Multilayered Composite Plates Research Articles

Efficient three-node triangular element based on a new mixed global-local higher-order theory for multilayered composite plates

An accurate and computationally attractive global-local higher-order theory (GLHT) is developed for the linearly elastic analysis of cross-ply multilayered composite plates. The theory is derived using the kinematic assumptions of GLHT in conjunction with the Reissner mixed variational principle. For a low-order linear element, it is difficult to accurately compute the transverse shear stresses even applying the three-dimensional equilibrium equation post-processing technique. The reason for this difficulty is that the higher-order derivatives of displacement variables are included in the transverse shear stress fields after using the post-processing technique. Thus, by employing the Reissner mixed variational principle, the higher-order derivatives of displacement variables have been removed from the transverse shear stress components before the finite element procedure is implemented. Based on the mixed GLHT, a computationally efficient C0-type three-node triangular plate element with linear interpolation function is proposed for the analysis of multilayered composite plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Performance of the proposed element is assessed by comparing with several benchmark solutions. Numerical results show that the present elements can robustly and accurately predict the displacements and stresses of multilayered composite plates.

Three-dimensional exact hygro-thermo-elastic solutions for multilayered plates: Composite laminates, fibre metal laminates and sandwich plates

Three-dimensional (3D) exact hygrothermal elasticity solutions are developed to study the behaviour of simply supported rectangular multilayered composite plates, considering any combination of orthotropic and/or isotropic layers, under hygro-thermo-mechanical loadings. In agreement with the 3D exact elasticity solutions derived by Pagano in the early 1970s, the form of the through-thickness exact solutions of any given layer depends, in fact, on whether the layer material is isotropic or (at most) orthotropic. The 3D exact thermoelastic solutions found, already available, consider either only isotropic layers or only (at most) orthotropic composite layers. This work aims to be all-inclusive, in addition to a further development by considering hygrothermal elasticity. The results here presented consider composite laminates, fibre metal laminates and sandwich plates with different side-to-thickness ratios under a series of hygro-thermo-mechanical loadings. A transverse mechanical load and/or thermal load and/or hygroscopic load are imposed on the multilayered plate top and bottom surfaces to study the effects of hygrothermal environments in the multilayered plate behaviour. These effects are demonstrated by the through-thickness distributions of displacements, stresses, temperature and weight percent moisture content for the selected multilayered plates under different hygro-thermo-mechanical loadings, which may serve as 3D benchmark exact solutions.

A refined sinusoidal theory for laminated composite and sandwich plates

This paper proposes a new zig-zag function to develop the refined sinusoidal theory. A refined sinusoidal shear deformation theory can be obtained by including the proposed zig-zag function and meeting the traction-free boundary conditions on the top and the bottom surfaces. Governing equations and boundary conditions are obtained by using the principle of virtual displacement. Using Navier’s method, analytical solutions are presented by solving the boundary value problem. By investigating the typical bending problems of laminated composite and sandwich plates, the effect of various parameters like aspect ratio, thickness ratio and material properties on the bending response of plate is studied in detail. Comparison of the present results with the three-dimensional elasticity solutions and the results calculated using other models published recently in the literature shows that the proposed theory can yield accurately the displacements and stresses of multilayered composite and sandwich plates. Moreover, the accuracy of the displacement and stresses are not impacted by the number of layers and the material properties.

Optimum design of perforated symmetric laminates using evolutionary algorithm

Here, analytical studies have been carried out to determine the optimal values of effective parameters on the stress concentration factor around a cutout using genetic algorithm. Optimum designs of single lamina as well as symmetric laminates with 4, 8 and 12 layers of graphite/epoxy and glass/epoxy plates containing a circular cutout with various sizes are presented. The work focuses on extending the analytical solution given by Greszczuk to determine the stress distribution in multilayered composite plates subjected to arbitrary in-plane loadings. This is achieved by introducing an arbitrary oriented uniaxial, biaxial and shear loading conditions into Greszczuk solution. In order to mimic as much as possible the real structural behavior, the finite-width correction factor given by Tan is used. Effective parameters on stress distribution around the circular cutout in composite plates considered as design variables include: load angle, fiber orientation, cutout size and stacking sequence of the laminate. The objective function in this study is the minimization of maximum stress concentration around the cutout which is calculated by the present analytical solution. The first ply failure load predicted using Tsai–Wu criterion is maximized for both single lamina and symmetric laminates. Also, the weight of the plates is minimized by increasing the hole size to width ratio. The results obtained by the present analytical solution compare favorably with those obtained using complex variable method. For laminated plate subjected to shear loading, the stress concentration factor decreased drastically by 48.79% compared to a single lamina. The failure load is also increased in most of the loading cases. The results also showed that the genetic algorithm code converges rapidly in most of the cases. The accuracy, quickness, low computational cost and the simplicity of the present solution encourage the designers to use it in practical applications.

Effect of rolling reductions on microstructure and properties of 2Cr13/316L multi-layered steel composite plate by accumulative roll-bonding

Abstract

Identification of mechanical and damage parameters of composite laminates based on a CPAM method

A new method combining experimental and numerical data is proposed to simultaneously determine the mechanical properties and damage parameters in multilayered composite plates. Studied parameters are mechanical properties of each layer, width and length of delamination zone, location of damage’s center, and interface location of the damage. In this method, the PSO optimization procedure based on a CPAM algorithm uses vibration test data along with their corresponding numerical solution. Vibration data are the plates’ natural frequencies and mode shapes obtained in the modal laboratory. In order to efficiently investigate the studied parameters, the numerical solution is investigated by a commercial finite element package. The error function constitutes two parts, one part is included by the sum of the squared differences between experimental and numerical natural frequencies and the other is based on the mode shapes data. The mode shapes’ curvatures are also utilized to achieve high sensitivity to small faults. Moreover, by applying a Gaussian disorder model to the vibrational data, the sensitivity of the method is evaluated in the presence of unwanted noises. The results confirm the robustness of the proposed study for identifying both mechanical constants and damage parameters in composite plates.

Wetting of Sn on Al-steel multilayered composite plate at 350-450 °C

Wetting of Al-steel multilayered composite plate by molten Sn was studied under high vacuum at 350-450 °C. Dissolution and reaction for liquid/Al interface and liquid/steel interface, respectively, induced the spreading. As a layered interface, the anisotropic wetting happened due to the physical and chemical heterogeneities. Three models, the classic Cassie model, the modified Cassie model with the consideration of Wenzel model or the local contact angles, were failed to fit the final contact angles. A modified Naidich’s model, also based on Cassie model, together with the consideration of metallurgical segregation, fits the results. Comparing to thermodynamic conditions of reaction and dissolution, the precipitation of reaction product is easier. Also, considering the wetting activation energies (almost the same in Sn/Al-steel multilayered composite and Sn/Al), we believed that the spreading may be limited by the dissolution of Al into liquid or the diffusion of Al in liquid.

Free vibration characteristics of multilayered composite plates in a hygrothermal environment via the refined hyperbolic theory

In this article, vibration characteristics of multilayered plates in a hygrothermal environment are discussed. The analysis considers the reduced properties of the lamina material at high concentrations of moisture and temperature. The multilayered plate is modelled in the context of a refined hyperbolic shear deformation theory that contains hygrothermal effects. The numerical results for dimensionless natural frequencies of multilayered composites under the action of both temperature and moisture concentration are investigated.

Experimental and numerical estimation of the damage level in multilayered composite plates

AbstractThe detection of the internal and surface damage and estimation of the critical delamination size is discussed. The problem is illustrated on examples of glass/epoxy and graphite/epoxy composite plates. Experimental static and fatigue tensile tests were performed for multi‐layered plates with a circular hole and a circular delamination with the passive thermography and the digital image correlation used simultaneously for full‐field monitoring of thermal and mechanical effects. Both techniques are compared and verified in the context of detection and prediction of damage under static and fatigue loads. The technique of critical delamination size calculation is presented on the example of a plate made of a graphite/epoxy material. The computations were performed for bi‐axial compression using the finite element analysis and multiaxial fracture criteria. Different criteria are compared. It was observed that only nonlinear‐interaction criteria are suitable for the analysis of glass/epoxy and graphite/epoxy composite structures. It was also found that the mixed form of all three gap opening modes may occur in a composite plate with internal delamination. The proposed procedure for detection and analysis of damage is applicable in structural health monitoring of composite structures.

The nondestructive evaluation of the GFRP composite plate with an elliptical hole under fatigue loading conditions

Abstract The accurate assessment of the fatigue strength for structures made of composite materials is difficult because of the great number of possible failure forms. The Structural Health Monitoring (SHM) systems are developed and applied in engineering structures for permanent monitoring the state of the constructions. In this paper the Lamb wave propagation method and the infrared thermography were applied to observe the fatigue damage evolution in the multilayered composite plate with an elliptical hole in the middle. The active pitch-catch measurement technique was introduced based on the surface mounted piezoelectric transducers. The localization of the piezoelectric actuator and sensors responsible for excitation and detection of the elastic wave was chosen based on the progressive failure analysis applied in finite element method. The multipoint measuring system was responsible for analysis of the elastic wave propagation phenomenon during the fatigue tests. The sequential measurement of the elastic wave parameters allow one to observe the state of the structure. The different parameters describing the wave propagation phenomenon like amplitude and time of flight was considered. The infrared thermography make possible of detection of the damage initiation and permanent monitoring of the structure. The measurement of the temperature distribution is straightforward and doesn’t need complicated algorithms and software. Application of the coupled approach to the damage detection (piezoelectric transducers in SHM system with the permanent surface temperature monitoring) allow one to build cost effective system for detection of the damage initiation and for monitoring failure form evolution.

Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions

A first order shear deformation theory based finite element approach is used in this paper to investigate the free vibration behaviour of functionally graded thin, moderately thick and thick multi-layer composite plates reinforced with graphene nanoplatelets (GPLs). The effect of four different layer-wise variations of GPL distribution along the thickness and all possible plate edge boundary condition combinations on the natural frequencies of the plate are investigated. The effective Young's modulus for each layer and distribution type is determined using the modified Halpin–Tsai model, and mass density and Poisson's ratio are calculated based on the rule of mixture. Initially, present results are verified by comparing with available reported results. Thereafter, the method is used to conduct a parametric study, focusing on the effect of length to thickness ratio, different boundary conditions, GPL distribution patterns, percentage weight fraction of GPL, and geometry and size of GPL on the natural frequencies and percentage increase in natural frequencies.

Advanced GDQ models and 3D stress recovery in multilayered plates, spherical and double-curved panels subjected to transverse shear loads

The present work shows a systematic comparison between different shell models in the case of static analysis of multilayered composite and sandwich plates and spherical shells. Transverse shear loads are applied on these structures. The behavior through the thickness direction is analyzed in terms of the three displacement components and the six stress components. Such evaluations allow to remark the typical zigzag effect of displacements and the interlaminar continuity conditions in terms of congruence and equilibrium equations in the multilayered plates and shells. The boundary load conditions at the external surfaces are also verified. The proposed 3D models are closed form solutions of 3D shell theories developed in the framework of analytical and semi-analytical approaches for differential equations in the thickness direction. The 2D numerical shell models are classical and refined models developed in both equivalent single layer and layer wise viewpoints. 2D numerical theories are solved by means of the Generalized Differential Quadrature (GDQ) model, which allows general solutions for different boundary conditions, load applications, lamination schemes and geometries. The advantages of this methodology are also clearly shown and discussed for complicated geometries such as double-curved shells.

Analytical solution and numerical validation of piezoelectric energy harvester patch for various thin multilayer composite plates

The study of vibrational energy harvesting using piezoelectric patch integrated on isotropic beam-like or plate-like thin structures has received significant attention over the past decade. Multilayer orthotropic composite plates are widely used in aerospace, automotive and marine applications, where they can be considered as host structures for vibration-based energy harvesting. In this paper, an exact analytical solution and numerical validation of a piezoelectric energy harvester structurally integrated to a thin multilayer orthotropic plate are presented. Electroelastic model of the thin multilayer composite plate with the piezoelectric patch harvester is developed based on a distributed parameter modeling approach with classical laminate plate theory assumptions for all-four-edge-clamped (CCCC) boundary condition. Closed-form steady-state expressions for coupled electrical outputs and structural vibration response are derived under harmonic transverse force excitation in the presence of a resistive load. Analytical electroelastic FRFs related to the voltage output as well as vibration response to force input are derived and generalized for different boundary conditions of host plate. The results of numerical and analytical models from multiple vibration modes are compared first for validating the analytical model with a case study employing a thin PZT-5A piezoceramic patch attached on the surface of a multilayer orthotropic composite CCCC plate. For this purpose, finite-element analysis is carried out by using ANSYS mechanical APDL software. Then, it is important to specify parameters in energy harvesting model, so positioning of piezoceramic patch harvester and excitation point force on the voltage output FRFs is discussed through an analysis of dynamic strain distribution on the overall plate surface. In addition, the effects of various composite laminate plates with different stacking sequences as host structures on generated power are discussed in details as well.

Vibration, Buckling and Aeroelastic Analyses of Functionally Graded Multilayer Graphene-Nanoplatelets-Reinforced Composite Plates Embedded in Piezoelectric Layers

This paper deals with the vibration characteristics and nonlinear aeroelastic response of the functionally graded (FG) multilayer composite plate reinforced with graphene nanoplatelets (GPLs) subjected to in-plane excitations and applied voltage. The different GPL nanofillers distribution patterns across the thickness are discussed, in which the effective Young’s modulus is determined by modified Halpin–Tsai model. Based on high-order shear deformation theory, the motion equations of the FG plate system considering the von Kármán geometric nonlinearity are derived using the Hamilton’s principle. The Galerkin method is applied to discretize the partial differential governing equations into the ordinary differential nonlinear system. The effects of many influential parameters, i.e., GPLs weight fraction, distribution pattern, geometry size, applied voltage and the number of layers, on the vibration and aeroelastic behaviors are presented in detail. Numerical results show that a small amount of GPLs reinforcement can have a significant enhancement effect on the performance of the composite plate structure. Moreover, the in-plane force and aerodynamic pressure play an opposite effect on the dynamic stability, and the jumping phenomena, quasi-periodic motion can be observed with the compressive force increased further.

High strain-rate behavior and deformation mechanism of a multi-layer composite textured AZ31B Mg alloy plate

There are currently very few studies on the high strain-rate properties of Mg alloys with multi-layer composite textures under dynamic loading. In present study, a multi-layer composite textured AZ31B Mg alloy plate was fabricated using the asymmetric twin-roll casting process. The high strain-rate (∼103 s−1) deformation behaviors of the AZ31B plate along the normal direction (ND) were investigated using split-Hopkinson pressure bar technique. The microstructural evolution and deformation mechanism were analyzed by optical microscopy, scanning electron microscopy, X-ray diffraction, and transmission electron microscopy methods. The experimental results show that the mechanical behaviors exhibit a power-law hardening response under high strain-rate deformation. The flow stress generally increases with increasing strain rate, whereas the strain-hardening rate decreases with increasing strain. An interesting feature is that the maximum flow stress at high strain rates is much lower than that at its corresponding quasi-static counterpart. Microstructure analysis demonstrates that the characteristic layered texture and microstructure along the ND determine its mechanical behavior. The plastic deformation is mainly controlled by the basal-type texture, where the predominant deformation mechanism is dislocation slip. Dynamic recrystallization (DRX) occurred unevenly in the material during dynamic deformation, resulting in a moderate increase in ductility. The fracture behaviors change from brittle fracture to ductile fracture as the strain rate increases. The energy absorption capacity is therefore enhanced due to the occurrence of both DRX and the brittle–ductile transition at high strain rates.

A general solution for stress resultants around a circular cutout in laminate plates under different in-plane loadings: analytical and experimental investigations

The current work focuses on extending the analytical solution given by Greszczuk to determine the stress distribution in multilayered composite plates subjected to arbitrary in-plane loadings. This is achieved by introducing an arbitrary oriented uniaxial, biaxial, and shear loading conditions into Greszczuk solution. The present solution has exactly reproduced most of the results of the analytical solution existing in the literature. The varying parameters, such as fiber orientation angle, type and load orientation, stacking sequence, and anisotropic modulus ratio $$E_{1}/E_{2}$$ , are examined. In the second part of this study, digital image correlation (DIC) technique is used to obtain full-field surface strain measurements in unidirectional E-glass/epoxy specimens with different fiber orientation angles, in order to show its effect on stress concentration and failure modes. The analytical results obtained by the present solution compare favorably with those obtained using DIC technique. Compared to the experimental data, the accuracy of the present approach is within 10%. The simplicity of the present solution gives the design engineer a useful tool for optimizing laminate plates in the presence of a circular cutout.

Modeling of simultaneous shape memory and pseudoelastic effects of shape memory alloys on nonlinear dynamic response of multilayer composite plate embedded with pre-strained SMA wires under thermal condition

ABSTRACTShape memory alloys as a kind of smart materials, have two unique characteristics entitled shape memory and pseudoelastic effects. In this paper, a nonlinear dynamic analysis of multilayered composite plate embedded with pre-strained SMA wires under thermal condition is implemented considering both effects of SMAs simultaneously, for the first time. The constitutive equation proposed by Brinson is used for modelling the behaviors of SMA wires. In this work, equations of motion are derived in the framework of Carrera's Unified Formulation, for robust analysis of the problem. In this regard, the nonlinear strains are employed for modelling the thermal effects and also the effect of recovery stresses in the SMA wires. In this study not only the material properties are instantaneous variable with respect to the time and location, but they are also unknown, which make the problem more complicated. For this aim, a transient nonlinear finite element in conjunction with incremental iterative algorithm proposed by the author is employed, in order to solve the equations. Results show that upon the thermal condition, the recovery stress is generated in the SMA wires and therefore reduce the amplitude of a damped response of the plate. One conclusion from this study is that, in contrast with many studies reported before, it cannot be always say that the stress recovery in SMA wires is increased with increasing the pre-strain of SMA wires. In other words, for a specified increasing in temperature, only a limit amount of pre-strain comes back to its original shape and not more. Also, several numerical examples upon effect of different thermal condition, different volume fraction of SMA wires and different boundary conditions have been analyzed.

A new mixed-field theory for bending and vibration analysis of multi-layered composite plate

A novel mixed-field theory with relatively low number of unknown variables is introduced for bending and vibration analysis of multi-layered composite plates. The presented plate theory is derived from a parametrized mixed variational principle which is introduced recently by the first author. A global-local kinematic with a layer-independent number of variables is assumed for the description of the displacements of the plate. The considered kinematic stratifies the displacement and transverse stress continuity conditions at the mutual interfaces of the layers. It also fulfill the homogenous boundary conditions of the shear stresses on the upper/lower surfaces of the plates without using the shear correction factor. One-unknown variable fields which satisfy a priori the continuity conditions at the adjacent interfaces between layers and the zero boundary conditions on the bounding surfaces are considered for the approximation of the transverse shear stresses. The transverse normal stress along the total thickness of the multi-layered plate is approximated via a quadratic polynomial. The presented mixed-field plate theory has been validated through comparison of the bending and vibration analysis results with those obtained from the three-dimensional (3D) theory of elasticity and the results of the other classical and high-order plate theories.

Calculation method for the determination of stress concentrations in fibre-reinforced multilayered composites due to metallic interference-fit bolt

Sophisticated analytical solution methods for the stress concentration problem in multilayered composites with interference-fit bolts have been developed on the basis of layer-related solutions. The model is based on a circular or elliptical isotropic bolt integrated in a fibre- or textile-reinforced multilayered composite plate. For the simulation of the interference between bolt and composite plate a modelling strategy has been proposed featuring the application of a defined temperature load to a metallic elastic inclusion. For analysing the stress concentration effects in the surrounding plate, complex-valued displacement functions in combination with the method of conformal mappings for the interface between inclusion and plate and a combination of boundary collocation and least squares method for the outer boundary are used. For the verification of the developed calculation methods, a number of experimental and numerical studies have been carried out and the decay behaviour of the distortions have been compared for different radians. For all combinations of multilayered composite plate and interference-fit bolt investigated so far, a good correlation of the analytically calculated and the numerically determined results can be observed.

P.1.h.036 - Do statins impair learning and memory after long-term treatment – comparative experimental study

The accurate assessment of the fatigue strength for structures made of composite materials is difficult because of the great number of possible failure forms. The Structural Health Monitoring (SHM) systems are developed and applied in engineering structures for permanent monitoring the state of the constructions. In this paper the Lamb wave propagation method and the infrared thermography were applied to observe the fatigue damage evolution in the multilayered composite plate with an elliptical hole in the middle. The active pitch-catch measurement technique was introduced based on the surface mounted piezoelectric transducers. The localization of the piezoelectric actuator and sensors responsible for excitation and detection of the elastic wave was chosen based on the progressive failure analysis applied in finite element method. The multipoint measuring system was responsible for analysis of the elastic wave propagation phenomenon during the fatigue tests. The sequential measurement of the elastic wave parameters allow one to observe the state of the structure. The different parameters describing the wave propagation phenomenon like amplitude and time of flight was considered. The infrared thermography make possible of detection of the damage initiation and permanent monitoring of the structure. The measurement of the temperature distribution is straightforward and doesn’t need complicated algorithms and software. Application of the coupled approach to the damage detection (piezoelectric transducers in SHM system with the permanent surface temperature monitoring) allow one to build cost effective system for detection of the damage initiation and for monitoring failure form evolution.