Unsymmetric Laminates Research Articles

Developing a thermomechanical and thermochemical model for investigating the cooling rate effects on the distortion of unsymmetrical viscoelastic polymeric composite laminates

An experimental and semi-analytical study of distortion of asymmetric composite laminates with different cooling rates and lay-ups has been presented. In this study, thermomechanical constitutive equations of thin composite laminates are developed using basic viscoelastic constitutive law considering chemical and thermal effects with time-temperature dependent material properties. To solve a fully scouple problem, both the thermochemical and thermomechanical constitutive equations are formulated. The general heat conduction equation known as the Fourier-Biot equation, viscoelastic laws, Boltzmann superposition principle and composite equations are utilized to formulate thin composite laminates. A static model with constant properties in ambient temperature and a transient model by obtaining constitutive equations are simulated. Results are compared with experimental data. Changing lay-up from cross-ply to angle-ply and then quasi isotropic will increase the value of maximum distortion. Results indicated that the increasing cooling rate will increase the value of the maximum distortion. The differences between FEM results with static analysis of different lay-ups and experimental specimens that cooled in the oven, environment and refrigerator is about 3%, 35% and 55% respectively. The differences between FEM simulation with transient analysis of different lay-ups and experimental specimens that cooled in the environment and the refrigerator is less than 9%.

An efficient semi-analytical framework to tailor snap-through loads in bistable variable stiffness laminates

Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.

On how unsymmetrical laminate designs with tailored ply clusters affect compression after impact strength compared to symmetric baseline

Out-of-plane loads induce unsymmetrical damage modes in the laminate thickness direction. Consequently, the authors have recently proposed overcoming the conventional laminate symmetry constraint by designing unsymmetrical laminates with zero coupling responses. While impact damage is able to be tailored with unsymmetrical laminates, comparing them to symmetric laminates and assessing their impact damage tolerances had yet to be addressed. In this paper, we study three unsymmetrical laminates with localized ply clusters positioned at different locations (at the impacted, at the middle and at the non-impacted sides), along with a standard symmetric laminate as a baseline. Using low-velocity impact, X-ray micro-computed tomography and compression after impact (CAI), we compared the impact and post-impact responses to understand the effect local ply clusters and the delamination location have on the CAI strength. Results revealed that the unsymmetrical laminate with the ply clusters in the middle, where the dominant delaminations also occured, improved the CAI strength by a maximum of 10% when compared to the symmetric baseline. Laminates with delaminations at the outer surfaces offered lesser resistance to buckling. While our study demonstrates that symmetric laminates are not the optimal damage tolerant solution for impact load cases, it also evidences the feasibility of unsymmetrical laminates.

Effect of extension-twisting and extension-bending coupling on a compressed plate with a cut-out

This paper investigates the behaviour of thin-walled composite plates with a cut-out under compression. The effects of lamina ply orientation on the critical state and the behaviour of the plates in the post-critical range were examined. The scope of the research involved numerical modelling of linear and non-linear stability problems by the finite element method, using the simulation software ABAQUS®. The created numerical models were then verified experimentally. The study was performed on a plate with an unsymmetric stacking sequence of plies. To force buckling into a higher mode, an unsymmetric laminate with extension-twisting and extension-bending coupling was used. This approach led to obtaining the natural, lowest mode of buckling (flexural-torsional), one that ensures stable performance of the structure in the post-critical range (no transition to flexural mode).

Green's functions for unsymmetric composite laminates with inclusions.

It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

Impact and damage behaviour of FRP-metal hybrid laminates made by the reinforcement of glass fibers on 22MnB5 metal surface

Hot stamping of 22MnB5 steel is know to yield very high strength of up to 1500 MPa depending on the final microstructure. In this work, different microstructures of 22MnB5 steel were produced by quenching with different cooling rates and then utilized to develop Fiber Reinforced Plastic (FRP)-metal hybrid laminates. By developing FRP-metal hybrid laminates using these hot stamped steels, the superior mechanical of it can be transferred to FRP-metal hybrid laminates. Two different types of FRP-metal hybrid laminates were developed in the study, one by reinforcing thermoplastic based glass/PA-6 FRP on steel surface using press-forming technique and other by reinforcing thermoset based glass/epoxy FRP using vacuum assisted resin transfer moulding process. By developing the FRP-metal hybrid laminates, optimal exploitation of the lightweight and high strength potential can be achieved. Both thermoplastic and thermoset based FRP-metal hybrid laminates developed by using heat treatment steel has better flexural properties compared to steel without heat treatment. In overall the PA-6 has better adhesion towards steel surface compared to epoxy polymer. The developed unsymmetrical hybrid laminates will consist of one side steel and other side with FRP and the influence of the damage behaviour with respect to the impacted side were investigated. Different failure behaviours were identified with respect to the impacted side. 22 J impact on the metal side of thermoplastic based FRP-metal hybrid laminates, developed by the hot stamped steel, requires 127.88% higher load compared to FRP laminates and 33.32% higher load compared to commercially available 22MnB5 steel.

Mitigating the weak impact response of thin-ply based thin laminates through an unsymmetrical laminate design incorporating intermediate grade plies

With aeronautic industries focussing on thinner structures and reducing manufacturing costs, recent research has been dedicated to the impact and post impact response of thin laminates (<2 mm) made of textile fabric composites. A recent study revealed that thin laminates based on thin plies exhibit extensive fibre failure and a reduced compression after impact strength. To mitigate this weakness, we propose a novel laminate concept based on combining plies of different thicknesses in an unsymmetrical configuration (intermediate grade plies are located only at the bottom of the laminate, i.e., the non-impacted face). C-scan inspection on impacted and quasi-statically indented specimens, allowed the damage sequence of the proposed unsymmetrical hybrid laminate to be compared with that of the thin-ply baseline. The hybrid laminate with intermediate plies at the bottom, delayed and reduced the fibre damage, decreased the projected delamination area and led to a 30% increase in the compression after impact strength in contrast to the thin-ply baseline laminate.

Unsymmetrical stacking sequences as a novel approach to tailor damage resistance under out-of-plane impact loading

In current composite design, stacking sequence symmetry around the laminate mid-plane is an unarguable constraint to avoid warpage during manufacturing. However, several load cases induce unevenly distributed stresses through the laminate thickness, such that symmetric laminates may not be the optimal solution. In this paper, we explore the damage resistance to out-of-plane low velocity impact loading of an unsymmetrical laminate with zero extension-bending coupling matrix ([B]), thereby assuring no undesired coupling deformations during mechanical or thermal loads. Using impact and quasi-static indentation tests, C-scan inspection and numerical modelling, we compare the damage pattern between an unsymmetrical laminate with ply clustering at the impacted face and a laminate with ply clustering at the non-impacted face (produced by flipping the former laminate upside down). The laminate with clusters at the impacted side exhibits better damage resistance for lower impact energies. More importantly, the location of the damage events obeys the predictions assumed when the laminate was designed, demonstrating the room for improvement by tailoring unsymmetrical laminates to particular load cases.

Inter-relationships among elastic constants for symmetrical or unsymmetrical laminates with cracked 90-plies

The relations between the stiffness components of a symmetrical or unsymmetrical laminate having trans-verse matrix cracks only in the 90-degree laminas are explored in this work. The crack closure condition for these laminates under membrane and bending deformations is established to obtain the interrelationships. These equations also link the in-plane equivalent Young’s moduli and the Poisson’s ratios of balanced symmetric laminates. Cracks in off-axis laminas are not considered here. The present relations are validated using numerical data reported in the literature. Each inter-relationship can be used to obtain one elastic property when other property was experimentally measured or analytically calculated.

Influence of different parameters on cured shapes and residual stresses of unsymmetric composite laminate reinforced by multi-wall carbon nanotubes

In this research, the curvature of three-phase unsymmetrical composite laminates was determined based on the Rayleigh–Ritz energy method. Three-phase composite laminate consists of glass fiber, epoxy resin and multi-walled carbon nanotubes (MWCNTs). Micromechanical models including Halpin–Tsai, modified Schapery, bridging and Schapery models have been employed to determine mechanical and thermal properties of nanocomposite plates. The influence of the thickness, curing temperature and weight fraction of MWCNTs were studied analytically. Then, some cross-ply composite specimens were fabricated and the analytical results were certified by experimental ones. Additionally, the results were compared with the Hyer model. It was observed that the proposed model can predict the curvature behavior better than the Hyer model. Study of the effects of mentioned parameters on the curvature of the cross-ply laminates revealed that addition of MWCNTs leads to increase in the elastic modulus and decrease in the CTE. So, the curvature of unsymmetrical cross-ply laminates decreases by addition of appropriate amount of nanoparticles.

An Improved Analytical Solution for Process-Induced Residual Stresses and Deformations in Flat Composite Laminates Considering Thermo-Viscoelastic Effects.

Dimensional control can be a major concern in the processing of composite structures. Compared to numerical models based on finite element methods, the analytical method can provide a faster prediction of process-induced residual stresses and deformations with a certain level of accuracy. It can explain the underlying mechanisms. In this paper, an improved analytical solution is proposed to consider thermo-viscoelastic effects on residual stresses and deformations of flat composite laminates during curing. First, an incremental differential equation is derived to describe the viscoelastic behavior of composite materials during curing. Afterward, the analytical solution is developed to solve the differential equation by assuming the solution at the current time, which is a linear combination of the corresponding Laplace equation solutions of all time. Moreover, the analytical solution is extended to investigate cure behavior of multilayer composite laminates during manufacturing. Good agreement between the analytical solution results and the experimental and finite element analysis (FEA) results validates the accuracy and effectiveness of the proposed method. Furthermore, the mechanism generating residual stresses and deformations for unsymmetrical composite laminates is investigated based on the proposed analytical solution.

Inter-relationships among stiffness matrix components for general laminates with transverse cracks in oblique plies

In this paper, nine inter-relationships linking the stiffness matrix components of symmetrical or unsymmetrical laminates having transverse matrix cracks in some of the off-axis plies is presented. The crack closure condition under membrane and bending deformations is established and used to obtain the inter-relationships. The derived crack closure conditions and inter-relationships are validated using a numerical model based on previous work by the authors. These inter-relationships include the eighteen stiffness matrix components and are exact within the assumptions made in the classical lamination theory. When using a two-scale finite element-based model, six loading cases would be needed to obtain the complete stiffness matrix. With the obtained inter-relationships, only four loading cases would be needed, thus saving a third of the total amount of information and computing time.

Nonlinear buckling analysis of variable stiffness composite plates based on the reduced order model

Abstract The variable-stiffness fiber composite plates which have an enhanced design flexibility, largely rely on laminate optimizations to maximize the buckling performance. The corresponding computational efficiency becomes a key issue, in particular when the nonlinear structural behavior is considered. The finite element method based on a full nonlinear analysis is a standard technique for nonlinear structural analysis, however the high computational complexities generated from both the incremental-iterative procedure and the very refined mesh needed for the discrete modeling of curved fibers, are still a decisive cost factor on modern computers. In this work, the Koiter-Newton method is further extended to nonlinear buckling analysis, including the pre and post buckling stage, of variable stiffness composite plates. A four-node quadrilateral element based on the classical laminated plate theory is developed in framework of the von Karman kinematics, for the finite element implementation of the proposed asymptotic method . The reduced order model , with or without imperfections, is constructed using the improved Koiter’s asymptotic expansion , for both the symmetrical and unsymmetrical laminates. The nonlinear response curve of loaded structure can be traced automatically, using the nonlinear predictor and corrections both generated from the reduced order model. This leads to a fairly large step size in the path-tracing process, compared to that for the classical Newton method . The reduced order model largely reduces the computational burden produced by the high-density FE mesh for the varied fiber path. Numerical results indicate the overall high quality and efficiency of the proposed method.

Snapthrough and free vibration of bistable composite laminates using a simplified Rayleigh-Ritz model

Abstract The snapthrough and free vibration response of bistable cross-ply [ 90 n / 0 n ] composite laminates is investigated. Thin unsymmetric composite laminates possess more than one equilibrium position when cooled to room temperature due to the difference in thermal expansion of the plies. Bistable cross-ply laminates have cylindrical shapes at room temperature provided appropriate side-length-to-thickness ratio is used. The laminate is modelled according to the classical lamination plate theory taking into account the von Karman geometric nonlinearity . The strains and displacements are approximated via a simplified Rayleigh-Ritz model that depends on only four time-dependent parameters for the general dynamic response. The simplified model is validated against experimental and finite element results and an acceptable agreement is obtained. The laminate’s length-to-thickness ratio is key to assess the existence of bistability. The model is used to investigate the snapthrough response of an 8-ply [ 90 4 / 0 4 ] laminate that is subjected to three loading schemes: concentrated moments, normal forces, and tangential forces . The variations of the principal curvatures and the lateral displacement of the laminate with the applied forces are shown. The significance of the force location is also found a crucial element in finding the snapthrough force. The free vibration that takes place in the vicinity of a stable equilibrium position is studied and the variation of the fundamental frequency with the laminate size is presented.

Variational analysis of free-edge stress and displacement fields in general un-symmetric and thin-ply laminates under in-plane, bending and thermal loading

A variational approach based on the minimization of complementary energy is developed to determine accurately a complete solution for both free-edge stress and displacement distributions of a laminate with arbitrary lay-ups (possibly un-symmetric and made of thin plies) under combined in-plane, bending and thermal loading. The key idea is partitioning the total stresses/displacements in a laminate with free edges into unperturbed (without free edges) and unknown perturbation stresses/displacements caused by the presence of free edges. It enables the theory of variational stress-transfer to deal easily with both applied traction and displacement boundary conditions. A methodology is introduced to obtain displacement fields for a stress-based variational approach. The resulting stress and displacement fields exactly satisfy local equilibrium equations, strain-displacement relations together with all traction/displacement boundary and continuity conditions. By comparing the results with those obtained from the finite element method, the accuracy and computational efficiency of the developed model, is confirmed.

Rectangular and Triangular Corrugated Composite Skins

A simple analytical model for the effective stiffness of rectangular and triangular corrugated composites is developed for the symmetrical and unsymmetrical laminates. The stiffness matrices for the corrugated composites were derived. The elongation and effective stiffness in the longitudinal and transverse directions for the rectangular and triangular corrugated composites were calculated and compared. The dimensions of the rectangular and triangular elements for unidirectional and plain woven fabrics made up of E-glass/Epoxy were investigated. The analytical model has been validated by experimental results from bending and tension tests. FEM models were used to predict the characteristics of rectangular and triangularly corrugated composites using ABAQUS. FEM and analytical models results are compared. Load displacement curves in tensile and bending tests are investigated. Four stages of their mechanical behaviour are identified. Finally ultimate strain and anisotropic behaviour of rectangular and triangular corrugated composites are investigated as experimentally. Results from FEM in ABAQUS, experimental findings, and analytical simulations show that corrugated composites laminates can afford larger deformations than their flat counterparts. Those laminates or skins have significant anisotropic behaviour and they are candidates for morphing applications.

Analysis of bistable composite laminate with embedded SMA actuators

The present work is aimed at the development of a finite element model of a composite laminate, to evaluate the possibility to snap between equilibrium configurations by means of shape memory alloy (SMA) wires. The underlying idea is to potentially take advantage of structures which possess multiple equilibrium configurations that can be achieved with a small energy input. Therefore, unsymmetric composite laminates that exhibit bistable response to actuation force are considered. Embedded SMA wires will provide the actuation force by virtue of Shape-Memory Effect i.e. restoring the original shape of a plastically deformed SMA wire by heating it. The Shape-Memory Effect is modelled in a simplified way using the Effective Coefficient of Thermal Expansion concept.

Inelastic damage using continuum damage mechanics in composite plate reinforced by unidirectional fibers

It is well that a finite element method is very popular simulation method to predict the physical behavior of systems and structures. In the last years an increase of interest in a new type of numerical methods known as meshless methods was observed. The paper deals with application of radial basis functions on modelling of inelastic damage using continuum damage mechanics of layered plate composite structures reinforced with long unidirectional fibers. For numerical simulations of elastic-plastic damage of layered composite plates own computational programs were implemented in MATLAB programming language. We will use the Newton-Raphson method to solve nonlinear systems of equations. Evaluation damage during plasticity has been solved using return mapping algorithm. The results of elastic-plastic damage analysis of composite plate with unsymmetrical laminate stacking sequence are presented.

A novel adaptive sun tracker for spacecraft solar panel based on hybrid unsymmetric composite laminates

This paper proposes a novel adaptive sun tracker which is constructed by hybrid unsymmetric composite laminates. The adaptive sun tracker could be applied on spacecraft solar panels to increase their energy efficiency through decreasing the inclined angle between the sunlight and the solar panel normal. The sun tracker possesses a large rotation freedom and its rotation angle depends on the laminate temperature, which is affected by the light condition in the orbit. Both analytical model and finite element model (FEM) are developed for the sun tracker to predict its rotation angle in different light conditions. In this work, the light condition of the geosynchronous orbit on winter solstice is considered in the numerical prediction of the temperatures of the hybrid laminates. The final inclined angle between the sunlight and the solar panel normal during a solar day is computed using the finite element model. Parametric study of the adaptive sun tracker is conducted to improve its capacity and effectiveness of sun tracking. The improved adaptive sun tracker is lightweight and has a state-of-the-art design. In addition, the adaptive sun tracker does not consume any power of the solar panel, since it has no electrical driving devices. The proposed adaptive sun tracker provides a potential alternative to replace the traditional sophisticated electrical driving mechanisms for spacecraft solar panels.

Modelling and experiment of process-induced distortions in unsymmetrical laminate plates

Process-induced distortions in composite structures lead to problems with dimensional control, which can be a major concern in the manufacturing. This paper focuses on the prediction of the warpages and curvatures in unsymmetrical laminate plates using closed-form solution and finite element method. A new characterization method that the shape of the deformed composite specimen is conducted in virtue of the coordinate measuring machine through contact method is adopted to experimentally measure the process-induced distortions in unsymmetrical laminate plates. The comparison of numerical and analytical prediction with experimental results for warpages in [06/906] and [09/903] unsymmetrical laminates indicates that shear layer between tool and part has a significant effect on the process-induced distortions, and PTFE release film and release agent between tool and part cannot eliminate effect of the tool-part interaction on the process-induced distortions in unsymmetrical laminate plates. Moreover, the comparison of analytically and numerically predicted development of curvature with experimental results presented by previous literature for unsymmetrical laminates further reveals the effect of tool-part interaction on the process-induced distortions and the accuracy of closed-form solution.