Theoretical analysis and numerical simulation of development length of straight steel fiber in cementitious materials

In fiber-reinforced concrete, it is important to choose an appropriate length in each fiber to develop its full yield strength without a failure in the bond strength between the fiber and the concrete. This length is called the fiber development length, L_df. The bond capacity is evaluated between the fiber and the concrete using the pull-out tests. This test evaluates the bond capacity of various types of steel fiber surfaces relative to a specific embedded length. If the steel fiber is smooth and straight, the distribution of tensile stresses will be uniform around the fiber at a specific section and varies along the anchorage length of the fiber and at a radial distance from the surface of the fiber. Pull-out tests can be performed on an embedded straight steel fiber in concrete matrix, in this case, the tensile force, P, is increased gradually and the number of cracks and their spacings and widths is recorded. The bond stresses vary along the fiber length between the cracks. The strain in the steel fiber is maximum at the cracked section and decreases toward the middle section between cracks. If the embedded length of the straight steel fiber is greater than the development length, the steel fiber may yield, leaving some length of the fiber in the concrete. The linear elastic behavior of the fiber-matrix system is interrupted by interface debonding which occurs due to overall weak bonding between the concrete matrix and the surface of the steel fiber. This paper introduces new developed shear lag model and explains simplified method to find the development length of straight steel fiber in concrete matrix using finite element model and analysis of shear lag stresses, where the maximum tension force which is applied on the steel fiber is resisted by another internal force related with the ultimate average bond stress, steel fiber diameter and its yield strength.     

Effect of matrix yield properties on fragmentation behavior of single fiber composites

Experimental and theoretical investigations have been conducted to study the dependence of fiber fragmentation behavior on matrix yielding properties. The cured Epikote 828 resins with two types of curing agents have almost similar elastic moduli, but different tensile yield strengths. The interfacial chemistry between fiber and epoxy resin is unchanged due to the same constituent of the epoxy resin. The experimental results indicate that the fragmentation behavior of the fibers embedded in the matrix is significantly different for the tested glass fiber treated by γ-glycidoxypropyltrimethoxysilane. The average fragment length decreased with increasing tensile yield strength of resin, which suggests that the interfacial shear strength determined in the fragmentation test should be different depending on the tensile yield strength of resin used. The important phenomenon observed is the transition of the micro-damage mode from matrix crack to interfacial debonding. An elastoplastic shear-lag model was used to calculate the shear stress and fiber tensile stress distributions considering different plastic behaviors of the matrices. The theoretical results indicate that the plastic behavior of the matrix has a large influence on stress transfer. Based on elastic and plastic properties of the matrix, the fiber fragmentation behavior in the matrix is predicted. Experimental and theoretical results are favorably compared.     

Interface end theory and re-evaluation in interfacial strength test methods

The experimental results of fragmentation, micro-indentation, pull-out and microdebond tests often exhibit large discrepancies. Since all specimens of the four test methods all have interface ends, the singularity theory of the interface end should be used to evaluate the exactness of the test methods. The eigenvalues of the specimens for the micro-indentation test, pull-out test and microdebond test are calculated and investigated. The results show that the stress singularity of the interface end depends on the Dundurs' parameters and the wedge angles. The interfacial shear strength (IFSS) obtained from the tests loses its rationality if the stress is singular at the interface end. In further analysis, for a carbon fiber-epoxy resin composite, it is found that the microdebond test gives the most reliable IFSS results, if the wedge angle of the resin droplet is less than 40°; the results from the pull-out test are dubious, due to the stress singularity at the interface end. In the micro-indentation test, there is a critical matrix stiffness value for a given fiber, above which the stress at the interface end will be non-singular. The fragmentation test assumes the interfacial shear stress on the fiber fragment of critical length is the IFSS. If debonding does not occur at the interface end, then apparently, the interfacial shear stress on the fiber fragment of critical length is less than the true value of IFSS.     

A refined method for estimating fiber and interfacial shear strength by using a single-fiber composite

In estimating interfacial shear strength from the fragmentation process of fibers in single-fiber composites, a problem arises as to the value of the fiber strength if the fiber strengths distribute widely and strongly depend on the fiber length. To overcome this problem, a refined analysis method for simultaneously estimating the fiber and the interfacial shear strength from the fragmentation process has been shown. Agreements between the values estimated with the proposed method and the results of the single-fiber tensile and the direct shear tests have been obtained. It has been shown that the estimation of the interfacial shear strength using the proposed method is insensitive to the matrix properties if the interfacial shear strength is unaltered by the matrix properties, and that the variations of the distribution parameters of the fiber strength is significantly smaller for the proposed method as compared with the single-fiber tensile tests. The results obtained by applying the proposed method to various carbon fibers have been shown.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

Role of weak interface to retain high strength of fiber in monofilamentary SiC fiber/titanium-aluminide composite

The tensile strength of monofilamentary weakly bonded SiC fiber/γ-TiAl intermetallic compound matrix composite, prepared by the sputtering method, was measured and analysed using a fracture mechanical technique. The main results are summarized as follows: (1) The fracture of TiAl occurred prior to that of fiber, resulting in formation of circumferential cracks on the fiber. Interfacial debonding occurred during tensile test, resulting in long pull-out of the fiber. (2) The strength of the fiber in the TiAl matrix was nearly the same as that of the bare fiber. (3) The fracture mechanical analysis showed that (i) the interfacial debonding grows unstably upon initiation and (ii) the stress distribution in the fiber in the cross-section, where the matrix is fractured, approaches to that of bare fiber with increasing debonded length. The reason why the fiber strength was maintained in spite of the formation of cracks on the fiber surface due to the premature fracture of the matrix was accounted for by the fully blunted crack-tip from the above calculation result.     

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber embedded in an elastic matrix is studied using the method of eigenfunction expansion. The dynamic stress concentration factors along the interface between the coated fiber and the matrix induced by the plane elastic wave and scattering cross section are derived and numerically evaluated. The interface stress, inhomogeneous material constants and thickness of the coated layer on the scattering of the elastic wave become much more important when the radius of the coated-fiber is reduced to the nanometer scale. These were confirmed by the use of numerical results. Our results can aid in understanding the dynamic mechanical properties of nano-composites. The proposed method has potential applications in the characterization of the interfacial layer that links reinforced fibers to their matrix.     

Enhancing the interfacial strength of glass/epoxy composites using ZnO nanowires

This paper investigated the application of ZnO nanowires (ZnO NW) to enhance the interfacial strength of glass/epoxy composites. ZnO NW were grown on glass fibers by hydrothermal method, tensile properties of bare and ZnO NW coated fibers were measured by single fiber tensile testing, wettability of fiber with resin was studied by contact angle measurements and finally the interfacial strength and mechanisms were determined by single fiber fragmentation testing of glass/epoxy composites. The surface coverage of ZnO NW on glass fibers was fairly uniform without formation of major clusters. The coating of ZnO NW slightly reduced the tensile strength and improved the tensile modulus of fibers. Wettability tests showed reduction in contact angles for ZnO NW coated fibers because of enhanced wetting and infiltration of epoxy resin into nanowires. In fragmentation testing of microcomposites, smaller and concentrated interfacial debonding zones for ZnO NW coated fibers indicated good stress transfer and strong interfacial adhesion. A new form of crossed and closely spaced stress patterns were observed for nanowires of high aspect ratios. The interfacial strength of ZnO NW coated fibers increased by at least 109% and by 430% on average, which was attributed to the increased surface area and mechanical interlocking provided by ZnO NW.     

Effects of residual stress and interfacial frictional shear stress on interfacial debonding at notch-tip in two-dimensional unidirectional composite

A calculation method based on the shear lag approach was presented to get an approximate estimate of influences of residual stresses and frictional shear stress at the debonded interface on the interfacial debonding behavior at the notch-tip along fiber direction in two-dimensional unidirectional double-edge-notched composites. With this method, the energy release rate for initiation and growth of debonding as a function of composite stress were calculated for some examples. The calculation results showed in outline how much the tensile and compressive residual stresses in the matrix and fiber along fiber direction, respectively, act to hasten the initiation and growth of the debonding when the final cut element in the notch is matrix, while they act to retard them when the final cut element is fiber, and how much the frictional shear stress at the debonded interface reduces the growth rate of the debonding.     

Determination of interfacial parameters in fiber-polymer systems from pull-out test data using a bilinear bond law

We propose a new model for characterization of strength properties of fiber-polymer interfaces by means of a single fiber pull-out test. Our model is based on shear-lag analysis using a bilinear bond law (stress–slip relationship) which, in turn, is a simplified representation of the true stress behavior as a function of strain for cold-drawing polymers. According to this law, the fiber-polymer interface is subjected to the following successive processes: (1) linear loading within the elastic region; (2) yielding and subsequent bond strengthening with increasing strain; (3) local debonding and interfacial crack propagation along the interface; (4) post-debonding friction. Both crack propagation and extension of the yielded zone can be stable and unstable, depending on the values of interfacial parameters and the load applied to the free fiber end. The procedure of construction of theoretical force–displacement curves for a pull-out test is described in detail. Theoretical curves exhibit such features as multiple kinks and non-linear regions, whose positions and shape are related to interfacial parameters. By fitting experimental curves with theoretical ones, these parameters can be determined for each separate pull-out specimen. Practical examples are provided for basalt fiber–polypropylene and glass fiber–polypropylene specimens.     

Stress transfer around a broken fiber in unidirectional fiber-reinforced composites considering matrix damage evolution and interface slipping

A shear-lag model is applied to study the stress transfer around a broken fiber within unidirectional fiber-reinforced composites(FRC) subjected to uniaxial tensile loading along the fiber direction.The matrix damage and interfacial debonding,which are the main failure modes,are considered in the model.The maximum stress criterion with the linear damage evolution theory is used for the matrix.The slipping friction stress is considered in the interfacial debonding region using Coulomb friction theory,in whic...     

Interphase characterization in polymer composites - monitoring of interphasial behavior in dependence on the mode of loading

Single fiber model composites consisting of epoxy resin matrix and differently sized glass fibers were investigated using pull-out tests, scanning electron microscopy (SEM), scanning force microscopy (SFM) and single fiber dynamic load test (SFDL). The inhomogeneous stress distribution along the embedded fiber length could be visualized by monitoring. SEM images showed either cohesive fracture or adhesive failure on pulled-out fibers with different sizings. The crack initiation and propagation were detected randomly and multiply distributed as the inhomogeneous interphase itself and depending strongly on the fiber-matrix model combination. The meniscus region acts as a material inhomogeneity and its appearence depends on the surface free energies of fiber and matrix and on the curing conditions of the resin. SFM in force modulation mode has visualized different interphase thicknesses and gradients of local stiffness. The SFDL test has been shown as a worthful tool for the comprehensive determination of fiber-matrix interaction.     

Micromechanical analysis of transverse damage of fibre-reinforced composites

The mechanical behaviour of fibre-reinforced composites under transverse tension, compression and shear is studied using computational micromechanics. The representative volume element is constructed for fibre’s random distribution. The Drucker–Prager model and cohesive zone model are used to simulate the matrix damage and interfacial debonding, respectively. The stress distribution along the interface is studied using the model with only one fibre embedded in the matrix. It is found that the interface tensile failure at the equators of fibre firstly occurs under transverse tension; the interface shear failure firstly occurs under transverse compression; both the interface tensile failure and shear failure occur under transverse shear. The direction of fracture plane is perpendicular to the loading direction under transverse tension, 52.5° with the perpendicular direction under compression and 7.5° with the perpendicular or vertical direction under shear, respectively.     

Investigation of a coated optical fiber strain sensor embedded in a linear strain matrix material

A theoretical model has been developed to study the mechanical behaviors of the interface between an embedded optical fiber with coating material and a linear strain matrix. The results show that the longitudinal stress and strain in the fiber optic sensor are different from that distributed in the host material and depend on the strain distribution and embedded length of the optical fiber as well as the material properties of the fiber coating. The distribution of interfacial shear strain between the coating and the glass fiber and the distribution of strain/stress of the glass fiber are given.     

Preparation of vertically aligned carbon nanotube arrays grown onto carbon fiber fabric and evaluating its wettability on effect of composite

Vertically aligned carbon nanotube (CNT) arrays have been grown onto the carbon fiber fabric using a catalytic chemical vapor deposition (CCVD) method. The as-synthesized CNT arrays are about 20 μm in height, and the nanotube has a mean inner and outer diameter of 2.6 nm, 5.5 nm, respectively. The CNT-grafted carbon fabric shows a hydrophobic property with a contact angle over 145°, and the single CNT-grafted carbon fiber shows a sharp increase of dynamic contact angle in de-ionized water from original 71.70° to about 103°, but a little increase does in diiodomethane or E-51 epoxy resin. However, the total surface energy of carbon nanotube-grafted carbon fiber is almost as same as that of as-received carbon fiber. After CNTs growth, single fiber tensile tests indicated a slight tensile strength degradation within 10% for all different lengths of fibers, while the fiber modulus has not been significantly damaged. Compared with the as-received carbon fibers, a nearly 110% increase of interfacial shear strength (IFSS) from 65 to 135 MPa has been identified by single fiber pull-out tests for the micro-droplet composite, which is reinforced by as-received carbon fiber or CNT-grafted carbon fiber.     

Interfacial adhesion and micro-failure phenomena in multi-fiber micro-composites using fragmentation test

Statistical fragments and micro-failure modes in the multi-fiber-reinforced micro-composites were investigated by fragmentation test. The specimen consisted of three fibers using carbon fibers (CFs) and glass fibers (GFs), embedded in the epoxy resin with three-dimensional arrangement. Fracture morphology and micro-failure behavior from the progressive fragmentation of fibers and fiber/matrix interfacial adhesion were observed via polarized-light microscope. The interfacial shear strength of CF/epoxy micro-composites is higher than that of the GF/epoxy micro-composites measured by the single fiber fragmentation test. The results show that fragment number on monofilament demonstrates obvious differences between multi-fiber and single fiber systems, and the location of the breakpoint is determined by the CFs that fracture firstly, indicating clustering fracture modes. This is because stress concentration around the breakpoints influences the stress redistribution on the adjacent fibers. Distinct micro-failure modes were observed in three-fiber and the hybrid systems, where matrix cracks around the CFs and interfacial debonding occurs around the GFs. The mixture of CFs and GFs demonstrates distinctive hybrid effect by the changes of the fragment number and initial fracture strain of fibers in hybrid systems.     

Improved mechanical properties of carbon fiber reinforced PTFE composites by growing graphene oxide on carbon fiber surface

The mechanical properties of carbon fiber reinforced polymer composites depend upon fiber-matrix interfacial properties. To improve the mechanical properties of ?bers/PTFE composites without sacri?cing tensile strength of ?bers, graphene oxide (GO) was introduced onto the surface of CFs by chemical vapour deposition (CVD). This hybrid coating increased the wettability and surface roughness of carbon fibers, which led to improved affinity between the carbon fibers and PTFE matrix. The resulting hybrid-coated carbon fiber-reinforced composites showed an enhancement in the short beam strength compared to un-coated carbon fiber composites. Meanwhile, a signi?cant increase of interlaminar shear strength (ILSS), interface shear strength tests (IFSS) and impact property were achieved in the 5-min-modi?ed CFs.     

Continuum Micro-mechanics of Estimating Interfacial Shear Strength in Short Fiber Composites

A new continuum approach to micro-mechanics of short fiber composites yielded two separate methods of estimating the apparent interfacial shear strength and fiber orientation efficiency. The methods exploit the compilation of the effects of fiber length distribution and interfacial shear strength on strengthening efficiency into a function of strain. The In-Built Method derives a unique combination of apparent interfacial shear strength and fiber orientation efficiency being able to reproduce the experimental stress–strain curve of a short fiber reinforced composite with a very low residual standard deviation. The Boundary Method accomplishes rapid interfacial shear strength screening in materials selection by constructing and utilizing the proposed selection chart.     

石墨烯/柔性基底复合结构双向界面切应力传递问题的理论研究

界面力学性能是影响石墨烯/柔性基底复合结构整体力学性能的关键因素,因此对该结构界面切应力传递机理的研究十分必要.考虑了石墨烯和基底泊松效应的影响,本文提出了二维非线性剪滞模型.对于基底泊松比相比石墨烯较大的情况,利用该模型理论研究了受单轴拉伸石墨烯/柔性基底结构的双向界面切应力传递问题.在弹性粘结阶段,导出了石墨烯双向正应变和双向界面切应力的半解析表达式,分析了不同位置处石墨烯正应变和界面切应力的分布规律.导出了石墨烯/柔性基底结构发生界面滑移的临界应变,结果表明该临界应变低于利用经典一维非线性剪滞模型得到的滑移临界应变,并且明显受到石墨烯宽度尺寸以及基底泊松比大小的影响.基于二维非线性剪滞模型建立有限元模型(FEM),研究了界面滑移阶段石墨烯双向正应变和双向界面切应力的分布规律.与一维非线性剪滞模型的结果对比表明,当石墨烯宽度较大时,二维模型和一维模型对石墨烯正应变、界面切应力以及滑移临界应变的计算结果均存在较大差别,但石墨烯宽度很小时,二维模型可近似被一维模型代替.最后,通过与拉曼实验结果的对比,验证了二维非线性剪滞模型的可靠性,并得到了石墨烯/聚对苯二甲酸乙二醇酯(PET)基底结构的界面刚度(100 TPa/m)和界面剪切强度(0.295 MPa).     

Microstructure and thermal residual stress analysis of SiC fiber through Raman spectroscopy

SiC fiber‐reinforced metal matrix composite is an interesting material for aerospace industry because of its excellent properties. However, these properties are greatly influenced by fiber microstructure and thermal residual stresses introduced by the preparation of the composites. Due to complicated preparation technology, microstructure and thermal stress along SiC fiber radius varies, which makes characterization difficult. Raman spectroscopy is a non‐destructive technique which provides information, at micrometer scale, on the phase composition and the crystalline state (structure and texture) of materials. Line scanning was used to assess microstructure along SiC fiber radius embedded in Ti64. The SiC coating is subdivided into three concentric parts across the fiber diameter, according to the differences in intensity and width of SiC transverse optical phonon (TO) band. Part 2 is considered to be a buffer zone connecting Part 1 and Part 3 with different deposition conditions, respectively. Amorphous Si is detected throughout fiber radius, while crystalline Si is only detected in the outer part. Thermal residual stress along fiber radius in the composite was calculated by using SiC TO band shifts with a bare fiber as reference. A cylindrical model was also used to compare with the stress data obtained from Raman shift. Copyright © 2013 John Wiley & Sons, Ltd.