Fibre Misalignment Angle Research Articles

Microscale and mesoscale modeling for compressive failure in unidirectional carbon fiber reinforced polymer composites with random distribution of fiber misalignments

AbstractCompressive strength and failure mode of carbon fiber reinforced polymer (CFRP) composites are affected by the severity of fiber misalignment. In this paper, numerical models based on computational micromechanics are proposed to investigate the correlation between fiber misalignment and compression failure. A single‐fiber micromodel including fiber, matrix, and interface phases is first developed to capture the influence of misalignment severity on the material failure mode. The failure longitudinal stress distribution in the fiber predicted by the micromodel indicates that the failure mode depending on the initial misalignment can be identified as uniform compression failure, compression‐bending combination collapse, and fiber buckle. A mesoscale 2D model with multiple fibers is then constructed to investigate the kink band formation. This model takes into account the distribution of fiber misalignments to capture the key geometric features of fiber misalignment that influent the compression failure in realistic composite materials at the structural scale. The results show that fiber misalignment angle amplitude, misalignment dispersion (characterized by the standard deviation), and misalignment wavelength are the key parameters of fiber misalignment, which have significant effects on compression strength and kink band geometry.Highlights Single‐fiber model to capture the effect of misalignment severity on failure mode. Multi‐fiber model with randomly distributed fiber misalignments. Failure mode depending on the severity of initial misalignment was identified. Key parameters of misalignment on compression strength and kink band geometry.

Probabilistic buckling assessment and reliability of fiber-metal laminate, composite and aluminum cylindrical panels under compression with load and fabrication uncertainties

The objective of this article is to study the buckling behavior and reliability of fiber metal laminated (FML), composite and aluminum cylindrical panels under uniaxial compression taking into account fabrication and loading uncertainties. A 3D finite element modeling with ANSYS software has been implemented for this purpose. The panels are discretized using shell elements and the eigenvalue buckling analysis is conducted for the prediction of elastic buckling. The influences of load and fabrication uncertainties on the buckling load factor are studied with probabilistic analyses and the reliability of the panels is calculated. It is found that the thickness of aluminum layers is the most significant uncertain variable for the critical buckling load factor of FML panels, whereas the fiber misalignment angle of their composite layers is insignificant. As the metal volume fraction decreases, the sensitivity of the elastic buckling load factor to variations of the axial load distribution is reduced whereas its sensitivity to variations of the thickness of composite layers is increased. Consequently, the metal volume fraction is an important design parameter for the uncertain buckling behavior of the panels.

Estimation of axial compressive strength of unidirectional carbon fiber-reinforced plastic considering the variability of fiber misalignment

The analytical method to calculate the axial compressive stress–strain relation of a unidirectional carbon fiber-reinforced plastic (UD CFRP) was presented considering the variability of the fiber misalignment angle. Because the compressive load-bearing capability of fibers surrounded by a matrix was different depending on the fiber misalignment angle, fibers were grouped based on the misalignment angle. The contribution to the load bearing was calculated and summed based on the area ratio of the fiber groups. All fibers supported a compressive load in the initial loading. However, with increased loading, the load-bearing capabilities of the different fiber groups decreased more dramatically with greater misalignment angles. The fibers with a misalignment angle of 0.5° showed a large load drop after their maximum loading, which triggered the ultimate failure. The variability of the fiber misalignment angle was indispensable to determining the axial compressive strength under the assumption of zero mean fiber misalignment angle.

An algorithm for automatically establishing a multi- parameter RVE model for z-pin composite laminates

Z-pinning is an effective method to improve the delamination resistance of composite laminates. The microstructure and manufacturing parameters have a great influence on the properties of z-pin composite laminates. In order to explore the influence of microscopic characteristic parameters on material properties and damage analysis, a parameterized RVE finite element model algorithm for automatic establishment of z-pin reinforced composites was proposed. The algorithm involves avoiding in-plane fibers to pin, generating fiber waviness, and assembling pin-fiber–matrix. Moreover, the statistical distribution of fiber misalignment angle can also be controlled. The developed program can generate RVE models with different parameters efficiently and quickly, such as fiber volume fraction, pin volume fraction, pin diameter, RVE size and fiber waviness. The statistical verification of the distribution of fiber misalignment angle can satisfy the probability distribution modeling of fiber angle. The generated model is divided into meshes, and finite element calculation can be realized. This work is of great significance to study the effects of microscopic characteristics on the properties and to optimize the design of z-pin reinforced composites.

Splitting failure of a composite under longitudinal tension

AbstractSignificant variation can be found in measurements for the longitudinal tensile strength of the same unidirectional (UD) composite. A splitting failure is one of the main reasons. It is shown in this paper that the shear stress component resulted from a longitudinal tension and a fiber misalignment can cause the matrix to fail before fiber break. The misalignment angle consists of an initial off‐axial angle and a further fiber rotation during the loading. Based on the micromechanics Bridging Model and the matrix true stress theory established by the author, splitting failure has been analyzed and predicted rigorously in this paper, only using the fiber and matrix properties together with the fiber misalignment angle. The fiber initial misalignment angle of a unidirectional plate can be obtained from testing statistics, or deducing from measured longitudinal compression strength. Our research indicates that the longitudinal tensile strength and the relevant failure mode can be significantly affected by the fiber initial misalignment.

Reduced order multiscale model for compression kink-band failure in composites

A multiscale model for compression kink band failure in fibrous composites is presented. The computational model predicts the progression of damage associated with the formation of kink bands, which experiments demonstrate to involve excessive shear straining of the matrix material and fiber fracture. The uniqueness of the study is establishing the concurrent treatment of nonlinear deformation and failure of the composite constituents at the scale of the material microstructure, and the formation of kink bands at the mesoscopic scale. The model incorporates computational homogenization of the material response, a nonlocal gradient regularization scheme, and a curvature-based criterion for macroscopic fiber break to predict kink band formation. The multiscale approach resolves mesoscale mechanisms associated with kink banding while offering computational benefits compared to direct mesomechanical approaches. An accessible implementation within finite element analysis software is presented and the model is verified with analysis of a mesoscale domain incorporating initial fiber waviness. In quasi-static simulations, the kink band initiates due to matrix softening that results in the onset of buckling and is completely formed when fibers break as a result of localized curvature. Results from parametric studies confirm that compression strength is not directly related to measures of the kink band morphology, but it is strongly correlated with the shear strength and initial fiber misalignment angle. The predicted effects of material properties representing various carbon fiber reinforced polymers and a range of fiber misalignment angles on kink band width and failure strength corroborate analytical and experimental results presented in the literature.

Analyzing the effect of misalignment on single-filament carbon fiber tensile testing via stereoscopic computer vision imaging

An understanding of the constitutive properties of carbon fibers (CFs) is critical to the accuracy of high-resolution composite simulations and to the development of CF derived from low-cost alternative precursor materials. Single-fiber tensile testing is a capable tool to measure CF properties and is well suited to research efforts where only a small number of fibers may be available. However, single-fiber tensile tests are challenging to conduct due to the difficulty in handling small diameter fibers (5–15 μm), the brittleness of single fibers, and the required nanoscale/microscale resolution of testing equipment. The accuracy of the measured properties depends on several factors, but a critical factor is fiber misalignment, especially at short gauge lengths. Current standards do not address the effect of tensile specimen misalignment on measured properties. This work presents a robust method of fiber alignment using stereoscopic computer vision that enables users to align fibers vertically for tensile testing to improve the accuracy of resulting mechanical properties. Additionally, an analytical relationship between fiber misalignment angle and measured properties is developed and validated against the experimental results. As a result, new best practices for single-fiber tensile testing of CF are recommended.

A microscale integrated approach to measure and model fibre misalignment in fibre-reinforced composites

Computational micromechanics of fibre-reinforced polymers (FRPs) relies on the ability of the representative volume elements (RVEs) to take into account the different features that characterise the geometry of the material system under consideration. Fibre misalignment has been proven experimentally to have a significant effect on the mechanical properties at the macroscale, but is not currently taken into consideration in models at the individual fibre level, perhaps due to the difficulty in statistically characterising the fibre misalignment. In this work, an integrated approach is presented to measure and model fibre misalignments in FRPs. A computed tomography (CT) scan is used to identify the fibre geometry and statistically characterise the fibre misalignment angle distribution. Using a methodology recently developed by the authors, three-dimensional (3D) RVEs were generated by requiring their misalignment angle distribution to fit the empirical distribution. The methodology proposed provides a framework for the systematic numerical analysis of the influence of fibre misalignment on mechanical properties of FRPs.

Compressive behavior of unidirectional FRP with spacial fibre waviness and non-uniform fibre packing

Longitudinal compressive strength of common engineering FRP is known to possess large stochastic variation which highlights the importance of accurate prediction on the compressive failure behaviour. This study employs non-linear 3D FE modeling to investigate the influence of spacial fibre waviness and non-uniform fibre packing on the compressive strength of UD FRP. Cuboid shaped FE model is constructed, and a region of sinusoidal fibre waviness is introduced in the model. Fibre is considered as materially linear-elastic but geometrically non-linear, while matrix is considered as elastic perfectly plastic. The results highlight that in the fibre kinking process fibre rotation may not necessarily occur in the plane with largest preliminary fibre misalignment angle (or fibre waviness plane). The compressive strength of FRP not only depends on fibre misalignment angle but also on fibre waviness direction, while non-uniform fibre packing seems to have insignificant influence on the compressive strength.

Uncertainty quantification in multiscale simulation of woven fiber composites

Woven fiber composites have been increasingly employed as light-weight materials in aerospace, construction, and transportation industries due to their superior properties. These materials possess a hierarchical structure that necessitates the use of multiscale simulations in their modeling. To account for the inherent uncertainty in materials, such simulations must be integrated with statistical uncertainty quantification (UQ) and propagation (UP) methods. However, limited advancement has been made in this regard due to the significant computational costs and complexities in modeling spatially correlated structural variations coupled at different scales. In this work, a non-intrusive approach is proposed for multiscale UQ and UP to address these limitations. We introduce the top-down sampling method that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields (RFs) where the hyperparameters of an ensemble of RFs is characterized by yet another RF. We employ multi-response Gaussian RFs in top-down sampling and leverage statistical techniques (such as metamodeling and dimensionality reduction) to address the considerable computational costs of multiscale simulations. We apply our approach to quantify the uncertainty in a cured woven composite due to spatial variations of yarn angle, fiber volume fraction, and fiber misalignment angle. Our results indicate that, even in linear analysis, the effect of uncertainty sources on the material’s response could be significant.

An experimental study of fibre waviness and its effects on compressive properties of unidirectional NCF composites

In this paper a comprehensive experimental study on effects of different fibre waviness characteristics on the compressive properties of unidirectional non-crimp fabrics (NCF) composites is presented. The fibre waviness ranges from periodic to random with medium to large misalignment angles. As expected, fibre waviness is found to strongly impair the compressive mechanical properties of the composite. It is demonstrated that the maximum fibre misalignment alone can be used to accurately predict strength with analytical kinking criteria. Furthermore, there is a direct correlation between waviness and a knock-down factor on stiffness with approximately 5%/degree mean fibre misalignment angle. Analysis of the extension of the misaligned regions (defects) provides additional evidence that defect extension in the transverse direction is more critical than in the longitudinal direction, supporting earlier theoretical predictions in the open literature.

Micro-Mechanical Analysis About Kink Band in Carbon Fiber/Epoxy Composites Under Longitudinal Compression

Kink band is a typical phenomenon for composites under longitudinal compression. In this paper, theoretical analysis and finite element simulation were conducted to analyze kink angle as well as compressive strength of composites. Kink angle was considered to be an important character throughout longitudinal compression process. Three factors including plastic matrix, initial fiber misalignment and rotation due to loading were considered for theoretical analysis. Besides, the relationship between kink angle and fiber volume fraction was improved and optimized by theoretical derivation. In addition, finite element models considering fiber stochastic strength and Drucker-Prager constitutive model for matrix were conducted in ABAQUS to analyze kink band formation process, which corresponded with the experimental results. Through simulation, the loading and failure procedure can be evidently divided into three stages: elastic stage, softening stage, and fiber break stage. It also shows that kink band is a result of fiber misalignment and plastic matrix. Different values of initial fiber misalignment angle, wavelength and fiber volume fraction were considered to explore the effects on compressive strength and kink angle. Results show that compressive strength increases with the decreasing of initial fiber misalignment angle, the decreasing of initial fiber misalignment wavelength and the increasing of fiber volume fraction, while kink angle decreases in these situations. Orthogonal array in statistics was also built to distinguish the effect degree of these factors. It indicates that initial fiber misalignment angle has the largest impact on compressive strength and kink angle.

Bolted Joints in Three Axially Braided Carbon Fibre/Epoxy Textile Composites with Moulded-in and Drilled Fastener Holes

Experimental behaviour of bolted joints in triaxial braided (0°/±45°) carbon fibre/epoxy composite laminates with drilled and moulded-in fastener holes has been investigated in this paper. Braided laminates were manufactured by vacuum infusion process using 12 K T700S carbon fibres (for bias and axial tows) and Araldite LY-564 epoxy resin. Moulded-in fastener holes were formed using guide pins which were inserted in the braided structure prior to the vacuum infusion process. The damage mechanism of the specimens was investigated using ultrasonic C-Scan technique. The specimens were dimensioned to obtain a bearing mode of failure. The bearing strength of the specimens with moulded-in hole was reduced in comparison to the specimens with drilled hole, due to the increased fibre misalignment angle following the pin insertion procedure. An improvement on the bearing strength of moulded-in hole specimens might be developed if the specimen dimensions would be prepared for a net-tension mode of failure where the fibre misalignment would not have an effect as significant as in the case of bearing failure mode, but this mode should be avoided since it leads to sudden catastrophic failures.

Determination of Material Parameters for Microbuckling Analysis of Fiber Reinforced Polymer Matrix Composites

This research focuses on studying the effect of the constitutive law adopted for a matrix material on the compressive response of a unidirectional fiber reinforced polymer matrix composite. To investigate this effect, a periodic unit cell model of a unidirectional composite with an initial fiber waviness and inelastic behavior of the matrix was used. The sensitivity of the compressive strength to the hydrostatic pressure, the flow rule and the fiber misalignment angle were presented. The model was verified against an analytical solution and experimental data. Results of this study indicate that a micromechanical model with correctly identified material parameters provides a useful alternative to theoretical models and experimentation.

Fibre Misalignment Measurement of Nanomodified-Unidirectional Carbon Fibre Laminates

This paper investigates the effect of nanosilica on the fibre waviness or misalignment angle distribution of carbon fibre reinforced polymer composite unidirectional laminates. The quality of the laminates was evaluated using image analyzer technique. The polished specimens were examined using Polyvar B-met optical microscope and analysed using KSRUN ZEISS software. The effect of 3, 7 and 13 vol.% nanosilica on the fibre misalignment angle distribution was determined. The results showed that, the fabricated laminates have average fibre volume fractionVfof 42%, low fibre waviness distribution (averageφo= 2.5o) and less than 1% void content. This implies that the fabrication technique, which was employed in the current work, successfully produced good quality laminates. The presence of nanosilica results in a narrow fibre angle distribution in the HTS40/828 laminate.

Characterization of microstructure in stitched unidirectional composite laminates

The internal geometry of stitched uniaxial multiply carbon-fiber preforms is investigated experimentally. The microstructure is parameterized by such four introduced parameters as distortion length, distortion width, minor axis and major axis. The quantificational measurements are performed for these parameters under different stitch densities and different stitch threads. A theoretical model, called fiber distortion model, is developed to describe the spatial distribution of in-plane fiber misalignment angle and inhomogeneous fiber volume fraction induced by stitching.

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

Abstract The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, G LT ∗ , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, G LT ∗ , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.

Modelling Lamina Longitudinal Compression Strength of Carbon Fibre Composite Laminates

The determination of the lamina longitudinal compression strength remains an unsolved problem. Non-valid failure modes are commonly observed in compression tests of unidirectional specimens. Micromechanical modelling has also proven to be a difficult task. It is believed that failure is initiated by fibre microbuckling, and that non-linear matrix behaviour and fibre misalignments play a major role. The main obstacles are thus the non-linear nature of the phenomenon and the scarcity of material data. Here 2D and 3D Finite Element models are presented. The Finite Element Method can easily deal with non-linear problems. The models are computationally inexpensive and can be easily implemented on a commercial code. A sensitivity analysis was performed using realistic input data. The model predictions are well above the unreliable experimental values so far available. Further, the most important variables were found to be the fibre misalignment angle and the matrix yield stress. The fibre spatial arrangement also affects the predicted results. Reliable strength data are essential to validate the models here presented. Nevertheless this study shows that accurate predictions should be expected to prove difficult, mainly because of the complex matrix stress-strain behaviour and the statistical nature of fibre misalignments and spatial distribution. In addition, the important role of the matrix in model results raises the question of the existence of a unique lamina longitudinal compression strength (LLCS). Lay-up dependent transverse and shear stresses acting on the load aligned laminae should accordingly yield lay-up dependent LLCSs, which is confirmed by experimental data.

Failure Behavior of Unidirectional AS4/3501-6 Carbon/Epoxy Laminates

The work is aimed at improved understanding of deformation and failure mechanisms of unidirectional carbon fiber reinforced plastics. Monotonic tension and compression experiments are conducted on 3501-6 epoxy resin and AS4/3501-6 carbon/epoxy composite at temperatures ranging from room temperature to 200°C. The goal is to better resolve the matrix modulus and matrix strength influence on the compressive strength and associated failure mechanisms. Two compressive failure mechanisms are observed. At temperatures below 100°C, the failure is governed by formation of longitudinal matrix cracks followed by transverse shear failure. Above this temperature, the failure is governed by localized kinking of fibers. The tensile and compressive strengths of both materials decreased with increasing temperature, the sensitivity to temperature was higher in compression versus tension. A deformation model based on Eshelby's equivalent inclusion theory is utilized to investigate the local and mean field stresses in the matrix as a function of fiber misalignment angle, fiber/matrix modulus mismatch and fiber volume fraction. Deformation maps are constructed to illustrate the link between local stresses and failure mechanisms. The results are compared to the models proposed by Argon and Budiansky.

Microbuckling of fiber composites with random initial fiber waviness

A fiber microbuckling calculation is presented for the effects of fiber misalignment and material nonlinearity on the compressive strength of fiber composites. The role of fiber bending stiffness is included by using a particular form of couple stress theory. In order to examine the effect of a distribution of fiber waviness, the fiber misalignment angle is assumed to vary along the fiber length but is taken to be uniform in the transverse direction. Thus, the effects of wavelength as well as amplitude of fiber waviness are taken into account. A consideration of sinusoidal initial waviness reveals that short wavelength imperfections are much less deleterious than long wavelengths. A statistical analysis is presented for the effect of random fiber waviness on compressive strength, using a Monte Carlo simulation technique. Compressive strength is found to be particularly sensitive to the area under the spectral density curve and to the minimum fiber wavelength.