Laminate Model Research Articles

Transient vibration and sound radiation analysis of simply supported functionally graded sandwich plates

Vibroacoustic response of simply supported functionally graded sandwich plates under transient loading is reported in this work. Simply supported square sandwich plate configurations of different thickness ratios and material property gradation in the core and face sheet are analyzed. The effective material properties of the sandwich plate are derived by considering an approximate laminate model where the Poisson’s ratio of the constituents of the sandwich are assumed to be constant and the plate kinematics is modelled using the first-order shear deformation theory. The structural system matrices of the functionally graded sandwich plate and plate deformations are computed using the finite element method. The time history of the structural response is obtained using the Newmark Beta time marching scheme. The radiated acoustic pressure in the far-field is determined using the time domain Rayleigh integral that is solved numerically by an elementary radiator approach. A detailed parametric study investigates the influence of the volume fraction index and thickness ratio on the transient vibroacoustic response of several sandwich configurations.

Behaviors of Composite Laminates Under Low-Energy Impact Using a Novel Analytical Framework

Carbon fiber-reinforced polymer (CFRP) composite laminates have the characteristics of orthogonal anisotropy and heterogeneity, so the failure mechanism under low-energy impact is very complex. As a supplement to the experiment, it is necessary to develop numerical tools to predict the mechanical behavior of composite laminates under low-energy impact. In this paper, the mechanical behavior analysis framework of composite laminates under low-energy impact load is established by using the micromechanics of failure (MMF) theory and the mixed mode exponential cohesive zone model (CZM). The failure modes of intralaminar components in composite laminates are determined by MMF theory. The damage onset and evolution process of interlaminar delamination is described by the mixed mode exponential CZM. The finite element model of composite laminates under low-energy impact is developed using the Python scripts on ABAQUS/Explicit platform. The user-defined material subroutine VUMAT is written in Fortran language. The impact responses of composite laminates with several impact energies are predicted. The intralaminar failure modes and interlaminar delamination behavior are discussed in detail. The results show that the tensile failure of matrix and interlaminar shear delamination failure are the main failure modes of composite laminates under low-energy impact load. The experimental results present better consistency with the numerical analysis, indicating that the constructed multiscale analysis method is efficient and accurate. This study expands the analysis method of mechanical behavior of composite laminates under low-energy impact. The constructed mixed mode exponential CZM also has guiding significance for the failure analysis of other bonding materials.

Numerical Investigation of the Dynamic Responses of Fibre-Reinforced Polymer Composite Bridge Beam Subjected to Moving Vehicle.

In modern industry, heavy traditional materials are being substituted with light and strong fibre-reinforced polymer composite materials. Bridges and railroads made of composite laminates are considerably affected by traffic loads. Therefore, it is very important to analyse this effect which would find practical applications in engineering designs. This paper explains the theoretical formulation that governs the dynamic response of a composite beam subjected to a moving load. The governing equations for the dynamic effect on the laminated composite bridge beam are explained here. The main theories in the micro–macro modelling of composite laminates are also described in the paper. Within the macro modelling, the Classical Laminate and Shear Deformation Laminate Theory of beams are presented. The symmetric cross-ply laminated bridge, made of boron/epoxy is under consideration. The computational two-dimensional model of the vehicle is adopted. The governing equations for the dynamic effect on the laminated composite bridge beam are explained. The calculation of the time response of the bridge for the characteristic speeds of the vehicle is performed in the environment of the MATLAB software. The maximum dynamic magnification factor for the dynamic analysis of a composite beam is found.

A novel estimation method for fitting fatigue data in the composite wearout model

S-N curves are used in the design of composite structures to estimate their fatigue behaviour. In this work, an empirical fatigue model has been developed based on one first proposed by Sendeckyj. To reduce the complexity of the nonlinear optimization in the Sendeckyj wearout model, a new constraint is derived based on the material S-N fatigue curve and a mathematical curve fitting. To improve the Sendeckyj model’s accuracy in all fatigue regions, a novel estimation method is used. In this method, an exponential model is used to determine the Sendeckyj model parameter for the low cycle fatigue region and a power-law model is used to determine the Sendeckyj model parameter for the high cycle fatigue region. The new model was compared against the original Sendeckyj model for glass fibre laminates with various polymer resins. The novel wearout method leads to more accurate parameters and more accurate S-N curve.

A robust and automated method for geometric modelling of thick laminates with multiple and asymmetric ply wrinkles

Ply wrinkles are often found in thick laminates and they are known to be a major failure cause of composite structures. To assess the criticality of the ply wrinkles accurately and efficiently, the complex wrinkle geometries - which are commonly simplified as a single sinusoidal, Gaussian or combined function, should be described precisely and preferably in an automated manner. This study presents a robust method for automated geometric reconstruction and finite element meshing of entire thick laminates with multiple, asymmetric out-of-plane ply wrinkles. We extract coordinate information of each data point along the plies from inspection images, subsequently, multiple Gaussian functions are used to best fit the complex wrinkle geometry. To reconstruct the entire laminate, we interpolate ply geometries of the intermediate layers based on the fitted layers. Finite element models of thick laminates with the concerned ply wrinkles are subsequently generated and analysed to assess structural criticality. The entire procedure is automatised and is implemented in MATLAB codes. The demonstration studies show the robustness and efficiency of the proposed method which can contribute to closing the gap between non-destructive testing and criticality assessment of thick laminates with ply wrinkles.

Research on buckling characteristics and placement processability of variable stiffness open-hole laminates

For variable stiffness open-hole laminates, the buckling characteristics and the placement processability are studied. In this study, the fiber reference path was defined by a linear variable angle function to generate variable stiffness laminates, and the grid density influence on the simulation results was explored. In order to improve the accuracy of the finite element model, a new open-hole laminate modeling method was proposed based on the Python language, and its accuracy of the analysis results and the fiber angle definition were investigated. Compared with classical open-hole laminates with constant stiffness, the buckling characteristics of open-hole laminates with variable stiffness under different placement paths were analyzed. In order to study the influence of the overlap and the gap ratio between the tows on the buckling performance of the laminates, the placement processability (defects of overlap and gap) was considered, and the fiber angle range without tow wrinkles was given. An open-hole laminates with a layer structure of [<0|±45>]2 s is taken as the example to show the distribution of fiber angles, overlaps and gaps. The results indicated that under ideal conditions, the buckling characteristics of most variable stiffness open-hole laminates are better than those of the constant stiffness open-hole laminates, and considering the placement processability of the laminates, the first-order buckling load of the laminates is positively correlated with the proportion of the overlap area, and when the overlap ratio is 50%, the stiffness of the laminates is the largest.

Effect of drilling-induced defects on progressive damage of open-hole composite laminates under compression

In this study, the effect of drilling-induced defects on open-hole compression progressive failure and buckling and post-buckling behavior of composite laminates was investigated numerically. First, drilling-induced defects were identified from X-ray computed tomography data using image processing software, from which delamination and fiber pull-out defects were quantified on the specimen. These defects were then incorporated into finite element mesh, and numerical analyses simulating ASTM open-hole compression tests were performed in Abaqus. Hashin failure criterion and energy-based linear softening law were employed to determine in-plane failure initiation and evolution. Interlaminar failure was accounted for by cohesive zone modelling inserting cohesive elements at delaminated interfaces. The numerical model with defects was validated against experimental results and very good agreement was obtained. Next, simulations were performed on both defect-free and defective open-hole composite laminate models to study the effect of drilling-induced defects on compressive strength and progressive failure behavior. Finally, analyses were performed with buckling deformation allowed and the effect of buckling and post-buckling on compression failure behavior was investigated.

Effects of planimetric position of delamination on compressive failure of composite laminates

Delamination is the main defect form of composite laminates. The strength and stiffness of composite laminates are greatly decreased due to delamination defects. In this paper, the FE model of composite laminates with delamination was established. And the nonlinear post-buckling response of composite laminates was investigated. The validity of the FE model was verified by comparing the analysis results with the experimental results. And a detailed parametric study was performed on the effects of planimetric position on the post-buckling behavior of laminates. Results show that the buckling mode does not depend on the planimetric position of the delamination; the closer the delamination is to the center, the greater the reduction of compressive strength.

Synthesis and characterization of fabricated fiber metal laminates for aerospace applications

The necessity for high-performance, lightweight materials in the aerospace sector has sparked a significant trend toward the formulation of sophisticated models for fiber-metal laminates during the last few decades. The fiber metal laminates are hybrid composite materials consisting of layers of thin metals and fibers in different orientation sequences. Generally, the composites are placed on top or sometimes both on top and bottom of the metal alloys (especially Al or Ti alloys). In the present study, Carbon fiber reinforced Aluminium sandwich composite laminates are fabricated in a traditional way i.e., compression molding method. The fabricated laminates are examined for assessment of the properties such as tensile, flexural, and impact strength for more usage in engineering applications. The assessments are accomplished under the ASTM standards. Scanning Electron Microscope (SEM) analysis is used to analyze the failure of the fabricated sandwich laminates. The microstructures of tested specimens evidently specify the fractured surface.

Establishment of Pollutant Concentration Model for Laminate Flooring Based on the Coupling Effects of Time and Temperature

Modern people are entering the third period of pollution, marked by indoor air pollution. The aim of this paper is to investigate the relationship between decorative materials and the pollution concentrations of typical indoor pollutants such as HCHO, C6H6 and VOC, using a combination of qualitative and quantitative methods. The environmental test chamber method is used to carry out the experimental measurement of the laminate flooring, and the numerical analysis is carried out according to the test release concentration and environmental parameters. The Levenberg-Marquardt optimization algorithm was selected to develop a first-order exponential (ExpDec1) mathematical model based on the concentrations of HCHO, C6H6 and VOC released from laminate flooring at different temperatures. The results show that the model predicts the characteristics of HCHO, C6H6 and VOC concentrations with time and temperature and there is a positive correlation between environmental parameters and release concentration, with correlation coefficients of 0.993, 0.925, 0.856, 0.992, 0.906 and 0.879 between measured and predicted values, and slopes of regression lines of 0.993, 0.932, 0.872, 0.994, 0.916 and 0.893. There is good consistency between measured and predicted values. The model provides a necessary basis for in-depth study of this issue and a solid evidence foundation for air quality.

Micromechanical study of the Scale Effect on composite material laminates

From the beginning of the application of composite materials, different theories to predict their behaviour and failure have been developed. The authors have already made a previous study, analyzing at the macroscopic level (both from an experimental and theoretical point of view), the failure of non-conventional laminates changing the thickness of the laminas that form it, in order to evaluate the &ldquo;scale effect&rdquo; (also known as &ldquo;in-situ strength&rdquo;) present in them. Results of this study proved the strength variation of the laminate with its configuration (scale effect) and it was found that the presence of laminas with fibres oriented in the direction of the load diminishes this effect. This paper is focused on the understanding of the aforementioned effect, conducting a study at &nbsp;micromechanical level (the level where the damages leading to the failure are generated) of the scale effect with an energetic approach, in order to progress in the understanding of this phenomenom. To this end, the Boundary Element Method (BEM) has been used. It has been applied to a laminate model with [0, 90n]S stacking sequence, where the influence of n at different stages of the generation and progression of damage has been studied: the beginning of the damage (that takes place when the debonding between fibre and matrix happens) and during the change of direction of the debonding crack towards the matrix (kinking). The models developed are multiscale, involving a mesoscale representation of the laminas of the laminates (modelled as homogeneous) and with micromechanics cells that simulate fibre and matrix and therefore with the capacity for collecting information about damage mechanisms observed experimentally.

On a phase‐field model of damage for hybrid laminates with cohesive interface

In this paper, we investigate a rate‐independent model for hybrid laminates described by a damage phase‐field approach on two layers coupled with a cohesive law governing the behaviour of their interface in a one‐dimensional set‐up. For the analysis, we adopt the notion of energetic evolution, based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading–unloading regimes is illustrated. The argument is based on time regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.

Hail ice impact simulation and damage response analysis in composite laminates

Hail ice impact and the induced damage are a real threat to the exposed composite laminates in the aircraft structures. In the present work, a nonlinear finite element (FE) model is proposed to investigate the mechanical behavior of carbon fiber reinforced plastic (CFRP) laminates under hail ice impact. Lagrangian FE and smooth particle hydrodynamics method (FE-SPH) is comprehensively applied to reproduce the impact behavior of hail ice and the equation of state (EoS) for liquid is introduced to describe the flow characteristics of hail failure. A rate-dependent constitutive model is adopted to identify the intra-laminar response of laminates and a bilinear cohesive zone model is used for modeling delamination of interface. A subroutine VUMAT is coded and executed to attain the numerical solution based on ABAQUS/Explicit solver. The transient dynamic process of CFRP laminates subjected to hail impact is replicated in detail. The failure threshold velocity (FTV) model and damage characteristics of CFRP laminates under different impact conditions are investigated thoroughly. The numerical results are mostly consistent with the available experimental data thus validates the effectiveness of the proposed hail ice impact model.

A material property degradation model of composite laminates considering stress level

Conventional phenomenological models of composite laminates often require a large amount of experimental data due to the dependence on stress level. In this study, a new generalized model capable of predicting the material property degradation at each stress level using a single set of parameters is proposed to dramatically subside the experimental cost. Furthermore, two sets of residual strength data and one set of residual stiffness data are adopted to validate the proposed model. The results show that the new model is capable of predicting both residual strength and stiffness at arbitrary stress levels using single set of model parameters.

Simulation of bridging mechanisms in complex laminates using a hybrid PF-CZM method

Delamination and cracking of matrix/fiber is a common failure phenomena reported in fiber reinforced composite materials. As complex stress states develop in laminated structures, they are prone to develop fracture phenomena. Therefore, designs with large damage tolerance are currently implemented in most of the industrial sectors. This can be achieved by designing such materials with superior fracture resistance, which requires a comprehensive understanding of failure mechanisms. Cohesive Zone Models (CZM) are a popular technique to study debonding and decohesion in composite structures. Furthermore, due to the accurate simulation of complex crack paths including crack branching, the Phase Field (PF) approach has gained notable relevance in fracture studies, including the interplay between debonding and crack propagation in the matrix. In order to get a further insight into these intricate scenarios, involving bridging mechanisms in intralayer and interlayer, crack simulation coupling the phase field approach and the cohesive zone model is herein exploited for identifying crack migration through material layers. The crack paths and the related force–displacement curves of 2D multilayered material models of complex laminates are predicted and compared.

Angle‐ply orientation‐dependent failure behaviors of carbon fiber reinforced polymer laminates

AbstractThis paper researches the micro‐failure behaviors of carbon fiber reinforced polymer (CFRP) laminates with different angle‐ply orientations subjected to tensile load. On the basis of the strain rates of 2.6 × 10−6 s−1 and 2.6 × 10−3 s−1, the significant difference in deformation behaviors of CFRP laminates with different angle‐ply orientations are investigated by using a miniature tensile tester. The scanning electron microscopy images are used to assess fracture damage modes of CFRP laminates, including matrix cracking, delamination, fiber‐matrix debonding, and fiber fracture, determined the “high‐low‐high” trend of the strength of laminates with the increase of ply angle. In order to analyze the crack propagation mechanism of laminates attributed to matrix micro‐crack under uniaxial tensile load, two wide applicable micro‐crack propagation models of laminates are proposed to explain the fracture damage failure behaviors of CFRP laminates with different angle‐ply orientations.

Topology optimization of laminated composite structures under harmonic force excitations

In this paper, a topology optimization approach for the design of laminated composite structures under harmonic force excitations is proposed. A novel method is developed to calculate the harmonic response for composite laminates, which consists of two steps: firstly, based on the strain energy approach, the damping matrix model of composite laminates is established with the proportional damping assumption; then, the displacement response is calculated by the mode acceleration method The design objective of topology optimization is to minimize the displacement amplitude at the concerning point with an excitation frequency or a frequency band. An extended polynomial interpolation scheme is introduced to penalize the stiffness, damped stiffness and mass of elements. The analytical sensitivities of the objective and constraint functions to the density variables are derived in detail, and the globally convergent method of moving asymptotes is used to solve the optimization problem. Numerical examples are performed to demonstrate the effectiveness and feasibility of the proposed topology optimization method in improving the dynamic performance of laminated composite structures. The influence rules of excitation frequency and layer sequence on topologic shape are also discussed.

Viscoelastic modeling and characterization of thin-ply composite laminates

Thin-ply composite laminates are promising materials for deployable spacecraft structures owing to their low mass and high folding curvature. However, the deployment force and the shape accuracy of the deployed configuration after a long duration of stowage is adversely affected by the inherent viscoelastic behavior of the polymer matrix. This paper presents a computational and experimental investigation into the effective viscoelastic response of thin-ply composite laminates made of woven carbon fabrics and an epoxy matrix intended for deployable spacecraft applications. A two-scale homogenization approach is utilized to model thin-ply composites as viscoelastic plates represented with relaxation ABD matrices. Micrographic analysis and relaxation tests are conducted to obtain the geometric and material characteristics that are incorporated into the model. The bending relaxation behavior is experimentally characterized using the recently developed column bending test methodology to compare against model predictions. The relaxation response is studied in two different orientations. The effects of ply phase arrangement, laminate thickness, fiber volume fraction, specimen width, and coordinate rotation are investigated.

Mechanical model and numerical simulation of composite laminates subjected to low velocity impact

A mechanical model of laminated plates subjected to low velocity impact is proposed in this paper. The model studies the attenuation of impactor velocity affected by air resistance, intra-laminar damage initiation based strain, intra-laminar damage evolution based on damage parameters and delamination damage. Based on this mechanical model and ABAQUS platform, the experiment of Shi is numerically simulated. It is found that the predicted contact force, energy absorption and delamination damage of laminates are in good agreement with the experimental results, indicating that the established mechanical model can be used to predict the mechanical response and damage characteristics of composite laminates subjected to low velocity impact.

Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure

As an effective and accurate method for modelling composite materials, mean-field homogenization is still not well studied in modelling non-linear and damage behaviours of UD composites. Investigated micro FE-simulations show that the matrix of UD composites exhibits different average plastic behaviour, named as average asymmetric matrix plasticity (AAMP), when the composite behaves different under shear, longitudinal and transverse loadings. In this study, a non-linear mean-field debonding model (NMFDM) combining a mean-field model and a fibre–matrix interface debonding model, is developed to simulate UD composites under consideration of AAMP, fibre–matrix interface damage and progressive failure. AAMP is considered by using so-called stress mode factor, which is expressed in terms of basic invariants of the matrix deviatoric stress tensor and is used as an indicator for detection of differences in the loading mode. The material behaviour of UD composites with imperfect interface is assumed identical as for perfect interface and stiffness reduced fibres. Progressive failure criteria are established with consideration of fibre breakage and matrix crack for different fibre orientations. As a representative example for the NMFDM, a C30/E201 UD composite is studied. To verify the model, experiments are conducted on polymers, carbon fibres and UD CFRPs. Finally, the model is applied to simulate a perforated CFRP laminate, which shows excellent prediction ability on deformation, debonding and progressive failure.