Waviness Angle Research Articles

Failure analysis of unidirectional CFRP composites with the coupled effects of initial fibre waviness and voids under longitudinal compression

This research delves into the failure mechanisms exhibited by unidirectional Carbon Fiber Reinforced Polymer (CFRP) composites under longitudinal compression, while considering the interplay of three types of manufacturing-induced defects: initial waviness of fibres, void volume fraction, and void size. The study employs 3D high-fidelity intact representative volume element (RVE) models, incorporating the initial waviness of fibres and voids based on Micro-CT imaging. A novel algorithm is proposed to generate more accurate 3D void shapes, departing from conventional circular or triangular approximations. The results highlight the substantial influence of the initial waviness angle on the reduction of predicted compressive stiffness and strength. The volume and size of voids play a significant role in determining damage initiation within the composites. The failure mechanisms of the composite under the coupled effects of initial waviness of fibres and voids are discussed, exhibiting reasonable agreement with experimental observations.

Mechanical behavior of nacre-inspired CFRP composites by 3D printing

High-performance carbon fiber reinforced polymer (CFRP) composites are essential for many structural applications, however, properties such as strength and toughness are often considered mutually exclusive in CFRP composites. Inspired by the biological structure of nacre, this study offers a new 3D printing strategy for manufacturing nacre-inspired CFRP composites, aiming to overcome the limitations of traditional materials. The geometric parameters of the nacre-inspired brick composites, including waviness angle and aspect ratio were considered to systematically investigate their respective roles in achieving both strength and toughness and reveal the failure and deformation mechanisms through tensile and three-point bending tests. The results indicated the interlocking and appropriate aspect ratio nacre-inspired CFRP composites provides distinct advantages in enhancing both the overall strength and toughness of the structure under tensile loading. It is further shown that the bending property exhibited a significant sensitivity to the waviness angle. As the waviness angle gradually increases from negative to positive, the bending resistance of the sample decreases. The findings regarding deformation, failure modes, and toughening mechanisms shed light on how geometric parameters affect the mechanical performance of the nacre-inspired CFRP composites.

Determining the role of microstructural topology on the mechanical performance of nacre-inspired composites using a phase-field model

Bio-inspired composites are celebrated for their remarkable strength and fracture toughness, often surpassing the properties of their constituent materials. A prime example of this inspiration is the nacre which is approximately three thousand times tougher than its components and showcases not only high toughness but also high strength. This extraordinary performance is largely attributed to its intricate microstructure. However, engineered composites have faced challenges in achieving similar levels of toughness. Attempts to replicate the “brick–mortar” microstructure of nacre revealed that mere imitation falls short. Recent studies emphasize the critical influence of specific parameters, such as volume fraction, aspect ratio, and tablet waviness angle, on the microstructure effectiveness. Prior investigations, whether experimental, numerical, or analytical, underlined the importance of these parameters in shaping composite mechanical properties. However, many of these studies relied on commercial software with some inbuilt fracture criteria, often overlooking the potential benefits of incorporating a phase-field model for a more comprehensive parametric analysis. Our research delves into the impact of these parameters on the mechanical performance of nacre-inspired composites, utilizing a phase-field model based on Griffith’s fracture criteria for complex crack propagation modeling. We notably reveal the superior performance of geometrically interlocking architecture compared to non-interlocking and rectangular architecture, marking a pioneering parametric exploration of this microstructure using a phase-field model. We validate our findings through experimental and numerical data. In summary, our work demonstrates that by strategically adjusting microstructural parameters, one can achieve optimal performance enhancements in nacre-inspired engineered composites. For instance, even a slight alteration of the waviness angle while maintaining constant volume fraction and aspect ratio can yield a remarkable 16.23% increase in fracture energy. Our open-source finite element codes, implemented using the Julia-based Gridap package, offer a “virtual” experimental tool for designing bio-inspired composites with high toughness and reasonable strength. This approach also provides valuable insights into creating exceptionally tough multilayered composites with diverse constituent combinations, holding significant promise for applications in automotive, aerospace, armor, and beyond.

The relation between in-plane fiber waviness severity and first ply failure in thermoplastic composite laminates

The influence of in-plane fiber waviness on the first ply failure of quasi-isotropic thermoplastic composite laminates was investigated. The failure mode and stress at first failure were studied by using a four-point bending test and an end-loaded bending (ELB) test. The experimental results confirm that no undesirable stress concentration due to load introduction occurred in the ELB test, thereby supporting the use of this test as an alternative method to measure stress at failure. The experiments demonstrated that waviness severity affects stress at first failure and compressive damage development. The stress at first failure initially decreases with increasing maximum waviness angle and levels off as the angle starts exceeding 20°. These results reinforce the hypothesis from previous research which suggests that wavy ply compressive strength is less sensitive to changes in severity at larger angles. Furthermore, it was found that kinking failure was the dominant failure mode for maximum waviness angle up to about 45°. No kink band was observed in wavy regions with maximum angles above 45° when there was another wavy region with a lower maximum angle in the same specimen. This means that failure is not necessarily initiated at the location where waviness is most severe.

The wavenumber imaging of fiber waviness in hybrid glass–carbon fiber reinforced polymer composite plates

Out-of-plane waviness is one of the most common defects which degenerates the strength, stiffness, and fatigue life of hybrid glass–carbon fiber–reinforced polymer composites (FRPs). An accurate and high-speed non-destructive testing method is highly desired for large composite structures in industries. Ultrasonic phased array is a great candidate for such application. This paper applies the wavenumber algorithm to image the waviness in hybrid FRP plates which are a multi-layered medium. The central frequency of 5 MHZ is chosen in order to maximize the ply resonance. Transducers are migrated virtually to each interface between glass and carbon plies in order to overcome the difficulty of wave propagation analysis in such multi-layered system. The wavenumber algorithm demonstrates a better computational performance compared to that of the traditional total focusing method (TFM) in time domain up to 6 times. The glass ply depth and waviness angle can be more accurately presented with relative errors less than 1.5% and 14.8%, respectively. In addition, the resin-rich defect characterization is also achievable with a maximum error of 14.4%.

Interaction effect of out of plane waviness and impact damages on composite structures – An experimental study

This publication provides the results of a test campaign with 105 specimens to investigate the interaction effect between manufacturing induced out of plane waviness (OoP) and low velocity impact damages on the compressive strength of a quasi-isotropic laminates (QI). The test campaign differs from existing experimental studies by examining the above-mentioned interaction as well as the waviness and impact effect on the compression strength in dependence on waviness angle, affected plies and affected 0°-plies. The geometry and layup of all Compression after impact (CAI) and plain strength compression (PSC) specimens were manufactured according to the Airbus standards, with the exception of the induced waviness in the defective specimens. The influencing factors of waviness, impact and their interaction were identified and meaningful physical relationships related to the interaction were derived experimentally. The results show that the effect of waviness on the residual strength of impacted specimens depends on various conditions, such the number of affected 0°-plies in dependence on the waviness angle and waviness morphology. Relevant parameters in case of individually considered defects are not necessarily relevant in case of damage interaction. The test results indicate that the interaction between impact and waviness of the investigated configurations represents a multiplicative relationship.

An experimental approach to reproduce in-plane fiber waviness in thermoplastic composites test coupons using a reverse forming method

In-plane fiber waviness is one of the defects that can occur from the stamp-forming process of thermoplastic composite (TPC) parts. The influence of this defect on the mechanical performance of multidirectional composites is not yet fully understood. The main challenge in determining the influence on mechanical properties lies in reproducing the waviness in test coupons that can subsequently be subjected to testing. This paper describes an experimental approach to reproduce representative in-plane waviness defects, specific for TPC, by reverse-forming of V-shape parts of various bend angles and inner radii. Characterization results show that this method enables the manufacturing of localized in-plane waviness in flat 24-ply quasi-isotropic C/PEEK composites with no voids. Furthermore, laminates having varying levels of maximum waviness angle ([Formula: see text]), between 14° to 64°, were successfully produced in this work. By comparing the [Formula: see text] value with the examples of industrial stamp-formed parts, it can be concluded that the developed coupon manufacturing method can reproduce waviness from TPC part production reasonably well. Finally, all of the produced laminates have defective region lengths smaller than 20 mm, localized within a predefined location which makes them well suited for standard compression test coupons.

Effect of in-plane fiber waviness defects on the compressive properties of quasi-isotropic thermoplastic composites

The influence of in-plane fiber waviness defects on the compressive properties of quasi-isotropic (QI) carbon polyether-ether-ketone (C/PEEK) composites was investigated experimentally. Specimens with localized waviness were manufactured using a stamp forming process resulting into laminates featuring multiple wavy plies, i.e. from one to three wavy 0° plies in a 24-ply QI composite and a range of maximum waviness angle between 23° to 60°. No significant influence of the waviness was found on the global laminate stiffness. Compression tests coupled with high-speed camera monitoring were performed to study the failure process. It was confirmed that the waviness defects act as a trigger for the initiation of damage, predominantly by the kinking mechanism, resulting into an early failure and significantly lower ultimate strength than the baseline when loading in 0° direction. Furthermore, it was found that all specimens with waviness and with the same layup have a similar strength, indicating that the maximum waviness angle within the range studied in this work did not significantly influence the ultimate compressive strength. However, the presence of waviness in multiple plies clearly affected the strength. It was found that the ultimate compressive strength decreased proportionally to the percentage of plies oriented in the loading direction that is wavy.

Three-Dimensional Stochastic Modelling of Wavy Carbon Nanotube Reinforced Epoxy Nanocomposites

Carbon nanotubes (CNTs) are frequently used as the nanoscale filler materials. It has been observed that when they are added to the polymer matrix by a small fraction, they are able to form a strong yet light-weight multifunctional composite materials. Previous studies found these properties to be significantly influenced by the morphology of CNTs embedded in the matrix. In general, long CNTs become wavy and randomly oriented when dispersed in the matrix material. Collectively, they form an interconnected network. Over the past several decades, many theoretical and computational studies have been carried out to capture the mechanics of CNT-reinforced nanocomposites. In most of these models, CNTs are modeled as straight fibers. In addition, a perfect interphase between CNT and epoxy is generally assumed. As such, these models may not capture the realistic morphology of CNT reinforced composites. In the current study, we have developed a method to construct stochastic three-dimensional finite element models of wavy CNT reinforced epoxy nanocomposites. Both aligned type and randomly distributed type are considered. Uniform random distributions are assumed for both waviness and orientation angles of the dispersed CNTs. To study the effect of waviness on the elastic properties, finite element models with maximum CNT waviness angles of 0° (straight), 10° , 20° , and 30° are generated for CNT volume fractions ranging from 0.1 to 1%. A significant decrease in the properties is observed as the maximum allowable waviness angle (θmax) of the embedded CNTs in the epoxy is increased. The obtained values are compared with the theoretical models available in the literature. The three-phase model including CNTs, CNT/epoxy interphase and matrix is also studied to evaluate the effect of ‘soft’ (Ei = 10–75% Em) as well as ‘hard’ interphase (Ei = 110–175% Em) on the composite modulus. These results suggest that due to ineffective load transfer between CNT and epoxy in the presence of CNT waviness, the elastic modulus of the CNT composites is compromised by 4–8%. The modulus is further decreased by nearly 2.5% as the CNT/epoxy interphase modulus decreases by 90%. The ‘hard’ interphase model confirms an efficient load transfer from matrix to CNT fibers, leading to the increase in composite stiffness. It is found that the composite modulus is more sensitive to the ‘soft’ interphase.

Evaluation of detectability of differential type probe using directional eddy current for fibre waviness in CFRP

This paper describes the detectability of eddy current testing (ECT) using directional eddy current for detection of in-plane fibre waviness in unidirectional carbon fibre reinforced plastic (CFRP) laminate. Three different types of probes, such as circular driving, symmetrical driving and uniform driving probe, were proposed, and the waviness angle was extracted from the contour map of the ECT signal by applying a Canny filter and a Hough transform. By comparing both the waviness angle estimated by ECT and that obtained by an X-ray CT image, the standard deviation (precision) and root mean square error (accuracy) were evaluated to discuss the detectability of these probes. The directional uniform driving probe shows the best detectability and can detect fibre waviness with a waviness angle of more than 2° in unidirectional CFRP. The probe shows a root mean square error of 1.90° and a standard deviation of 4.49° between the actual waviness angle and the angle estimated by ECT. This article is part of the theme issue 'Advanced electromagnetic non-destructive evaluation and smart monitoring'.

Combination of stiffness, strength, and toughness in 3D printed interlocking nacre-like composites

Constituted by mineral tablets and organic interlayers, nacre is known for its attractive combination of stiffness, strength, and toughness. The impressive mechanical property of nacre can be attributed to the ‘brick-and-mortar’ structure which is usually defined with two geometric parameters: tablet aspect ratio and volume fraction of the stiff phase. Inspired by the interlocking tablets found in red Abalone and Hyriopsis cumingii, we study the effect of interlock by introducing a third parameter: tablet waviness angle. Tension tests and single edge notched bend fracture tests are performed on the specimens of interlocking and non-interlocking nacre-like composites that are fabricated using a high-resolution multi-material 3D printer. Stress distribution, deformation pattern and parameter analysis reveal the mechanical behavior of interlocking and non-interlocking nacre-like composites and how these three parameters affect the performance. Two failure patterns (soft phase failure and tablet break) and three toughening mechanisms (uncracked-ligament bridging, constrained microcracking, and crack deflection/twist) are found in three-point bending fracture tests, which uncovers the key to high toughness. Interlocking nacre-like composites clearly show enhanced tensile and fracture performance with an unusual combination of stiffness, strength, and toughness.

Non-contact visualization of fiber waviness distribution in carbon fiber composites using eddy current testing

Fiber waviness is a process-induced defect that greatly decreases the compressive strength of carbon fiber composites. In this study, we developed eddy current techniques that enable non-contact visualization of waviness distribution. To visualize in-plane waviness in a carbon fiber composite, we visualized the path of eddy current flowing along the carbon fiber by measuring the magnetic field. Finite element analyses show that the shape of the in-plane waviness can be visualized in the distribution of the magnetic field from the eddy current. However, with increasing distance between the surface of the tested material and measurement plane, the visualization increasingly underestimates the in-plane waviness angle. To avoid this underestimation, we propose a magnetic imaging method that can reconstruct the magnetic field at the surface. The surface magnetic field was reconstructed by using the magnetic field data measured away from the surface. Experiments were performed on a cross-ply laminate with artificially induced in-plane waviness. The distribution of in-plane waviness can be successfully visualized from the measured magnetic field. Using this magnetic field imaging method to enable non-contact measurements, the angle of waviness can be measured with an error of only 1°.

Modeling of a biological material nacre: Waviness stiffness model

Nacre is a tough yet stiff natural composite composed of microscopic mineral polygonal tablets bonded by a tough biopolymer. The high stiffness of nacre is known to be due to its high mineral content. However, the remarkable toughness of nacre is explained by its ability to deform past a yield point and develop large inelastic strain over a large volume around defects and cracks. The high strain is mainly due to sliding and waviness of the tablets. Mimicking nacre's remarkable properties, to date, is still a challenge due in part to fabrication challenges as well as a lack of models that can predict its properties or properties of a bulk material given specific constituent materials and material structure. Previous attempts to create analytical models for nacre include tablet sliding but don't account for the waviness of the tablets. In this work, a mathematical model is proposed to account for the waviness of the tablet. Using this model, a better prediction of the elastic modulus is obtained that agrees with experimental values found in the literature. In addition, the waviness angle can be predicted which is within the recommended range. Having a good representative model aids in designing a bio-mimicked nacre.

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.

Compression properties and damage mechanisms of stitched carbon/epoxy composites

Abstract The effect of stitching on compression properties and damage mechanisms of carbon/epoxy composites is experimentally investigated. The waviness angle of load-bearing tows is also measured in both in-plane and out-of-plane directions, and a correlation is made between compression strength and the waviness angle. It is found that stitching generally reduces the compression strength of carbon/epoxy composites of up to 16%. The average compression strength has a stronger correlation with the in-plane waviness angle rather than the out-of-plane one. A comparative damage assessment, which studies the initiation, progression and final failure in stitched and unstitched composites under axial compression, reveals that the early cracking in resin-rich region is responsible for the lower compression strength experienced by the stitched composites. The interaction between resin cracking and fiber splitting near the flank of wavy fibers accelerates the development of fiber kinking, and causes an early failure in stitched composites.

Influence of Fibre Architecture on Impact Damage Tolerance in 3D Woven Composites

3D woven composites, due to the presence of through-thickness fibre-bridging, have the potential to improve damage tolerance and at the same time to reduce the manufacturing costs. However, ability to withstand damage depends on weave topology as well as geometry of individual tows. There is an extensive literature on damage tolerance of 2D prepreg laminates but limited work is reported on the damage tolerance of 3D weaves. In view of the recent interest in 3D woven composites from aerospace as well as non-aerospace sectors, this paper aims to provide an understanding of the impact damage resistance as well as damage tolerance of 3D woven composites. Four different 3D woven architectures, orthogonal, angle interlocked, layer-to-layer and modified layer-to-layer structures, have been produced under identical weaving conditions. Two additional structures, Unidirectional (UD) cross-ply and 2D plain weave, have been developed for comparison with 3D weaves. All the four 3D woven laminates have similar order of magnitude of damage area and damage width, but significantly lower than UD and 2D woven laminates. Damage Resistance, calculated as impact energy per unit damage area, has been shown to be significantly higher for 3D woven laminates. Rate of change of CAI strength with impact energy appears to be similar for all four 3D woven laminates as well as UD laminate; 2D woven laminate has higher rate of degradation with respect to impact energy. Undamaged compression strength has been shown to be a function of average tow waviness angle. Additionally, 3D weaves exhibit a critical damage size; below this size there is no appreciable reduction in compression strength. 3D woven laminates have also exhibited a degree of plasticity during compression whereas UD laminates fail instantly. The experimental work reported in this paper forms a foundation for systematic development of computational models for 3D woven architectures for damage tolerance.

Flange Delamination Prediction in Composite Structures with Ply Waviness

A fracture-mechanics-based delamination prediction strategy for load-carrying composite structures is proposed. This strategy relies on the knowledge of failure modes and local structural details to predict failure based on coupon-level test data. The methodology presented effectively predicted delamination initiation of a composite hat stringer based on fracture toughness test data. In addition, ply waviness was identified as a critical factor influencing the delamination failure load. The finite element modeling technique was used to model the skin-flange region, which included the ply waviness effect. The finite element analysis results were used to calculate the total strain energy release rate and its mode I and II components. The finite element analysis predicted unstable delamination growth for positive waviness angles and stable delamination growth for negative waviness angles. The same trends for the relationship between ply waviness angle and the critical load for delamination initiation were observed in the pull-off specimens previously tested. The predictions captured the trend of the test results.

Fourier analysis for estimating probability of sliding for the plane shear failure mode : Miller, S M Proc 23rd Symposium on Rock Mechanics, Berkeley, 25–27 August 1982, P124–131. Publ New York: AIME, 1982

The probabilistic nature of appropriate geologic variables can be included in analyzing the stability of potential slope failure modes. Random variables in the two-dimensional plane shear analysis of a specified structural discontinuity include the shear strength and waviness angle of the discontinuity and, in some cases, the rock mass density. Estimated probability density functions that describe these random variables are combined by Fourier analysis to produce an estimate of the safety factor probability density function, which appears to approximate a gamma distribution. The probability that sliding will occur along the specified structure is equal to the area under this density function where the safety factor is less than one. For the covering abstract of the symposium see TRIS 452576. (Author/TRRL)