Bending Of Laminates Research Articles

Impact of layer orientation and interlayer inhomogeneity on the bending properties of plain weave CFRP laminates

AbstractPlain weave carbon fiber reinforced polymer (CFRP) laminates have garnered widespread attention in the aerospace and automotive industries due to their exceptional mechanical properties and lightweight structure. During the production of laminates, the thickness of each layer is often nonuniform. In traditional finite element analysis (FEA), the laminates are usually assumed to be uniformly layered, which can introduce some errors. Thus, there is room for improvement in prediction accuracy. This study explores the bending performance of plain weave CFRP laminates at different orientation angles of the layers, employing both experimental and FEA. In contrast to traditional methods, using images of weave structures captured by metallographic microscopy to create the representative volume element (RVE) model can improve the precision of FEA. Bending tests are conducted on specimens with orientation angles at 0° and 45°, while the bending modulus for orientation angles at 15° and 30° are predicted through FEA methods. This research enhances the accuracy of the mechanical performance analysis of plain weave CFRP laminates and also uncovers the relationship between the bending modulus changes and the orientation angles. It provides a theoretical foundation and guidance for optimizing the structural design and improving the mechanical properties of woven laminates.Highlights Investigated plain weave CFRP laminate mechanics via homogenization. Microscopy‐based RVE model improves FEM bending modulus prediction. Effects of orientation angles on plain weave CFRP laminate bending performance.

Geodesic planes in a geometrically finite end and the halo of a measured lamination

Recent works [22,23,3,33] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifold M of infinite volume. In this paper, we focus on the remaining case of geodesic planes outside the convex core of M, giving a complete classification of their closures in M.In particular, we show that the behavior is different depending on whether exotic roofs exist or not. Here an exotic roof is a geodesic plane contained in an end E of M, which limits on the convex core boundary ∂E, but cannot be separated from the core by a support plane of ∂E.A necessary condition for the existence of exotic roofs is the existence of exotic rays for the bending lamination. Here an exotic ray is a geodesic ray that has a finite intersection number with a measured lamination L but is not asymptotic to any leaf nor eventually disjoint from L. We establish that exotic rays exist if and only if L is not a multicurve. The proof is constructive, and the ideas involved are important in the construction of exotic roofs.We also show that the existence of geodesic rays satisfying a stronger condition than being exotic, phrased only in terms of the hyperbolic surface ∂E and the bending lamination, is sufficient for the existence of exotic roofs. As a result, we show that geometrically finite ends with exotic roofs exist in every genus. Moreover, in genus 1, when the end is homotopic to a punctured torus, a generic one (in the sense of Baire category) contains uncountably many exotic roofs.

Damage behavior and mechanical property investigation of CFRP/CFRP washer-bushing riveted joints

Carbon fiber reinforced composites (CFRP) are prone to occur riveting damage. Therefore, the damage behaviors and mechanical properties of CFRP/CFRP washer-bushing riveted joints were investigated experimentally in this paper. Results showed that due to the uneven expansion of rivet shank and local pressure caused by upsetting head, CFRP/CFRP riveted joints occurred multiple damage modes by using net riveting method and bushing method. The damage was mainly located in the layer around the CFRP hole near the upsetting head. However, washer-bushing riveting method effectively limited the uneven expansion and the local pressure of upsetting head, and no obvious damage was observed. Load-displacement curves of direct riveted joints and washer-bushing riveted joints exhibited obvious linear stage, progressive damage stage and final failure stage in both tensile shear and pull-off tests. However, the bushing reduced the effective fastening area of upsetting head, and load-displacement curves of bushing riveted joints only included linear and failure stages. Besides, the tensile shear and pull-off peak load were also the lowest. Tensile failure modes of both net riveted joints and washer-bushing riveted joints were dominated by the coupling failure mode of shear failure and rivet pull-off. The CFRP connecting hole was observed with obvious shear damage and extrusion deformation area. Besides, pull-off failure modes were laminate fracture and ply delamination, and also accompanied by laminate bending deformation. In contrast, bushing riveted joints failed by rivet pull-off in both tensile shear and pull-off tests.

Study on the Effect of Free-edge Conditions on Bending Properties of Composite Materials

The glass fiber is selected as the reinforcement, and the structural design of the composite is carried out to enhance the continuity of the edge fiber of the laminate. The influence of the width of the edge fiber on the bending mechanical properties is discussed. It is found that when the edge fiber of the laminate is continuous, the failure mode of the laminate bending can be changed to a certain extent, and the strength of the reinforcement and the matrix bonding is strengthened. The width of the laminate is not the influence factor in improving the bending strength.

Realisation of Bending Measured Laminations by Kleinian Surface Groups

Abstract For geometrically finite Kleinian surface groups, Bonahon and Otal proved the existence part, and partly the uniqueness part of the bending lamination conjecture. In this paper, we generalise the existence part to general Kleinian surface groups including geometrically infinite ones. Along the way, we also prove the compactness of the set of Kleinian surface groups realising an arbitrarily fixed data of bending laminations and ending laminations. Our proof is independent of that of Bonahon and Otal.

The Effect of Hybridisation on Carbon and Glass Fibres Reinforced Composites Under Quasi-Static Loading

Fibre hybridisation in composite structures is a promising strategy to control the stiffness and energy absorption characteristics. The hybrid structure could offer a better balance of appropriate mechanical properties tailored to specific application. Carbon fibre is extremely strong compared to glass fibre, and to overcome the challenges of replacing conventional materials in respect of the appropriate mechanical properties, hybridisation seems to be a good approach. In this study interlaminar hybrid composites were produced with carbon and glass fibres as reinforcement and non-hybrid samples of carbon fibre reinforcement. All the composite plates were tested under quasi-static loading and the results obtained were plotted as load – displacement graphs for loading and un-loading; the slope of the loading curve taken as estimate for the bending stiffness. The results of the laminate bending stiffnesses were 312 kN/m, 407 kN/m, 224 kN/m and 223 kN/m for the configurations [90C/0C/±45C]S, [90C/0C]2S, [90C/0G/±45CG]S and [90C/0G]2S, respectively; which showed reduction with the introduction of glass fibres. Hence, the process of hybridisation could be used to modify a couple of the characteristics of composite structures including the natural frequencies and damping properties. Micro-photograph of the damaged section revealed matrix crack and ply debonding.

Uniformity Prediction of Bending Stiffness of Composite Space Mirrors With Ply Angle Misalignments by Deflection Angle

Based on the classical lamination theory, the principal moment direction of the laminate is derived. It is 45° apart from the generalized ply angle, which is the orientation of the ply where the ply angle misalignment occurs nominally. After adding a fixed one-ply angle or random multiple ply angle misalignments to six quasi-isotropic and symmetric stacking sequences, out-of-plane deformations of mirrors were simulated and compared. The result shows an angle difference between the principal moment and curvature directions. It is referred to as the deflection angle, approximately appearing as a trigonometric curve, which varies with laminates and is dependent on the generalized ply angle within each laminate. The deflection angle directly reflects the consistency of bending stiffness or laminate bending anisotropy; the smaller the deflection angle, the better will be the uniformity of bending stiffness. Consequently, it is an efficient approach to obtain a laminate with more uniformity of bending stiffness by comparing the deflection angle. These results enrich the research of out-of-plane deformation and could objectively promote the study of quasi-isotropic laminates for bending stiffness.

A finite element unified formulation for composite laminates in bending considering progressive damage

This works proposes a novel approach to develop higher-order finite elements by taking progressive damage into account in the formulation. The approach is based on Carrera’s unified formulation (CUF) while the damage model is based on continuum damage mechanics (CDM) principles, which is implemented as a UEL (User Element subroutine) written in FORTRAN and linked to Abaqus. The approach is assessed by simulating a plate under distributed and sinusoidal loads. Besides, a progressive damage analysis of a composite coupon under three-point bending is simulated, and the numerical predictions are compared against experimental results, showing good correlation. The main findings show that the implemented UEL is accurate and fast enough to predict progressive failure events and the in-plane damage mechanisms for composite laminates under bending loadings.

Design of laminated conical shells using spectral Chebyshev method and lamination parameters

This study presents a modeling approach to accurately and efficiently predict the dynamics of laminated conical shells. The governing equations are derived based on the first order shear deformation theory kinematic equations following the Hamilton’s principle. To express the strain energy of the shells, in-plane and bending lamination parameters are used. A two-dimensional spectral approach based on Chebyshev polynomials is implemented to solve the governing equations. The developed framework including the spectral-Chebyshev approach and lamination parameters results in an accurate and computationally efficient solution method. To demonstrate the performance of the presented solution approach, various case studies including straight panels, curved shells, and truncated conical shells are investigated. The benchmarks indicate that the calculated non-dimensional natural frequencies excellently match the results found using finite element method and the simulation duration can be decreased by 100 folds. To leverage the computational performance of the presented approach, a stacking sequence optimization is performed to maximize the fundamental frequency of a shell geometry, and the corresponding fiber angles are retrieved from the optimized lamination parameters. Furthermore, a parametric analysis is performed to investigate the effect of geometry on the optimized lamination parameters (and fiber angles) based on fundamental natural frequency maximization.

Size-dependent bending modulus of fibre composite laminates comprising unidirectional plies

Heterogeneous materials can show size-dependent behaviour in which the bending modulus depends on sample size. In fibre composite materials the interaction between fibre and matrix can lead to such a size effect.Then the effective modulus calculated by the rule of mixtures can either underestimate or overestimate the bending modulus of the laminate, depending on the fibre/matrix material mismatch, the microstructural morphology (fibre distribution) and the laminate thickness. In this work, the bending behaviour of a laminate comprising unidirectional fibre composite plies is considered using Euler-Bernoulli beam theory and the influence of size on the bending modulus is investigated. The effective bending modulus of each ply is calculated and used to formulate the overall bending modulus of the laminate. The results show that the laminate bending modulus depends on the number of plies, the number of fibres through the thickness of each ply, the fibre spacing and radius, and the mismatch of fibre and matrix material properties in each ply. Our analysis shows that accounting for the ply microstructure (fibre spacing and radius and number of fibres per ply) can lead to a 10% difference in the predicted bending modulus in a three ply laminate, when there are less than four fibres through the thickness in each ply.

The Energy-absorbing Characteristics of Single Spherical-roof Contoured-core (SRCC) Cell with Composite Materials

It is a challenging task to manufacture the novel lightweight sandwich panel with different composite materials. The aim of this paper is to study the energy-absorbing characteristics of single spherical-roof contoured-core cell with carbon, glass and aramid fibre reinforced plastics, which were fabricated through compression moulding technique. The quasi-static compression test was carried out to investigate the compressive properties and crushing behaviour of the single contoured-core cell. It was demonstrated that the single spherical-roof contoured-core with aramid fibre reinforced plastic provided the highest specific energy absorption value of 0.69 kJ and the lowest compressive stiffness of 30.43 kN/mm compared to carbon and glass fibre reinforced plastics. Furthermore, it was observed that matrix cracks, fibre fracture and laminate bending are the main failure modes of the single contoured-core cell under quasi-static loading.

A Method of Stiffness Calculation and Optimization Design of Marine Composite Sandwich Plates Based on Ocean Environment

Fu, X.; Mei, Z.Y.; Zhang, F.; Chen, G.T.; Bai, X.F., and Lu, C., 2020. A method of stiffness calculation and optimization design of marine composite sandwich plates based on ocean environment. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. JournalofCoastalResearch, Special Issue No. 115, pp. 549-555. Coconut Creek (Florida), ISSN 0749-0208.In order to improve the performance of the ship's dome in the complex marine environment, this paper takes the optimization design of the shell plate of the sonar dome as the background, aiming to solve the problem that the structure of the ship's dome bears large flow shock load and occasional attack load in the negative pressure area, as well as the contradiction between the sound transmission and the rigidity design of the composite shell plate of the ship caused by the problem, therefore, a scheme of carbon fiber reinforced floating core sandwich shell is put forward Through the combination of theoretical analysis, numerical simulation and experimental verification, the research on the stiffness change law of acoustic sandwich plate is carried out. According to the research, it is found that the formula of composite laminate bending stiffness is also applicable to sandwich plate. Sandwich plate has the best efficiency in the stiffness optimization, and the accuracy of the stiffness optimization scheme can be verified by combining the material acoustic tube test data. The results show that the proposed optimization scheme can basically meet the needs of the marine environment, and can guide the optimization design of the stiffness of the acoustic sandwich plate in accordance with the best stiffness efficiency.

Probabilistic bending behaviour of a symmetric multi-directional composite laminate subjected to moisture induced material property asymmetry

In practical applications, moisture diffusion in a composite laminate occurs one dimensional, which results in moisture content asymmetry through-the-thickness of the laminate. The effect of such moisture content asymmetry on the bending behaviour of the laminate is investigated in this study. The bending response of the laminate is numerically simulated by following the first-order shear deformation theory and is experimentally validated. The probabilistic simulation was conducted by developing a surrogate model for the laminate bending response using the Polynomial Chaos Expansion method, and concurrently applying the Monte Carlo simulation. The necessity for a probabilistic simulation is also discussed in detail. The moisture diffusion through the thickness of the laminate is predicted using the Fick diffusion model, and the extent of moisture asymmetry is established for different ageing periods. The moisture asymmetry in the laminate resulted in the unwanted bending-extension coupling, which diminished as the laminate approached moisture equilibrium. Further, the moisture asymmetry introduced a material property asymmetry in the laminate, which affected the ply stresses. The study concludes that the ply stresses are dependent on the moisture content, position of the ply in the laminate, and the moisture induced stress redistribution.

Understanding the influence of laminate stacking sequence on strain/stress concentrations in thin laminates at repair holes with large scarf angles

Scarf repair is widely used in the restoration of structural performance of damaged aircraft secondary structures. Such repairs result in reduced thickness sections which are significantly larger than those associated with typical fastener holes. Significant literature exists on the distribution of strain/stress concentration in fastener hole geometries, both straight sided and countersunk, but is lacking for the geometries associated with shallow scarf angles and thin laminates. Hence, herein three-dimensional finite element models are developed to understand the influence of stacking sequence and scarf angle on strain/stress concentrations. The results demonstrate and quantify for the first time that strain concentrations are not only dependant on the laminate membrane stiffness but also on laminate bending stiffness, due to the anisotropy created as a result of scarfing angle, hole geometry and laminate thickness. Scarfing is demonstrated, for typical repair geometry associated with foreign object damage (hole diameter 20 mm, scarf angles 3° to 7°), to elevate strains by up to 2.5 times when compared to equivalent diameter straight-sided holes in laminates of thickness ≈1 mm.

Prediction of delamination propagation in polymer composites

Delamination within composite laminates has been typically characterized by the critical strain energy release rate, or fracture toughness, by performing double cantilever beam (DCB) tests. However, significant variations of the fracture toughness can occur across the width of a DCB test article due to the anticlastic curvature of composite laminates in bending. To obtain more accurate fracture toughness values, this study demonstrates a Lagrangian cross-correlation method that uses strain measurements directly from the delamination front in a DCB test to estimate the internal fracture toughness. Unmodified optical fibers were embedded in DCB test articles fabricated from non-crimped carbon fabric using a VARTM process. The variation in the strain energy release rate along the delamination front is obtained using multiple optical fiber passes. Predicted crack lengths, fracture toughness, and flexural moduli are in excellent agreement with those from surface measurements.

Thickness effect on spring-in of prepreg composite L-profiles – An experimental study

This paper presents the results and analysis of an experimental study of laminate thickness effects on the spring-in and shape distortion of thermoset composite L profiles. The primary objective is to achieve a broader understanding of how shape distortion is affected by laminate bending stiffness and part thickness of L-shaped laminates whose thickness varies between 1 and 12 mm. The larger thicknesses in particular have not received much attention in previous research. This work further aims at distinguishing the pure (geometrical) thickness effect from that of the coupled laminate bending stiffness by comparing laminates with different lay-ups. The work is performed on test specimens subjected to both a standard cure cycle and post-cure heat treatment at elevated temperatures. In parallel, finite element (FE) analysis is performed to evaluate if variation in the bending stiffness or the laminate thickness affects the predicted spring-in angle. The results clearly show spring-in dependence on laminate thickness and bending stiffness, whereas this dependence is not well predicted by the FE approaches. It is concluded that both effects exist and that shape distortions are more strongly related to bending stiffness than to laminate thickness.

Three-dimensional stress analysis in torsion of laminated composite bar with general layer stacking

Abstract A general laminated composite bar with rectangular cross-section which is subjected to torsional torque is studied and the three dimensional stress state, specially the out of plane stresses is investigated. A reduced displacement field is obtained for the long laminated bar in which the global and local deformation response of the laminate are separated. This reduced displacement field is obtained from integration of the strain components. In order to obtain the three dimensional stress state and free edge effect, the displacement based layer-wise method is employed for formulation of the problem and the governing equations are solved analytically. The numerical results are compared with the predictions of multi-term extended Kantorovich method and mixed-field multi-term extended Kantorovich method which is available in the open literature and with an analytical series solution, and very good agreements are achieved. The twisting, extension, and bending of laminate due to torsion torque, and the out of plane and in-plane stresses are studied for various layers stacking. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations.

On the geometric transferability of the delamination shear limit for CFRP laminate in bending

The laminate load bearing capability is often compromised when delamination occurs even though the laminae remain intact. The out-of-plane components of the stress tensor, defined at the interfaces between plies, are typically responsible for the delamination of multi-layered materials. Commonly used failure criteria for delamination make use of both shear and normal interlaminar stresses. In this work the out-of-plane stresses inside a woven laminate were numerically evaluated using a micromechanical model. Under three point bending the existence of local normal interlaminar stress related to the fabric architecture was demonstrated. The influence of the due to texture normal interlaminar stress on the fracture occurrence was discussed. The reduction of the apparent interlaminar shear strength as effect of the span-to-depth ratio increase was successfully reproduced introducing a dependence of the delamination shear limit from the stress triaxiality gradient.

Modeling and Experimental Assessment of Bending Characteristics of Laminated Bilayer Sheet Materials

Many mathematical models based on the advanced theory of bending to predict bending characteristics for monolithic sheet materials are available in the literature. In this work, a similar approach is utilized to develop bending models for a bilayer laminated sheet material. The principal stresses and strains through the thickness and change in relative thickness, at specified bend curvatures, are obtained as a function of increasing curvature during bending. Additionally, three-dimensional (3D) finite element (FE) based models for bilayer laminate bending are developed to overcome simplifications of the analytical models. In order to experimentally validate the two models, a new experimental bend test-jig is developed and experiments are performed on bilayer steel–aluminum laminate for different clad to matrix thickness ratios. These experiments have enabled continuous measurements of strain along the width at the bend line and through the laminate thickness at one of the specimen edges using an online strain mapping system based on digital image correlation (DIC) method. Analytical model results indicate how the through-thickness strain distribution and relative thickness of the specimen in bending are influenced by the location and thickness of the soft clad material. The FE model and experimental results exhibit similar trends in the relative thickness change for different geometric arrangements of steel–aluminum layers. The tangential and radial stresses decrease in magnitude with increasing aluminum clad thickness ratios. The 3D FE model of laminate bending provided strain predictions across the specimen width at the bend line on the tension and compression sides that increased with increasing clad thickness ratios. Also, relative thickness data from the 3D FE model showed uniaxial and plane strain stress states at the edge and midwidth sections of the test specimen. The results from analytical and FE models and from DIC and microscopic thickness measurements indicate that thickness at the bend line increases with increasing clad thickness for the case of clad layer on the compressive side of the laminate (i.e., C-C case) and vice versa for clad layer on the tensile side (C-T).

816 層内不均質性を考慮した織物複合材料積層板の曲げおよび面外せん断特性の有限要素解析(GS4-3 材料力学・計算力学)

In this study, bending and transverse shear properties of plain weave fabric composite laminates are investigated through the finite element analysis considering the intra-lamina inhomogeneity due to the weave architecture of constituent yarns. Using the homogenization method, the effective Reissner-Mindlin plate stiffness of the composite laminate is calculated. Then, the effect of the number of plies on the laminate bending elastic modulus and the transverse shear modulus is evaluated. For the bending property, the experimental evaluation is also conducted to validate the numerical analysis. Through the numerical and experimental investigations, it is found that in case the number of plies is large (eight-plies or more), these moduli are constant independent of the number of plies, however in case the number of plies is very small (three-plies or less), these moduli significantly decrease.