Multilayered Composite Laminates Research Articles

Evolutionary topology optimization of fiber reinforced composite laminates for maximum stiffness

In this study, a topology optimization technique based on the bi-directional evolutionary structural optimization (BESO) method is developed to maximize the stiffness of fiber reinforced composite laminates. The elastic properties of single-layer and multi-layer composite laminates are characterized and a composite material interpolation scheme is introduced. The effectiveness of the developed BESO method for the single-layer and multi-layer composite laminates are verified by three classical examples, namely a cantilever, a Michell-type structure, and an L-bracket. Then, based on the analysis of the topological results, a selection suggestion and verification criteria for layers with appropriately matched fiber angles are proposed and verified by two additional examples. This study proves that the BESO method is an effective technique for the topology optimization of composite laminates for maximum stiffness, and the proposed suggestion and criteria are useful for avoiding large computational costs and empirical selection of layers.

Transient Structural Thermo-Mechanical Response of Multi-Layered Viscoelastic Composite Laminates with Non-Idealized Interfacial Conditions Based on New Fractional Derivatives

Multi-Layered viscoelastic composite laminates are commonly designed as damping structures in non-isothermal environments to avoid unnecessary vibration and ensure the safety of structures working in vibration engineering, such as reducing the unwanted vibration and noise of aircraft structures and vehicles. In recent years, there have been extensive research works that contributed to evaluate and predict the influences of relaxation time parameters, nonlocal elastic/thermal parameters, and temperature related material properties on the dynamic thermo-viscoelastic responses of such structures. Nevertheless, the effects of fractional derivatives and related parameters are rarely reported on this topic. This paper aims to construct a mathematical model of transient structural thermo-mechanical response of multi-layered viscoelastic composite laminates with non-idealized interfacial conditions (i.e., the thermal contact resistance and elastic wave impedance) by introducing the new definitions of the Caputo-Fabrizio (CF), Atangana-Baleanu (AB), and Tempered-Caputo (TC) fractional derivatives. The Laplace transform method is applied to obtain the transient solutions. The dimensionless results reveal that the new fractional derivatives, non-idealized interfacial conditions and material constants ratios significantly affect the wave propagations and transient thermo-viscoelastic responses, and the harmful heat/stress isolation at interface are improved to some extent.

Fractional-order non-Fick mechanical-diffusion coupling model based on new fractional derivatives and structural transient dynamic responses of multilayered composite laminates

Fractional-order non-Fick mechanical-diffusion coupling model based on new fractional derivatives and structural transient dynamic responses of multilayered composite laminates

Collaborative optimization for variable stiffness composite laminates using a fiber angle description method based on Archimedean spiral function

When optimizing the fiber orientation of multilayer composite laminates, with the increasing number of layers, the number of design variables increases sharply, resulting in a large amount of computational cost. To address this challenge, this paper proposes a novel discrete fiber angle optimization method based on the Archimedean spiral function and applies it to a collaborative design framework of topology and fiber orientation. The proposed method uses the normal distribution function as the angle selection function in every layer. To prevent convergence issues in optimizing the fiber angle, a new candidate angle weighting formula is proposed. Further, a discrete fiber angle parameterization method based on the Archimedean spiral function for the thickness direction of laminates is presented, which requires only one variable to represent the fiber angle of any two layers in the element. To circumvent the issue of local optima and expand the design space, a collaborative optimization strategy is employed to improve the discrete fiber angle optimization results. Finally, the numerical examples indicate that in comparison to conventional approaches, the correlation of the proposed method with initial values is significantly reduced (σ2=0.00188). Under identical initial conditions, this method can improve the structural stiffness by over 20% at maximum.

On the ultrasonic characterization of the stacking sequence of CFRP laminates

Ultrasound in pulse-echo scan mode has already been demonstrated for the extraction of local fiber angle distribution in composite laminates. Depending on the ultrasonic (scan) parameters employed, different sensitivity, spatial resolution, and dynamic depth range can be reached.This study investigates the use of pulse-echo ultrasound testing in different frequency ranges to characterize the in-plane fiber angle distribution and ply stacking sequence in a multi-layer composite laminate. Minimization of the Mumford-Shah functional is performed as an edge-preserving smoothing procedure for the recorded ultrasonic dataset, followed by the application of a Gabor Filter-based Information Diagram approach to extract a 3D tomographic image of the fiber angles. The performance of the method is experimentally studied on ultrasonic datasets, recorded at various center frequencies, of a 5.5 mm thick 24-layer quasi-isotropic carbon fiber reinforced polymer laminate with stacking sequence [+45/0/−45/90]3s. For quantitative analysis, statistical metrics are employed to evaluate the accuracy and precision of the extracted angles over depth, and to better understand the interfering influence of adjacent plies. For the given case study, a 15 MHz ultrasound frequency is recommended as it provides a good balance between precision, accuracy, and depth range. To understand the influence of scan parameters on the fiber angle characterization, the 15 MHz ultrasonic dataset is analyzed for various noise conditions as well as different spatial step size of the scan.

Terahertz Spectroscopic Characterization and Thickness Evaluation of Internal Delamination Defects in GFRP Composites

The use of terahertz time-domain spectroscopy (THz-TDS) for the nondestructive testing and evaluation (NDT&E) of materials and structural systems has attracted significant attention over the past two decades due to its superior spatial resolution and capabilities of detecting and characterizing defects and structural damage in non-conducting materials. In this study, the THz-TDS system is used to detect, localize and evaluate hidden multi-delamination defects (i.e., a three-level multi-delamination system) in multilayered GFRP composite laminates. To obtain accurate results, a wavelet shrinkage de-noising algorithm is used to remove the noise from the measured time-of-flight (TOF) signals. The thickness and location of each delamination defect in the z-direction (i.e., through-the-thickness direction) are calculated from the de-noised TOF signals considering the interaction between the pulsed THz waves and the different interfaces in the GFRP composite laminates. A comparison between the actual and the measured thickness values of the delamination defects before and after the wavelet shrinkage denoising process indicates that the latter provides better results with less than 3.712% relative error, while the relative error of the non-de-noised signals reaches 16.388%. Also, the power and absorbance levels of the THz waves at every interface with different refractive indices in the GFRP composite laminates are evaluated based on analytical and experimental approaches. The present study provides an adequate theoretical analysis that could help NDT&E specialists to estimate the maximum thickness of GFRP composite materials and/or structures with different interfaces that can be evaluated by the THz-TDS. Also, the accuracy of the obtained results highlights the capabilities of the THz-TDS for the NDT&E of multilayered GFRP composite laminates.

The displacement view of a multilayered HSDT plate

This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the center of plate for both fixed and simply supported edges is verified with reported literature and a good conformity is found. An attempt has been made to observe the minimum value of maximum deflection in the laminate for attaining the maximum strength of laminate with a suitable combination of stacking sequences with a constant volume of material.

Dichotomy property of dispersion equation of guided waves propagating in anisotropic composite plates

Accurate prediction of dispersion curves for ultrasonic guided waves propagation in multi-layered composite laminates is crucial for the deployment of nondestructive testing procedures and structural health monitoring algorithms dedicated to aerospace composite materials. However, existing efforts mainly focused on finding ways to build complex-valued dispersion equations for guided waves (see transfer matrix method (TMM), global matrix method (GMM) and stiffness matrix method (SMM) for example) with little focus on developing efficient and stable numerical solving methods associated with the derived complex-valued equations. In this paper, the conditions under which complex-valued dispersion equations are either real- or purely imaginary-valued equations (termed as dichotomy property) are derived for both single- and multi-layered composite plates. With such a property, the complex-valued dispersion equations can be efficiently numerically solved within the real number field via the standard bisection method or the corrected phase change method. It is thus now possible to overcome numerical issues frequently reported in literature. Besides, a parallel computing technique is proposed in this paper to improve the computational efficiency of the traditional GMM. The proposed methodology provides a new standard framework to solve the dispersion equations which is stable, multipurpose, and numerically efficient.

Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media.

There has been an increase in the use of ultrasonic arrays for the detection of defects in composite structures used in the aerospace industry. The response of a defect embedded in such a medium is influenced by the inherent anisotropy of the bounding medium and the layering of the bounding medium and hence poses challenges for the interpretation of the full matrix capture (FMC) results. Modeling techniques can be used to understand and simulate the effect of the structure and the defect on the received signals. Existing modeling techniques, such as finite element methods (FEM), finite difference time domain (FDTD), and analytical solutions, are computationally inefficient or are singularly used for structures with complex geometries. In this paper, we develop a novel model based on the Gaussian-based recursive stiffness matrix approach to model the scattering from a side-drilled hole embedded in an anisotropic layered medium. The paper provides a novel method to calculate the transmission and reflection coefficients of plane waves traveling from a layered anisotropic medium into a semi-infinite anisotropic medium by combining the transfer matrix and stiffness matrix methods. The novelty of the paper is the developed model using Gaussian beams to simulate the scattering from a Side Drilled Hole (SDH) embedded in a multilayered composite laminate, which can be used in both immersion and contact setups. We describe a method to combine the scattering from defects with the model to simulate the response of a layered structure and to simulate the full matrix capture (FMC) signals that are received from an SDH embedded in a layered medium. The model-assisted correction total focusing method (MAC-TFM) imaging is used to image both the simulated and experimental results. The proposed method has been validated for both isotropic and anisotropic media by a qualitative and quantitative comparison with experimentally determined signals. The method proposed in this paper is modular, computationally inexpensive, and is in good agreement with experimentally determined signals, and it enables us to understand the effects of various parameters on the scattering of a defect embedded in a layered anisotropic medium.

Study on intralaminar crack propagation mechanisms in single- and multi-layer 2D woven composite laminate

The intralaminar crack propagation of the carbon/epoxy two-dimensional plain woven composite material has been experimentally investigated. It was found that the propagation direction is insensitive to pre-crack tip locations. The propagation path direction is aligned along the intersecting position of warp fibers and weft fibers weaving, and the extends forward along the crack tip until the final fracture failure. The crack propagation process has two major stages, the maximum energy accumulation stage (stage A) and the gradual release of energy stage (stage B). In stage B, there are many single or several fiber bundles breakage during these stages due to the characteristics of reinforcing fibers woven from multiple fiber bundles. The warp fiber bundles gradually break under the axial tensile loading. Analysis of the images obtained by the optical microscope and scanning electron microscope, the fracture surfaces of the specimens are all sawtoothed, the fracture damage of the plain woven single-layer laminate is mainly fiber bundles separation, breakage of the fiber, and debonding of the fiber and the matrix. In addition, the validity of the intralaminar crack propagation mechanisms is further verified by multi-layer laminate experiments.

Mechanical characterization of a woven multi-layered hyperelastic composite laminate under uniaxial loading

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

Recent Advances in the Laser Forming Process: A Review

Laser forming is an emerging manufacturing process capable of producing either uncomplicated and complicated shapes by employing a concentrated heating source. The heat source movement creates local softening, and a plastic strain will be induced during the rise of temperature and the subsequent cooling. This contactless forming process may be used for the simple bending of sheets and tubes or fabrication of doubly-curved parts. Different studies have been carried out over recent years to understand the mechanism of forming and predicting the bending angle. The analysis of process parameters and search for optimized manufacturing conditions are among the most discussed topics. This review describes the main recent findings in the laser forming of single and multilayer sheets, composite and fiber-metal laminate plates, force assisted laser bending, tube bending by laser beam, the optimization technique implemented for process parameters selection and control, doubly-curved parts, and the analytical solutions in laser bending. The main focus is set to the researches published since 2015.

Influence of environmental relative humidity on the polarization behaviour of paper and paper-dielectric structures

In paper containing multilayer composite structures and laminates, polarization is usually investigated under dry environmental conditions. The aim of this research is to determine polarization dependence of paper and paper-dielectric structures on environmental relative humidity (RH). The role of each component was identified. The obtained and recorded data are used for identification and clarification of the physical mechanism of polarization. The polarization was studied by applying a dosed charging and forced discharge method and was evaluated by a depolarization potential and its formation kinetics. The polarization level of investigated structures increases with RH and is determined mainly by the paper (cellulose) and moisture content in it. In composite structures of the paper between dielectric films and dielectric on paper the polarization dependence on RH correlates with moisture absorption isotherm. It was found that the surface electrical conductivity of paper distorts the results of the paper and structure paper on dielectric. Analysis of the formation kinetics of the depolarization potential together with the potential decay of the charged paper has determined the role of orientation polarization and space charges. The formation of space charges is faster than orientation polarization and dominates in polarization process at higher RH. The process modeling by superposition of two exponents confirms this polarization mechanism.

Analysis of Damage and Crack Propagation in Unidirectional Composite Laminates with a Peridynamic Model

A continuous function was applied to establish a peridynamics model to study the damage of unidirectional composite laminate, a kind of transverse isotropic material with three-dimensional (3D) structure. To express the interaction of nonadjacent layers and the influence of thickness on elastic deformation and damage, this paper employed a spherical material horizon. The spherical harmonics function was applied to express the relationship of the micro-elastic modulus and the bond-fiber angle, as well as critical bond stretch and the bond-fiber angle, respectively. Spatial stress or strain conditions were employed to calculate the strain energy density and solve the bond stiffness constant. The model was verified with unidirectional multilayer composite laminate with orifice. The damage mode and the crack propagation process of laminates with orifice were also consistent with that of experimental.

The dynamic performance of novel multilayered hybrid composite laminate

Due to an increase in the need for improvement of impact resistance of conventional composites, hybrid composites are evolved. This research article presents the dynamic characteristics of a novel two-component hybrid composite plate under transverse impact loading. The multilayered hybrid composite laminate is fabricated using woven fibreglass fabric as skin material and thermoplastic polycarbonate sheet as the core. High strength, medium viscous epoxy matrix is used for bonding the skin and core materials. The hand layup followed by a compression molding technique is used for producing the laminate. The test samples are impacted with a minimum energy of 45 J to a maximum energy of 60 J to obtain rebound, penetration and perforation phenomenon at room temperature. Load–energy–displacement–time curves are plotted to understand the transient behaviour of the composite plates. Results are compared with the pure counterparts available in the literature in terms of impact resistance. It is inferred that the novel multilayered laminate being in lightweight about 19.17% as compared to conventional laminate presented by Evci and Gulgec (J Compos Mater 48:3215–3236). Further, the novel composite has provided less damage area with 16.66% of enhanced impact resistance in terms of energy required for complete perforation. The investigation revealed the possibility of replacing conventional materials with hybrid laminates in structural, defense and automotive applications, where impact resistance and light weight has much importance.

Progressive multi-damage analysis of composite laminate using higher order zig-zag plate theory

In this article, a finite element model of multi-layer composite laminates with delamination based on higher order zig-zag theory is studied for the progressive delamination analysis. The degrees of freedom are simplified by the continuity conditions of shear stress between layers and the free-surface conditions at the bottom and top of laminates. The numbers of degrees of freedom are not reduced with this method while the model can take the initiation of delamination into consideration in return. Static loading analysis is implemented to simulate the performance in delamination resistance with two different plies and under two different boundary conditions. The present model can present good performance in the prediction of delamination phenomenon.

Enhancement of Fracture Properties of Composite Laminate with Si C Additive

ASTM standards for short beam test, double cantilever beam and end notched specimen test are followed to compare control specimen with different percentage of Si C test data. Present study shows interlaminar shear strength (ILSS) and delamination fracture toughness values of multilayered composite laminate can be enhanced considerably with the use of Si C admixture in epoxy resin system as nonpolar elements compatible with to polar glass fiber. With respect to control specimen one percentage by weight of Si C w.r.t resin can bring up the ILSS value by as much 70% while the DCB test data on the critical energy release rate of mode I increases by 85% and mode II toughness value becomes double for 1% by weight of Si C. The bidirectional cloth provides more resistance for mode-I delamination fracture toughness when compared to UDL reported in literature and hence for higher fracture properties. The study is useful for design of rocket nozzles and input required for the cohesive zone model to assess the residual strength of composite structures with of delamination.

Numerical optimizing and experimental evaluation of stepwise rapid high-pressure microwave curing carbon fiber/epoxy composite repair patch

Numerical models of multi-layer composite laminates with various fiber orientations and fiber layers were investigated under adhesively bonded repair condition by ABAQUS. Stress intensity factors (SIF) of bonded structure systems were calculated by J integral method. Results indicated that composite laminate with [90/90/90] fiber orientation and three fiber layers exhibited the lowest numerical SIF value. The laminates reinforced by carbon fiber with corresponding orientation were experimentally prepared in a two-step high-pressure microwave curing and traditional thermal curing methods on the basis of simulated results, respectively. Mechanical and curing properties of laminates prepared by two curing methods were characterized and compared by means of tensile tests and differential scanning calorimetry (DSC). In comparison to the thermal curing method, the laminate can be prepared more effectively by means of microwave curing method, and the laminate with [90/90/90] fiber orientation and three fiber layers showed the optimal static mechanical performance and the highest curing degree due to the synergistic effect of dipolar induced effect and heating effect generated by microwave, which was in well agreement with the results of numerical simulation.

Modeling guided wave propagation in multi-layered anisotropic composite laminates by state-vector formalism and the Legendre polynomials

This research presents a numerical method to analyze the propagation characteristics of guided waves in multi-layered anisotropic composite laminates. The dispersion equations were derived theoretically, while the displacement and stress components of each layer are expressed in the form of state vectors, by combining the state-vector formalism and the Legendre polynomials (SVF-LP). The displacement fields are fitted approximately by Legendre polynomials, and the system of linear equations are constructed by the orthogonal projection. The eigenvalue/eigenvector solution is established to compute the phase dispersion curves instead of solving the transcendental dispersion equations. This overcomes the problem of missing roots in traditional matrix method effectively. In order to verify the robustness of the SVF-LP, three cases of multi-layered laminates, formed by isotropic material, unidirectional carbon-fiber epoxy prepreg and fiber-metal laminate (GLARE 3-3/2) are investigated, respectively. The influences of fiber angle change and the stacking sequence are primarily analyzed, on the dispersion characteristics and the displacement and stress profiles. The matrix method is also carried out to compare the accuracy of this proposed method, which is done by the commercial software Disperse. Finally, the displacement and stress profiles of fundamental modes of the guided waves in an arbitrary lay-up quasi-isotropic plate at a given frequency is discussed in details.

Effect of hybridisation in laminated composites on the first ply failure behaviour: Experimental and numerical studies

First ply failure analysis of hybrid laminated plate panels subjected to transversely applied static load is carried out and presented in this article. Hybrid laminates are fabricated in the laboratory as a combination of carbon and glass fabrics along with epoxy resin for this purpose. Strength and elastic properties of epoxy based laminates with carbon fibre (CFRP) and glass fibre (GFRP) are determined experimentally according to ASTM standard. Various multilayered hybrid laminates (HFRP) and GFRP laminates having all edges fixed boundary condition are tested under transverse static load. An improved eight noded quadratic isoparametric plate bending element based on refined higher order zigzag theory (HRZT) has been developed in the present study to evaluate the interlaminar stresses of multilayered composite laminates. The warping function has been considered in the displacement field to formulate a C° continuous plate bending element. The transverse shear stresses are computed in a simplified manner using the three dimensional differential equations of stress equilibrium. The first ply failure load is determined within linear and elastic range. The correctness and competence of the present finite element model is verified by comparing the solutions with relevant published data and also experimental outcome. The comparison between HFRP and GFRP laminates in terms of failure load has been made to identify the effectiveness of hybridisation.