Symmetric Composite Laminates Research Articles

Non‐isometric deformation in double curvature and symmetric composite laminates due to shrinkage

AbstractApplication of the global Gauss–Bonnet theorem for the prediction of changes in Gaussian curvature for double curvature laminate geometries due to shrinkage is developed for non‐isometric deformation states where in surface area change accompanies changes in curvature. The transition between isometric and non‐isometric deformation is strongly influenced by the ratio of the principal radii of curvature of the double curved surface and a relationship is proposed by the authors to accommodate the transition. Examples for the radii of curvature ratios of 2, 3, and 4 are compared to results from finite‐element simulations and the developed relationship is shown to be accurate within 0.55%. Furthermore, these results demonstrate that isometric deformation state can be taken as an adequate representation for double curvature toroidal laminate geometries of >10 and the class of materials studied in this work.Highlights Shrinkage induced deformation in multi‐curvature composite laminates is a recurring issue in polymer composite manufacturing. Thermal, crystallization and cure shrinkage are the dominant sources of shrinkage deformation in polymer composite systems. Isometric deformation of multi‐curvature, symmetric laminates composite is defined by the absence of membrane strain. The Gauss–Bonnet theorem provides a platform for determining radii of curvature changes in multi‐curvature symmetric laminates, Non‐isometric deformation of symmetric laminates can be treated by the Gauss–Bonnet theorem for radii of curvature ratios that correspond to geometric self‐constraint. The above highlights yield insight into the anticipated geometric distortions due to shrinkage in polymer composites.

A comprehensive formulation for determining static characteristics of mosaic multi-stable composite laminates under large deformation and large rotation

Multi-stable composite laminates are composite materials that exhibit multi-stable states, making them highly suitable for use in morphing structures. These materials are capable of maintaining each stable state without expending any energy. As a result, they are used extensively in numerous applications and garnered the interest of scholars and aerospace organizations. In the context of practical applications, such as morphing structures, it is insufficient for designers to rely solely on common bi-stable composite laminates that exhibit large deformations and medium rotations to achieve their desired objectives. Consequently, based on the objectives of the design, there are two potential resolutions to address this limitation. A designer may utilize mosaic multi-stable composite laminates to achieve a morphing structure that exhibits high flexibility, significant deformation, and substantial rotation. The utilization of a series connection between a bi-stable composite laminate and a symmetric composite laminate results in the formation of a mosaic bi-stable composite laminate with variable stiffness. Furthermore, the amalgamation of two asymmetric composite laminates with inverted orientations engenders a mosaic tri-stable composite laminate. The present research examines the static characteristics of mosaic bi-stable and tri-stable composite laminates. It also seeks to analyze the factors affecting the behavior of these types of laminates. A geometrically exact model was formulated for this objective. Apart from the geometrically exact model, a widely used and uncomplicated model relying on the conventional Classical Laminated-Plate Theory (CLPT) and Von-Karman nonlinear strains was employed. The proposed models were validated through finite element simulations. The system's static equations were derived using the virtual work principle and the Rayleigh-Ritz method. The present study examines and explores quasi-static snap-through behavior between stable states through the application of concentrated forces. The findings indicate a high level of concurrence between the outcomes derived from the geometrically exact model and the finite element analyses, particularly in composite laminates exhibiting significant deformations and rotations.

Non-uniform spacing of transverse cracks in symmetric composite laminates

Non-uniform spacing of transverse cracks in symmetric composite laminates

Free flexural vibration of cracked composite laminated plate using higher-order XFEM

In this work, a higher-order XFEM approach is presented and implemented to analyze free flexural vibration in cracked composite laminated plate using higher-order shear deformation theory. The composite laminated plate experiences flexural vibration during its service life due to transverse shear loading. Out-of-plane modulus of the plate is much lesser than the in-plane modulus, so the free vibration study of the plate has become a crucial parameter for a safe service environment. The proposed methodology introduce higher-order tip enrichment functions (r2 terms) for crack simulation in laminated plate. These enrichment functions efficiently capture all conceivable displacements and rotations near the crack tip region. A comparative analysis between higher-order XFEM and conventional XFEM approach is presented in terms of computational accuracy. Several numerical examples are presented to demonstrate the accuracy of these higher-order enrichment functions, which contain variations in natural frequency with respect to crack sizes for different symmetric ply composite laminate plates under varied boundary conditions. The numerical results demonstrate that the proposed higher-order XFEM approach is significantly enhancing computational accuracy than the classical XFEM approach.

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.

Modeling lamb wave propagation in visco-elastic composite plates using a fifth-order plate theory

A new extension of the shear deformation theory to fifth order in order to calculate the spectrum of Lamb waves in orthotropic media over a wide frequency range is developed and analyzed. The aspiration of the proposed method is to create an alternative framework to exhaustive 3D elasticity based solutions by increasing computational efficiency without losing accuracy, nor robustness. A new computational framework is introduced which allows to estimate the dispersion curves for the first nine symmetric and nine anti-symmetric Lamb modes. Analytically calculated dispersion curves using 5-SDT for different propagation directions and polar plots for selected frequency of different materials are compared with the results from both the semi analytical finite element method, and lower order shear deformation theories. Careful analysis for individual laminae and for symmetric composite laminates exhibits a good agreement between the new higher order plate theory and the semi analytical finite element method over an extensive frequency range. In addition, attenuation plots show that the proposed method can also be used for visco-elastic materials (or highly damped materials). The advantage of the new higher order plate theory and its numerical implementation is that it is much more computationally efficient compared to comprehensive methods as Lamb wave polar plots of composite plates as function of incidence angle, polar angle and frequency can be calculated in less than a second on a standard laptop. Consequently, the use of this framework in inversion routines opens up the possibility of quasi real-time Structural Health Monitoring for visco-elastic composites covering a sufficiently wide frequency range.

A novel experiment-based approach on nonlinear bending analysis of thermoplastic composite laminates

A novel experiment-based approach, in which we proposed a new physical model for the carbon fibre reinforced thermoplastic (CFRTP) composite with stress-strain nonlinearity and material bimodularity, is presented for the nonlinear bending analysis of CFRTP composite laminates. The nonlinear stress-strain curves in tension, compression and shear are determined by experiments. The bimodular nonlinear model is validated through comparisons of tensile, compressive and three-point bending experimental data against the finite element analysis results firstly. Numerical investigations are then carried out for the symmetric angle-ply CFRTP composite laminates. The effects of the material nonlinearity, bimodularity, fibre orientation, plate aspect ratio, width-to-thickness ratio, boundary conditions and load distributions on the nonlinear bending load-central deflection and load-bending moment curves of CFRTP laminate plates are discussed in detail.

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.

Matrix cracking initiation, propagation and laminate failure in multiple plies of general symmetric composite laminates

This paper formulates an analytical model based on intrinsic material properties to predict ply cracking initiation and propagation in multiple plies and its impact on laminate strength in general symmetric laminates (possibly made of thin-plies) under combined triaxial normal loads and in-plane and out-of-plane shear loads while the effect of thermal residual stresses and statistical distribution of fracture energies are considered. To do so, a novel complete homogenization technique combined with recently developed accurate stress transfer models is implemented in conjunction with multi-axial energy-based failure criteria, Monte Carlo type of simulation and a strain-based fiber failure criterion. The model predictions show very good agreement with experimental results.

Feasibility of ultrasonic guided waves for detecting surface-breaking cracks in laminated composite plate structures

Ultrasonic guided waves are attractive for rapid inspection of laminated composite structures, where the cracks developed transverse to the loading direction are the serious type of damage. In this context, the paper presents studies of guided wave interaction with transverse cracks in symmetric and non-symmetric cross-ply composite laminates. In view of this, a two-dimensional finite element approach is used to gain physical insight into the reflection regime. Reflection ratios for GFRP/CFRP cross-ply laminates with various surface-breaking/transverse crack sizes are calculated, and results are presented in frequency spectrum, which shows that the minimum crack depth of 0.0093 of the operating wavelength has been successfully detected. Effect of different ply layup orientations is also considered. This work will be useful for practical guided wave-based inspection of composite plate structures. These points have been added at the abstract section of the revised manuscript.

Thickness effect of carbon nanotube interleaves on free-edge delamination and ultimate strength within a symmetric composite laminate

This paper utilizes carbon nanotube (CNT) buckypaper (BP) as a modified interleaf and incorporates it into the potential delaminated interfaces within the [±θn]S laminates, and then how the CNT BP affects the interlaminar stress and induces free-edge delamination is considered. According to the measured in-put mechanical parameters, a numerical model is firstly developed. Results show that the thickness of the CNT-based interleaf has an obvious effect on the interlaminar stress and corresponding delamination. It just changes the relative value of stress or strength but doesn’t change the patterns of stress distribution or delamination. More importantly, the CNT-based interleaf with a reasonable thickness would significantly decrease the interlaminar stresses (less than 16 μm), delay initiation of delamination and enhance the ultimate strength (less than 40 μm) of the laminates. Simultaneously, the obtained experimental results are coherent with the numerical results, which further prove the thickness effect of the CNT-based interleaf.

Review on Thermal Buckling of Symmetric Cross-Ply Laminated Plate

In the present work thermal buckling of symmetric cross-ply composite laminates is investigated. In this study, a square plate element is employed for the thermal buckling analysis of composite laminated plates. The maximum buckling temperature of symmetric cross-ply laminates under various sides to thickness ratios, aspect ratios, stacking sequence and boundary condition are studied in detail. The maximum buckling temperature analysis of square composite eight and four layered plates under uniform temperature rise is investigated using the classical laminated plate theory & first order shear deformation theory and material properties (Stiffnesses, Poisson’s ratio and Coefficient of thermal expansion) are considered to be temperature dependent. The classical laminated plate theory and first order shear deformation theory in conjunction with the Rayleigh-Ritz method is used for the evaluation of the thermal buckling parameters of structures made out of graphite fibers with an epoxy matrix. The post-buckling response of symmetrically cross-ply laminated composite plates subjected to a combination of uniform temperature distribution through the thickness and in-plane compressive edge loading is presented. The maximum buckling temperature is obtained from the solution. The computing is done by using MATLAB.

Stress analysis of symmetric laminates containing elliptical or circular holes under inplane loading

An analytical method, for determining the behavior under inplane loading of symmetric composite laminates containing an elliptical or a circular hole, is proposed in this article. This method is developed using conformal mapping and the complex variable approach which is based on the parametric representation of a given ellipse. The results obtained by this method are compared with those obtained by finite elements. This method allows the better understanding of the behavior of composite plates under in plane loading for different ratios of the minor axis to the major axis of the hole, different types of loading, different load ratios, and different types of materials.

Interlaminar failure investigations on delamination growth of composite laminates

The investigation of the interlaminar damage evolution on multi-layered composites as well as the numerical modelling techniques available for the simulation of the interface delamination are still a current concern. The complexity of modelling the mechanical behaviour and fracture modes of composite laminates is increased because of the anisotropic behaviour of the material, the fibre arrangement or other important parameters, such as stacking sequence, fibre orientation angle and the configuration of the composite laminates. Different failure modes may occur on multi-layered composites, which can lead to significant stiffness and strength reduction or to the complete loss of the load carrying capacity. The interlaminar stresses are the main factors responsible for the initiation and growth of the interlaminar failures such as delamination. They may occur as a result of manufacturing defects, low-velocity impacts or as an effect of the presence of the free edges. The delamination onset can lead to serious problems such as the premature buckling of the laminates, moisture infiltration, and stiffness degradation or even to progressive delamination growth and the separation of the layers of the composite laminates. The paper presents the numerical modelling of a multi-layered composite subjected to the tensile opening fracture mode as well as the investigation of the delamination growth. The purpose of the analysis is to study the delamination evolution on a symmetric composite laminate, starting from a pre-existing initial crack, at the interface between the adjacent layers from the middle plane. Thenumerical modelling approach for the simulation of the delamination evolution is conducted based on the Cohesive Zone Method. The results are presented in terms of the total displacement jump and equivalent stress distributions on the layers of the composite laminates.

Predicting the matrix cracking formation in symmetric composite laminates subjected to bending loads

The present study investigates analytically the effects of matrix crack formation on the properties of composite laminates subjected to bending loads, using a crack density-based model. For this purpose, by assuming that the plies prone for matrix cracking are sufficiently thin, the relationships of the stiffness reduction due to matrix cracking formation is applied. Then, by considering the equivalent damaged lamina and using the relationships of classical laminates theory (CLT), the variation of mechanical properties of symmetric laminates in the presence of matrix crack is calculated. In addition, a method is proposed to estimate the fracture toughness caused by the matrix crack in composite laminates by using the concept of finite fracture mechanics and calculating the energy release rate due to a matrix crack in a laminate under bending loading. Finally, the progressive growth of matrix crack in the cross-ply symmetric composite laminates is studied by applying the developed relationships into the nonlinear finite element code. The credibility of the proposed method is verified by comparing the obtained results with those achieved numerically and experimentally.

Mechanical properties of hybrid composites reinforced by carbon and basalt fibers

In virtue of higher thermal resistance, superior ductility, and lower cost than carbon fiber, basalt fiber has attracted extensive attention recently to be an alternative to reinforcement materials. Nevertheless, relatively fewer works have been reported on the mechanical properties of such fibers and their hybrid forms with other fibers available on the market. In this study, mechanical properties of carbon/basalt fiber reinforced epoxy hybrid composite were investigated through experimental, analytical and numerical methods. Seven symmetric composite laminates with different hybrid ratios and stacking sequences were fabricated by the vacuum assisted resin transfer molding (VARTM) technology and tested under tensile and bending loads, respectively. The test results showed that the stacking sequences had an evident influence on strength and flexural modulus, but less influence on tensile modulus. Tensile properties extracted from the experimental data exhibited good agreement with the results obtained from the analytical model. Further, the finite element analysis (FEA) was carried out in ABAQUS/Explicit through developing a VUMAT subroutine program to investigate the flexural properties in detail. The numerical simulation and experimental tests show good correlation for the flexural modulus. A modified analytical model was derived for predicting flexural strength by comparing with the FEA and experimental results. Both analytical model and numerical results are validated against the experimental results. In this study, scanning electron microscopy (SEM) study on the failed specimens revealed that use of ductile basalt fiber may to a considerable extent prevent cracks from propagation across the thickness and alter the failure modes from a no-kink pattern, commonly seen in pure carbon composites, to a kink band pattern. This indicated that the failure resistance of pure carbon fiber composites was improved after inserting basalt fiber layers.

Modelling the electrical resistance change in a multidirectional laminate with a delamination

In this work, the electrical response of a multidirectional symmetric composite laminate with a delamination is studied analytically, numerically and experimentally.An analytical model is initially developed to predict the electrical resistance of the composite laminate as a function of the delamination extent. The model was first validated against the results of a bulk of finite element analyses, considering different lay-ups and electrical resistivity. The model predictions were then compared to experimental data obtained through a dedicated experimental campaign performed on unidirectional and multidirectional Double Cantilever Beam (DCB) specimens. A satisfactory agreement was found in all the cases, thus supporting the accuracy of the analytical model.

Theory of variational stress transfer in general symmetric composite laminates containing non-uniformly spaced ply cracks

Ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. Such randomness in microstructure and in failure evolution generally leads to non-uniform distributions of ply cracks. Modeling this non-uniformity is a crucial factor in predicting the initiation and propagation of matrix cracks. Therefore, a novel stress-based variational model is developed to accurately predict stress transfer and stiffness reduction in general symmetric laminates containing non-uniformly spaced ply cracks. In contrast to available approaches for uniformly spaced ply cracks based on the unit cell, the analysis is carried out for the entire laminate. Results derived from the developed method for thermo-elastic properties of the cracked laminates show an excellent agreement with finite element results. Moreover, the accuracy of predictions based on an approximate approach is discussed using a comprehensive analysis of various laminates and crack patterns for both carbon and glass fibre systems.

A variational approach for predicting initiation of matrix cracking and induced delamination in symmetric composite laminates under in-plane loading

Abstract This paper discusses the formation of matrix cracking and induced delaminations in a [ ϕ m ( 2 ) / ψ n ( 1 ) ] s $[\phi _m^{(2)}/\psi _n^{(1)}]s$ laminate subject to arbitrary in-plane loading using a variational approach. To this end, the effects of delaminations coming from the tips of transverse cracks in the middle sublaminates are considered to specify the critical crack density points and finally understand which modes of damage are prospects for various lay-ups in the presence of transverse cracks as well as induced delamination. After deriving a very good approximation of the principle of minimum complementary energy by considering complex equations, the stress fields are provided. In this analysis, a unit cell in the ply level of a composite laminate containing both matrix cracking and delamination is considered. Then, the values of the admissible stresses and compliance of cracked laminate are employed to evaluate the energy release rate of each mentioned damage mode. Eventually, the graphs for different lay-ups in such symmetric laminate are drawn, which indicate important points for designers in practical applications. Afterwards, the effects of thickness on the dislocation of critical crack density points are checked. It can be emphasized that the current approach opens a new insight for perceiving the composites’ structural behavior in vulnerable positions.

A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates

A variational model is developed to exactly determine both stress and displacement fields at free edges of general symmetric composite laminate strips under thermomechanical loads. By partitioning the total stresses in a composite with free edges into unperturbed (without free edge) and perturbation stresses and using the minimum complementary energy principle, the optimal stress and displacement fields are derived that exactly satisfy equilibrium, compatibility, boundary and continuity conditions. The paper extends the theory of stress-based variational stress transfer so that the effects of both applied traction and displacement loads can be considered. It has been also shown how the displacement field can be determined for a stress-based variational approach. The results are compared to refined finite element results. The superiority of the developed method over finite element method, both in terms of accuracy and computational efficiency, is discussed. The method is also applicable to thin-ply laminates and is computationally efficient.