Analysis of a pull-out test with real specimen geometry. Part I: matrix droplet in the shape of a spherical segment

We compared two models of the pull-out specimen – the ‘equivalent cylinder’ and the platelet models in which the matrix droplet is represented as a set of thin parallel disks with the diameters varying along the embedded fiber to approximate the real droplet shape. Analytical expressions for the profiles of the fiber tensile stress and the interfacial shear stress have been derived for the matrix droplet in the shape of a spherical segment, including the effects of residual thermal stresses and interfacial friction. Using these expressions, we analyzed the process of crack initiation and propagation in the platelet model and investigated the effect of the specimen shape on the force–displacement curves. The interfacial stress near the loaded fiber end in the platelet model is higher than in the equivalent cylinder model, which gives rise to earlier crack initiation and smoother shape of the force–displacement curve. As a result, the calculated interfacial shear strength values may be underestimated by 10–20%, if the equivalent cylinder is used instead of the real droplet shape. A method of correction to the equivalent cylinder model in order to avoid this underestimation is proposed.     

Peak force as function of the embedded length in pull-out and microbond tests: effect of specimen geometry

We have derived the equations which explicitly express the peak force, F _max, and the apparent interfacial shear strength, τ _app, measured in the pull-out and microbond tests, as functions of the embedded length. Three types of test geometries were considered: (1) a fiber embedded in a cylindrical block of the matrix material; (2) microbond test with spherical matrix droplets; and (3) pull-out test in which the matrix droplet had the shape of a hemisphere. Our equations include the local interfacial shear strength (IFSS), τ _d, and the frictional interfacial stress, τ _f, as parameters; the effect of specimen geometry appeared in the form of dependency of the effective fiber volume fraction on the embedded length. The values of τ _d and τ _f were determined by fitting our theoretical curves to experimental F _max (l _e) plots by using the least squares method. Our analysis showed how the local IFSS and the frictional interfacial stress affected the measured F _max and τ _app values. In particular, it was revealed that intervals of embedded lengths could exist in which frictional interfacial stress had no effect on F _max and τ _app, even if the τ _f value was high. We also derived an equation relating the scatter in the interfacial strength parameters (τ _d and τ _f) to the scatter in τ _app, which is experimentally measurable, and proposed a procedure to determine the standard deviations of τ _d and τ _f from experimental pull-out and/or microbond test data.     

Indirect estimation of fiber/polymer bond strength and interfacial friction from maximum load values recorded in the microbond and pull-out tests. Part I: local bond strength

The techniques aimed at adhesion strength measurement between reinforcing fibers and polymer matrices (the pull-out and microbond tests) involve the measurement of the force, F _max, required to pull out a fiber whose end is embedded in the matrix. Then, this maximum force value is used to calculate such interfacial parameters as the apparent bond strength, τ_app, and the local interfacial shear strength (IFSS), τ_d. However, it has been demonstrated that the F _max value is influenced by interfacial friction in already debonded regions, and, therefore, these parameters are not purely 'adhesional' but depend, in an intricate way, on interfacial adhesion and friction. In the last few years, several techniques for separate determination of adhesion and friction in micromechanical tests have been developed, but their experimental realization is rather complicated, because they require an accurate value of the external load at the moment of crack initiation. We have developed a new technique which uses the relationship between the maximum force and the embedded length ('scale factor') to separately measure fiber-matrix interfacial adhesion and friction. Using the equation for the current crack length as a function of the applied load, based on a stress criterion of interfacial debonding, we modeled the pull-out and microbond experiments and obtained the maximum force value versus the embedded length. By varying τ_d and interfacial friction, τ_f, to fit experimental plots, both interfacial parameters were estimated. The micromechanical tests were modeled for three types of specimen geometries (cylindrical specimens, spherical droplets, and matrix hemispheres in the pull-out test) with different levels of residual thermal stresses and interfacial friction. The effect of all these factors on the experimental results is discussed, and the importance of specimen geometry is demonstrated. One of the most interesting results is that the 'ultimate' IFSS (the limiting τ_app as the embedded length tends to zero) is not always equal to the 'local' bond strength.     

Theory and Analysis of Fracture Energy in Fiber Reinforced Composites

A micro-mechanics model is developed to analyze the stress distributions and fracture energies associated with crack propagation and fiber pull-out in reinforced composites. The stress and work mechanisms of interfacial debonding, fiber deformation, and the frictional work of fiber pull-out are considered as semi-independent contributions to fracture toughness. The theoretical expressions of Cottrell for frictional work W_F and Outwater and Murphy for fiber deformational work W_D are obtained as special relations in a general relation for the total work W_T = W_s + W_F + W_D where W_s defines the matrix shear work for interfacial debonding of fiber and matrix. Three dimensional diagrams of fracture energies W_T, W_s, or W_r versus interfacial shear bond strength λ₀ and frictional shear stress λ_f identify regions of optimized fracture energy. The influence of environmental degradation of bond strength upon fracture energy is analyzed in terms of the theory.     

Indirect estimation of fiber/polymer bond strength and interfacial friction from maximum load values recorded in the microbond and pull-out tests. Part II: Critical energy release rate

A new approach to experimental data treatment in the pull-out and microbond tests has been developed. It uses the relationship between the maximum force recorded in these tests and the embedded length ('scale factor') to separately determine adhesional interfacial parameters (critical energy release rate, local bond strength) and interfacial friction in debonded regions. The new method does not require the measurement of the debond force, which corresponds to interfacial crack initiation, and is, therefore, much more convenient and simpler than 'direct' techniques involving continuous monitoring of crack growth. Using the equation for the current crack length as a function of the load applied to the fiber, based on a fracture mechanics analysis of interfacial debonding, we modeled the pull-out and microbond experiments and obtained the maximum force versus the embedded length. By varying the critical energy release rate and interfacial frictional stress to fit experimental plots, both interfacial parameters were determined for several fiber-polymer pairs. Effects of specimen geometry, residual thermal stresses, and interfacial friction on the measured values are discussed. The results are compared with those obtained with our similar stress-based approach. The energy criterion works when the embedded length is not very short, and in this range of embedded length it is better than the stress criterion. Both criteria can be complementarily used for interface characterization.     

Calendar of events

—A fracture mechanics approach to the problem of single fiber pull-out is formulated in terms of the critical energy release rate. The solution is more general than that of Outwater and Murphy [1] since the matrix compressive and shear rigidities are more realistic and stress distribution is taken into consideration. The model also takes into account frictional forces between the filament and the matrix along the debonded surface. The shear-lag method is used for stress analysis. A relationship between the filament pull-out force, the critical value of the energy release rate and the position of the tip of the cylindrical crack is established. Numerical examples show the effects of fiber and matrix rigidities and diameters on the apparent average debonding stress predicted by the model. The results of a computer study on the relationship between the pull-out force and the notch size are presented along with the analysis of the model sensitivity to different parameters.     

Evaluation of Adhesion Property of UHMWPE Fibers/Nano-epoxy by a Pullout Test

Ultrahigh-molecular-weight polyethylene (UHMWPE) fibers have poor wetting and adhesion properties to polymer resins because of the inert surface of the fibers. In our previous study, a reactive nano-epoxy matrix, developed by making a modification on the matrix with reactive graphitic nanofibers (r-GNFs), showed improved wettability to UHMWPE fibers. In this work, fiber bundle pullout tests were conducted to evaluate the adhesion property between the UHMWPE fibers and the nano-epoxy matrices. Analysis of load-displacement curves from pullout tests shows that debonding initiation load and ultimate debonding load increased considerably, because of effective improvement of adhesion between the UHMWPE fibers and nano-epoxy matrix. Stress-controlled and energy-controlled models of interfacial debonding were applied for theoretical analyses. Results from ultimate IFSS, frictional shear stress, and critical energy-release rate are in good agreement with experimental results. Nano-epoxy matrix with 0.3 wt% r-GNFs shows effective improvement in terms of adhesion property between UHMWPE fiber and epoxy.     

Modified shear lag model for fibers and fillers with irregular cross-sectional shapes

For fibers with irregular cross sections such as ultrahigh modulus polyethylene (UHMPE) fibers and ribbon-like carbon fibers, the original shear lag model would not provide accurate calculations for interfacial shear stress because it assumes a circular fiber cross section. In this study, a modified shear lag model is proposed to calculate the interfacial shear stress that reflects the change of fiber cross-sectional shape. Microbond test on a UHMPE fiber/epoxy system was used for verification of the model. The difference between the interfacial shear strength (IFSS) calculated using the modified model and that using the original model assuming an equivalent fiber diameter was found to be as high as 15% and it linearly increased as the irregularity of the cross-sectional shape increased. When the irregularity constant exceeds 1.12, the error in IFSS involved in using the original shear lag model and an equivalent fiber diameter is greater than 10%.     

Interfacial properties of kevlar-49 fiber-reinforced thermoplastics

A single-filament pull-out test was used to study adhesion of Kevlar-49 fibers to thermoplastic polymers. The test involved pulling a partially embedded fiber out of a polymer film. Kevlar-49 fibers with three different surface treatments were used with five thermoplastic materials. The test resulted in the measurement of two properties, an interfacial bond strength and a frictional shear strength. The interfacial bond strength is an essential factor in determining the critical aspect ratio of discontinuous fibers in a composite. The frictional shear strength was found to correlate with the tensile strength of discontinuous fiber composites which fail by fiber pull-out. Scanning electron microscopy was used to examine the fiber pull-out specimens after testing. Observations of the fiber showed that the failure mode at the fiber–matrix interface was complex. The predominant failure mode was fracture at the interface (or in some weak boundary layer). In some cases, cohesive failure of the fiber surface was observed, with the result that strips of material were torn from the fiber surface.     

Measuring effective interfacial shear strength in carbon fiber bundle polymeric composites

Adhesion in composite materials is often quantified using the single fiber fragmentation (SFF) test. While this method is believed to provide accurate values for the fiber–matrix interfacial shear strength (IFSS), these may not accurately reflect the macroscopic mechanical properties of specimens consisting of tows of thousands of tightly spaced fibers embedded in a resin matrix. In these types of specimens, adhesion may be mitigated by fiber twisting and misalignment, differences in the resin structure in the confined spaces between the fibers and, most importantly, by any incompleteness of the fiber wetting by the resin. The present work implements fiber band fragmentation (FBF) testing to obtain effective interfacial shear strengths, whose values reflect the importance of these factors. The fiber fragmentation in these specimens is tracked through the counting and sorting of acoustic emission (AE) events occurring during the tensile testing of the specimen and yields the average critical fiber fragment length. AE results, in conjunction with stress-strain data, show that fiber breakage events occur at acoustic wavelet amplitudes substantially greater than those generated by fiber/matrix debonding. Kelly–Tyson analysis is applied, using the measured critical fiber fragment length together with known values for the fiber diameter and tensile strength to yield the effective IFSS. FBF tests are performed on carbon fiber/poly(vinyl butyral) (PVB) dog-bone fiber-bundle systems, and effective IFSS values substantially lower than those typically reported for the single fiber fragmentation testing of similar systems are obtained, suggesting the importance of multi-fiber effects and incomplete fiber wetting.     

不同龄期钢纤维增强水泥砂浆纤维拉拔试验与模拟研究

钢纤维增强水泥基复合材料作为一种多相复合材料,其增强增韧效果的发挥依赖于钢纤维与基体之间的界面粘结性能。通过开展不同龄期的钢纤维增强水泥基复合材料单根纤维拉拔试验及数值模拟研究,分析了龄期对钢纤维增强水泥砂浆界面粘结性能的影响,建立了不同龄期的单根纤维拉拔细观模型,通过将模拟结果与试验结果进行对比验证模型的有效性。根据所建立的细观模型分别对不同龄期钢纤维增强水泥砂浆纤维-基体间的界面粘结作用机理及纤维-基体间粘结表面在纤维拔出过程中的应力变化进行了分析。结果表明:所建立细观模型模拟得到的纤维最大拉拔力及荷载-滑移曲线与试验结果吻合较好,钢纤维的最大拉拔力及钢纤维-水泥砂浆基体的界面粘结强度均随着龄期的增加而增加;在7 d龄期内界面粘结强度的增长速度较快,7 d龄期后增长速度放缓;随着龄期的增加,不同龄期段的界面粘结强度的增长率逐渐减小并趋于稳定。采用拟合得到的粘结表面材料参数能够有效模拟各龄期下单根钢纤维从水泥砂浆中的拔出过程。     

微脱黏法在碳纤维/环氧树脂界面性能评价中的应用

利用微脱黏法测定碳纤维/环氧树脂复合材料的界面剪切强度,并分析了造成测试结果分散的影响因素.结果表明:在脱黏过程中,最大脱黏力随碳纤维埋人环氧树脂内长度的增加而线性递增,当埋人长度超过一定值后最大脱黏力趋于稳定:碳纤维与环氧树脂间的接触角对复合材料界面剪切强度有一定影响,接触角越大,界面剪切强度越高;测试结果的分散性与树脂微球的半月板区域、钳口区等因素有关;未经表面处理的碳纤维增强环氧树脂复合材料的界面剪切强度仪为39.4 MPa,低于处理后的复合材料(60.6 MPa).     

Experimental Observations of Frictional Heating in Fiber-Reinforced Ceramics

The influence of fatigue loading history and microstructural damage on the magnitude of frictional heating and interfacial shear stress in a unidirectional SiC fiber/calcium aluminosilicate matrix composite was investigated. The extent of frictional heating was found to depend upon loading frequency, stress range, and average matrix crack spacing. The temperature rise attained during fatigue can be significant. For example, the temperature rise exceeded 100 K during fatigue at 75 Hz between stress limits of 220 and 10 MPa. Analysis of the frictional heating data indicates that the interfacial shear stress undergoes an initially rapid decrease during the initial stages of fatigue loading: from an initial value over 20 MPa, to approximately 5 MPa after 25 000 cycles. Over the range of 5 to 25 Hz, the interfacial shear stress was not significantly influenced by loading frequency. The implications of frictional heating in fiber-reinforced ceramics are also discussed.     

Fiber-stretching test: a new technique for characterizing the fiber–matrix interface using direct observation of crack initiation and propagation

A new micromechanical technique for experimental determination of fiber-matrix interfacial properties is presented. This technique consists in tensile loading of the fiber, with a matrix droplet on it, at both ends, accompanied by continuous direct observation of interfacial crack propagation. In comparison with the well-known microbond test, the new method has two important advantages. First, crack propagation is stable for any embedded fiber length and any relation between adhesion and friction at the interface. Second, compliance of the test equipment does not affect the results, and specimens with long free fiber ends can be successfully tested. A similar result can be reached using the pull-out or microbond test with an 'infinite' (very long) embedded fiber length. An algorithm for separate determination of the interfacial adhesion and friction from experimental relationships between the crack length and applied load is described. The new test was employed to determine the interfacial parameters for composites of glass fibers with polypropylene, polystyrene, and polycarbonate. For each fiber-polymer system investigated, the following parameters were calculated: ultimate interfacial shear strength; critical energy release rate for crack propagation; and adhesional pressure. Our approach to the estimation of the work of adhesion, WA, from micromechanical tests, based on the concept of adhesional pressure, allowed us to calculate the WA values for several thermoplastic matrix-glass fiber pairs and to obtain values consistent with previous estimations made according to other approaches.     

Effects of cyclic tensile loading on the rupture behavior of orthogonal 3-D woven SiC fiber/SiC matrix composites at elevated temperatures in air

This study examined the rupture mechanisms of an orthogonal 3D woven SiC fiber/BN interface/SiC matrix composite under combination of constant and cyclic tensile loading at elevated temperature in air. Monotonic tensile testing, constant tensile load testing, and tension–tension fatigue testing were conducted at 1100 °C. A rectangular waveform was used for fatigue testing to assess effects of unloading on the damage and failure behavior. Microscopic observation and single-fiber push-out tests were conducted to reveal the rupture mechanisms. Results show that both oxidative matrix crack propagation attributable to oxidation of the fiber–matrix interface and the decrease in the interfacial shear stress (IFSS) at the fiber–matrix interface significantly affect the lifetime of the SiC/SiC composites. A rupture strength degradation model was proposed using the combination of the oxidative matrix crack growth model and the IFSS degradation model. The prediction roughly agreed with the experimentally obtained results.     

Enhanced interfacial adhesion via interfacial crystallization between sisal fiber and isotactic polypropylene: direct evidence from single‐fiber fragmentation testing

Bioresource natural sisal fiber (SF) was used to prepare single fiber‐reinforced isotactic polypropylene (iPP) composites. Three kinds of interfacial crystalline morphologies, spherulites, medium nuclei density transcrystallinity (MD‐TC) and high nuclei density transcrystallinity (HD‐TC), were obtained in the single fiber‐reinforced composites by implementing quiescent or dynamic shear‐enhanced crystallization and by modulating the compatibility interaction between SF and iPP. The development of interfacial shear strength (IFSS) during the interfacial crystallization process was demonstrated for the first time using a combination of single‐fiber fragmentation testing and optical microscope observation. A close correlation between IFSS and morphological characteristics of interfacial crystallization was well elucidated. The increases in IFSS were very different for spherulitic, MD‐TC and HD‐TC morphologies. The highest IFSS obtained was 28 MPa, after the formation of HD‐TC, which was about 62% of the tensile strength of neat iPP (45 MPa). These results offer powerful and direct evidence that interfacial crystallization could play an important role in the enhancement of interfacial adhesion of real SF/iPP composites. © 2013 Society of Chemical Industry     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part III. Experimental observation of crack propagation in the microbond test

A direct observation of crack propagation in the microbond test was carried out for five different fiber/polymer matrix systems. This technique appeared to be a very effective tool for interface characterization. Experimental plots of the force required for further crack propagation as a function of debond length were analyzed using both energy-based and stress-based models of debonding. The fracture mechanics analysis was used to construct families of crack resistance or R-curves which showed the variation of energy release rate, G, with the debond length, and included the effect of interfacial friction in debonded regions. For the first time, analogs of the R-curves were created within the scope of the stress-based model to present the local shear stress near the crack tip, τ, as a function of crack length. In both models, the behavior of the interfacial parameter (G or τ) strongly depends on the assumed value of the interfacial frictional stress (τ_f). However, for each matrix/fiber system there exists such a τ_f value for which the investigated parameter is nearly constant over the whole region of stable crack propagation (70–90% of the embedded length). Moreover, these best-fit τ_f values for each specimen appeared to be practically the same for both energy-based and stress-based approaches. Thus, both interfacial toughness, G _ic, and local interfacial shear strength, τ_d, adequately characterize the strength of a fiber/matrix interface. Extrapolation of R-curves and their analogs to zero crack length allows measurement of the interfacial parameters with good accuracy.     

Improvement of interfacial shear strengths of polybenzobisoxazole fiber/epoxy resin composite by n‐TiO2 coating

Smooth polybenzobisoxazole (PBO) fiber has limited interfacial interaction with resin matrix. In this article, nano‐TiO₂ coating on PBO fiber is applied to improve the interfacial adhesion between PBO fiber and epoxy resin. The test results suggest that the PBO fiber had good interaction with epoxy resin matrix after its treatment with n‐TiO₂ sol. Nano TiO₂ particle embedded onto PBO fiber surface, acting as a chock, which made fiber implanted into the resin better. This greatly improved the shear strengths (IFSS) of PBO fiber/epoxy resin composite. It has been found that a 56% increase in interfacial IFSS has achieved without sacrificing mechanical properties of fiber. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

The pull-out and failure of a fiber bundle in a carbon fiber reinforced carbon matrix composite

The interfacial failure is examined for a unidirectionally reinforced carbon fiber/carbon matrix composite. A novel tensile test is conducted which realizes the processes of interfacial debonding and subsequent pull-out of a fiber bundle from the surrounding composite medium. The critical stress at the onset of delamination cracking is related to the fracture energy (the critical energy release rate for mode II cracking). A force-balance equation of a fiber bundle, which is quasi-statically pulled-out of the composite socket, is formulated in terms of the inter- and intra-laminar shear strengths of the composite. This equation is successfully used to estimate the delamination crack length along the debonded fiber bundle, as a function of the stress applied to the bundle.     

Surface ammonification of the mutual‐irradiated aramid fibers in 1,4‐dichlorobutane for improving interfacial properties with epoxy resin

The mutual irradiated aramid fibers in 1,4‐dichlorobutane was ammoniated by ammonia/alcohol solution, in an attempt to improve the interfacial properties between aramid fibers and epoxy matrix. Scanning electron microscopy (SEM), X‐ray photoelectron spectroscopy (XPS), dynamic contact angle analysis (DCA), interfacial shear strength (IFSS), and single fiber tensile testing were carried out to investigate the functionalization process of aramid fibers and the interfacial properties of the composites. Experimental results showed that the fiber surface elements content changed obviously as well as the roughness through the radiation and chemical reaction. The surface energy and IFSS of aramid fibers increased distinctly after the ammonification, respectively. The amino groups generated by ammonification enhanced the interfacial adhesion of composites effectively by participating in the epoxy resin curing. Moreover, benefited by the appropriate radiation, the tensile strength of aramid fibers was not affected at all. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44924.