Fiber Strength Distribution Research Articles

Design of Pseudoductile Unidirectional Hybrid Composites Based on the Model of a Dry Bundle

An analytical method for designing layered high-modulus and high-strength fibrous hybrid composite materials with a highly nonlinear mechanical behavior is put forward. The elastic and strength characteristics of unidirectional layers of the composites were determined experimentally. Then, the parameters of Weibull distribution of the strength of carbon and glass fibers were estimated using test results for specimens of hybrid structure with a preliminary calculated number of carbon plastic layers in the composite. Using the criterion of maximum structural strength with a restricted elastic modulus and proportionality limit, the structure of a hybrid composite with thin CFRP and GFRP layers is optimized. A kinematic loading of a hybrid composite in which all layers deform together without stratification is considered. The Daniels model of dry bundle, with account of Weibull distribution of fiber strength, is employed to consider the decrease in the stiffness of composite layers and of the composite as a whole caused by microdefects. The approach offered was used in the design of a $$ \left[{0}_m^{\mathrm{c}}/{0}_{1-m}^{\mathrm{g}}\right] $$ pseudoductile hybrid carbon/glass plastic with the highest structural strength. It was found that m ≈ 0.30, which agreed with experimental data.

Prediction of strength and constitutive response of SiC/SiC composites considering fiber failure

A constitutive model of SiC/SiC composites is developed which considers fiber failure and broken fibers’ load carrying capability. To obtain the in situ properties of SiC fibers, tensile tests are performed on the heat-treated fibers. A more universal fiber strength model is developed to describe the strength distribution of SiC fibers. In the constitutive model of SiC/SiC composites, the stress distribution of broken fibers is analyzed. To validate the in situ fiber strength distribution and the constitutive model, a tensile test is performed on SiC/SiC minicomposites. The predicted strength and stress-strain response of SiC/SiC minicomposites are in good agreement with the experimental results. The numerical calculations show that fiber failure nearly has no effect on the nonlinearity of SiC/SiC composites although the strength of composites will increase to infinity without fiber failure, and that the strength of the composites will decrease greatly if broken fibers do not carry the load.

Stochastic micromechanical modeling of transverse punch shear damage behavior of unidirectional composites

Punch shear in unidirectional composites is induced by transverse shear loading that progressively perforates the laminate within a narrow shear annulus. At lower micromechanical length scales, punch shear loading creates unique micromechanical damage mechanisms dominated by transverse fiber shear failure, fiber–matrix interphase debonding and large inelastic deformation and cracking of the matrix. A new punch shear experimental method has been developed to test unidirectional S glass/DER353 epoxy composite ribbons at sub-millimeter length scale. The experimental data consist of a statistical measurement of the continuum response (load-deformation and punch shear strength) and the characterization of micromechanical damage modes. A simplified 2D micromechanical finite element model incorporating Weibull fiber strength distribution has been developed and correlated with the experimental data. The 2D micromechanical finite element model can simulate the punch shear failure of the ribbon incorporating mixed mode fiber fracture, and fiber–matrix debonding mechanisms using zero thickness cohesive elements. Results from stochastic simulations of punch shear experiments show that an equivalent 2D micromechanical finite element model can predict the micromechanical damage mechanisms and the statistical distribution of punch shear strength of the continuum with favorable correlation with the experiments. This paper presents a combined experimental and computational approach in simulating the stochastic non-linear progressive punch shear behavior of unidirectional composites for the first time in the literature.

A study of stress concentrations around fiber breaks in unidirectional CF/epoxy composites using double-fiber fragmentation tests

The prediction of tensile strength of unidirectional CF/epoxy composites requires appropriately determining the tensile strength distribution of carbon fibers and calculating the stress concentrations around the fiber breaks. In this study, double-fiber fragmentation tests were performed to investigate the stress concentration factor in adjacent fibers around a broken fiber. Simulation results obtained by considering the additional stress concentration due to the matrix cracks correspond well with the fiber breakage behavior observed in experiments. Furthermore, using an additional stress concentration factor and a bimodal Weibull distribution, which has a narrow strength distribution at the short gauge length, the prediction of tensile strength of the unidirectional CF/epoxy composite exhibited a good agreement with experimental results. These results showed that double-fiber fragmentation tests are a valid means of estimating the stress concentrations around fiber breaks.

Effective simulation of the mechanics of longitudinal tensile failure of unidirectional polymer composites

An efficient computational model to simulate tensile failure of both hybrid and non-hybrid composite materials is proposed. This model is based on the spring element model, which is extended to a random 2D fibre packing. The proposed model is used to study the local stress fields around a broken fibre as well as the failure process in composite materials. The influence of fibre strength distributions and matrix properties on this process is also analysed. A detailed analysis of the fracture process and cluster development is performed and the results are compared with experimental results from the literature.

Effect of fiber volume fraction on longitudinal tensile properties of SiCf/Ti-6Al-4V composites

The longitudinal tensile properties of SiCf/Ti-6Al-4V composites with different fiber volume fractions were simulated by the Monte Carlo 2-D finite element model. The random distribution of fiber strength was expressed by the two-parameter Weibull function. Meanwhile, contact elements and birth-death elements were used to describe the interfacial sliding process after debonding and fiber breakage (or matrix cracking) respectively, which was realized by subroutine complied in ANSYS-APDL (ANSYS Parametric Design Language). The experimental results show that the yield stress and ultimate tensile strength of SiCf/Ti-6Al-4V composites increase with increasing fiber volume fraction, while the corresponding strain of them is just on the contrary. In addition, almost the same failure mode is obtained in SiCf/Ti-6Al-4V composites with various fiber volume fractions when the interfacial shear strength is fixed. Finally, the tensile strength predicted by finite element analysis is compared with that predicted by Global load-sharing model, Local load-sharing model and conventional rule of mixtures, thus drawing the conclusion that Local load-sharing model is very perfect for the prediction of the ultimate tensile strength.

In situ modulus and strength of carbon fibers in C/SiC composites

The in situ elastic modulus and strength distribution of carbon fibers in C/SiC composites were studied. To obtain the in situ property data, fibers were heat treated according to the fabrication process of C/SiC composites. Tensile tests were performed on the single fibers and fiber bundles. The equivalent in situ modulus and strength were proposed considering the loose and unparallel fibers in the composites. The experimental and numerical results showed that the equivalent elastic modulus and average strength of in situ fibers are much lower than that of the original fibers. In addition, the equivalent strength distribution of in situ fibers is more dispersive.

On weakest link theory and Weibull statistics

AbstractThis communication addresses some common misconceptions about weakest link theory and Weibull statistics as they pertain to strength distributions of brittle fibers. After describing the nature of the problem, the flaws in ensuing proposed models of strength distributions are highlighted and discussed. A way forward that obviates the problems is suggested.

Accurate determination of fiber strength distributions

AbstractTensile strengths of small‐diameter ceramic fibers are commonly obtained from measured fracture loads on individual fibers and the average cross‐sectional area of the entire fiber population. The goal of the present article is to provide a critical assessment of the consequences of using the average fiber area in the inferred strength distribution. The issues are addressed through established theorems in convolution and uncertainty propagation as well as Monte Carlo simulations. Systematic errors introduced by using the average area are well‐represented by simple analytical formulae. The formulae are couched in terms of the coefficient of variation in fiber area and the dispersion in fiber strengths, characterized by the Weibull modulus. In turn, the formulae are used to determine the true values of Weibull modulus and reference strength from their nominal values. Random uncertainties associated with a finite number of tests decay slowly with number, in accordance with an inverse root scaling. When systematic errors are conflated with random uncertainties, accurate determination of the true Weibull modulus becomes increasingly challenging, even for seemingly large numbers of strength measurements. The results are used to assess the fidelity of previously‐reported experimental results based on nominal strength data.

Micromechanical damage analysis in laminated composites with randomly distributed fibers

Damage mechanisms in uni-directional fiber-reinforced plastics have been studied at the micro-scale by developing three-dimensional-repeating unit cells with randomly distributed fibers. Three damage mechanisms have been considered, viz., matrix damage, fiber failure and fiber-matrix interface debonding. The development of these damage modes and their effect on the overall stress–strain response of the micro-structure due to varying fiber volume fractions, loading conditions (longitudinal, transverse and combined transverse tension and shear), spatial distribution of fibers and fiber strength distributions (deterministic and Weibull) are of interest. A numerical framework has been developed that allows for conducting such studies for the chosen parameters. Microscopic images of real micro-structure of uni-directional fiber-reinforced plastics have been used to develop the random micro-structure for the three-dimensional-repeating unit cell. In the longitudinal loading scenario, fibers with Weibull strength distribution are closer to reality. While the three-dimensional-repeating unit cell under longitudinal loading fails in predominantly fiber failure mode, debonding and matrix damage play a major role in determining the average response of the micro-structure under transverse and combined transverse and shear loading.

Fracture process of a fiber bundle with strong disorder

We investigate the effect of the amount of disorder on the fracture process of heterogeneous materials in the framework of a fiber bundle model. The limit of high disorder is realized by introducing a power law distribution of fiber strength over an infinite range. We show that on decreasing the amount of disorder by controlling the exponent of the power law the system undergoes a transition from the quasi-brittle phase where fracture proceeds in bursts to the phase of perfectly brittle failure where the first fiber breaking triggers a catastrophic collapse. For equal load sharing in the quasi-brittle phase the fat tailed disorder distribution gives rise to a homogeneous fracture process where the sequence of breaking bursts does not show any acceleration as the load increases quasi-statically. The size of bursts is power law distributed with an exponent smaller than the usual mean field exponent of fiber bundles. We demonstrate by means of analytical and numerical calculations that the quasi-brittle to brittle transition is analogous to continuous phase transitions and determine the corresponding critical exponents. When the load sharing is localized to nearest neighbor intact fibers the overall characteristics of the failure process prove to be the same, however, with different critical exponents. We show that in the limit of the highest disorder considered the spatial structure of damage is identical with site percolation—however, approaching the critical point of perfect brittleness spatial correlations play an increasing role, which results in a different cluster structure of failed elements.

Micromechanical modelling of the progressive failure in unidirectional composites reinforced with bamboo fibres

A multiscale approach based upon the micromechanical analysis of multiple damage events at the fibre/matrix scale is developed to investigate the mechanical behaviour of unidirectional composites subjected to tensile loading. The composites are reinforced with bamboo fibres under conditions of fibre breakage and matrix transverse cracking, by considering longitudinal splitting derived from the weak interfacial bonding between fibre and matrix. Due to the statistical nature, an improved Weibull model is employed to describe fibre strength distributions affected by the diameter change in the fibres. A simulation scheme coupled with the Monte Carlo method is performed to characterise the progressive failure in the composite. Compared with experimental results, the validity of the model for composite strength prediction is examined as well.

The local strength of microscopic alumina reinforcements

We measure, using an adaptation of a method designed for ceramic ball bearings, the local strength of a brittle second phase that serves to reinforce a metal. The method uses focused ion beam milling and a nanoindentation device, and is free of artifacts commonly present in micromachined specimens. It is demonstrated on Nextel 610™ nanocrystalline alumina fibers embedded in an aluminum matrix composite. Results reveal a size effect that does not follow, across size scales, usual Weibull statistics: the fiber strength distribution differs between measurements at the microscale and macroscopic tensile testing. This implies that, in micromechanical analysis of multiphase materials, highly localized events such as the propagation of internal damage require input data that must be measured at the same, local, microscale as the event; the present work opens a path to this end.

Quantification of Foreign Object Damage and Electrical Resistivity for Ceramic Matrix Composites and Tensile Residual Strength Prediction

SiC-based ceramic matrix composites (CMC) in turbine engine applications must sustain certain foreign object impacts (FOIs) that might occur in services. Experiments and nondestructive evaluation (NDE) have illustrated good correlations between impact energy and foreign object damage (FOD) assessed using electrical resistivity (ER), acoustic emission (AE), and microscopy. A progressive failure dynamic analysis (PFDA) method is explored in understanding and predicting the damage states, ER, and residual strength after impact of CMCs. To accurately correlate the damage state with ER, the PFDA tool has been improved to incorporate the physical damage mechanisms in CMCs, which are matrix microcrack density due to both longitudinal and transverse tensile loads and the fiber breakage due to probabilistic fiber strength distribution. The predicted damage states and ER are correlated with the measurement of FOD and validated with tension after impact tests using high temperature ER. The PFDA tool has demonstrated a great potential for CMCs' FOD and residual strength predictions.

Modelling of textile composites with fibre strength variability

Abstract Scatter in composite mechanical properties is related to variabilities occurring at different scales. This work attempts to analyse fibre strength variability numerically from micro to macro-scale taking into account the size effect and its transition between scales. Two micro-mechanical models based on the Weibull distribution were used within meso-scale finite element models of fibre bundles which were validated against experimental results. These models were then implemented in a meso-scale model of an AS4 carbon fibre plain weave/vinyl ester textile composite. Monte Carlo simulations showed that fibre strength variability has a limited effect on the strength of the textile composite at the meso-scale and introduces variability of less than 2% from the mean value. Macro-scale strength based on the predicted meso-scale distribution was lower than the strength of the composite without variability by 1–4% depending on the model. The presented multi-scale approach demonstrates that a wide fibre strength distribution leads to a narrow distribution of composite strength and a shift to lower mean values.

Tensile strength distribution of carbon fibers at short gauge lengths

In this study, we determined the strength distribution of high-strength polyacrylonitrile-based carbon fibers of different short gauge lengths (~1 mm) using both the single-fiber-composite four-point bending test and the single-fiber tensile test. We employed the bimodal Weibull model to explain the experimental data. We found that the value of the Weibull shape parameter for short gauge lengths was higher than that for long gauge lengths. This implies that the tensile strength distribution of carbon fibers is governed by two different flaw populations. The tensile strength of resin-impregnated fiber bundles predicted on the basis of the bimodal Weibull distribution was in better agreement with the experimental result than the tensile strength of those predicted on the basis of the unimodal Weibull distribution.

Analysis on the process of stress transferring in single fiber composite and Monte-Carlo simulation on the process of single-fiber fragmentation

In this study, the shear-lag model considering the micro-structure “interphase” and the two separate micro-damages, “interphase” debonding and matrix damage, in single fiber composite is developed firstly. So the more actual stress distribution on the fiber fragmentations during the process of stress transferring in single fiber composite is obtained. Then based on the present shear-lag model, the Monte-Carlo simulation for the process of the single-fiber fragmentation is established to predict the number of fiber fragmentation during the process of the test. The predicted result of the simulation is in accordance with the result of the single-fiber fragmentation test. At last, the factors including the statistical parameter of fiber strength distribution, the properties of the matrix and the state of the “interphase” in the single fiber composite, which affect the process of single-fiber fragmentation are analyzed.

Bamboo fibres for reinforcement in composite materials: Strength Weibull analysis

A recently developed mechanical method for extracting long bamboo fibres opens the possibility to exploit this new material as reinforcement in composite materials for high end uses. The strength distribution of the fibres was characterized in a novel approach to evaluate the effect of defects introduced by the extraction process as function of different scale variables: fibre length, fibre surface area and fibre volume. The modified Weibull distribution, a practical model requiring only three parameters, described accurately the fibre strength distribution of the fibres at different gauge lengths. The average fibre strength decreased with increasing gauge length, from 943MPa at L=1mm to 733MPa at L=40mm and it was nearly independent of the mean fibre volume. The Weibull shape parameter was found to be 7.6 for all tested fibres, showing low strength variability in comparison with other natural fibres and some synthetic fibres, indicating their high quality.

Commensal microbiota triggers spontaneous autoimmune encephalomyelitis

A recently developed mechanical method for extracting long bamboo fibres opens the possibility to exploit this new material as reinforcement in composite materials for high end uses. The strength distribution of the fibres was characterized in a novel approach to evaluate the effect of defects introduced by the extraction process as function of different scale variables: fibre length, fibre surface area and fibre volume. The modified Weibull distribution, a practical model requiring only three parameters, described accurately the fibre strength distribution of the fibres at different gauge lengths. The average fibre strength decreased with increasing gauge length, from 943 MPa at L = 1 mm to 733 MPa at L = 40 mm and it was nearly independent of the mean fibre volume. The Weibull shape parameter was found to be 7.6 for all tested fibres, showing low strength variability in comparison with other natural fibres and some synthetic fibres, indicating their high quality.

Factors controlling the strength of carbon fibres in tension

We have investigated the fracture mechanisms of different types of carbon fibres, in terms of skin-core differences in single fibres, flaw size and fracture toughness. The fibre strength distribution was measured precisely using the fragmentation test for single-fibre composites. The failure probability for intermediate/high modulus types fibres was found to be constant with fibre strength in the range 2–4GPa, but in contrast the strength scatter for high modulus type fibres was reduced. The fracture toughness of the carbon fibres, determined by introducing notches with lengths in range 60–200nm, was found to be about 1.1MPam1/2. The average flaw size of the carbon fibres increased with increasing fibre modulus, suggesting that the crack growth of surface flaws on the tens-of-nm scale occurred. This appears to be the main reason for the reduction in tensile strength during the carbonisation treatment.