar, 35Hui C.Y. Liu Z. Phoenix S.L. King D.R. Cui W. Huang Y. Gong J.P. Mechanical behavior of unidirectional fiber reinforced soft composites.Extreme Mech. Lett. 2020; 35: 100642https://doi.org/10.1016/j.eml.2020.100642Crossref Scopus (10) Google Scholar On the other hand, although traditional soft composites made from laminated rubbers can theoretically have very large lT values implying the existence of a size-appropriate sub-lT region, interfacial delamination between the matrix and fibers results in a separate failure mechanism, preventing this study.36Pan R. Wati D. Tear resistance of sparsely reinforced elastomer sheets.Polym. Compos. 1996; 17: 486-491https://doi.org/10.1002/pc.10637Crossref Scopus (5) Google Scholar, 37Mehan M. Schadler L. Micromechanical behavior of short-fiber polymer composites.Compos. Sci. Technol. 2000; 60: 1013-1026https://doi.org/10.1016/S0266-3538(99)00194-3Crossref Scopus (37) Google Scholar, 38Meng Q. Chang M. Interfacial crack propagation between a rigid fiber and a hyperelastic elastomer: experiments and modeling.Int. J. Sol. Struct. 2020; 188: 141-154https://doi.org/10.1016/j.ijsolstr.2019.10.006Crossref Scopus (5) Google Scholar, 39Illeperuma W.R. Sun J.Y. Suo Z. Vlassak J.J. Fiber-reinforced tough hydrogels.Extreme Mech. Lett. 2014; 1: 90-96https://doi.org/10.1016/j.eml.2014.11.001Crossref Scopus (73) Google Scholar Therefore, fiber-reinforced viscoelastic polymers are uniquely suited for investigating this region. Discerning the material and structural parameters governing the fracture mechanism in the sub-lT region is of great significance and will facilitate the rational design and development of materials for use in size-limited applications that require high strength and crack resistance.40Shepherd R.F. Stokes A.A. Nunes R.M. Whitesides G.M. Soft machines that are resistant to puncture and that self seal.Adv. Mater. 2013; 25: 6709-6713https://doi.org/10.1002/adma.201303175Crossref PubMed Scopus (141) Google Scholar,41Keten S. Xu Z. Ihle B. Buehler M.J. Nanoconfinement controls stiffness, strength and mechanical toughness of β-sheet crystals in silk.Nat. Mater. 2010; 9: 359-367https://doi.org/10.1038/nmat2704Crossref PubMed Scopus (932) Google ScholarIn this work, we establish a quantitative empirical relationship to show that the tearing toughness of soft composites, T, scales with the sample width, w, matrix toughness, Tm, and fiber bundle geometry factor, K. This relationship is based upon a simple fiber-reinforced soft composites model with a perfect interface and can accurately calculate T for the limiting case that the soft composites fail through a single-mode fiber pullout mechanism due solely to matrix fracture, with no fiber fracture or interfacial debonding. The relationship has been proven experimentally for a variety of elastomers, fabrics, sample widths, and testing rates, with a total of 76 composite testing combinations. The results demonstrate that the presence of a stiff, reinforcing phase can result in significant toughness amplification when compared with a neat soft elastomer, even when both materials fracture solely through matrix rupture. We believe that the results of this study should give insight into the failure mechanisms of other traditional FRPs in which lT is too small to study the size-dependent fracture behavior experimentally. This work also provides a clear guide toward the future design of miniaturized soft materials devices by exploiting the benefits of FRPs at size scales that have previously been ignored.ResultsMicrostructural analysis of region I soft FRPsViscoelastic matrices are synthesized through a copolymerization of ethylene glycol phenyl ether acrylate (PEA, M1) or 2-(2-phenoxyethoxy) ether acrylate (PDEA, M2) as a soft segment, and isobornyl acrylate (IBA) as a hard segment (Figure S1). Tensile and tearing mechanical properties of the matrices are shown in Figures S3 and S4, respectively, and the results are summarized in Table S1. Two types of carbon fiber (CF) fabrics with the same weave pattern but different fiber bundle geometries are used (Figure S5), which we refer to as thick carbon fiber (CF) and thin carbon fiber (t-CF) fabric, respectively. The structural parameters of the fabrics are summarized in Table S2. Soft FRPs made from different matrices and fabrics are coded as x-f/y, where x represents the soft segment chemistry, f represents the molar fraction of the hard segment, IBA, to the total monomer concentration, and y represents the type of fabric.For each matrix and fabric combination, the occurrence of at least one fiber bundle fracture was the criterion for determining the transition point from region I to region II. This critical width is denoted as w1, and the corresponding value for each sample is listed in Table S3. By utilizing the mechanical and structural parameters of the matrix and fiber bundle (Figures S3 and S6; Table S2), we can also estimate w1 through a force balance between the force applied to a single fiber bundle and the shear resistance by the surrounding matrix during fiber pullout (see Figure S7A and related appendix in supplemental information for details). The experimental w1 is plotted as a function of the theoretical w1 in Figure S7B. The result shows that the experimental w1 follows an empirical relationship:w1,exp=0.76w1,theo=0.76σfAfσmc,(Equation 1) where σf and σm are the fracture stress of a fiber bundle and the matrix, respectively, and Af and c are the cross-sectional area and circumference of a fiber bundle, respectively. Note that a coefficient of 0.76 exists in the equation, indicating that the theoretical w1 is overestimated. The coefficient is required because Equation 1 is based on a unidirectional fiber-reinforced soft composite, whereas the practical soft composites possess a woven structure, with fibers existing in both the longitudinal and lateral direction. During the tearing of a soft composite, the transverse fiber bundles are deformed by the tensile stress along the fiber bundle, as well as by the perpendicular compressive stress from the longitudinal fiber bundles. The additional compressive stress could lead to premature fracture. Such a geometrical difference should account for the existence of the coefficient in Equation 1. Since every parameter of the matrix and fiber bundle is measurable, we can estimate w1 for any material combination using Equation 1, ensuring that all samples fall within region I.A composite sheet is formed when the monomers are synthesized in the presence of the CF fabric, as shown in the scanning electron microscopy (SEM) images taken from a cross-section of an as-prepared M1-0.2/CF sample (Figure 2). Since fiber fracture does not occur at limited specimen size, it is important to explicitly demonstrate that the fibers and matrix are strongly adhered, which ensures effective load transfer. The cross-section was made by cutting the sample with scissors. As a control sample, we first examined the morphology of the two interlaced fiber bundles in a neat CF fabric without matrix. Figure S8 shows that there is an obvious gap between the longitudinal (parallel to crack) and transverse (perpendicular to crack) fiber bundles, and that numerous voids exist within the longitudinal fiber bundle, providing space for the precursor monomer solution to enter. For the soft composite, the SEM observation shows two interwoven fiber bundles that are surrounded by matrix (Figure 2A). A corresponding illustration is given in Figure 2B for clarity. Inside the longitudinal fiber bundle, individual fibers are encompassed by matrix (Figure 2C). The matrix also exists within the crossover region of the two perpendicularly aligned and interwoven fiber bundles (Figure 2D). The SEM observation reveals that the fibers are thoroughly imbedded in the soft matrix to form strong bonding, owing to the good wettability of the precursor monomers onto the fabric.Figure 2The microstructure of the soft FRPs by SEM observationShow full caption(A) A cross-sectional view of the fiber bundles of the soft FRP made from P(PEA-co-IBA) (f = 0.2) and thick carbon fiber fabric.(B) Corresponding illustration of the SEM image in (A).(C) SEM image of a longitudinal fiber bundle at position “c” as shown in (B). The magnified image shows that individual fibers inside the fiber bundle are fully surrounded by the matrix.(D) SEM image of two interlaced fiber bundles at position “d” shown in (B). The magnified image shows that the interlaced fiber bundles are connected by the matrix with some voids.View Large Image Figure ViewerDownload Hi-res image Download (PPT)After confirming the structure and interface, we aimed to clarify the fracture mechanism for soft FRPs that exhibit only fiber pullout (region I). The typical fiber pullout failure behavior of a soft FRP before, during, and after a tearing test is shown in Figure 3. For the tearing test, the sample was cut to the required geometry with a laser cutter. One leg was fixed to the bottom of the tensile tester, and the other leg was fixed to the crosshead with mechanical grips. Displacement was applied at 50 mm min−1 and the force was measured until the sample completely failed. The resulting force-displacement curve is shown in Figure 3A, and SEM images were taken at the crack tip region at different tearing times (Figures 3B–3D). Before the test, the longitudinal fiber bundles appeared to be intimately connected with the transverse fiber bundle through the matrix (Figure 3B). When the transverse fiber bundle undergoes pullout, the matrix existing within the crossover region becomes greatly deformed, resulting in prominent fibrillation (Figure 3C). Owing to the strong interface between components (resulting from two physical effects: van der Waals adhesion and topological interlocking),26Cui W. King D.R. Huang Y. Chen L. Sun T.L. Guo Y. Saruwatari Y. Hui C.Y. Kurokawa T. Gong J.P. Fiber-reinforced viscoelastomers show extraordinary crack resistance that exceeds metals.Adv. Mater. 2020; 32: 1907180https://doi.org/10.1002/adma.201907180Crossref PubMed Scopus (43) Google Scholar cracks tend to be initiated in the matrix between the fiber bundles, rather than at the fiber/matrix interface, and propagate as fiber pullout proceeds. SEM images of a longitudinal and a transverse fiber bundle after pullout are shown in Figure 3Di and Dii, respectively. The fiber bundles remain intact while the matrix between the bundles is fractured, with the residual matrix still bonded to the fiber bundle surface. The above results confirm that the fiber/matrix interface is strong and that the failure behavior of the soft FRPs with w < w1 is fiber pullout-induced matrix rupture.Figure 3The fiber pullout fracture behavior of the soft FRPs around the crack tipShow full caption(A) Force-displacement curve of the tearing test of the soft FRP (w = 10 mm). The letters b, c, and d on the curve correspond to the (B), (C), and (D), respectively. The first peak of this curve indicates the onset of fiber pullout.(B) SEM image of two interlaced fiber bundles in the original soft FRP before loading at point b.(C) SEM image and corresponding magnified region of two interlaced fiber bundles during deformation at point c. Significant fibrillation of the matrix is observed in the interlaced region, which accounts for large energy dissipation.(D) SEM images of a longitudinal (i) and a transverse (ii) fiber bundle after pullout at point d. The fractured matrix remains adhered to the fiber bundles, indicating strong bonding at the fiber/matrix interface.View Large Image Figure ViewerDownload Hi-res image Download (PPT)A simple model for understanding toughness in the fiber pullout limitSince the fracture behavior of soft FRPs in region I is governed by fiber pullout-induced matrix rupture and that the fiber is much stiffer than the matrix, we can estimate the fracture energy (toughness) of the composites by only considering the energy dissipation of the matrix as:19Huang Y. King D.R. Cui W. Sun T.L. Guo H. Kurokawa T. Brown H.R. Hui C.Y. Gong J.P. Superior fracture resistance of fiber reinforced polyampholyte hydrogels achieved by extraordinarily large energy-dissipative process zones.J. Mater. Chem. A. 2019; 7: 13431-13440https://doi.org/10.1039/C9TA02326GCrossref Google ScholarT=Wρt(w