Composite panels containing multiple through-the-width delaminations and subjected to compression. Part I: Analysis

An analytical and experimental investigation was performed to study the compression response of laminated composite panels containing multiple through-the-width delaminations. Both flat and cylindrical panels were considered. The major objective of the study was to develop an analytical model for simulating the deformations of the laminated panels from initial loading to final collapse. The model consists of three parts: a stress analysis, a contact analysis, and a failure analysis. A nonlinear finite element code was developed based on the model. Extensive experimental work on T300/976 composites was also conducted during the investigation to verify the model and the numerical calculations.

The results of the study will be presented in two parts: I — Analysis and II — Experiments. In this paper, the development of the analytical model, the implementation of the model into the finite element code, and comparisons between the calculations based on the model and the existing analytical and experimental results will be presented. The experiments performed during the investigation, and the comparisons between the calculations and the test data will be given in the second paper.     

Post-buckling behaviour of thermoplastic matrix composite laminates subjected to pure shear

The present study focuses on the determination of the buckling load and post-buckling behaviour of simply supported laminated composite rectangular panels loaded in shear. The nonlinear structural response is studied with a non-linear finite element approach. In order to determine the accuracy of the procedure, several tests have been performed comparing the finite element solutions for isotropic and laminated composite rectangular panels with existing ones, adopting different sequences of lamination and different length to width ratios. The analysis then considers the behaviour of laminates produced with innovative thermoplastic matrix composites developed in the frame of a national research program.     

Modelling delaminations in postbuckling stiffened composite shear panels

 A method has been developed to predict the effect of delaminations in a postbuckling stiffened structure manufactured from laminated composite materials. The emphasis of the technique, driven by aircraft certification requirements, was towards establishing whether delamination growth would initiate under given loading conditions. A geometric nonlinear finite element analysis was used to calculate the strain energy release rate around the circumference of a circular delamination using the virtual crack closure technique. In order to deal with the complex structural response in a computationally efficient manner, the structure was modelled using plate elements with two layers of plate elements used in the delaminated region. The effect of delamination size on the strength of postbuckling panels was shown to be a complex phenomenon in which trends were difficult to predict. Large delaminations could significantly affect the global and sub-laminate buckling modes and therefore be less critical than smaller delaminations. It was concluded that the method could accurately predict the load and location at which delamination growth would initiate, given suitable critical strain energy release rate data. Received 16 February 2000     

Damage prediction in composite sandwich panels subjected to low-velocity impact

The paper illustrates the application of a finite element tool for simulating the structural and damage response of foam-based sandwich composites subjected to low-velocity impact. Onset and growth of typical damage modes occurring in the composite skins, such as fibre fracture, matrix cracking and delaminations, were simulated by the use of three-dimensional damage models (for intralaminar damage) and interfacial cohesive laws (for interlaminar damage). The nonlinear behaviour of the foam core was simulated by a crushable foam plasticity model. The FE results were compared with experimental data acquired by impact testing on sandwich panels consisting of carbon/epoxy facesheets bonded to a PVC foam. Good agreement was obtained between predictions and experiments in terms of force histories, force–displacement curves and dissipated energy. The proposed model was also capable of simulating correctly nature and size of impact damage, and of capturing the key features of individual delaminations at different depth locations.     

Numerical characterization of compressive response and damage evolution in laminated plates containing a cutout

A micromechanical constitutive model [Liang Z, Lee HK, Suaris W. Micromechanics-based constitutive modeling for unidirectional laminated composites. Int J Solid Struct 2006;43:5674–89], based on the concept of the ensemble-volume average for laminated composites, is implemented into a finite element program to numerically characterize the compressive response and damage evolution in laminated plates containing a cutout. Prior to the implementation of the model into the finite element program, the predicted moduli of laminated composites are compared with analytical bounds and experimental data for the validation and verification of the constitutive model. A series of numerical simulations for a uniaxial test of laminated plate specimens containing a cutout are conducted using the implemented constitutive model. The predictions are compared with experimental data [Lessard LB, Chang FK. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part II-Experiment. J Compos Mater 1991;25:44–64; Chang FK, Lessard LB. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part I-Analysis. J Compos Mater 1991;25:2–43] to verify the accuracy of the implemented constitutive model. A parametric study is also carried out to illustrate the influence of the geometry of the specimens on the behavior of laminated plates. It is shown that the implemented constitutive model is suitable for the analysis of the constitutive behavior of laminated plates having a dilute or moderate fiber volume fraction.     

Interlaminar stresses in laminated composite plates, cylindrical/spherical shell panels damaged by low-velocity impact

Prediction of damage caused by low-velocity impact in laminated composite plate cylindrical/spherical shell panels is an important problem faced by designers using composites. Not only the in-plane stresses but also the interlaminar normal and shear stresses play a role in estimating the damage caused. The work reported here is an effort in getting better predictions of damage in composite plate cylindrical/spherical shell panels subjected to low-velocity impact.

The low-velocity impact problem is treated as a quasi-static problem. First, the in-plane stresses are calculated by 2-D nonlinear finite element analysis using a 48 degrees of freedom laminated composite shell element. The damage analysis is then carried out using a Tsai-Wu quadratic failure criterion and a maximum stress criteria. Interlaminar normal and shear stresses are predicted after taking into account the in-plane damage caused by low-velocity impact. The interlaminar stresses are obtained by integrating the 3-D equations of equilibrium through the thickness. The deformed geometry is taken into account in the third equation of equilibrium (in the thickness direction). After evaluating the formulation and the computer program developed for correctness, the interlaminar stresses are predicted for composite plates/shell panels which are damaged by low-velocity impact.     

Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites

The reliability of impact simulations for aircraft components made with triaxial braided carbon fiber composites is currently limited by inadequate material property data and lack of validated material models for analysis. Methods to characterize the material properties used in the analytical models from a systematically obtained set of test data are also lacking. A macroscopic finite element based analytical model to analyze the impact response of these materials has been developed. The stiffness and strength properties utilized in the material model are obtained from a set of quasi-static in-plane tension, compression and shear coupon level tests. Full-field optical strain measurement techniques are applied in the testing, and the results are used to help in characterizing the model. The unit cell of the braided composite is modeled as a series of shell elements, where each element is modeled as a laminated composite. The braided architecture can thus be approximated within the analytical model. The transient dynamic finite element code LS-DYNA is utilized to conduct the finite element simulations, and an internal LS-DYNA constitutive model is utilized in the analysis. Methods to obtain the stiffness and strength properties required by the constitutive model from the available test data are developed. Simulations of quasi-static coupon tests and impact tests of a represented braided composite are conducted. Overall, the developed method shows promise, but improvements that are needed in test and analysis methods for better predictive capability are examined.     

Active damping of laminated thin cylindrical composite panels using vertically/obliquely reinforced 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite panels using vertically and obliquely reinforced 1–3 piezoelectric composite materials as the material of the constraining layer of the ACLD treatment. A finite element model has been developed for analyzing the ACLD of laminated antisymmetric cross-ply and antisymmetric angle-ply thin composite panels integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. The analysis revealed that the vertically reinforced 1–3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart thin composite panels.     

Finite element micromechanical modelling of unidirectional fibre-reinforced metal-matrix composites

Typical finite element formulations and models for unidirectional composite materials are reviewed. The application of micromechanical finite element analysis to the modelling of unidirectional fibre-reinforced metal-matrix composites is demonstrated by presenting some studies from recent publications. It is shown that while analytical models offer a simple tool for obtaining the overall response of composites, finite element analysis provides more accurate and detailed characterisation of composite properties for complicated geometries and constituent property variations. Various effects that influence the stress/strain response and fibre/matrix deformation of composites are studied through modelling. These effects include the fibre coating and reaction layer, fibre shape and distribution, metallurgical and environmental factors, stress distributions and damage. It is demonstrated that the properties and constituent phase interaction of metal-matrix composites are best modelled by finite element analysis. It is emphasized that in order to obtain good predictions, the models must be coupled with first-hand characterisations of the constituent phases and their interactions, including the thermal history of the specimens.     

Application of DQM as an effective simulation tool for buckling response of delaminated composite plates

The application of differential quadrature method (DQM), as an effective and robust numerical method, for the analysis of buckling of delaminated composite plates is introduced. The analysis investigated the response of laminated composite plates hosting a circular or an elliptical delamination. The delaminations were assumed to be fairly thinner than the plate hosting them, and thus, they could be treated as plates with clamped edges. Several case studies were used to verify the integrity of DQM in predicting the buckling strain of the plates. The investigation included the examination of several parameters influencing the buckling strength. The results obtained from DQM were compared with those obtained by the Rayleigh–Ritz and finite element solutions of other workers.     

The effects of three-dimensional states of stress on damping of laminated composites

A three-dimensional finite element method is developed for the characterization of the effects of three-dimensional states of stress on the damping of laminated composites. The calculation of laminate damping is performed by the use of a strain energy method and the damping properties of the individual laminae. Particular attention is paid to the effects of interlaminar stresses on laminate damping. These effects are studied by varying the fiber orientation and the laminate width-to-thickness ratio. The predicted damping and natural frequency data from the finite element analysis are compared with experimental results obtained from an impulse-frequency response technique. This study shows that the three-dimensional finite element method is a powerful technique for the determination of damping of laminated composites, and that it provides considerable potential for full three-dimensional characterization in more complex structures and loading situations.     

Constitutive description of Bulk Metallic Glass composites at high homologous temperatures

Experimental stress–strain responses of La-based in situ Bulk Metallic Glass (BMG) composites within the supercooled liquid region reveal initial post-yield hardening, followed by softening and subsequent strain-hardening. This behavior contrasts with that of monolithic La-based BMGs, which reach a steady stress level after an initial overshoot. XRD analysis of BMG composites shows the formation of intermetallic compounds during compressive deformation. These intermetallic compound formation/interactions are associated with storage of energy in the material and affect the stress–strain response. In this study, an elastic–viscoplastic, three-dimensional, finite deformation constitutive model is also established to describe the behavior of a recently developed La-based in situ BMG (La–Al–Cu–Ni) composite, within the supercooled liquid region, at ambient pressure and a range of strain rates. The constitutive model is incorporated into a finite element program (ABAQUS/Explicit) via a user-defined material subroutine. Numerical predictions are compared with compression test results on BMG composites cast in-house. The comparison shows that the model is able to describe the material behavior observed.     

Progressive failure and ultimate collapse of laminated composite plates in bending

A method is presented to study the non-linear behaviour, first ply failure and ultimate collapse of laminated composite plates with clamped edges, subjected to transverse pressure. Several failure criteria, including Hashin's and Tsai-Wu's, are used to predict the failure mechanisms. The effect of aspect ratio on the strength and stiffness of laminated composite plates is studied. Non-linear strain-displacement relations that contain large strain and large rotation are used in the analysis. The general purpose finite element program ABAQUS is used for the analysis. The stiffness reduction is carried out at the Gauss points of the finite element mesh depending on the mode of failure. The predictions of the model correlate well with experimental data for different aspect ratios.     

Buckling analysis for delaminated composites using plate bending elements based on higher‐order zig‐zag theory

A finite element based on the efficient higher‐order zig‐zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig‐zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig‐zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher‐order zig‐zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three‐dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd.     

Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually.     

Weight optimal design of lateral wing upper covers made of composite materials

The present investigation is devoted to the development of a new optimal design of lateral wing upper covers made of advanced composite materials, with special emphasis on closer conformity of the developed finite element analysis and operational requirements for aircraft wing panels. In the first stage, 24 weight optimization problems based on linear buckling analysis were solved for the laminated composite panels with three types of stiffener, two stiffener pitches and four load levels, taking into account manufacturing, reparability and damage tolerance requirements. In the second stage, a composite panel with the best weight/design performance from the previous study was verified by nonlinear buckling analysis and optimization to investigate the effect of shear and fuel pressure on the performance of stiffened panels, and their behaviour under skin post-buckling. Three rib-bay laminated composite panels with T-, I- and HAT-stiffeners were modelled with ANSYS, NASTRAN and ABAQUS finite element codes to study their buckling behaviour as a function of skin and stiffener lay-ups, stiffener height, stiffener top and root width. Owing to the large dimension of numerical problems to be solved, an optimization methodology was developed employing the method of experimental design and response surface technique. Optimal results obtained in terms of cross-sectional areas were verified successfully using ANSYS and ABAQUS shared-node models and a NASTRAN rigid-linked model, and were used later to estimate the weight of the Advanced Low Cost Aircraft Structures (ALCAS) lateral wing upper cover.     

Embedded delamination growth in composite panels under compressive load

In this paper, crack growth analyses on composite panels containing embedded delaminations has been performed using a geometrically non linear FEM code, based on the total Lagrangian formulation. The code has been improved with an effective virtual crack closure technique to evaluate energy release rate and with penalty method to evaluate contact forces. Validation of the proposed tool has been performed with experimental and numerical data available in the literature for double cantilever beam (DCB) specimens. Finally, the influence of the geometrical parameters of the delamination (size and location along the thickness) on the energy release rate distribution and delamination growth stability in composite panels under compression has been analyzed.     

Delamination modeling in doubly curved laminated shells for free vibration analysis using zigzag theory-based facet shell element and hybrid continuity method

We present a finite element (FE) formulation for the free vibration analysis of doubly curved laminated composite and sandwich shells having multiple delaminations, employing a facet shell element based on the efficient third-order zigzag theory and the region approach of modeling delaminations. The methodology, hitherto not attempted, is general for delaminations occurring at multiple interfacial and spatial locations. A recently developed hybrid method is used for satisfying the continuity of the nonlinear layerwise displacement field at the delamination fronts. The formulation is shown to yield very accurate results with reference to full-field three-dimensional FE solutions, for the natural frequencies and mode shapes of delaminated shallow and deep, composite and highly inhomogeneous soft-core sandwich shells of different geometries and boundary conditions, with a significant computational advantage. The accuracy is sensitive to the continuity method used at the delamination fronts, the usual point continuity method yielding rather poor accuracy, and the proposed hybrid method giving the best accuracy. Such efficient modeling of laminated shells with delamination damage will be of immense use for model-based techniques for structural health monitoring of laminated shell-type structures.     

The effects of geometric parameters on the failure strength for pin-loaded multi-directional fiber-glass reinforced epoxy laminate

A numerical and experimental study was carried out to determine the failure of mechanically fastened fiber-reinforced laminated composite joints. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties and strengths of the composite were obtained experimentally. Tests have been carried out on single pinned joints in [0/90/0]_s and [90/0/90]_s laminated composites. A parametric study considering geometries was performed to identify the failure characteristics of the pin-loaded laminated composite. Data obtained from pin-loaded laminate tests were compared with the ones calculated from a finite element model (PDNLPIN computer code). Damage accumulations in the laminates were evaluated by using Hashin's failure criteria combined with the proposed property degradation model. Based on the results, ply orientation and geometries of composites could be crucial for pinned laminated composite joints.