Lay-up Configurations Research Articles

Ballistic Impact and Virtual Testing of Woven FRP Laminates

The aim of the work was to investigate the numerical simulations correlation with the experimental behaviour of steel ball high velocity impact onto a 2 × 2 twill woven carbon composite laminate. The experimental set up consisted of a pressurised gas-gun able to shot steel ball projectiles onto two different composite plate layup configurations of plates made of the same composite material fabric. Subsequently, the experiments were replicated using the LSDYNA explicit finite element analysis software package. Progressive failure numerical models of two different fidelity levels were constructed. The higher fidelity model was simulating each of the plys of the composite panels separately, tied together using cohesive zone modelling properties. The lower fidelity model consisted of a single layer plate with artificial integration points for each ply. The simulation results came out to be in satisfactory agreement with the experimental ones. While the delamination extent was moderately under predicted by the higher fidelity model, the general behaviour was complying with the experimental results. The lower fidelity model was consistent in representing the damage of the panel during the impact and better predicted the impactor residual velocities due to the better matching of the pane stiffness. Despite the competency of the higher fidelity model to capture the damage of the laminate in a more detailed level, the computational cost was 80% higher than the lower fidelity case, which rendered that model impractical against the lower fidelity one, to use in larger models representing more substantial or more complex structures.

Structural Analysis of Composite Conical Convex-Concave Plate (CCCP) Using VAM-Based Equivalent Model

Compared with the ordinary foundation plate, the composite conical convex-concave plate (CCCP) has obvious anisotropic characteristics, and there is less research on the relationship between its mechanical properties and structural parameters. In this article, a numerical model for the equivalent stiffness of a typical unit cell with conical convex is established by using the variational asymptotic method. Then, the 3D finite element model (3D-FEM) of CCCP is transformed into 2D equivalent plate model (2D-EPM) with the effective plate properties obtained from the constitutive analysis of unit cell. The accuracy of 2D-EPM is verified by comparing with the displacement, natural frequencies, and buckling results from 3D-FEM under different boundary conditions. Then, the influence of geometric parameters and layup configurations on the effective performances of CCCP are investigated. Finally, the buckling loads and natural frequencies of bidirectional CCCP are compared with those of CCCP by using the present model. The present model is particularly useful in the early design stage of CCCP where many design trade-offs need to be made over a vast design space in terms of material selection, ply angles, and geometric parameters.

On the elastic buckling of cross-ply composite closed cylindrical shell under hydrostatic pressure

This paper focuses on the elastic buckling of cross-ply composite closed cylindrical shell subjected to hydrostatic pressure. The analytical model for buckling of composite cylindrical shell is derived by using the First Order Shear Deformation Theory (FOSDT) and considering the pressure stiffness. Several types of shells including thin, thick, long, and short shells are investigated. Two composite materials i.e. Carbon/Epoxy and Glass/Epoxy and several layup configurations are employed. The results of the derived FOSDT-based model are compared with those obtained from a Shell Buckling Equation (SBE) used in earlier studies and the Classical Shell Theory (CST). For verification, the results of the derived FOSDT-based model are compared with the results found in literature and also with the results obtained from finite element analysis. The difference among the results of the SBE and FOSDT, and the CST and FOSDT increases with the increase of the thickness in the case of all layup configurations and materials. For thin shells, the difference between the results of the CST and FOSDT almost vanishes, while for thin and large shells, the difference between the results of the SBE and FOSDT is still significant.

Critical Load Prediction in Notched E/Glass-Epoxy-Laminated Composites Using the Virtual Isotropic Material Concept Combined with the Average Strain Energy Density Criterion.

This paper attempts to validate the application of the Virtual Isotropic Material Concept (VIMC) in combination with the average strain energy density (ASED) criterion to predict the critical load in notched laminated composites. This methodology was applied to E/glass–epoxy-laminated composites containing U-notches. For this purpose, a series of fracture test data recently published in the literature on specimens with different notch tip radii, lay-up configurations, and a number of plies were employed. It was shown that the VIMC–ASED combined approach provided satisfactory predictions of the last-ply failure (LPF) loads (i.e., critical loads).

Static and dynamic analysis of Isogrid Stiffened Composite Plates (ISCP) using equivalent model based on variational asymptotic method

The isogrid stiffened composite plate (ISCP) can be used to resist bending and buckling loads while being lightweight. In order to reveal the relationship between structural parameters and static/dynamic behavior, the original geometrical nonlinear problem of ISCP is decoupled into a linear constitutive modeling over the unit cell and a geometrically nonlinear analysis over the two-dimensional equivalent plate model (2D-EPM). The equivalent stiffness, static deformation, natural vibration frequencies and buckling mode of ISCP under different layup configurations and structural parameters are calculated based on 2D-EPM, and verified by comparing with the results of three-dimensional finite element (3D-FEM). The results show that the equivalent stiffness, buckling load and natural frequency of ISCP increase with the increase of stiffener thickness and height, while decrease with the increase of stiffener spacing due to the special structural form. Compared with the orthogonal stiffened composite plate and honeycomb stiffened composite plate, the bending stiffness and buckling load of ISCP are greater. More importantly, the model can effectively improve the calculation efficiency under the premise of ensuring sufficient accuracy, which is very important for the preliminary design of ISCP.

High efficiency analysis model for composite honeycomb sandwich plate by using variational asymptotic method

In this article, an equivalent model (called the two-dimensional equivalent plate model (2D-EPM)) of a composite honeycomb sandwich plate (CHSP) is developed using the variational asymptotic method (VAM). The three-dimensional (3D) geometric nonlinear problem of the CHSP is decoupled into a linear constitutive model over a unit cell and a geometric nonlinear problem defined in the 2D-EPM. In the linear constitutive model, the equivalent plate properties are calculated and imported into the 2D-EPM to carry out static, buckling, and vibration analysis. The effects of the layup configurations of the face sheet, geometric parameters of the honeycomb core, and boundary conditions on the equivalent stiffness and the static, buckling, and free-vibration responses are systematically studied. Compared with the 3D finite element method and 3D traditional equivalent model, the 2D-EPM possesses the merits of high precision and calculation efficiency. The equivalent stiffness and anisotropy of the CHSP are very sensitive to the layup configuration as well as the side length and cell corrugation angle of the honeycomb core. The present model can accurately capture the local field distribution within the unit cell as well as provides an effective method for the design and optimization of the CHSP.

Continuous evolution of processing induced residual stresses in composites: An in-situ approach

Processing induced residual stresses are often responsible for causing warping, undesired distortion, dimensional instability, and delaminations in composite structures. Monitoring the evolution of residual stresses throughout the cure is essential to understand their effect on the mechanical behavior of the composites. In the present work, a novel in-situ experimental approach is used to measure the dimensional changes in the laminates during cure and combined with temperature-dependent moduli obtained from Dynamic Mechanical Analysis (DMA) to calculate the continuous evolution of residual stresses during composite processing. Five symmetric and asymmetric layup configurations are analyzed to investigate the effect of ply orientation on the residual stress evolution. The maximum average residual stress of 110 MPa in the longitudinal direction is observed for symmetric cross-ply [0/90]s configuration and the maximum average warpage of 1.46 mm is observed for balanced un-symmetric [30/−30/60/−60] layup configuration.

A Numerical Investigation on Stress Modal Analysis of Composite Laminated Thin Plates

Because of the light weight and high strength, composite laminates have many advantages in aircraft structures; however, they are frequently subjected to severe dynamic loadings during flight. To understand the dynamic properties of composite laminated thin plates at the stress scale, this paper studies the stress modal analysis (SMA) of composite laminated thin plates by finite element method (FEM). Firstly, the basic theory on SMA of composite laminates was given from the classical displacement modal analysis. Secondly, a square laminated thin plate was numerically studied to obtain some distribution laws of the stress mode shapes (SMSs) from the layup and stress component perspectives. Then, based on the characteristics of SMSs in different plies, a modified layup configuration was conducted for possible lower magnitude and more uniform distributions of SMSs. Results indicate that ±45° layups can improve the performance of SMSs of the square plate, without excessively decreasing the modal frequencies. Such fact manifests that ±45° layups are critically vital for the dynamic stress reduction of the square composite laminated plates. Modal participation factor and strain energy were evaluated to assist the determination of critical modes. Lastly, the aspect ratio of the composite plate on layup design was considered. Numerical investigation in this study can serve as a preliminary step of SMSs perspective for the analysis and optimization of dynamic composite laminates.

Modelling damage in multidirectional laminates subjected to multi-axial loading: Ply thickness effects and model assessment

A meso-scale damage modelling framework for composite laminates is assessed against multi-axial experimental data obtained from specimens subjected to combined tension/compression and shear loading using a modified Arcan fixture (MAF). Two laminates made from unidirectional carbon fibre-reinforced epoxy plies of different thickness are considered to investigate the ply thickness effect on the damage behaviour of modified open-hole specimens. Intra-laminar damage is predicted using a continuum damage model combined with a fibre-aligned mesh, while cohesive zones are used to account for inter-laminar damage. The multi-axial open-hole specimen strength is predicted with a mean relative error of 15% across all the investigated lay-up and loading configurations, while the predicted damage maps show encouraging agreement with full-field measurements obtained using digital image correlation (DIC). However, the assessment reveals limitations of the assumption of small strains and rotations in the formulation of the model that lead to spurious model behaviour for shear-dominated damage modes.

Effect of interfacial fibre orientation and PPS veil density on delamination resistance of 5HS woven CFRP laminates under mode II loading

This paper presents an experimental study on the effect of interfacial fibre orientation and interleaved thermoplastic veil on Mode II interlaminar fracture toughness of 5-harness satin woven carbon fibre reinforced polymer composite laminates. Three-point End-Notched Flexure tests were carried out to determine delamination resistance, GIIC, of specimens with five fibre orientation biases and two veil densities at the midplane. Results show that delamination resistance of 5-harness satin woven laminates depends on the layup configurations at the midplane with 90/45 fibre orientation bias exhibiting the greatest resistance. The delamination resistance enhancement from polyphenylene sulfide (PPS) veil interleaves is also fibre orientation dependent but a further increase of the veil density from 10 gm−2 to 20 gm−2 offers little extra benefit. Fracture surface morphologies were examined under SEM to understand the failure mechanism and fracture process of the woven laminate under the combined effects of the interfacial fibre orientation and the veil density. Fibre orientation relative to the delamination path, surface texture misfit, and veil density are the three main contributors identified for the variation of delamination resistance of 5HS woven laminates.

Experimental, semi-analytical and numerical nonlinear analysis of compression-loaded laminates with different boundary conditions

The aim of this study is to investigate the nonlinear response of composite square laminates with different boundary conditions and under compressive loading using experimental, semi-analytical and finite element methods. In order to perform the experimental tests, a new fixture was designed and fabricated for simulation of the nonlinear response of composite laminates. The fixture has the ability to model all kinds of boundary conditions such as simply-support, clamp, and free on longitudinal edges. Nevertheless, in the loaded ends, the boundary conditions are only of clamped type. The desired composite laminates have been prepared with different numbers of layers (8, 12 and 16 layers) and as asymmetrical layup configuration, which finds out-of-plane displacement response as soon as compressive load is exerted. To get the nonlinear results of the composite plates, in addition to experimental results, finite element numerical method has also been used through ABAQUS software alongside another semi-analytical method. In the semi-analytical method, the displacement fields of the plates have been estimated through the first-order shear deformation theory and by Legendre polynomials. Next, through minimum of total potential energy principle, the nonlinear system governing the behavior of the laminates has been obtained and solved. Comparison between all experimental, numerical, and semi-analytical results suggested accuracy of the calculations through the simulations against the experimental results obtained from the new fixture.

Nonlinear lay-up optimization of variable stiffness composite skew and taper cylindrical panels in free vibration

In the present study, the fundamental natural frequencies of curvilinear fiber composite skew and taper cylindrical panels are optimized applying genetic algorithm (GA). Later, the fundamental amplitude-dependent nonlinear frequency behavior of the optimized curved fiber layup configurations is studied and compared with the reference unidirectional fiber layup. The variable stiffness behavior is obtained by altering the fiber angles continuously according to the curvilinear fiber path function in the composite laminates. A nonlinear structural model is utilized based on the virtual work principle. Green’s nonlinear kinematic strain relations are used to account for the geometric nonlinearities and the first-order shear deformation theory (FSDT) is adopted to generalize the formulation for the case of moderately thick cylindrical panels including transverse shear deformations. The goal is to determine how the variable stiffness parameters affect the linear and nonlinear free vibration behavior of the skew and taper cylindrical panels. Consequently, one may find the optimum fiber path with improved structural characteristics for the cylindrical panel. Eight-layered composite skew and taper cylindrical panels at two different boundary condition sets are considered in this research. Generalized Differential Quadrature (GDQ) method of solution is employed to solve the nonlinear governing equations of motion. Numerical results demonstrate the degree of effectiveness for fiber angle paths, boundary conditions, and geometrical non-uniformities on the fundamental frequencies of the cylindrical panel. Eventually, optimum fiber angles of each layer in free vibration analysis are presented.

Phosphoric acid derived efficient reclaimation of carbon fibre for re-manufacturing high performance epoxy composites reinforced by highly-aligned mat with optimized layup

This study presented an economic and closed-loop recycling approach of carbon fibre reinforced polymers (CFRP) comprising phosphoric acid derived efficient reclaimation of recycled CF (rCF) and re-manufacture of high performance epoxy (EP) composites reinforced by highly-aligned rCF mat. The integral rCF with clean surface and intact graphitization structure showed the high retention ratios of 97.1 and 99.5% in tensile strength and modulus, respectively, as well as highly-aligned arrangement of rCF mat with preferential alignment degree (PAD) of 83.5% much contributed to increasing its maximum volume fraction up to ~ 40% in composites. Thus, through fully utilizing the property anisotropy and structural designability of aligned rCF, mechanical and EMI shielding performance of rCF/EP composites were significantly enhanced via optimizing mat layup configurations.

Flexural bearing capacity and failure mechanism of CFRP-aluminum laminate beam with double-channel cross-section

Abstract In this study, the flexural bearing capacity and failure mechanism of carbon fiber-reinforced aluminum laminate (CARALL) beams with a double-channel cross-section and a 3/2 laminated configuration were experimentally and numerically studied. Two types of specimens using different carbon fiber layup configurations ([0°/90°/0°]3 and [45°/0°/−45°]3) were fabricated using the pressure molding thermal curing forming process. The double-channel CARALL beams were subjected to static three-point bending tests to determine their failure behaviors in terms of ultimate bearing capacity and failure modes. Owing to the shortcomings of the two-dimensional Hashin failure criterion, the user-defined FORTRAN subroutine VUMAT suitable for the ABAQUS/Explicit solver and an analysis algorithm were established to obtain a progressive damage prediction of the CFRP layer using the three-dimensional Hashin failure criterion. Various failure behaviors and mechanisms of the CARALL beams were numerically analyzed. The results indicated that the numerical simulation was consistent with the experimental results for the ultimate bearing capacity and final failure modes, and the failure process of the double-channel CARALL beams could be revealed. The ultimate failure modes of both types of double-channel CARALL beams were local buckling deformation at the intersection of the upper flange and web near the concentrated loading position, which was mainly caused by the delamination failure among different unidirectional plates, tension and compression failure of the matrix, and shear failure of the fiber layers. The ability of each fiber layer to resist damage decreased in the order of 90° fiber layer > 0° fiber layer > 45° fiber layer. Thus, it is suggested that 90°, 0°, and 45° fiber layers should be stacked for double-channel CARALL beams.

Multi-objective design exploration using self-organization map for composite structures made by automated fiber placement

In this study, we apply the sequential approximate multi-objective optimization (SAMOO) to an open-hole laminated plate with partially different lay-up configurations for assuming fabrication by the AFP equipment. The SAMOO is a method to search for the optimal design with a small number of evaluations of the objective function while adding appropriate sample points to the response surface. When the optimization problem deals with many objective functions, it becomes difficult to visualize the design candidates and to understand the relationship between the objective functions. Thus, the self-organizing map (SOM) which displays multi-dimensional data in two dimensions is employed for visualization and clustering of obtained non-dominated solutions. Numerical results showed that the trade-off relationships among the three objectives were clarified and design alternatives could be explored according to the design tastes, and it was confirmed that the SOM was effective for the present optimization problem.

Modeling and Optimal Control of Piezoactuated Rotating Box Beams with Sophisticated Couplings

The mathematical modeling and active control of piezoactuated pretwisted thin-walled rotating beams with a circumferentially asymmetric stiffness layup configuration are addressed. The effects induced by rotation (for example, dynamic stiffening, tennis-racket effects, etc.) are highlighted. The geometrical pretwist effect-induced additional inertial and elastic couplings are specifically discussed. A better idea of the relationship between control effectiveness and the synergistic effect devoted by elastic, inertial, and actuation couplings is obtained based on the linear quadratic regulator control strategy. It can be found that elastic couplings have a significant effect on control effectiveness of the system (especially on that controlled by the piezoelectrically induced transverse shear), whereas the influence of the rotation-induced centrifugal effects on control effectiveness is weaker. On the other hand, elastic couplings will reduce the sensitivity of the control authority to the piezoelectrically induced actuation couplings. And, the geometrical pretwist effect will further reduce this sensitivity since it will introduce more elastic couplings to the system.

Effect of lay-up configuration on the microwave absorption properties of carbon fiber reinforced polymer composite materials

Multidirectional carbon fiber reinforced polymer (CFRP) composites, stacked by multiple layers of unidirectional prepregs, are generally considered to be microwave reflective, but we have found that it is not always the case. In this paper, the microwave response of many CFRP laminates has been investigated, considering the effect of the fiber orientation and the laminate thickness. An analytical model was developed to establish the relationship between the lay-up configuration and the effective impedance of composite laminates. The result indicated that if carbon fibers inside the headmost layer(s) are parallel to the incident electric field, the material will reflect the microwave power regardless of the subsequent fiber orientation and laminate thickness, due to the high conductivity of carbon fibers in the axial direction. Otherwise, the response of the CFRP laminates will strongly associate with the position of its internal cross-ply and the laminate thickness, as they have a significant influence on the impedance of the laminate. When the position of the cross-ply is far from the surface radiated by microwave, the multidirectional CFRP laminate can be changed to microwave absorbers, because it has a relatively matched impedance with air. The findings in this paper may be applied to design lay-up configurations of CFRP laminates for a specific microwave performance, besides mechanical properties.

Non-convex layup optimization of the composite laminates with fast and robust FEA model and modified SPEA-II

The biggest design challenge regarding composite laminates is the selection of a stacking sequence such that the cost and/or weigth of the laminate to be minimized subject to constraints like failure criteria. The layup optimization of the composite laminates involves a very complex multidimensional solution space which is usually non-exhaustively explored using heuristic computational methods like genetic/evolutionary algorithms. To ensure the convergence of the prefered method it is necessary to evaluate a lot of layup configurations during the optimization process which involves that the evaluation of a single configuration should be fast enough to keep the overall optimization time to an acceptable level. On the other hand the mechanical behaviour of the composite laminates is very complex and it is analyzed with expensive computational tools such as finite element analysis. In this paper we propose a computational efficient framework which combines a very fast and robust Matlab-based FEA model with a non-convex evolutionary algorithm (strength pareto evolutionary algorithm II). We speed up the convergence by modifying the standard algorithm to generate new potentially pareto-optimal individuals. Also, a detalied numerical example is presented in order to highligth the steep computational time improvement between our method and a convex genetic algorithm.

The Effect of Non-Conservative Compressive Force on the Vibration of Rotating Composite Blades

This paper investigates the effectiveness of a resonance avoidance concept for composite rotor blades featuring extension–twist elastic coupling. The concept uses a tendon, attached to the tip of the blade, to apply a proper amount of compressive force to tune the vibration behavior of the blade actively. The tendon is simulated by applying a non-conservative axial compressive force applied to the blade tip. The main load carrying part of the structure is the composite spar box, which has an antisymmetric layup configuration. The nonlinear dynamic behavior of the composite blade is modelled by using the geometrically exact fully intrinsic beam equations. The resulting nonlinear differential equations are discretized using a time–space scheme, and the stationary and rotating frequencies of the blade are obtained. It is observed that the proposed resonance avoidance mechanism is effective for tuning the vibration behavior of composite blades. The applied compressive force can shift the frequencies and the location at which the frequency veering take place. Furthermore, the compressive force can also cause the composite blade to get unstable depending on the layup ply angle. Finally, the results, highlighting the importance of compressive force and ply angle on the dynamic behavior of composite blades, are presented and discussed.

Influence of metal/composite interface on the damage behavior and energy absorption mechanisms of FMLs against projectile impact

This paper focuses on the interface failure in metal/GFRP laminates on account of the high-velocity impact phenomenon by a hemispherical projectile. The study considers three laminates in which the failure inside the 8-layer 0/90 GFRP laminate is compared with the other two laminates that include metal layers in their layup configuration. The metal layers were placed on the top and bottom on one type of laminates while in the other additional metal layers are placed symmetrically inside the layup as well. They were subjected to high-velocity impact by a hemispherical projectile at different energy levels and the idea is not to perforate the laminate configuration instead to account for the damage incurred in these laminates and the role of metal layers in providing resistance to damage within these laminates. The study utilizes experimental findings and proposes a rate-dependent Finite Element (FE) model consisting of the Hashin-Puck failure scheme for composite and the Johnson-Cook damage model for metal layers. The results of the model satisfactorily agree with their experimental counterparts and provide valuable insight into the damage resistance inside the laminates. It has been observed that the 8-layer GFRP laminate was good in terms of elastic recovery and prevention of propagation of damage inside the laminates only, till the impact energy was lower. For higher impact energy, they show poor damage resistance as the fiber failure is triggered in them. However, laminates with metal layers are shown to protect the laminate by dissipating energy in the delamination of metal/GFRP interface, shear failure of the metal layer, and on account of metal plasticity. The study further shows that the through-thickness compressive stresses were responsible for the failure of laminates and also triggering the delamination in them. A damage energy study was performed to investigate the amount of energy dissipating in various failure modes like delamination, matrix cracking, fiber failure, etc.