Fiber Strength Distribution Research Articles

Evaluation of the relationship between the number of surface and internal defects and stress in inorganic fibers

To better utilize the mechanical properties of ceramics fibers, it is very important to understand the ceramics fiber distribution. The strength distribution of ceramics fibers is strongly dependent on defects that are present in or on the surface of the material. When the defects are large, the location of the defects is identified by observing the fracture surface, and the strength of the material is analyzed based on the results. However, in recent years, defects in high-strength ceramics such as carbon fibers have become so small that it is very difficult to analyze the location of such defects. To overcome this problem, a defect analysis method has been developed based on the observation that the tensile strength of fibers decreases when tensile tests are performed in liquids. In this study, a new model that considers both surface and internal defects of fibers was introduced into this analysis method, and the newly developed method was applied to quantitatively separate surface and internal defects of polyacrylonitrile-based fibers, pitch-based carbon fibers, SiC fibers, and glass fibers in air, water, and organic solvents. The number of internal and external defects was expressed as a function of stress. Based on the number of defects, the influence of surface defects was significant for glass fibers, polyacrylonitrile-based carbon fibers, silicon carbide fibers, and pitch-based carbon fibers, in that order. This method is useful for analyses of surface defects in fibers.

Time-dependent mechanical behavior analysis using Weibull models of cellulose hollow fiber membranes produced by green solvent

The mechanical behavior of sustainable (“green”), bio-based cellulose hollow fiber membranes (hereafter, hollow fiber) produced using green solvent, which is potential for desalination and solvent-resistant nanofiltration, can be evaluated either in dry or water-conditioned (wet) states. However, the effect of conditioning time on the mechanical behavior of hollow fibers has not been conclusive. In this work, an extensive evaluation involving an experimental campaign and rigorous application of statistical models for cellulose hollow fibers produced using green solvent (1-ethyl-3-methylimidazolium diethyl phosphate or [EMIM][DEP]) via a dry-jet spinning technique is reported. First, we evaluated the microstructures and separation performance (water permeation, solute rejection) of hollow fibers made of different cellulose concentrations (10–15 wt%) in both pristine and conditioned states. Then, the strength, stiffness, and ductility of hollow fiber samples of different gauge lengths (25 and 50 mm) were measured by a standard tensile test device. Here, the effect of conditioning time on mechanical properties was evaluated after the hollow fiber samples were water-immersed at different times (from 30 s to 2 months). The strength distribution of conditioned hollow fibers was modeled and analyzed using two-parameter and three-parameter Weibull models. Our results showed that the cellulose content of 15 wt% in the hollow fibers produced a denser microstructure, providing the lowest molecular weight cut-off (MWCO). The cellulose content and gauge length slightly modified the mechanical properties of hollow fibers when they were evaluated in pristine, dry conditions. The mechanical properties of hollow fibers were drastically reduced after 10 min of water immersion, beyond which their properties were stabilized. Weibull modeling of mechanical reliability showed that two- or three-parameter Weibull could estimate the failure probability of hollow fibers quite well. Nonetheless, the three-parameter Weibull is better than the two-parameter one in terms of accuracy in determining the threshold strength located at the “lower-end tail.” Our analysis provides a rigorous demonstration of Weibull modeling in evaluating the time-dependent mechanical behavior of ductile, cellulose-based hollow fiber membranes, which is essential to support the design and development of future hollow fiber membranes in desalination industries.

Strength response investigation of defective C/C composite materials based on the Weibull model

In this study, the issue of random fiber strength resulting from initial fiber defects and matrix pore defects in the strength response of C/C composite materials is addressed. A method for generating random numbers following the Weibull distribution is proposed and an improved random sequence adsorption (RSA) algorithm is employed to describe pore defects in the matrix, ultimately leading to the development of a representative volume element (RVE) model for C/C composite materials. The influence of fiber strength distribution and pore defects on the mechanical properties of unidirectional C/C (UD-C/C) composite materials is analyzed. This study offers a new approach to investigate the mechanical behavior of C/C composite materials, taking into account both fiber initial defects and pore defects.

The strength prediction model of unidirectional fiber reinforced composites based on the renormalization group method

When unidirectional fiber reinforced composites are subjected to longitudinal tensile loading and reach a critical failure state, they experience a sudden transition from local damage to catastrophic failure, commonly termed as an avalanche event. This paper integrates the self-organized criticality theory (SOC) concepts into the prediction of longitudinal tensile strength of composites and establishes a strength prediction model of composites based on the renormalization group method (RGM). The predictions of the RGM model are successfully validated against experimental results in the literatures, and it demonstrates relatively acceptable predictive accuracy compared to classical strength criteria. Compared to other state-of-the-art prediction models considering stochastic fiber strength distribution, the RGM model effectively provides strength statistics for fiber bundles of any size and describes the occurrence of composites avalanche failure induced by local stress concentration. This present model can be very conveniently implemented as a User Material Subroutine (UMAT) for finite simulations, facilitating practical prediction of the strength of composites structures.

Tensile Strength Statistics and Fracture Mechanism of Ultrahigh Molecular Weight Polyethylene Fibers: On the Weibull Distribution.

To study the distribution of ultrahigh molecular weight polyethylene fiber (UHMWPE) strength, three groups of UHMWPE fibers were spun by the gel spinning method, which was undrafted raw fibers (with high strain at break) and fibers with different prespinning and postspinning draw ratios. It is found that even when the strain at break (εb) > 46%, the tensile strength of the fiber still obeys the Weibull distribution. The draw ratio has a great influence on the distribution of fiber strength, especially the draw ratios of the spinneret in the prespinning process. It may be that different drafting processes affect the fracture mechanism of the fibers. This paper analyzes and discusses that and proves it by differential scanning calorimetry and the taut tie molecules (TTMs) fractions. The parameters of the Weibull distribution suggest the quality of the fiber. The Weibull modulus is closely related to the dispersion of the fiber properties and processing parameters. The characteristic strength is similar to the test average strength, which is more suitable for the judgment of fiber reliability in actual use. At the same time, the normality of the samples was tested by Kolmogorov-Smirnov, Shapiro-Wilk, Jarque-Bera test, and quantile-quantile (Q-Q) plots, and the strength distribution was visually displayed by the bell curve. The results show that the Gaussian distribution is not so suitable to describe the strength distribution of the stretched fiber compared to the Weibull distribution.

Variability of sub-regional fibre strength in 3D orthogonal SiC fabrics and its effect on the constitutive response of composites

Various fibre damage may occur during 3D orthogonal SiC woven weaving, leading to the variability of sub-regional fibre strength. In this study, different types of yarns were divided into several subregions along the cross-section according to the possible damage modes. The fibres in different subregions were extracted, and the monofilament strength test was carried out. The results showed that the fibre strengths of yarns and yarn subregions followed normal distributions. The correlation between the fibre strength distribution of the in-situ yarns and the subregion fibre strength difference was verified by using the Monte Carlo simulation method. Finally, the sub-regional fibre strength difference was considered in the tensile simulation of 3D orthogonal woven SiC/SiC composites. The simulation results agree with the experimental results and showed that the variability of sub-regional fibre strength significantly affects the composite's constitutive behaviour.

Novel continuous fiber bending experiment to determine size- and spatial-distribution of surface defects in glass fibers

Tensile strength models for unidirectional composites require scaling of fiber strength distributions to small length scales in the range of the fiber radius to the ineffective length (5–200 μm). No test methods currently exist to measure and validate fiber strength at these length scales. In this paper, a novel continuous fiber bending test method is developed to measure the size and spatial distribution of defects in S-glass fibers. For this test method, a single glass fiber was placed between Kapton film and tape, and the sample is subjected to a sequence of controlled radii of curvatures ranging from 350 μm to 25 μm in a confocal microscope. From the bending tests, the number of defects and spacings between the defects over 780 mm length of fiber are obtained for each level of flexural stress. The Kapton film confines the fiber fragments and maintains fiber alignment allowing the same sample to be tested at lower radius of curvature (higher flexural strain/stress). The associated defect size is calculated using fracture mechanics. These results are used to map the size- and spatial-distribution of critical defects on the tension surface of a glass fiber. A methodology is presented to map additional defects around the circumference of the fiber, while maintaining the size and spatial distribution obtained from the bending tests. The results show that the lognormal distribution best fits the spatial distribution of defects along the fiber axis. The results also indicate that extrapolating the Weibull strength distribution (be it bimodal or unimodal) to gage lengths less than 200 μm leads to serious errors in fiber strength prediction.

Characterization of metal-core piezoelectric fiber/aluminum composite in a large-strain region

To evaluate the suitability of metal-core piezoelectric fiber/aluminum composites for structural health monitoring, their output characteristics and mechanical properties were evaluated in large strain regions exceeding 10%. Tensile vibration tests were adapted to the composites to evaluate the output charges in large strains; simultaneously, the mechanical properties were evaluated. Consequently, it was possible to obtain outputs even at approximately 20%, and the output was divided into three stages. The fracture behavior of the fiber was related to the change in output. The first stage involves the region where fiber fragmentation occurs due to mechanical load on the fiber and the fragmentation reduces the stress, resulting in a decrease in output charges. The second stage is a region where the fragment length reaches a critical length and the stress transmitted from the matrix becomes constant, resulting in a constant output. The third stage involves a sudden decrease in output due to core rupture. Further, the effect of residual stress was confirmed. The Weibull distribution of fiber strength, decreased with relaxation of the residual stress in the scale parameter from 9.31 MPa to 6.36 MPa, indicating that residual stress has a significant effect on the mechanical properties of the fiber.

Numerical and Experimental Investigation on Bending Behavior for High-Performance Fiber Yarns Considering Probability Distribution of Fiber Strength

The performance of fiber-reinforced composite materials is significantly influenced by the mechanical properties of the yarns. Predictive simulations of the mechanical response of yarns are, thus, necessary for fiber-reinforced composite materials. This paper developed a novel experiment equipment and approach to characterize the bending behavior of yarns, which was also analyzed by characterization parameters, bending load, bending stiffness, and realistic contact area. Inspired by the digital element approach, an improved modeling methodology with the probability distribution was employed to establish the geometry model of yarns and simulated bending behavior of yarns by defining the crimp strain of fibers in the yarn and the effective elastic modulus of yarns as random variables. The accuracy of the developed model was confirmed by the experimental approach. More bending behavior of yarns, including the twisted and plied yarns, was predicted by numerical simulation. Additionally, models revealed that twist level and number of plies affect yarn bending properties, which need to be adopted as sufficient conditions for the mechanical analysis of fiber-reinforced composite materials. This efficient experiment and modeling method is meaningful to be developed in further virtual weaving research.

Experimental determination of bimodal strength distribution of S-glass fibers

Tensile strength distribution of S-Glass fibers at small gage lengths on the order of the ineffective length is required for both analytical and numerical models of composite unidirectional tensile strength. Historically unimodal Weibull strength distributions measured at large gage lengths are extrapolated to smaller length scales (5–200 μm). The accuracy of this approach is assessed by using 2 different experiments – the filament tensile test (gage lengths > 4 mm) and a continuously-monitored Single Fiber Fragmentation Test (SFFT, gage length = 544 μm). Extrapolation of the unimodal Weibull distribution to the 544 μm gage length leads to significant overprediction of fiber strengths (by ∼60%). The Weibull distribution obtained from SFFT also shows a significantly higher Weibull Modulus (12.9) as opposed to the tension dataset (4.5). This indicates that a different population of defects dominate at the shorter gage lengths. A bimodal Weibull equation has been fit to the combined data to account for the 2 different defect populations to provide accurate strength predictions over fiber lengths from ∼500 μm to 30 mm. An independent validation experiment was performed at 2 mm gage length to validate the Bimodal Equation.

In-situ synchrotron computed tomography tensile testing of composite specimens to estimate fibre strength Weibull parameters

A methodology is presented for the retrieval of fibre strength Weibull parameters using in-situ synchrotron computed tomography tensile testing of unidirectional composite specimens. Only fibre breaks that did not fail due to stress concentrations caused by other breaks are considered in this methodology. After the selection of the fibre breaks, the Weibull strength parameters were estimated through non-linear regression as well as least-squares fitting of linear regression in logarithmic scale. The two methods yield different estimated parameters, with the non-linear regression showing a better correlation with the observed fibre strength probability. The estimated Weibull parameters differed between specimens of the same fibre and matrix type, indicating that the strength distribution of fibres can vary within a given material batch. The measured Weibull scale parameters of the carbon fibres was estimated to be larger than the parameters measured in the single fibre tensile testing. This strength increase can be evidence of the higher strength of fibres when embedded in resin compared to when tested in air. The effect of fibre pre-selection in single fibre tensile tests was eliminated in the performed impregnated specimen tests, removing one source of uncertainty of the fibre strength Weibull parameters.

Environmental Effects on Strength and Failure Strain Distributions of Sheep Wool Fibers.

Sheep wool is an eco-friendly, renewable, and totally recyclable material increasingly used in textiles, filters, insulation, and building materials. Recently, wool fibers have become good alternatives for reinforcement of polymer composites and filaments for 3D printing. Wool fibers are susceptible to environmental degradation that could shorten their lifetime and limit applications. This study reports on the mechanical properties of sheep wool fibers under the impact of humid air and UV irradiation. The results of single fiber tensile tests showed a noticeable gauge length effect on the fibers’ strength and failure strain. Long (50 mm) fibers possessed about 40% lower characteristics than short (10 mm) fibers. Environmental aging decreased the elastic modulus and strength of the fibers. Moisture-saturated fibers possessed up to 43% lower characteristics, while UV aging resulted in up to a twofold reduction of the strength. The most severe degradation effect is observed under the coupled influence of UVs and moisture. The two-parameter Weibull distribution was applied for the fiber strength and failure strain statistical assessment. The model well predicted the gauge length effects. Moisture-saturated and UV-aged fibers were characterized by less extensive strength dependences on the fiber length. The strength and failure strain distributions of aged fibers were horizontally shifted to lower values. The results will contribute to be reliable predictions of the environmental durability of sheep wool fibers and will extend their use in technical applications.

An innovative micromechanics-based multiscale damage model of 3D woven composites incorporating probabilistic fiber strength distribution

An innovative micromechanics-based multiscale damage model for investigating the complex failure behaviors of 3D woven composites is proposed in this paper. The microscale and mesoscale representative volume cells (RVC) are established to sequentially define the fiber arrangements within yarns and the intertwined yarn architecture of realistic composites. The micromechanics of failure criteria (MMF) are adopted to identify the damage initiations of fibers and matrix constituents, and the damage evolvements are governed by the equivalent displacements and fracture toughnesses to alleviate the mesh dependency. The loading direction effects on the stress distributions of micro RVC with hexagonal fiber arrangements are studied by conducting a suite of micromechanics analyses. Instead of using deterministic values, the stochastic strengths of fiber filaments are characterized by adopting a Weibull probabilistic distribution. Particularly, the influences of fiber strength distributions on the performance of woven composites are parametrically investigated. The proposed multiscale damage model is integrated to ABAQUS with a user-defined subroutine to analyze the quasi-static damage responses of 3D woven composites. The numerical predictions exhibit a good correlation with the relevant experiments.

Direct comparison between monofilament and multifilament tow testing for evaluating the tensile strength distribution of SiC fibers

The tensile strength distributions of five types of silicon carbide (SiC) fiber, namely, Nicalon, Hi-Nicalon, Hi-Nicalon TypeS, Tyranno ZMI and Tyranno SA, were evaluated by monofilament and multifilament tow tensile testing with the estimated Weibull parameters being compared from each method. Whereas values for the Weibull scale parameter were found to be similar for both the monofilament and multifilament test methods, the Weibull shape parameter obtained from multifilament tow testing tended to be greater than that obtained from monofilament testing. The effect of diameter variation within individual fibers on the multifilament tow test results was investigated by Monte-Carlo simulations. In contrast with the experimentally obtained results, the shape parameters calculated by Monte-Carlo simulation exhibited good agreement with the monofilament test results.

Detailed experimental validation and benchmarking of six models for longitudinal tensile failure of unidirectional composites

Longitudinal tensile failure of unidirectional fibre-reinforced composites remains difficult to predict accurately. The key underlying mechanism is the tensile failure of individual fibres. This paper objectively measured the relevant input data and performed a detailed experimental validation of blind predictions of six state-of-the-art models using high-resolution in-situ synchrotron radiation computed tomography (SRCT) measurements on two carbon fibre/epoxy composites. Models without major conservative assumptions regarding stress redistributions around fibre breaks significantly overpredicted failure strains and strengths, but predictions of models with at least one such assumption were in better agreement for those properties. Moreover, all models failed to predict fibre break (and cluster) development accurately, suggesting that it is vital to improve experimental methods to characterise accurately the in-situ strength distribution of fibres within the composites. As a result of detailed measurements of all required input parameters and advanced SRCT experiments, this paper establishes a benchmark for future research on longitudinal tensile failure.

Determination of the composite’s representative volume for longitudinal tensile test simulations

In this study the proper size of the composite material’s representative volume element is addressed. Longitudinal tensile test simulations are conducted for a range of sizes and several variants of material models for matrix, fibre and interface. It is found, that matrix and interface degradation with prescribed properties do not influence the value of failure engineering stress for the cell in comparison with model, where only fibre damage model is set, and the adequate size of the cell is shown to be 80 µm. In contrast, variant contained stochastic fiber strength distribution shows different value for engineering failure stress and strain and suggests larger size of the material cell for simulations. Received results might be useful for accurate micromechanical modelling of material testing.

Accurate Tensile Strength Distribution of PAN-based Carbon Fibers

Accurate Tensile Strength Distribution of PAN-based Carbon Fibers

Determination of Carbon Fiber Strength Distribution Using Bundle Fiber Tensile Test: Correction of Measurement System Elongation and Kinetic Friction Between Fibers in the Fiber Bundle

In this study, we investigated the improvement in carbon fiber (CF) bundle tensile tests. To effectively evaluate the mechanical properties of CF using the fiber bundle tensile test, measurement of system elongation correction considering nonlinear behavior and Weibull analysis using fitting of stress–strain curves was conducted. Shear-lag theory analysis revealed that the elongation in the nonlinear measurement system was largely governed by the adhesive layer deformation within the tabs. A nonlinear measurement elongation correction method was proposed that can be applied to specimens of different widths. Weibull parameters were extracted by fitting the stress–strain curves, while considering the effect of the kinetic frictional force. The obtained parameters from the fiber bundle tensile test corresponded to those obtained from the SFTT. Thus, the proposed fiber bundle test can be a simple method for evaluating fiber strength distribution.

Особенности статистических распределений прочностей моно- и полифиламентных ультраориентированных высокопрочных волокон сверхвысокомолекулярного полиэтилена

The patterns of the statistical distributions of tensile strength of high-strength ultraoriented mono-and multifilament fibers, consisting of several hundred single fibers of ultra-high-molecular-weight polyethylene (UHMWPE), have been analyzed using the Weibull and Gaussian models by considering a large number of measurements (50 identical samples in each series). It has been shown that the strength distribution of the multifilament UHMWPE fibers can be described both within the normal Gaussian distribution and the standard Weibull distribution function. At the same time, the strength distribution of the UHMWPE monofilaments oriented to a final draw ratio of 120 is not subject to the normal distribution. The reasons for the revealed differences in the types of the statistical strength distributions of the mono- and multifilaments of high-strength UHMWPE during fracture are discussed.

Особенности деформации стекло- и углепластиков с матрицей Т-107 при растяжении

The article presents the results of a study on the mechanical properties of glass (T-10-14 filler) and carbon-fiber (Formosa TC-35 12K) reinforced plastics in an epoxy matrix T-107. It was found that the mechanical properties of carbon fiber were superior to fiberglass. Regardless of the composition of the composite, there are two distinct stages on the deformation curves of experimental samples based both on carbon and glass fibers, which correspond to elastic deformation and softening stages associated with the failure of composite fibers. Taking account for the significant difference between the elastic moduli and tensile strength of carbon and glass fibers, on the one hand, and the polymer matrix, on the other, it was suggested that the observed effect of softening of the composites is associated with the process of sequential breaking of the fibers as the applied load increases. Basing on the proposed idea, a model of deformation of a polymer composite material based on the sequential fracture of the filler fiber with increasing the applied load has been developed. According to this model, the observed increase in the applied load at the stage of strain hardening is associated with the presence of dispersion of the fibers of the samples by the values of strength, i. e. there is a distribution of the strength characteristics of the fiber along the length. With an increase in the length of a fiber in the sample, and, consequently, the length of the sample itself, the probability of appearance of thread sections with an even lower level of strength increases. Thus, in general, the tensile strength of the composite measured in the experiment should decrease. This dependence of the strength characteristics of the composite on the geometrical parameters of the product is determined by the fiber strength distribution function along its length, which can be determined from the experimental curves of tensile specimens of composites. Taking into account the proposed model, the obtained experimental results are used to estimate the distribution function g(f) of the probability of detection of its strength value per unit length of fiber.