Composite Plies Research Articles

Explicit multiscale modelling of impact damage on laminated composites – Part II: Multiscale analyses

This work describes a multiscale impact damage prediction methodology for laminated composite structures which is based on the HFGMC micromechanical model and the MMCDM damage formulation. The numerical approach is intended for application within explicit finite element analyses and has been employed for modelling of high-velocity impact damage in laminated composite structures. Structural-scale applications and the multiscale framework of the method are presented in this paper whereas introduction and validation of the methodology have been presented in Part I of the paper.By applying the described method, the micromechanical model calculates the local stress/strain fields within the unidirectional composite material, whereas the structural-scale computations have been performed employing Abaqus/Explicit. The Mixed Mode Continuum Damage Mechanics (MMCDM) theory has been utilised as to model the damage and failure modes of the composite material at the micromechanical level. As demonstrated in the Part I paper, the HFGMC and MMCDM model enable modelling of the microdamage nonlinearities at in-plane shear and transverse compressive loading of the composite plies. The micromechanical damage modelling approach has been employed at high-velocity soft-body impact on CFRP and GFRP composite plates in this work. Results of the multiscale damage model have been validated using available experimental data and by comparison with the numerical results obtained using the commonly used ply-level failure criteria and damage models.

On plane stress and plane strain in classical lamination theory

Classical Lamination Theory combines the specially orthotropic nature of unidirectional composite plies with the assumptions of Kirchhoff plate theory to arrive at the in-plane properties of the laminate. Traditionally, the derivation assumes a plane stress state in each lamina prior to performing the rotational transformation from the lamina coordinates to the laminate coordinates, resulting in an incomplete formulation of the out-of-plane properties. In this work the rotational transformation of each lamina is performed prior to applying the plane stress or strain simplifications, resulting in an accurate formulation of the out-of-plane properties. Both plane stress and plane strain are considered. To illustrate the new formulation's ability to accurately predict out-of-plane properties, an optimization is performed to find laminates that exhibit the extrema of the out-of-plane Poisson's ratios. Verification of nearly optimal laminates with finite element analysis and experimental testing demonstrates improved accuracy of the new formulation.

Engineering method to build the composite structure ply database

In this paper, a new method to build a composite ply database with engineering design constraints is proposed. This method has two levels: the core stacking sequence design and the whole stacking sequence design. The core stacking sequences are obtained by the full permutation algorithm considering the ply ratio requirement and the dispersion character which characterizes the dispersion of ply angles. The whole stacking sequences are the combinations of the core stacking sequences. By excluding the ply sequences which do not meet the engineering requirements, the final ply database is obtained. One example with the constraints that the total layer number is 100 and the ply ratio is 30:60:10 is presented to validate the method. This method provides a new way to set up the ply database based on the engineering requirements without adopting intelligent optimization algorithms.

Cutting Mechanism of Drilling CFRP Laminates—Effect of Ultrasonic Torsional Mode Vibration Cutting

Cutting mechanism of drilling CFRP laminates and effects of ultrasonic torsional mode vibration cutting are investigated. CFRP laminates are made of carbon fiber reinforced/epoxy-resin matrix composite ply. Challenges in drilling CFRP laminates arise because of anisotropy due to carbon fiber orientation and heterogeneousness between carbon fiber and epoxy-resin. Experimental works are performed to characterize major hole quality parameters and cutting mechanism encountered when conventional drilling CFRP laminates. Some craters of about 100 μm depth are found at the particular position on inner surface of drilled hole and the mechanism for the crater to be generated is revealed based on cutting mechanism of both anisotropic and hheterogeneous composite material. In order to improve hole quality and tool life, the specific drilling assisted by ultrasonic torsional mode vibration of 27 kHz is examined. The ultrasonic torsional mode vibration cutting is considerably effective to restrain the generation of crater and also to elongate tool life about five times.

Structural Analysis of Composite Laminates using Analytical and Numerical Techniques

A laminated composite material consists of different layers of matrix and fibres. Its properties can vary a lot with each layer’s or ply’s orientation, material property and the number of layers itself. The present paper focuses on a novel approach of incorporating an analytical method to arrive at a preliminary ply layup order of a composite laminate, which acts as a feeder data for the further detailed analysis done on FEA tools. The equations used in our MATLAB are based on analytical study code and supply results that are remarkably close to the final optimized layup found through extensive FEA analysis with a high probabilistic degree. This reduces significant computing time and saves considerable FEA processing to obtain efficient results quickly. The result output by our method also provides the user with the conditions that predicts the successive failure sequence of the composite plies, a result option which is not even available in popular FEM tools. The predicted results are further verified by testing the laminates in the laboratory and the results are found in good agreement.

A unit circle failure criterion for carbon fiber reinforced polymer composites

A novel invariant-based approach to describe elastic properties and failure of composite plies and laminates has been recently proposed in the literature. An omni strain failure envelope has been defined as the minimum inner failure envelope in strain space, which describes the failure of a given composite material for all ply orientations. In this work, a unit circle is proposed as a strain normalized failure envelope for any carbon fiber reinforced polymer laminate. Based on this unit circle, a failure envelope can be generated from the longitudinal tensile and compressive strains-to-failure of a unidirectional ply. The calculated failure envelope was found in good agreement with experimental data published in the well-known World Wide Failure Exercise.

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

The higher-order, equivalent single-layer model developed in Part I is applied to the stretching and bending of exemplar multilayered flat plates, where the results are compared with different 3D models, and trends and insights are subsequently drawn. The present mixed displacement/stress-based model is derived from inherently equilibrated 3D stress fields that satisfy the interlaminar and surface traction equilibrium conditions. A new set of governing equations is derived from a contracted Hellinger–Reissner functional that only enforces the classical membrane and bending equations via Lagrange multipliers. Combined with the fact that the same set of stress resultants is used for all stress fields, the number of unknown variables of the theory reduces, while maintaining sufficient fidelity to capture higher-order transverse shearing and zig-zag effects. A wide range of stacking sequences are considered ranging from orthotropic straight-fibre laminates to sandwich panels with variable-stiffness face sheets, i.e. composite plies in which the reinforcing fibres describe curvilinear paths. Hence, the model is used to study laminated plates with 3D heterogeneity, that is laminates comprising layers with material properties that can differ by multiple orders of magnitude and that vary continuously in-plane. The governing equations are solved both analytically using trigonometric expansions and numerically using the pseudo-spectral differential quadrature method. The 3D stress fields predictions correlate closely with 3D elasticity and 3D finite element solutions and are accurate to within a few percent for thick plates with characteristic length to thickness ratios as small as 5:1. In fact, the results suggest that 3D stress fields from our model satisfy Cauchy’s 3D equilibrium equations more accurately, and at a three-order degree of freedom reduction in computational cost, compared to high-fidelity 3D FEM models.

A Three-Phase Shear-Lag Model for Longitudinal Cracking of a Ceramic Matrix Composite Ply With Thick Fiber Coatings

During progressive cracking of cross-ply ceramic matrix composites (CMCs), load is transferred from the fiber to the matrix in the longitudinal (0 deg) ply via shear through a compliant interphase layer, also referred to as the coating. In the material system of interest, this coating has significant thickness relative to the fiber diameter. The damage process in the cross-ply CMC is observed to be as follows: (1) elastic deformation, (2) cracking of the transverse plies, (3) matrix cracking within the longitudinal plies, (4) failure of longitudinal fibers, and (5) pullout of the cracked fibers from the matrix. In this paper, the focus is on the longitudinal (0 deg) ply. Existing shear-lag models do not fully represent either the stress transfer through the coating or the true accumulations of shear and normal stresses in the matrix. In the current study, a model is developed that takes into account both of these factors to provide a more accurate, analytical representation of the stress distribution and progressive damage accumulation in a longitudinal CMC ply.

EFFECT OF HYBRIDIZATION ON OPEN-HOLE TENSION PROPERTIES OF WOVEN KEVLAR/GLASS FIBER HYBRID COMPOSITE LAMINATES

Hybrid laminates consisting of woven Kevlar/glass fiber composite plies were studied in terms of their residual tensile strength, stiffness and fracture surface. Residual tensile strength and stiffness were determined from the open hole tension test according to ASTM D5766. The laminates of Kevlar fiber reinforced polymer (KFRP), glass fiber reinforced polymer (GFRP) and hybrid of Kevlar-glass fiber reinforced polymer (KGFRP) were fabricated using a vacuum bagging process. Three different ratios of Kevlar to glass fiber plies were prepared in this study which were 20:80, 50:50, and 80:20. Results showed that hybrid laminate consisting of 80:20 Kevlar to glass fiber plies, produced higher residual tensile strength and stiffness when compared to the other hybrid system. Furthermore, strength and stiffness of hole specimens were reduced within 50-63% when compared to unhole specimens due to existence of the hole. In addition, the effect of adding nanosilica to the hybrid system was also studied. 5 wt% of nanosilica was added to the hybrid composite laminates and results showed that higher tensile strength and stiffness was observed in GFRP and 20:80 KGFRP specimens, while the tensile strength was decreased with an increased number of Kevlar fiber. This research was conducted as there are limited number of studies that have been done on the tensile strength of woven hybrid composite laminates so far, especially on hybridization of Kevlar and glass fiber with consideration on the effect of hole and addition of nanofillers.

Multi-objective design optimization strategies for small-scale vertical-axis wind turbines

Extracting energy from wind has been an interesting and serious topic over the last few decades and a lot of work has been done on the subject. This paper discusses in detail possible approaches to optimization of a somewhat less known type of wind turbines, particularly suitable for small consumers. In order to perform full aerodynamic and structural shape optimization of a small-scale vertical-axis wind turbine, a Double-multiple streamtube model code, known to provide good results in stationary working regimes, was complemented by a finite element analysis and implemented into a multi-objective particle swarm algorithm. For the purpose of shortening the total time needed for aerodynamic computation, the performed numerical simulations were two-dimensional and experimentally measured static airfoil data were used. The used aerodynamic model was validated against the available experimental data of similar wind turbines. The subsequent structural analyses of the composite turbine blades were performed by applying computed maximal aerodynamic forces together with gravitational and inertial loads. By employing various input and output parameters different multi-objective optimization strategies were analyzed and compared and their applicability was demonstrated. Investigated input parameters included: wind turbine rotor diameter, blade length, chord and airfoil, composite shell thickness, laminate lay-up and ply orientations, while optimization goal functions and constraints comprised rated power, cut-in and optimal wind speed, blade mass, tip deflection, failure index and blade natural frequencies. The fidelity and accuracy of proposed methodologies can be increased by employing more complex numerical models which can easily be implemented into the code.

Characterization and modeling of the polymerization-dependent moisture absorption behavior of an epoxy-carbon fiber-reinforced composite material

The creation of defects (internal porosity) inside epoxy-based carbon fiber-reinforced composites during the curing process is well known to have a harmful impact on most of the mechanical properties of those materials. One of the main sources of void creation is the moisture absorption of the composite plies during the manufacturing process steps before the composite part cure. In order to get a better control of manufacturing, the moisture absorption behavior of a carbon-epoxy prepreg, which is submitted to a wet environment, is investigated. Moreover, the impact of the resin polymerization state on the water absorption behaviors of the plies will be highlighted. The moisture content is therefore measured as a function of time, temperature and relative humidity for uncured and for different partially polymerized materials. An original model was established in order to predict the moisture content in function of time, temperature, relative humidity and polymerization degree. As a major conclusion, it is demonstrated that the water coefficient of diffusion decreases when the polymerization degree increases.

Automated In-Process Inspection System for AFP Machines

In many existing AFP cells manual inspection of composite plies accounts for a large percentage of production time. Next generation AFP cells can require an even greater inspection burden. The industry is rapidly developing technologies to reduce inspection time and to replace manual inspection with automated solutions. Electroimpact is delivering a solution that integrates multiple technologies to combat inspection challenges. The approach integrates laser projectors, cameras, and laser profilometers in a comprehensive user interface that greatly reduces the burden on inspectors and decreases overall run time. This paper discusses the implementation of each technology and the user interface that ties the data together and presents it to the inspector.

The compressive response of ultra-high molecular weight polyethylene fibres and composites

Measurements are reported for the compressive response of ultra-high molecular weight polyethylene (UHMWPE) fibres and laminated composites loaded along the fibre direction. The compressive strength of the fibres was measured by both recoil tests and knot (or bend) tests. The strength of the fibres is governed by micro-kinking of the fibrils within the fibres. The recoil tests suggest that this kinking occurs at a compressive stress of approximately 340MPa. Consistent with observations of other fibres such as Kevlar and carbon fibres, the compressive strength inferred from bending tests is approximately a factor of two higher than that from a direct compression test, such as the recoil test. The in-plane compressive response of laminated UHMWPE composites was measured using notched specimens. Two grades of composites with shear strengths of about 1.5 and 0.5MPa were investigated and found to have compressive strengths of about 12MPa and 3MPa, respectively. Thus, unlike Kevlar composites, the composite compressive strength is not governed by the compressive strength of the fibres but by the micro-buckling of the composite plies. Detailed experimental measurements are reported for the kink-band width, fibre rotation within the band and its subsequent broadening after lock-up due to fibre rotation. These are shown to be adequately modelled by traditional kinking theory while a net section stress analysis models the propagation of the micro-buckle with sufficient fidelity.

Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO

This paper presents an output only damage diagnostic algorithm based on frequency response functions and the principal components for health monitoring of laminated composite structures. The principal components evaluated from frequency response data, are employed as dynamical invariants to handle the effects of operational/environmental variability on the dynamic response of the structure. Finite element models of a laminated composite beam and plate are used to generate vibration data for healthy and damaged structures. Three numerical examples include a laminated composite beam, cantilever plate made of carbon–epoxy and a laminated composite simply supported plate. Varied levels of delamination of laminated composite plies and matrix cracking at varied locations in the plies are simulated at different spatial locations of the structure. Numerical investigations have been carried out to identify the spatial location of damage using the proposed principal component analysis (PCA) based algorithm. In order to limit the number of sensors on the structure, an optimal sensor placement algorithm based on PCA is employed in the present work and the effectiveness of the proposed algorithm with a limited number of sensors is also investigated. Finally, the inverse problem associated with the detection of delamination and matrix cracking is formulated as an optimization problem and is solved using the newly developed dynamic quantum particle swarm optimization (DQPSO) algorithm. Studies carried out and presented in this paper clearly indicate that the proposed SHM scheme can robustly identify the instant of damage, spatial location, the extent of delamination and matrix cracking even with limited sensor measurements and also with noisy data.

A simplified micromechanics model for predicting the stiffness degradation in symmetric composite laminates

AbstractRecently, the authors of this paper have developed a new micromechanics approach to evaluate the stress fields and material properties of an orthotropic composite ply containing specified matrix cracking density under multi‐axial loading condition. In this study, more complementary details of approach are obtained, and a closed form solution for evaluating the stress fields and stiffness degradation of a damaged ply will be presented and applied for analysing several composite laminate with general symmetric lay‐ups. The obtained results will be compared with the available experimental results. The major advantage of the mentioned micromechanics approach is its capability for analysing an arbitrary composite ply containing specified matrix crack independent of its adjacent plies. This preference can be applied for bridging the proposed micromechanics model into the finite element analysis for progressive modelling of matrix cracking in general symmetric laminates with the least computational effort and the most accuracy.

A design of laminated composite plates using graded orthotropic fiber-reinforced composite plies

A new lamination scheme is proposed through the design of a graded orthotropic fiber-reinforced composite ply for achieving continuous variations of material properties along the thickness direction of laminated composite plates. First, a micro-structure of graded unidirectional fiber-reinforced composite ply is designed and its effective graded elastic properties are estimated using finite element procedure. Next, the new lamination scheme is demonstrated through the conversion of a conventional laminated composite plate (CLCP) into a conventional-graded laminated composite plate (CGLCP) utilizing presently designed graded orthotropic composite ply. The suitability of this conversion/proposed lamination scheme is substantiated through the bending analysis of both the plates (CLCP and CGLCP).

An efficient approach to the modeling of compressive transverse cracking in composite laminates

A wedge-shaped failure mechanism occurs when a composite ply in a laminate is loaded under transverse compression. Therefore failure models developed for tension are not straightforwardly applicable to compression. For models that represent matrix cracks as discontinuities, the inclined crack topology complicates algorithms considerably. In this paper, a method is introduced to approximate the behavior of inclined cracks while avoiding these complications. Rather than adapting the crack topology, a transformation is applied in the evaluation of the cohesive law. The method is applied on predefined interface elements in a 2D model, as well as on cohesive segments in the extended finite element method in a 3D model. It is found that the compressive failure of composite laminates including the wedge effect can be approximated accurately with this method using a vertical crack plane. In 3D, a variable fracture plane angle is taken into account with the method, which means that the whole range of failure modes, from tensile through shear-dominated to compressive failure can be covered in a single approach.

Analytical prediction of damage due to large mass impact on thin ply composites

This article presents analytical models for predicting large mass impact response and damage in thin-ply composite laminates. Existing models for large mass impact (quasi-static) response are presented and extended to account for damage phenomena observed in thin-ply composites. The most important addition is a set of criteria for initiation and growth of bending induced compressive fibre failure, which has been observed to be extensive in thin ply laminates, while it is rarely observed in conventional laminates. The model predictions are compared to results from previous tests on CFRP laminates with a plain weave made from thin spread tow bands. The experiments seem to confirm the model predictions, but also highlight the need to include the effects of widespread bending induced fibre failure into the structural model.

Parametric constitutive model of plain-weave fabric reinforced composite ply

A computational model that allows to explicitly determine orthotropic elastic constants of plain-weave fabric-reinforced composite ply as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic representative volume element is employed. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Advanced numerical modelling techniques for the structural design of composite tidal turbine blades

Tidal stream turbine blades must withstand both extreme one-off loads and severe fatigue loads during their 20–25 year required lifetimes in harsh marine environments. This necessitates the use of high-strength fibre reinforced composite materials to provide the required stiffness, strength and fatigue life, as well as resistance to corrosion, whilst minimising the mass of material required for blade construction and allowing its geometric form to provide the required hydrodynamic performance. Although composites provide superior performance to metals, potential failure mechanisms are more complicated and difficult to predict. A dominant failure mechanism is interfacial failure (delamination) between the composite layers (plies). This paper demonstrates how the development of numerical techniques for modelling the growth of interfacial cracks can aid the design process, allowing the effects on crack growth from potential manufacturing defects and the effect of stacking sequence of composite plies to be analysed. This can ultimately lead to reduced design safety margins and a reduction in the mass of material required for blade manufacture, essential for reducing lifecycle costs. Although the examples provided in this article are specific to tidal turbine blades, the analysis techniques are applicable to all composite structures where fatigue delamination is a primary failure concern.