Brittle Fibers Research Articles

Inclination Angle Effect of Carbon Fibers in Cementitious Composites

This paper presents an analytic model, which describes the bridging load and fiber stress developed when an inclined brittle fiber bridges a crack. The coupled effect of fiber bending and axial loading is explicitly accounted for. The model also considers matrix spalling and concentration of friction load at the point where the fiber bends over the matrix. With this model, it is possible to test the influence of fiber and matrix parameters on the bridging load and fiber stress, in order to achieve more efficient use of the fibers. Good comparison of the model predictions with experimental results of the inclined carbon-fiber test was achieved, both for the bridging load and the spall length. The model can serve as a useful tool to predict the efficiency of inclined fibers bridging a matrix crack.

Scalings in the statistical failure of brittle matrix composites with discontinuous fibers—I. Analysis and Monte Carlo simulations

This paper addresses the statistical aspects of the failure of unidirectional composites having brittle matrices reinforced with discontinuous brittle fibers. The failure process involves quasi-periodic matrix cracking, frictional sliding of the fibers in fiber break zones and fiber bridging of matrix cracks in a global load-sharing framework. We consider a composite section of “characteristic” length and develop its distribution for strength in terms of certain characteristic stress and length scales. Continuous sections of the fibers follow the usual Weibull distribution for strength. We also introduce random discontinuities along the fiber, originating say from processing damage whose spacins follow a Poisson process where the rate α is the mean number of discontinuities per characteristic length of the fiber. We derive two approximations for the mean and standard deviation of such characteristics composites. A realistic Monte Carlo simulation model is developed to test these analytical results and to study the fiber pull-out properties. The composites turn out to be quite insensitive to initial damage. The mean pull-out length is found to increase with increasing α and becomes independent of the Weibull modulus for large values of α.

Creep rupture of brittle matrix composites reinforced with time dependent fibers: Scalings and Monte Carlo simulations

This paper addresses statistical aspects of the lifetime in creep rupture of unidirectional composites having brittle matrices reinforced with brittle fibers. Time dependence enters through the fibers, which fail following a probability model due to Coleman, involving power law dependence on stress level, Weibull shape and a memory integral of the load history. The creep rupture model has many features similar to the model for composite strength of earlier work, which involves quasiperiodic cracking of the matrix, frictional sliding of fibers in fiber break zones, and fiber bridging of matrix cracks in a global load-sharing framework. No time dependence is assumed at the fiber-matrix interface, though progressive slippage does occur in time as fibers fail and load is redistributed. Starting from an “equivalent” short term strength model we identify characteristic strength and length scales which depend on strain rate and other model parameters. We are then able to identify a characteristic length for the composite for purpose of developing a scaling analysis relating parameters of strength to creep-rupture lifetime. Through Monte Carlo simulation we are able to establish key parametric relationships and distributional forms not accessible through analysis. The power law scaling that allows us to write the lifetime of a single fiber in terms of the ratio of the load level to the short term strength is preserved remarkably well in the composite, though with a different power law exponent. An interesting and unexpected result is the emergence of an asymptotic log-normal distribution for the lifetime of a composite of characteristic length in contrast to the asymptotic normal distribution for strength. We also study through analysis and simulation the size effect relating composite lifetime distribution and its median to overall composite volume.

Creep models for metal matrix composites with long brittle fibers

Creep models for metal matrix composites reinforced by long brittle fibers with weak interfaces are presented. These models extend the work of McLean (1985) to include effects of fiber breaks and the consequential stress relaxation in the broken fibers. The creep strain and the creep rupture time are calculated when global load sharing occurs. Analyses are conducted for composites with a wide range of fiber volume fractions, Young's modulus of the fibers and the matrix, interfacial sliding stress and Weibull properties for the strength of the fibers. The results derived from this study are compared with those predicted by McLean's (1985) model. The creep life is found to be sensitive to the extent of fiber stress relaxation in the broken fibers. Models, which ignore this effect overestimate the creep rupture time especially when the composite is subjected to a low or moderate level of stress.

Bond Properties of Carbon Fibers in Cementitious Matrix

The interfacial bond properties of two carbon fibers, having diameters of 10 μm and 46 μm, were tested for cement matrices of different water-to-binder ( w /b) ratios and silica-fume contents. The pullout test was conducted using a special technique that prevented the brittle fiber from breaking during specimen handling. An environmental scanning electron microscope (ESEM) was used to determine the nature of the fiber-matrix bond. The results show a friction-based bond mechanism for the fiber of 10 μm, with a bond strength of 0.5 MPa for the high w /b matrix and without silica fume. Densifying the matrix by lowering the w /b ratio or by using silica fume improved the bond by 50–100%. For the larger-diameter fiber, silica fume had a very strong effect on the bond (an increase of 370–670%). It appears that long grooves along the fiber surface creates a mechanical anchorage, which is strongly affected by the presence of silica fume.

Impact damage prediction in carbon composite structures

This paper describes a strategy for predicting the extent of internal damage in a brittle carbon fibre laminated composite stucture, when subjected to low velocity impact by a single mass. The success of the predictions, which avoid expensive three-dimensional analysis, is validated by test for a wide range of structures from small stiff plates through to large flexible stiffened compression panels whose residual strength is affected much more by internal delamination than tension structures. It is shown that a numerical model needs to incorporate nonlinear behaviour due to both gross deformations and to in-plane material degradation.

A Shear Stress Relaxation Model for Continuous Fiber Reinforced Unidirectional Metal Matrix Composites with Fiber Breakages.

A model is presented to express the relaxation of the interfacial shear stress acting on the ineffective part of a broken fiber in a unidirectional metal matrix composite reinforced with long brittle fibers. A cylindrical cell containing a broken fiber is considered, and a bilinear approximation of the fiber stress distribution in the broken fiber is employed to derive a simple differential equation for the relaxation of the interfacial shear stress. The resulting equation is applied to the cell subjected to constant or increasing strain. It is thus shown that the interfacial shear stress relaxes very slowly in comparison with the axial stress in the matrix, and that the analytical solution obtained in the case of constant strain agrees well with the numerical analysis performed by Du and McMeeking. The effect of the radial gradient of matrix shear stress on the interfacial shear stress relaxation is also discussed.

Fracture propagation near a frictionally - constrained fiber interface

This work provides a three-dimensional numerical fracture mechanics analysis of a crack periphery as it propagates through a brittle matrix and encounters an individual brittle fiber. The surface integral method, based upon a distribution of singular fundamental solutions, is used to represent both the cracks and the coupled interfacial sliding zone. The interfacial frictional tractions are assumed to satisfy a Coulomb relationship and are determined iteratively from the stress induced by the matrix crack, the stress induced by the developing slip, and the initial normal compressive interfacial stress (i.e. from setting or thermal mismatch). Simulations of an initially long straight crack front moving toward and past a fiber for different interfacial frictional characteristics were conducted. The implications for tailoring fiber/matrix interfaces to optimize the global toughening effect are discussed. If the interface between fiber and matrix is cohesive enough (but not too cohesive) then tractions which develop at the interface may effectively retard the local growth of a matrix crack. Raising the friction coefficient (or cohesion) at the interface must, however, be balanced against the potential for fiber failure in the high stress zone near the matrix crack periphery. The implications frictional slippage holds for inhibiting and possibly arresting small matrix cracks are emphasized.

Prediction of deformative and thermal properties of hybrid fiber composites with polymer matrix

AbstractA theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermal characteristics of hybrid polymer composites reinforced with anisotropic fibers of several types. The theoretical solutions were obtained by generalizing the self‐consistent method for the case of a three‐phase model. The effects of brittle fiber breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of short‐term loading and long‐term creep. A variant of the solution is proposed for predicting the thermal deformation of a hybrid composite containing not only elastic, but also viscoelastic thermorheologically simple components with different temperature–time shift factors. The experimental confirmation of the predicted results was done on specimens of organic/glass, organic/carbon, glass/carbon and organic/boron polymer composites with different ratios of volume contents of fibers.

Influence on fiber inclination and interfacial conditions on fracture in composite materials

Dynamic photoelasticity has been used to study the effect of the fiber-matrix interface and fiber orientation on dynamic crack growth in fiber composites. Two types of fiber-matrix interfaces are considered: well bonded and partly debonded. The fiber-matrix interface is characterized by conducting fiber pullout tests. Partly debonded fibers aligned with the loading direction, result in higher fiber debonded lengths, lower dynamic stress-intensity factorKID and lower fracture surface roughness compared to well bonded fibers. Orientation of brittle fibers, with respect to the loading direction, impairs their ability to lowerKID, while oriented ductile fibers produce no significant change inKID. Misalignment of fibers from the loading direction reduces the fiber debonded length due to kinding of the fiber at the crack face.

Concrete Reinforced with Deformed Steel Fibers, Part I: Bond-Slip Mechanisms

Bond-slip characteristics were investigated for three deformed steel fibers bonded in concrete matrixes with different strengths. Fibers were aligned at 0, 15, 30, 45, and 60 deg with respect to the loading direction, and complete load-versus-slip curves were obtained. It was found that the bond-slip characteristics of fibers aligned with respect to the loading direction were signifcantly superior to those for inclined fibers. Inclined fibers supported smaller peak pullout loads and absorbed less pullout energy than the aligned fibers. A high-strength matrix often caused brittle fiber and matrix failures, and led to reductions in the energy-absorption capability. The paper provides interpretations of the bond-slip curves based on various micromechanical processes in the matrix and fiber, and identifies the conditions that lead to a brittle response. The bond-slip information generated in this study for the various deformed fibers will be correlated to the actual behavior of fiber reinforced concrete in the second part of this paper.

Fatigue and Fracture of Nickel Aluminide Composites

AbstractThe results of preliminary investigations of the room-temperature fatigue and fracture mechanisms in model NiAl composites are presented. The composite systems studied include: NiAl reinforced with ductile second phase particles (Mo); ductile fibers (Mo); brittle second phase particles (zirconia partially stabilized with yttria) and brittle fibers+particles (Al2O3 + zirconia). Mechanisms of fatigue crack growth in heat treated specimens of the fiber-reinforced composites are also elucidated. The investigations indicate that both ductile and brittle reinforcements can enhance the toughness of NiAl significantly, and the ductile phase particulate reinforcement may even contribute to room-temperature ductility in the composite.

連続繊維マット強化ＣＰレジン複合材の静的力学および破壊特性に及ぼす母材および繊維含有率の影響

The purpose of the present work is to reveal the behavior of two kinds of different matrix resins in composite materials through the experimental results of mechanical and fracture properties and observation of macro and micro fracture surfaces. The composite specimens are made of ductile or brittle resin and continuous glass fiber mats with various fiber contents. The elastic modulus and the tensile strength of these two resins are nearly of the same values, while the elongation is different.The results obtained are as follows:(1) The tensile strength of the ductile matrix resin composites is higher by 20-30% than that of the brittle matrix resin composites. The values of both composites with fiber content 20wt%, however, are lower than those of the matrix resins. These results can be understood based on the observations of macro fracture processes and fracture surfaces.(2) The fracture toughness Kin at crack growth initiation increases with increasing fiber content for both composites. The values of Kin for the ductile matrix resin composites with fiber contents 0wt% and 20wt% are higher than those of the brittle ones. For the composites with fiber contents 40wt% and 60wt%, the values of Kin for both composites scatter randomly.

Multifibre polymer composites: Prediction of deformation and thermophysical properties

A theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermophysical characteristics of hybrid polymer composites reinforced with anisotropic fibres of several types. The theoretical solutions were obtained by generalizing the self-consistent method for the case of a three phase model. The effects of brittle fibre breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of a short-term loading and a long-term creep. It has been shown that a creep of viscoelastic fibres plays a principal role in creep of the hybrid composite. It is just this creep that significantly increases the fibre damage during creep of the composite.

Effect of water on the mechanical adhesion of the glass/epoxy interface

In recent years, the quality of the fibre/matrix bonding in polymer composites has been quantified by means of a single mechanical parameter, the interfacial shear strength, based on measurements made using micromechanical techniques. It has gradually appeared, however, that this parameter is both ambiguous in terms of its physical meaning and, at the same time, difficult to measure reliably in many cases. Moreover, different micromechanical techniques yield differing values of the interfacial shear strength. Finally, it has been suggested in a few studies that it may not be the critical factor governing fibre/matrix debonding. In this paper an energy balance approach is proposed, by which the degree of fibre/matrix bonding is now quantified by means of the interfacial energy, as a function of the fibre geometrical and mechanical characteristics, the stress transfer length and the debonding length. The validity of the approach is discussed in the case of the single-fibre composite test, in which progressive fragmentation of a single brittle fibre in a more ductile polymeric matrix takes place, using data for E-glass fibres embedded in epoxy, both in the dry state and in the presence of hot distilled water.

Model studies of fibre breakage and debonding in a metal reinforced by short fibres

F or a metal reinforced by short, brittle fibres the development of damage by fibre cracking or decohesion is studied, taking into account the interaction between these two types of damage. The metal matrix composite, containing a periodic array of aligned fibres, is represented in terms of a cell model, and solutions for the stress and strain fields are determined numerically. Failure at the interface is modelled in terms of a cohesive zone model that accounts for decohesion by normal separation as well as by tangential separation, whereas fibre fracture is simply represented by a critical value of the average tensile stress on a cross-section. The effect of various material parameters and of the macroscopic stress state on the two types of damage is investigated, together with the subsequent mode of void growth.

Loss of strength of boron fibers in interaction with the matrix

A model of loss of strength of brittle fibers by the products of their interaction with the matrix is proposed. The model is based on the assumption that the rigid products of interaction form with the original surface cracks of the fibers paired defects leading to an increase in stress concentration at the crack tips. In this case the strength of the fibers is determined by the sizes of the original cracks and of the reaction products and also by the distance between them. A specific example of calculation of the strength of boron fibers using the proposed method is given.

Characterization of a Fiber-Optic Evanescent Wave Absorbance Sensor for Nonpolar Organic Compounds

A fiber-optic evanescent field absorbance sensor (EFAS) is described, for which the sensing element consists of a commercially available silicone-clad quartz glass fiber, coiled on a Teflon® support. The polydimethylsiloxane cladding fulfills various functions. It protects the brittle fiber core against fracture induced by mechanical stress. Moreover, as a lower-refractive-index medium, it causes total reflection in the fiber and acts as a hydrophobic membrane that enriches nonpolar organic compounds, whereas polar species like water cannot penetrate. Coupled to an NIR spectrometer, the sensor has a potential for remote in situ measurements of organic pollutants in drainage waters originating from contaminated areas. In this study aqueous solutions of typical drainage-water contaminants like dichloromethane, chloroform, and trichloroethylene were measured in the 900–2100 nm spectral range. The influence of refractive index, fiber length and diameter, bend radius, polysiloxane swelling, and ambient temperature on the sensor signal is described and qualitatively compared with theoretical predictions. Kinetics measurements are presented, which allow explanation of the diffusion mechanism of CHC13 enrichment in the polysiloxane cladding. The data show that the rate-determining step for penetration of this substance into the sensor polymer layer can be described mainly by film diffusion through the aqueous boundary layer. In most cases no remarkable influence of gel diffusion in the polysiloxane membrane was observed.

Aligned short-fibre reinforced thermosets: Experiments and analysis lend little support for established theory

Experiments with epoxy resins reinforced with aligned short carbon fibres give results which disagree sharply with traditional fibre reinforcement theory based on interface yielding and slip and the concept of the critical fibre aspect ratio. Earlier results and evidence from interface studies are therefore reviewed, and it is shown that, as the carbon/polymer interface is brittle, the progressive interface failure process previously envisaged almost certainly does not take place. Furthermore, a careful reading of the sources of data relating to the yielding and slip theory indicates that the evidence in support of it is very weak. Thus, the idea of the critical fibre aspect ratio, borrowed from the metallurgists, may not be appropriate for short-fibre reinforced plastics. Instead, a process involving brittle fibre debonds should be considered. These debonds could trigger matrix cracking and hence explain the anomalously low composite breaking strains observed when the breaking strain of the fibre is greater than that of the polymer, and other properties of aligned short-fibre composites.

Statistical issues in the fracture of brittle-matrix fibrous composites

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional sliding of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. First, we review the overall statistical features of the failure process, and identify certain issues in terms of critical geometric, statistical and mechanical parameters. This leads to two interesting cases, one where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider ‘characteristic’ bundles in the composite which capture essential features of the statistics of the failure process, and develop their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arrangement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section. This scale, though not precisely quantified, depends on such things as the stiffness of the matrix relative to the fibers, the volume fraction of the matrix and the spacing of periodic cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fracture as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experimental results.