Angle-ply Laminates Research Articles

Minimum weight design of CNT/fiber reinforced laminates subject to a frequency constraint by optimal distribution of reinforcements across the thickness

Present work involves minimization of the weight of a three-phase, glass and carbon nanotubes (CNT) reinforced angle-ply laminate, subject to a fundamental frequency constraint. Design variables include the optimal (nonuniform) distributions of the fibers and the CNTs across the laminate thickness, the stacking sequence, ply angles and ply thicknesses. In order to assess the effect of different design variables on weight minimization, a sequence of five different optimization problems is solved with an increasing number of design variables. The present approach has the advantage of comparing and assessing the effectiveness of different sets of design variables on the design efficiency and identifying the ones which are more effective in minimizing the weight. Design efficiency is defined as the ratio of the weight of the optimal laminate to the weight of a plate which is not reinforced, but subject to the same frequency constraint. It is observed that fiber and CNT reinforcements are used most effectively if placed close to or in the outer layers. It is also observed that CNT reinforcement affects the optimal values of the ply angles due to the fact that the directional properties of the fibers become less pronounced as the matrix is reinforced by CNTs.

Tension–compression biaxial test with ±45° symmetric angle-ply laminates for determining the pure shear response in principal material directions of a lamina

The tension–compression biaxial test with cruciform specimens using ±45° symmetric angle-ply laminates is proved to be suitable for determining the in-plane pure shear response of a lamina in principal material directions. The full stress–strain evolution presents a linear stage followed by an inelastic region with high shear deformations. At the linear stage a pure and homogeneous shear strain state is measured by Digital Image Correlation (DIC). Afterwards, the DIC registers the initiation of a shear band in the measurement region at 45° from the loaded directions that leads to the final failure plane. It is verified that the arms of the specimen, which are uniaxially loaded, do not develop pseudo-ductile effects during testing that could affect the central response. For comparison purposes, the ability to obtain an accurate shear elastic response from uniaxial loading with ±45° angle-ply laminates is investigated. Based on the elastic strain energy involved in the linear stage of the testing process, it is concluded that both uniaxial tensile and compressive tests could overestimate the shear stiffness. Moreover, if the material has higher tensile than compressive elastic properties, the uniaxial tensile tests should provide a slightly better approximation of the shear elastic modulus than uniaxial compressive tests.

Lévy-type solutions for the buckling analysis of unsymmetrically laminated plates with rotational restraints for various plate theories

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups.

Trade-off between ordinary differential equation and Legendre polynomial methods to study guided modes in angle-ply laminate

Trade-off between ordinary differential equation and Legendre polynomial methods to study guided modes in angle-ply laminate

A New Shear Deformation Theory in Axiomatic Framework for Bending and Buckling Analysis of Cross-Ply and Angle-Ply Laminated Composite Plates

Abstract In this study, a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multilayered plates is developed. Analytical solution to the static and buckling responses of symmetric and anti-symmetric composite laminates is presented. The proposed theory considers secant hyperbolic function of thickness coordinate in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero shear stresses. The equilibrium equations are obtained by applying the principle of virtual work. The stiffness characteristics of cross-ply and angle-ply laminates are taken into account when solving these governing equations. The closed-form Navier solution satisfying the corresponding boundary conditions is derived for simply supported (SS) composite plates. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loading force are used to evaluate critical buckling loads. Furthermore, the impact of span thickness ratio, aspect ratios, fiber orientation, modulus ratio, etc. on static and buckling analysis plates is also studied. The validity of present formulation is demonstrated by comparing our results with some of the available results in the literature.

Isogeometric analysis of stress concentrations and failure strength in composite plates with circular holes using RHT-splines

This paper studies the stress concentration factors (SCFs) to predict the first ply failure (FPF) of cross and angle-ply laminate composite plates with single circular holes. The rational splines over hierarchical T-meshes (RHT-splines) were chosen as a surface design methodology for Isogeometric Analysis (IGA) due to their ability to exactly represent the geometry, efficient and simple local refinement algorithm, and reduction of the superfluous control points of the NURBS surface. The Bézier extraction concept was used as an element structure for IGA that allows mapping the Bernstein polynomials basis functions on Bezier elements to be performed on RHT-splines geometries. Several failure criteria and composite materials are employed in numerical examples for different fiber orientation angles through Matlab® implementation. The results obtained by the IGA based on RHT-splines showed very good conformity with those obtained by the analytic approach and finite element method (FEM) published in the literature, which demonstrates the robustness and accuracy of the IGA using RHT-splines and provides an effective and realistic way to determine SCF and failure strength. The Matlab® program for the analytical approach and failure theories is made an open-source and can be downloaded from (Github Website).

Study on out-of-plane tensile strength of angle-plied reinforced hybrid CFRP laminates using thin-ply

Thin-plies are generally defined as composites with ply thicknesses below 100 μm. These materials are rapidly gaining interest for high-performance applications, for example, the aerospace sector. Many practical techniques have been proposed to prevent delamination and improve the strength of composite laminates. A recent study has shown that the delamination could be postponed by replacing layers of CFRP with thin-ply in a unidirectional composite laminate, a configuration known as hybrid laminates reinforced with thin-plies. Since fiber orientation is known to be one of the most important parameters in composite laminate design, this study investigates the effect of oriented layers of thin-ply or both thin-ply and conventional CFRP in a hybrid laminate under out-of-plane tensile loading. A numerical Representative Volume Element (RVE) model for CFRP and thin-ply was generated, considering the unidirectional [0], cross-ply [45/−45], and [0/90] in order to better understand the effect of angle-plied hybrid composite laminates. Experimental results show that angle-plied composite laminates present higher failure load under out-of-plane tensile loading compared to the unidirectional ones. This can be attributed to the fact that an initiated crack is faced with a significantly more complex crack path in an angle-plied laminate to advance in the through-the-thickness direction.

Solid Particle Erosion Behavior on the Outer Surface of Basalt/Epoxy Composite Pipes Produced by the Filament Winding Technique

Basalt/epoxy composite pipes in a [±55]4 winding configuration were produced on CNC filament winding machines (10 N fiber tension and ~11 mm bandwidth). In the experiments, a 34 m/s impact velocity was set using the double-disc method, and five different particle impingement angles (30, 45, 60, 75, and 90°) were used to determine the erosive effect on the outer surfaces of filament wound composite pipes under the influence of 600 μm erodent particles with angular geometry in the test set, complying with the ASTM G76-95 standard. The winding patterns in the lamina (±55 angle-ply laminate region) and zigzag (±55 zigzag region) regions of BFR/EP pipes were determined to have significant effects on solid particle erosion resistance, as evidenced by the SEM images.

Experimental Investigation on the Effect of Stacking Sequence on Damage Resistance and Post-indentation Performance of Glass/Epoxy Laminates Under Different Loading Planes Using Acoustic Emission Monitoring

This research work focuses on the experimental investigation of indentation damage resistance and post-indented performance of different stacking sequence of glass/epoxy laminates using mechanical and acoustic responses. The laminates with stacking sequence, namely [0]12, [0/90]6S, [+45/-45]6S and [0/+45/-45/90]3S were subjected to normal and inclined indentation with acoustic emission monitoring. Quasi-static indentation (QSI) test was conducted on the center of the laminates using a hemispherical steel indenter with 12.7 mm diameter. The residual strength of the laminates was computed by conducting flexural after indentation test. Mechanical responses such as peak force, residual dent, linear stiffness and absorbed energy were employed to assess induced damages. The results reveal that the quasi-isotropic (QIS) laminates having better indentation damage resistance under 0o and 10o loading planes, whereas the angle-ply (AP) laminates performed well at 20o. Moreover, the normalised cumulative counts, energy rate, peak frequency, AE hits and sentry function were used to evaluate the damage initiation and propagation. Further, AE results show that the shear induced damage has been reduced in AP as compared with QIS laminates under 20o indentation plane. Finally, this study concluded that the QIS and AP laminates exhibited better indentation resistance under 0o and 10o, and 20o loading planes respectively.

Modelado micromecánico del comportamiento no lineal de laminados angle-ply ante diferentes estados de tensión plana

The non-linear behaviour ocurring in symmetrical angle-ply laminates formed by unidirectional layers of carbon fiber reinforced polymeric matrix (CFRP), known as pseudo-ductility, has been previously studied numerically and experimentally under different uniaxial, biaxial and bending loads. This phenomenon is associated with different mechanisms which affect the mechanical behaviour of the material: large permanent strains, fiber reorientation and matrix cracking. The present study is based on a microscale approach through simulations based on the Finite Element Method (FEM), with the aim of predicting the homogenized response of these laminates subjected to multiaxial in-plane. The micromechanical model is based on a Representative Volume Element (RVE) where Periodic Boundary Conditions (PBC) are applied, together with a non-linear material model of the matrix and a cohesive interface between fibre and matrix. In addition, the implementation of the model is updated to be able to reproduce any plane stress state in a [±45]S laminate, without the need to add other meso- or macroscale models.

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Bending analysis of antisymmetric angle-ply laminates using HSDTs and the radial point interpolation method – Part I: Literature review and formulation

Influence of shear direction on the buckling of CFRP composite perforated plate

The shear buckling performance of CFRP composite perforated plates taking due account of the influence of the flexural anisotropy is examined in this paper using the finite element analysis procedure. Typical laminated composite lay-up causes many complexities but can easily be dealt with in the numerical simulations. The results from the finite element models are shown to agree favourably with the buckling curves from the independent simulations using finite strip method of analysis. Results in the paper clearly show that care should be taken seriously for the case of composite structural members having opening in their webs. Depending on the nature of the applied shear loading, openings, and varied symmetric angle ply laminates, the buckling behavior and capabilities have also been altered.

Three-dimensional scaled boundary finite element method to study interfacial imperfections in thick laminated composite plates undergoing bi-axial bending

In this work, the scaled boundary finite element method (SBFEM) is employed to model weakly bonded thick laminated composite plates subjected to bi-axial bending. A three-dimensional modelling technique incorporated in the SBFEM framework is used for thick laminated plates, where two-dimensional plate models cease to provide accurate results. Weakly bonded interfaces are modelled using spring layer models with the incorporation of zero-thickness interface elements between the layers. The interface element is subjected to behave in a linearly elastic manner capturing the slippage between the layers. Using SBFEM, it is possible to have fewer discretisation in the through thickness direction of the plate (or individual lamina) without compromising the accuracy of the results. Additionally, the size of interface elements can be kept small without altering the size of the adjoining bulk element. Validation examples covering symmetric, anti-symmetric cross ply and angle ply laminates have been solved using the proposed approach. Results from the proposed method using SBFEM are compared with well-established methods for modelling thick laminated composite under bi-axial bending.

Auxetic Composite Laminates with Through-Thickness Negative Poisson's Ratio for Mitigating Low Velocity Impact Damage: A Numerical Study.

Auxetic materials are those that exhibit negative Poisson’s ratios. Such a unique property was shown to improve the indentation and impact resistances. Angle-ply composite laminates can be designed to produce negative Poisson’s ratio at the laminate level due to the large anisotropicity of the individual layer and the strain mismatch between adjacent layers. This paper investigates the effect of through-thickness negative Poisson’s ratio on the low velocity impact behaviors of carbon fiber reinforced polymer matrix composite laminates, including the global impact behaviors, as well as the delamination, and the fiber and matrix damage. Results from numerical investigations show consistently reduced fiber and matrix tensile damage in the auxetic laminate in all plies, in comparison to the non-auxetic counterpart laminates (up to 40% on average). However, the auxetic laminate does not present a clear advantage on mitigating the delamination damage or the matrix compressive damage.

A comparative analysis of thermos-mechanical behavior of CNT-reinforced composite plates: Capturing the effects of thermal shrinkage

In this study, an analytical model based on the classical laminate theory (CLT) is developed for the prediction of the effective thermal expansion coefficients (ETECs) of general angle-ply laminates (symmetrical and asymmetrical). The applications of the derived model are shown by solved examples for the prediction of ETEC of carbon nanotube-reinforced (CNTRC) angle ply laminates for various ply angles. CNTRC laminates with a negative thermal coefficient (NTC) are obtained and considered as a special case. For an extreme case, a laying angle of (35/-35)3T and (55/-55)3T, along with an NTC of −0.79 × 10−5/K is achieved. Meanwhile, the Reddy shear plate model is extended to the framework of Von Kármán nonlinearity. The corresponding dynamic equations are analytically established. With the help of the two-perturbation approach, the deflection time history curves of the forced vibration are obtained. Numerical results show that the thermal-vibration behaviors may be adjusted and controlled by changing the TEC and functionally graded pattern. The presented analytical results not only are theoretically fundamental for understanding the thermal-vibration behavior of FG-CNTRC but also serve as guidelines for NTC design of composited laminated structures.

Vibration Analysis of Composite Laminated Plates Using Analytical and APDL ANSYS Codes

The aim of this work is to investigate analytical (Classical theory) and [ANSYS Parametric Design Language (APDL)] analysis of laminate composite plate. The free vibration analysis with two boundary conditions simply supported (SSSS) & clamped ends (CCCC) are taken into account in this work. The equations of motion that governs the predication of dynamic behavior of cross and angle ply composite are solved theoretically using [Matlab] software. Three degrees of freedom are included in computing the natural frequency and mode shapes of cross and angle ply laminate. The significant effect of various parameters such as number of layers of fibers, aspect ratios, fiber orientation, and modulus ratio on natural frequency is evaluated theoretically and APDL (ANSYS). The numerical analysis is carried out by commercially available ANSYS software. The boundary conditions can significantly affect the natural frequency of the composite laminate plate due to the restraint effect at the edges. In this work a relatively new modeling technique will be adopted. Good agreement is achieved between the analytical and ANSYS results.

Modelling damage in half-hole pin bearing cross-ply and angle-ply composite laminates

This paper presents the development and validation of a mesoscale numerical model to predict the bearing failure of composite laminates reinforced by unidirectional continuous fibers, focusing on specimens that show a significant non-linear response prior to failure. Half-hole pin bearing tests were carried out with multiple instrumentation for the comprehensive characterization of the failure process. Three-dimensional finite element models were used for the simulation of plastic deformation and damage of the cross- and angle-ply specimens using fiber-aligned mesh for the composite plies. To consider the non-linear material behavior prior to crack propagation, the constitutive model proposed includes a bi-linear elastoplastic model to represent the non-linear response under longitudinal shear. For the prediction of the peak and post-peak behavior, 3D invariant-based failure criteria and mechanism-based continuum damage models were used for intralaminar damage, together with a discrete cohesive zone model for delamination. Thorough analyses and comparisons of the experimental and numerical results show a good correlation of the bearing strengths and overall deformation, as well as good agreement in terms of damage size and damage shape. Relevant limitations include difficulties in predicting the post-peak plateau stresses and the loading displacements in some configurations, setting the stage for additional future research.

Influence of Bending-Twisting Coupling Deformation on Pure Bending Strength and Fracture Morphology of CFRP Angle-Ply Laminate

The purpose of this study is to investigate the effect of bending-twisting coupling deformation on the bending strength of CFRP in which laminate configuration has symmetricity and angled fiber orientation. In this study, a novel type of test fixture for pure bending test that permit the coupled bending-twisting deformation is newly developed. Test results showed that the pure bending strength of the angle-ply laminates was decreased when bending-twisting coupled deformation was permitted. The normalized bending strength when the bending-twisting coupled deformation is permitted was decreased with increase of coupled component of angle-ply laminate. Observations of fracture morphology of specimen also showed that the specimen was firstly failure at the 0° layer on the compression side, no matter if the coupled deformation was permitted or constrained. However, when the coupled deformation was permitted, the failure was occurred at lower applied bending stress compared with when coupled deformation was constrained. Moreover, when the coupled deformation was permitted, the failure of 0° layer was occurred at the diagonal portion of specimen. These results suggested that the existing of in-plane shear stress at 0° layer affects the fracture morphology of specimen.

Verification of Puck's criterion for CFRP laminates under multiaxial loads at ambient and cryogenic temperatures

Objective of the present study is the verification of Puck's failure criterion for multiaxial mechanical loading situations in the ambient and cryogenic thermal regimes. The assessment is based on the material data and the failure envelope determined in a previous study on uniaxially loaded single-ply specimens study. Here, the pre-existing experimental data base is complemented by experiments on specimens made from angle ply laminates featuring holes, tapered sections and combinations thereof. The specimens were tested at ambient temperature and in a liquid Helium environment at 4.2 K. For determination of the local stress states in the individual plies at the stress concentrations induced by the holes and tapered sections, the experiments were simulated numerically by the finite element method. It is found that Puck's criterion in most cases provides conservative results. Unresolved additional safety margins may develop if a structural failure in an inter-fiber mode requires development of larger delaminations of adjacent plies to form a through crack.

Effect of Non-Uniform Fibre Distribution along Thickness and Non-Uniform Ply Thicknesses on Frequencies of Symmetric Angle-Ply Laminates

Effect of Non-Uniform Fibre Distribution along Thickness and Non-Uniform Ply Thicknesses on Frequencies of Symmetric Angle-Ply Laminates