Fiber Strength Distribution Research Articles

Statistical dynamic tensile strength of UHMWPE-fibers

Dynamic tensile properties of UHMWPE fiber bundles were studied at two strain rates and two temperatures. The integral stress–strain curves were obtained. Experimental data show that UHMWPE fiber bundle has strain rate and temperature sensitivity. A fiber-bundle constitutive equation was used to describe the tensile behavior of UHMWPE fiber bundles at high strain rates. The good consistency between the simulated results and experimental data indicates that the 5-parameter Weibull function can represent the tensile strength distribution of UHMWPE fibers and the method of extracting Weibull parameters from fiber bundles stress–strain data is valid.

Simplified stochastic modeling and simulation of unidirectional fiber reinforced composites

Stochastic prediction of the failure strength of composite materials has been the subject of research for the last four decades. These studies have generally focused on expensive materials with high quality control for use in aerospace applications. For these applications it has been economically feasible to obtain reliable statistical data. To extend this research to the analysis of composites with widespread use in civil engineering, the complicated models developed in the past need to be simplified. This paper proposes a simplified stochastic two-dimensional model to predict the strength distribution of single-ply unidirectional composites. The model is studied via Monte Carlo simulation and accounts for the following parameters: specimen size, fiber strength distribution, fiber–matrix properties and load transfer at broken fibers. The classical load sharing rules to model the load redistribution at broken fibers are modified to consider different material properties. A parametric study investigating the parameters that affect the strength and the failure pattern of the composite is presented. The numerical results are consistent with experimental data analyzed. The study is used to quantify the effect of various material and geometric characteristics on resultant performance and failure properties.

単一炭素繊維強化プラスチックの繊維破断挙動に及ぼす負荷速度の影響

Fiber fragmentation behavior in a single carbon fiber reinforced epoxy composite is investigated experimentally and analytically. Strength distribution of the carbon fiber is also measured. Fiber fragmentation process is observed during tensile loading on the composites. The effect of loading rate on the fiber fragmentation behavior is discussed. The statistical prediction model of fiber fragmentation behavior assuming that the constant interfacial shear stress presents is used to estimate the interfacial shear stress. It is found that the fiber fragmentation behavior is well predicted by using the measured fiber strength distribution and an assumed interfacial shear stress. A Monte Carlo simulation technique in which a stress transfer model based on the linear elasticity is used is also conducted to describe the fiber fragmentation behavior. The effect of loading rate on the failure process around the fiber breaks is also discussed.

FAILURE PROPERTIES OF FIBER BUNDLE MODELS

We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cut-off. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

Strength of SCS-6 fibers in a Tiβ21s/SCS-6 composite before and after fatigue

The strength distributions of SCS-6 fibers extracted from both as-received (AR) and fatigued Tiβ21s/SCS-6 composite specimens have been characterized by single-fiber-tension tests and have then been analyzed statistically. With the assistance of fractography, the whole population of SCS-6 fibers in the composite can be cataloged into three subpopulations with fracture strengths, σF, of <2000, 2000 ≤ σF <3700, and ≥ 3700 MPa, respectively. Each subpopulation has distinctive statistical parameters, which do not appear to change markedly after fatigue. However, cyclic loading can reduce the average strength of the whole population by decreasing the percentage of high-strength fibers present. In addition, cyclic loading can also break some of the low-strength fibers. By using a trimodal Weibull function, the degradation of the strength of the fibers after fatigue, as well as the influence of such degradation of fiber strength on the fiber-bundle strength and then on the predicted fatigue crack growth resistance of the composite, have been analyzed.

Mechanical properties of alumina Nextel™ 720 fibres at room and elevated temperatures: tensile bundle testing

Tensile tests on alumina Nextel 720™ fibre bundles were performed and results were analysed using Weibull statistics to calculate the tensile strength and elastic modulus of the fibres as a function of temperature and gauge length. A compliance-correction technique was used to deduce the net fibre strain from the recorded experimental data separately for room and high-temperature tests; the latter tests were performed under inert (argon) gas environments. The Weibull parameters, calculated in terms of strain values, yielded the mean failure strain and the initial compliances yielded the elastic moduli. Both parameters allowed to obtain the mean fibre strength. Statistical analysis was performed to provide a high and low confidence limit for both the Weibull modulus and the strength. Fibre strength was projected to a reference gauge length of 25-mm using the Weibull gauge length correction to allow for comparison with results from single-fibre tests. Room-temperature tests showed that gauge lengths larger than 75 mm are associated with a non-smooth fibre failure regime that can be explained by the larger amount of energy stored in the tested volume at the onset of failure. Results from relevant tests yielded an elastic modulus of 260 GPa and a Weibull modulus of 5.6, 20% less than the value reported by the manufacturer. Fibre strength was substantially less than the value quoted by the manufacturer for both room and high-temperatures; the room-temperature value corresponding to only 53% of the value reported. The observed divergence is a direct effect of the fundamental characteristic of the fibre bundle testing technique which, contrary to the single-fibre test used in the reference studies, is associated with minimal fibre handling and damage and, as such, is believed to fully assess the fibre strength distribution by not eliminating weaker fibres from the population before testing.

Phase transition in fiber bundle models with recursive dynamics.

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

Strength and adhesion characteristics of elementary flax fibres with different surface treatments

It is known that the best flax fibres can compete in terms of mechanical properties with glass fibres. However, during the manufacturing process flax fibres are often damaged, and hence, the properties can be lowered. Furthermore, these properties change from batch to batch (depending on the time and place of harvest), which means that they are somewhat unpredictable. The most affected fibre property is strength, which can vary in very wide interval due to defects introduced by the manufacturing process. Therefore, there is a need for a simple but reliable testing procedure that allows the estimation of the strength of flax fibres, so called quality control. Regarding the final goal, that is the development of natural fibre composites, another crucial property is the fibre/matrix adhesion. The objective of this study is to investigate the possibility to use the single fibre fragmentation test to characterize strength distribution of flax fibres and to evaluate the adhesion. Untreated flax fibres and fibres coated by a special surface treatment are used. Fragmentation tests are performed on flax fibres embedded in thermoset, vinylester and polyester, resins. Results show that there is a definite improvement in interfacial strength when a fibre surface treatment is applied. Fibre strength distribution is obtained from SFFT and compared with limited results available from single flax fibre tests.

Statistical analysis of the failure stresses of ceramic fibres: Dependence of the Weibull parameters on the gauge length, diameter variation and fluctuation of defect density

The strength distribution of ceramic fibres is commonly described using a two-parameter Weibull distribution function. This study shows that the determination of these parameters from around 30 tensile tests obtained at one single gauge length (L0) does not allow the strength distribution at other gauge lengths to be correctly predicted. The reliability in the Weibull parameter determination is lowered by variations in fibre diameter (D) and the insufficient number of fibres tested. An effective failure stress σE = σ · (π D · L0)1/m is first introduced to take into account fibre diameter variations and to extract the two Weibull parameters from the 180 tests obtained at 6 gauge lengths. It is then shown that the linear size effect, which is expected from the standard Weibull model, is not appropriate to fit correctly this experimental strength distribution. The length dependence follows a power law (L0β) leading to an effective failure stress σE = σ · (π D · L0β)1/m. Diameter variations along the gauge length cannot be responsible for this non linear variation with the length, which is attributed to a large scale fluctuation of the density of defects. The value of β can bring valuable information about fluctuations in the fibre processing conditions.

Size effect on the fiber strength of composite pressure vessels

In this study, experimental tests and an analytical approach are conducted to verify the size effect on the fiber strength of a composite pressure vessel. As an analytical method, the Weibull weakest link model and the sequential multi-step failure model are considered and mutually compared. In the case of carbon fiber tensile strength, there is no large difference between the analytical methods for the volumetric size effect. To verify the validity of the analytical approach, experimental tests were performed using fiber strand specimens, unidirectional laminate specimens and composite pressure vessels. Good agreement for fiber strength distribution was shown between the test data and predicted results. The volumetric size effect shows the clearly observed tendency towards fiber strength degradation with increasing stressed volume. Because the volumetric size effect depends on material and processing factors, the reduction of fiber strength due to the stressed volume shows different values according to the variation of material and processing conditions.

Size effect on tensile strength of unidirectional CFRP composites— experiment and simulation

The present paper studies the size effect on the strength of unidirectional carbon fiber reinforced plastic (CFRP) composites both experimentally and numerically. The main aim of the present study is to validate the recent micro-mechanical model for internal damage occurring in composites. The relationship between the composite size and strength was experimentally evaluated, and the composite strength decreased as the composite size increased. Microscopic damage observation showed the existence of localized damage (i.e. a cluster of fiber breakage). Based on a 3D shear-lag model considering the matrix-yielding properties, we conducted a Monte Carlo simulation of the damage process using the measured fiber strength distribution for several gage lengths. The simulation shows that Weibull of Weibull (WOW) statistics considering the fiber-to-fiber strength variation is appropriate for predicting the present composite failure, rather than a traditional Weibull model. The simulated result showed a good agreement with the upper bounds of the experimental data. It was found that the size-dependent strength of composite could be predicted based on the microscopic models.

Fatigue crack growth in a Tiβ21s/SCS-6 composite

The fatigue crack growth resistance of a Tiβ21s/SCS-6 composite at room temperature has been characterised experimentally and analysed theoretically. Particular attention has been paid to the transition from crack-arrest (CA) to catastrophic specimen failure (CF), and emphasis has been placed on the influence of the extrinsic factors of initial notch length, specimen width and loading configuration, and of the intrinsic fibre strength distribution on this transition. Experimental results show a marked influence of extrinsic factors on the CA/CF transition, and they also reveal the importance of fibre strength on the fatigue crack growth resistance of the composite. The stress in bridging fibres has been analysed theoretically, and the results have been used to explain the experimental observations.

Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model.

The random fiber bundle (RFB) model, with the strength of the fibers distributed uniformly within a finite interval, is studied under the assumption of global load sharing among all unbroken fibers of the bundle. At any fixed value of the applied stress sigma (load per fiber initially present in the bundle), the fraction U(t)(sigma) of fibers that remain unbroken at successive time steps t is shown to follow simple recurrence relations. The model is found to have stable fixed point U*, filled (sigma) for applied stress in the range 0 < or = sigma < or = sigma(c), beyond which total failure of the bundle takes place discontinuously [abruptly from U*, filled (sigma(c)) to 0]. The dynamic critical behavior near this sigma(c) has been studied for this model analyzing the recurrence relations. We also investigated the finite size scaling behavior near sigma(c). At the critical point sigma = sigma(c), one finds strict power law decay (with time t) of the fraction of unbroken fibers U(t)(sigma(c)) (as t--> infinity). The avalanche size distribution for this mean-field dynamics of failure at sigma < sigma(c) has been studied. The elastic response of the RFB model has also been studied analytically for a specific probability distribution of fiber strengths, where the bundle shows plastic behavior before complete failure, following an initial linear response.

In situ analysis of delayed fibre failure within water-aged GFRP under static fatigue conditions

A stress corrosion model has been applied to the microscopic analysis of the delayed fibre failure processes occurring within a water-aged unidirectional glass/epoxy composite under static fatigue loading (i.e. relaxation). By means of in situ microscopic observations, the individual fibre failures within an elementary volume located on the tensile side of the flexural specimens have been quantified as a function of time under various applied strain levels. It was found that the time dependence of the in situ fibre failure processes obeyed a stress corrosion model. From the microscopic observations, it was possible to assess consistent values of the parameters characterising the in situ fibre strength distribution and the subcritical crack propagation law. A comparison with separate static fatigue experiments using unimpregnated fibre bundles demonstrated that the specific physico-chemical environment encountered by the glass fibres within the aged epoxy matrix can induce significant changes in the subcritical crack propagation rates, as compared to stress corrosion cracking data collected in humid air.

Characterization of interfacial and mechanical properties of green composites with soy protein isolate and ramie fiber

Environment-friendly fiber-reinforced composites were fabricated using ramie fibers and soy protein isolate (SPI) and were characterized for their interfacial and mechanical properties. Ramie fibers were characterized for their tensile properties and the parameters for the Weibull distribution were estimated. Effect of glycerol content on the tensile properties of SPI was studied. Interfacial shear strength (IFSS) was determined using the microbond technique. Based on the IFSS results and fiber strength distribution, three different fiber lengths and fiber weight contents (FWC) were chosen to fabricate short fiber-reinforced composites. The results indicate that the fracture stress increases with increase in fiber length and fiber weight content. Glycerol was found to increase the fracture strain and reduce the resin fracture stress and modulus as a result of plasticization. For 10% (w/w) of 5 mm long fibers, no significant reinforcement effect was observed. In fact the short fibers acted as flaws and led to reduction in the tensile properties. On further increasing the fiber length and FWC, a significant increase in the Young's modulus and fracture stress and decrease in fracture strain was observed as the fibers started to control the tensile properties of the composites. The experimental data were compared to the theoretical predictions made using Zweben's model. The experimental results are lower than the predicted values for a variety of reasons. However, the two values get closer with increasing fiber length and FWC.

Glass fibre strength distribution determined by common experimental methods

The tensile strength of brittle fibres is routinely described by the Weibull distribution. The parameters of the distribution can be obtained from tests on single fibres and fibre bundles or from model composite tests. However, there is growing evidence that the distribution parameters obtained by different experimental techniques differ systematically. In order to investigate the possible causes of such discrepancies, single-fibre tension, fibre bundle, and single-fibre fragmentation tests are employed in this study to obtain strength distribution of commercial E-glass fibres. The results reveal parameter dependence on the approach used to extract the distribution parameters from experimental data. Particularly, in the case of single-fibre tension tests, the shape parameter obtained from average fibre strength vs. length data is larger than that obtained at a fixed gauge length. It is assumed that the apparent fibre strength scatter is caused by both the inherent flaw structure along a fibre and by the fibre-to-fibre strength variability within a batch, due to slightly differing processing and handling history of the fibres. Fibre fragmentation test results are used to derive the Weibull distribution parameters applicable to the fibre batch. The strength distribution obtained is compared with strength data for the single fibres, and reasonably good agreement is observed.

Electromechanical modeling of unidirectional CFRP composites under tensile loading condition

The present paper addresses the correlation between mechanical damage and the change in electrical resistance of CFRP under tensile loading. A linear relation between the strain and the electrical resistance of single carbon fibers was obtained experimentally, and the electrical behavior of CFRP under tensile loading was investigated. At stresses approaching the failure stress, the composite resistance rises non-linearly, which is attributed to damage in the form of broken fibers. These experiments lead to the concept of electrical ineffective length over which a broken fiber does not carry electric current, in analogy to the well-established mechanical ineffective length over which a broken fiber carries reduced stress. Based on this concept, a DC circuit model consisting of a serial array of discrete parallel cells of length equal to the electrical ineffective length is proposed to explain the resistance evolution in the composite. An analytical model for fiber damage evolution within the electrical ineffective length is constructed using the Global Load Sharing model and the Weibull fiber strength distribution, The model successfully explains the experimental results on the resistance change of CFRP under tensile loading with an electrical ineffective length of 5 mm. (C) 2001 Elsevier Science Ltd. All rights reserved.

In situ strength distribution of carbon fibers in unidirectional metal-matrix composites-wires

Based on an etching method and the fiber-bundle tensile testing technique, a new method has been developed for the testing and characterization of the strength distributions of in situ fibers in unidirectional aluminum-matrix-composite wires. According to this method, a systematic study on in situ properties of T300 fiber and M40J fibers in MMCs wires have been performed at strain rates ranging from 0.001 to 1300 1/s. Experimental results show that both T300 fiber and M40J fibers are strain-rate insensitive materials. Results also show that the modulus, ultimate strength and unstable strain of two fibers have been degraded to some degree by high-temperature processing. Micrographs indicate that there are obvious crack distributions on the surfaces of in situ fibers and this is the main reason for the decreasing fiber strength. On the basis of the fiber-bundles model and the statistical theory of fiber strengths, the distribution parameters for in situ fiber strength have been obtained. The evaluated stress/strain curves from the theoretical model are in good agreement with the test data. Statistical analysis results show that the high-temperature manufacturing processing only affects the Weibull scale parameter, σ 0, of T300 fibers and does not affect the shape parameter, β whereas for M40J fibers, both the shape and scale parameters have been changed by high-temperature manufacturing processing.

Micromechanics-based deformation and failure prediction for longitudinally reinforced titanium composites

Two models to account for fiber breakage in longitudinally loaded composite materials have been incorporated into NASA Glenn's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) (Arnold SM, Bednarcyk BA, Wilt TE, Trowbridge D. MAC/GMC Users Guide: Version 3.0. NASA/TM- 1999-209070, 1999). The first is Curtin's widely used effective fiber breakage model (Curtin WA. Ultimate strengths of fibre-reinforced ceramics and metals. Composites 1993;24(2):98–102; Curtin WA. Theory of mechanical properties of ceramic-matrix composites. J Am Ceram Soc 1991;74(11):2837–45). This model treats all fibers in the composite as one effective fiber whose properties degrade in accordance with the statistical strength distribution of the actual fibers. The second is a new discrete model that considers failure of many individual fibers in a composite repeating unit cell. This model explicitly includes the important feature of local stress unloading in fractured fibers, even as global loading of the composite continues. MAC/GMC was employed to simulate the longitudinal tensile deformation and failure behavior of several silicon-carbide-fiber/titanium-matrix (SiC/Ti) composites using both models. Through comparison with experiment, MAC/GMC, in conjunction with the incorporated fiber breakage models, is shown to be quite realistic and capable of accurate predictions for various temperatures, fiber volume fractions, and fiber diameters.

Tensile properties of short fiber composites with fiber strength distribution

The influence of fiber rupture, fiber pull-out and fiber tensile strength distribution on the post-cracking behavior of short-randomly-distributed fiber reinforced brittle-matrix composites has been analyzed using an approach based on the Weibull weakest-link statistics. The analysis led to the development of a predicting model for the composite bridging stress-crack opening displacement (σc − δ) law—a fundamental material property necessary for the analysis of steady-state cracking in the composites. The proposed σc − δ relationship can be used to relate the composite tensile and fracture properties to the microstructural parameters. The model revealed the importance of fiber strength distribution as described by the Weibull weakest-link statistics in governing the post-cracking response of the composite. The proposed model was able to reproduce the results of an earlier model for a limiting case where fiber tensile rupture was accounted for assuming a deterministic fiber tensile rupture strength. Model-predicted post-peak σc − δ curve was also in close agreement with those obtained from uniaxial tensile tests of a Kevlar fiber reinforced cementitious composite where fiber tensile rupture was reported. The model provided physical insights as to the micro-mechanisms controlling the post-cracking response of short-fiber reinforced brittle-matrix composites where fibers have a tensile strength distribution described by the Weibull weakest-link statistics.