Fiber Strength Distribution Research Articles

Fibre fragment distribution in a single-fibre composite tension test

Abstract Single fibre fragmentation tests are performed for brittle fibres with Weibull strength distribution and different surface treatments. The fragmentation process is modelled and closed-form expressions for break spacing distribution are obtained. The model accounts for the effect of finite fibre length on the initial fragmentation as well as for break interaction on the advanced fragmentation stage. It is assumed that the exclusion zone due to fibre–matrix interface failure and stress recovery in the fibre is linearly dependent on the applied load. This assumption is validated experimentally. The derived theoretical average fragment length dependence on applied load is used to determine the fibre strength distribution parameters and the effective interfacial shear stress for carbon/epoxy single fibre composites with different fibre surface treatment and for glass/vinylester single fibre composite. Fragment length distribution is predicted for several load levels. Predictions are in good agreement with experimental data.

The estimation of statistical fiber strength by fragmentation tests of single-fiber composites

Both evaluation of interfacial properties and statistical strength theories for the failure of unidirectional composites require information about fiber strength distributions and, in particular, the Weibull scale and shape parameters, σ L and m, at some characteristic gauge length, L, such as the critical fiber length. In this paper, the in situ strengths of E-glass fibers with five different kinds of surface treatments in epoxy matrix have been estimated by fragmentation tests on single-fiber composites (SFC). The number of fiber breaks as a function of applied stress is simulated according to the Curtin theory for SFC with various fiber strengths and interfacial properties. The Weibull scale parameter, σ o, and shape parameter, m, at short gauge lengths are determined for each type of fiber through best-fit of the calculated and measured numbers of fiber breaks versus applied fiber stress. Lower values of σ o and higher values of m are obtained when compared with those obtained from single-fiber tension (SFT) tests for all kinds of fibers. However, the effects of surface treatments and gauge length on the fiber strength showed similar trends for both methods. It is found that the relatively low values of interfacial shear strengths calculated from SFC data are considered to be reasonable than those from SFT tests.

Effects of debonding and fiber strength distribution on fatigue-damage propagation in carbon fiber-reinforced epoxy

In order to design new fatigue-resistant composites, the underlying fatigue damage mechanisms must be characterized and the controlling microstructural properties should be identified. The fatigue-damage mechanisms of a unidirectional carbon fiber-reinforced epoxy has been studied under tension-tension loading. A ubiquitous form of damage was one or a few planar fiber breaks from which debonds or shear yield zones grew in the longitudinal direction during fatigue cycling. This leads to a change in stress profile of the neighboring fibers, and an increase in failure probability of these fibers. The breakage of fibers in the composite is controlled by the fiber strength distribution. The interaction between the fiber strength distribution and debond propagation leading to further fiber breakage was investigated by a numerical simulation. It was found that a wider distribution of fiber strength and a higher debond rate lead to more distributed damage and a higher fracture toughness. Implications to fatigue life behavior are discussed, with reference to constituent microstructure.

Prediction of the fracture toughness of fibrous composites

A statistical/micromechanical model is developed for the prediction of the fracture toughness of fibrous composites. The fracture resistance of the material is assumed to be related to the statistical distribution of the fiber pull-out length. The distribution of the fiber pull-out length is derived from the fiber strength distribution. The R-curve behavior of the fibrous composite is predicted and interpreted based on the present model. The limiting fracture toughness is predicted to be proportional to the square root of the ineffective length, or proportional to the square root of the fiber length if the fiber length is less than the ineffective length.

Comparison of fibre/matrix interface strength for a 3D woven SiC/SiC composite

The fibre/matrix interface shear strength, τ P, was determined by analysis of fibre pullout length distributions for a 3D woven SiC/SiC-based composite that had undergone tensile testing between room temperature and 1300°C in vacuum and air. Data was compared with the fibre/matrix interface shear strength, τ S, obtained previously for this system by analysis of in situ fibre strength distributions. τ P was found to follow the same general trend as that of τ S and this was explained in terms of the carbon-rich fibre/matrix interface region. However, τ P was smaller than τ S by a factor of 3-4 for all cases, but the reason for this remains unclear although several tentative suggestions have been put forward.

Influence of Fiber Structure on Properties of Thermally Point Bonded Polypropylene Nonwovens

Carded webs with a basis weight of 30 g/m2 are prepared from Hercules T-196 and Hercules T-101 polypropylene fibers, then thermally point bonded with "Novonette" rolls at various temperatures and pressures. A subset of samples is studied in relative detail using various methods. In particular, the distribution of bridging fiber strengths after bonding is measured directly. Bonding at higher temperatures reduces single fiber strength and increases its variability while increasing the effectiveness (strength) of the bonds. These competing effects appear to explain the maximum fabric-strength-versus-bonding temperature relationship. Bonding performance differences between these two fibers appear to depend on the fact that nonfailing bonds can be produced at lower temperatures in the T-196, where fiber strength degradation is less, and possibly to a lesser extent on the higher elongation and concave-down curvature of the stress-strain relationship.

Size and heterogeneity effects on the strength of fibrous composites

Probabilistic fiber composite strength distributions and size scalings depend heavily on both the stress redistribution mechanism around broken fibers and properties of the fiber strength distribution. In this study we perform large scale Monte Carlo simulations to study the fracture process in a fiber composite material in which fibers are arranged in parallel in a hexagonal array and their strengths are given by a two-parameter Weibull distribution function. To calculate the stress redistribution due to several broken fibers, a realistic 3D shear-lag theory is applied to rhombus-shaped domains with periodic boundary conditions. Empirical composite strength distributions are generated from several hundred Monte Carlo replications, particularly for much lower values of fiber Weibull modulus γ, and larger composite sizes than studied previously. Despite the localized stress enhancements due to fiber failures, predicted by the shear-lag model, composite response displays a transition to equal load sharing like behavior for approximately γ≤1. Accordingly, the results reveal distinct alterations in size effect, failure mode, and weak-link scaling behavior, associated with a transition from stress-driven to fiber strength-driven breakdown.

Experimental and theoretical study on the strain rate and temperature dependence of mechanical behaviour of Kevlar fibre

Abstract The tensile impact experiments on Kevlar 49 fibre bundles were carried out at strain rates 140, 440, 1350 s −1 and at temperatures −60, −20, 15, 50 and 90°C. It was found that the tensile mechanical properties of Kevlar 49 fibre bundles depend both upon the strain rate and the temperature. A bimodal Weibull distribution statistical model of the strain rate and temperature dependence of fibres, and a test method of determining mechanical properties and Weibull parameters of fibres from the fibre bundle test were adopted to characterize the combined effects of strain rate and temperature on Kevlar 49 fibre strength distribution. The simulated results are in good agreement with the experimental data, which proves that the bimodal Weibull distribution function is suitable to represent the statistical strength distribution of Kevlar 49 fibre which has peculiar ‘skin–core’ physical structure, and that the test method is valid and reliable.

Creep of SiC/Ti-1100 composite in a vacuum environment

This study examines the longitudinal creep behavior of a unidirectionally reinforced SiC fiber/Ti-1100 composite at 540°C in a vacuum. Primary creep behavior is predicted by the McLean creep model for elastic fibers in a creeping matrix provided the initial damage in the composite is taken into account and no damage accumulates during creep. At higher stresses, where the composite accumulates damage and eventually fails, both the strain and time to rupture can be predicted using the Bundle model, a modification of the McLean/Curtin creep model. In predicting rupture, the strength distribution of the weakest fibers in the composite is the controlling factor.

Mechanical behavior of SiC fiber reinforced brittle-matrix composites

The failure process of unidirectional BN-coated HI-NICALONTM SiC fiber reinforced glass matrix composites was examined under tensile loading. In situ observation of the mean matrix crack interval was conducted by the replica observation during tensile testing. Axisymmetric cylindrical models extended to the system considering the strength distribution of fibers were proposed to predict the whole stress-strain curve for comparison with the experimental results.

ESTIMATION OF TENSILE STRENGTH DISTRIBUTION FOR CARBON FIBER WITH DIAMETER VARIATION ALONG FIBER

Tensile strength distribution of carbon fibers was investigated for different gauge lengths ranging from 2 to 100mm. In tensile tests, the fiber diameter was determined as the three-point minimum diameter d3 at neighborhoods of both ends and the center of gauge section by using an optical microscope. Weibull analysis of the data and the effective volume model for tensile strength of carbon fiber showed that the shape parameter a was not constant for different gauge lengths and the effective volume model could not be applied effectively to the results. It was found that these were caused by the fact that the diameter was never constant along a carbon fiber. Consequently, in this study, it was aimed to derive the distribution of the tensile strength σ0 for the true minimum diameter d0 along the gauge length. In order to do this, two-dimensional distributions of d3 and d0 were derived from the data of diameter measured at every 0.1mm along a single fiber with the gauge length of 100mm. Combining these distributions of d3 and d0 with the distribution of the tensile strength σ3 for the diameter d3, the distribution of the strength σ0 was derived analytically, and calculated by using numerical values of included parameters. The distributions of σ0 obtained for respective gauge lengths mutually agreed very well and could be represented by a single normal distribution, and this showed the validity of the present analysis.

SiC繊維強化TiAl基複合材料の引張強度に及ぼす繊維強度分布および残留応力の影響

SiC繊維強化TiAl基複合材料の引張強度に及ぼす繊維強度分布および残留応力の影響

The effect of thermal exposure on the strength distribution of B4C coated carbon fibers

The effect of thermal exposure on the strength distribution of B4C coated carbon fibers was evaluated using the loose bundle tensile test. These tests were performed on the as-received T300 carbon fibers and on the coated fibers before and after thermal exposure at 700°C and 750°C. The heating times ranged between 15 and 180 min in an industrial, and in a pure nitrogen atmosphere. The fiber strength distributions were analyzed using the S−ε curve, in relation to the microstructural state of these fibers. It was shown that the local overthicknesses of the B4C coating make the fibers more brittle, leading to a premature failure of these carbon fibers. However, a significant improvement in the mechanical properties of the coated carbon fibers is observed for a heating time of 30 min at 700°C and 15 min at 750°C in an industrial nitrogen atmosphere. Using XPS analysis and microscopy observations, it was demonstrated that this effect is due to a reaction between the B4C coating and the environment which tends to form compliant protective layers, like BN and BxOy. Thermal treatments in controlled exposure conditions in a pure nitrogen atmosphere can lead to the formation of a compliant protective layer giving comparable mechanical properties to as-received T300 fibers.

Experimental assessment of fatigue life and failure modes in a SiC/Ti composite

An experimental investigation of the fatigue life and the associated failure modes in a fiber-reinforced titanium-matrix composite (TMC) has been conducted. Tests have been performed over a wide range of loading conditions, characterized by stress ratios (minimum/maximum) of R=0–0·8, and the results presented in the form of a Goodman diagram. The failure modes include: (i) catastrophic fracture following damage initiation; (ii) the formation and propagation of multiple bridged cracks, leading to the development of hysteresis and permanent strain and, in some instances, fiber bundle fracture; and (iii) the development of similar damage but without the occurrence of fiber bundle fracture. There exists a damage-initiation threshold, associated with a critical value of the stress amplitude, below which there is no apparent microstructural damage and the fatigue life is effectively infinite. There is also a fracture threshold following matrix cracking which is dictated by the fiber strength distribution. The fibers degrade somewhat upon cycling in the presence of matrix cracks, as manifested in a slight reduction (∼10%) in the mean strength of extracted fibers as well as the occurrence of composite fracture well after the attainment of a saturation in the matrix crack density. The results indicate that the damage-initiation threshold is likely to be the single most important property from the viewpoint of design and life prediction under high cycle fatigue.

Coulomb friction controlled bridging stresses and crack resistance of ceramic matrix composites

Bridging stresses in ceramic matrix composites (CMC) are calculated taking into account the effect of Poisson contraction of fibre and matrix during loading and a two parameter Weibull distribution of fibre strength. A parameter study is performed in order to assess the influence of the constituent properties. The bridging stress curve provides the link from the micromechanical analysis to the prediction of macroscopic composite behaviour. The load–deflection behaviour of pre-notched CMC specimens is derived by application of the method of weight functions. The predictions are compared with experimental results giving information about the actual properties of the material.

Diameter and Strength Distributions of Merino Wool in Early Stage Processing

In this paper, we investigate fiber diameter and strength distributions in early-stage processing. We have processed two lots of merino wool from scouring to top finishing. Fiber samples collected at each processing stage are measured for diameter on an optical fiber diameter analyzer, and fiber strength is measured on a modified WIRA single fiber strength tester. Fiber diameter conforms to a lognormal distribution, and this conformity persists throughout early-stage processing. Single fiber strength also conforms to a lognormal distribution in general, but this conformity may be distorted by fiber damage in processes such as carding. Furthermore, we have established a formula to estimate the coefficient of variation of single fiber strength once we know the coefficient of variation of the fiber diameter.

Characterization of Nicalon fibres with varying diameters Part II Modified Weibull distribution

Diameters vary significantly in a tow of commercial NicalonTM fibres, which is one of the most attractive ceramic reinforcements for structural composites. It was found that the strength distribution of Nicalon fibres could not be adequately characterized using either single- or bi-modal Weibull distribution. A recently proposed modified Weibull distribution can account for the effect of varying diameter in the characterization of fibre strength. To verify the validity of the modified Weibull distribution, comprehensive mechanical testing and fractographic studies have been conducted on Nicalon SiC fibres with diameters varying from 8 to 22 μm. The experimental results have been reported in Part I. Part II of this paper further modifies the derivation of the modified Weibull distribution to yield a relationship which is similar in form, but soundly based on experimental findings. Factors considered in the modified Weibull distribution include the dependence of fracture toughness and flaw density on fibre diameter, both of which may vary with fibre diameter, as reported in Part I. Comparison with experimental data shows that the current modified Weibull distribution works very well, while both single-modal and bi-modal Weibull distributions are inadequate for describing Nicalon fibres with varying diameters. © 1998 Chapman & Hall

Experimental evaluation of the strength distribution of fibers under high strain rates by bimodal Weibull distribution

This paper proposes a bimodal Weibull distribution model for strain- rate- and temperature-dependent fiber strength. The relationships of the mechanical quantities between fiber and fiber bundles at different strain rates and temperatures under tensile impact are established. A method for determining mechanical parameters of fibers by tensile impact tests of fiber bundles is established. Experiments on E-glass bundles have been performed at six strain rates (90, 300, 800, 1100, 1300 and 1700s−1) at three different temperatures (−70, 14, 80°C). According to the statistical analysis and models, the mechanical parameters for the fiber and their relationships with strain rate and temperature are obtained from the tensile impact experimental results. The emulated stress/strain curves from the model are in good agreement with the test data. The theoretical model and test results show that the shape parameters, βd1 and βd2, are not only strain rate independent but also temperature independent. The scale parameters σd01 and σd02, which change with strain rate and temperature, are not constant.

The single-filament-composite test: a new statistical theory for estimating the interfacial shear strength and Weibull parameters for fiber strength

For over two decades the single-filament-composite (SFC) test has been an important tool in the study of the failure of fibrous composites. The SFC test itself involves a single brittle fiber embedded along the center-line of a matrix specimen of both large cross-sectional area and strain to failure. With increasing strain, the fiber fractures progressively, breaking into an increasing number of shorter and shorter fragments. Surrounding each break a shielded or exclusion zone develops within which no further breaks typically occur. At some strain level ‘saturation’ occurs abruptly as the shielded zones finally occupy the whole fiber, thus leaving a final distribution of fiber fragments end-to-end. Two uses for the SFC test have emerged: one has been to estimate the interfacial shear stress, τ, in the exclusion zone, sometimes called the interfacial shear strength and usually idealized as a constant over this zone. The other has been to estimate the fiber strength distribution and in particular the Weibull shape and scale parameters, ρ and σl, for fiber strength appropriate to some characteristic ‘gage’ length, l, such as the mean fragmentation length. In the past, theoretical bases for these estimates have handled the statistics of shielding in ways that have led to quite large biases. The purpose of the present paper is to use some recent theoretical advances to develop more sophisticated estimation procedures for τ and the Weibull fiber strength parameters ‘in situ’, and thus to eliminate various errors in previous methods. Straightforward computer programs (written in release 3 of Maple), which calculate the various quantities in the paper, will be provided by the first or second author on request.

Strength variability in alumina fiber-reinforced aluminum matrix composites

The strength variability of an Al2% Cu alloy matrix reinforced with 65 vol.% Nextel -610 Al 2O 3 fibers has been investigated, with the aim of identifying and separating the contributions associated with the variabilities in both the fiber bundle strength and the fiber volume fraction. Strength distributions have been measured using three test geometries, including three- and four-point flexure and uniaxial tension. The measured distributions are rationalized on the basis of a fiber strength distribution that follows Weibull statistics and a fiber volume fraction distribution characterized by a Gaussian. The fiber bundle strength distribution is found to be extremely narrow, with a Weibull modulus in the range of ∼ 50–60. In addition, the coefficient of variation in the fiber volume fraction distribution is inferred to be ∼ 6%; by comparison, measurements made on relatively large specimens yield a coefficient of variation of ∼ 3%. The differences in these values are attributed to local volume fraction variations which are not detectable by the global measurements. The measured strengths are compared with the predicted values based on the theoretical work of Curtin and co-workers, incorporating the effects of local load sharing between broken fibers and their neighbors. Good correlations are obtained between the experimental data and the model predictions.