Delamination detection in laminated composite beams using the empirical mode decomposition energy damage index

Fiber reinforced plastic composite (FRPC) beams have been widely used as effective stand-alone structural elements and/or reinforcing agents in various engineering applications. Such lightweight, stiff and strong structural elements may suffer, however, from inter-ply defects (referred to as delaminations), arising from various causes and factors. A delamination in such structural components could propagate into severely large damage zone, thus compromising the structural integrity. Therefore, detection of delamination at an early stage is of paramount importance.     

Thermal buckling behavior of composite laminated plates

Thermal buckling behavior of composite laminated plates was studied by making the use of finite element method. The thermal buckling mode shapes of cross-ply and angle-ply laminates with various E₁/E₂ ratios, aspect ratios, fiber angle, stacking sequence and boundary condition were studied in detail. The results indicate that the high E₁/E₂ and α₂/α₁ ratios of AS4/3501-6 and T 300/5208 laminates produce higher bending rigidity along the fiber direction and higher in-plane compressive force in a direction perpendicular to the fiber direction. Therefore, the higher thermal buckling mode shapes are formed. The thermal buckling mode that composite laminated plate will buckle into is mainly dependent on the E₁/E₂ ratio, α₂/α₁ ratio, fiber orientation and aspect ratio of the plate.     

Analysis of laminated composite beams using layerwise displacement theories

Within the displacement field of a layerwise theory, two laminated beam theories for beams with general lamination are developed. In the first theory, an existing layerwise laminated plate theory is adapted to laminated beams. The procedure used in the second theory is simple and straightforward and similar to the one used in the development of plate and shell theories. These theories can also be used in developing simpler theories such as classical, first, and higher-order shear deformation laminated beam theories. Equations of motions are obtained by using Hamilton’s principle. For the assessment of the accuracy of these theories, analytical solutions for static bending and free vibration are developed and compared with those of an existing three-dimensional elasticity solution of cross-ply laminates in cylindrical bending and with the three-dimensional finite element analysis for angle-ply laminates.     

Cohesive models for damage evolution in laminated composites

A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.     

Delamination damage analyses of adhesively bonded lap shear joints in laminated FRP composites

Three-dimensional non-linear finite ele- ment analyses have been carried out to evaluate the out-of-plane stresses in the adhesive layer existing between the lap and the strap adherends of the Lap Shear Joint (LSJ) in laminated FRP composites for varied delamination lengths. The delaminations are presumed to be pre-embedded in the thin resin rich layer existing between the first and second plies of the strap adherend. Sublaminate technique has been used to model the LSJ with the delamination. Contact finite element analyses have been performed in order to avoid interpenetration of delaminated surfaces. The effects of varied delamination lengths on the peel and interlaminar shear stresses and the individual modes of Energy Release Rate (ERR) in the delamination zones are highlighted in this paper. It is seen that three-dimensional effects exist near the free edges of the overlap end of the joint. The delamination propagation significantly affects the stress distributions in the adhesive layer existing between the lap and the strap adherends of the LSJ. The variations of interlaminar stresses and ERRs on both the delamination fronts are found to be significantly different and thus, indicate that the propagation of delamination does not occur at same rate at the two delamination fronts. This may throw some light to the evaluation of structural integrity of the LSJ in the presence of pre-embedded delaminations.     

Delamination detection in laminated composite beams using hybrid elements

This investigation pursues two goals. One of them is developing a three-dimensional finite element with an embedded interface for analyzing the laminated composite structure. The composite element efficiency is numerically proven. Delaminatoin is an important failure mechanism in certain types of composite structures. Detecting this type of damage is currently a problem of interest to the structural health monitoring community. The second goal of the paper is presenting a novel and well-organized procedure for the identification of delaminatoin in laminated composite beams. The damage identification scheme is formulated by an inverse problem, where analysis data from related finite element modeling, are used to quantify the magnitude and local of delaminatoin. The inverse problem is then transformed to an optimization statement, and the optimum delaminatoin parameters are found by minimizing the objective function. In this study, a genetic algorithm is used for the optimization process. Several numerical examples are analyzed for the accuracy test, and a few of them are presented here.     

A quantitative identification approach for delamination in laminated composite beams using digital damage fingerprints (DDFs)

Digital damage fingerprints (DDFs) are a set of optimised and digitised characteristics of structural signatures, which are able to exactly and uniquely define a certain kind of structural healthy status. The DDF-based damage recognition technique includes the extraction of DDFs, assembly of damage parameters database (DPD) and subsequently inverse recognition in virtue of artificial intelligence. In this study, DDFs extracted from Lamb wave signals were employed to quantitatively assess delamination in carbon fibre-reinforced laminated beams. Characteristics of Lamb wave signals in the laminated beams were first evaluated, and DPD hosting DDFs for selected damage scenarios was constructed through numerical simulations, which was used to predict delamination in the composite beams with the aid of an artificial neural algorithm. The diagnostic results have demonstrated the excellent performance of DDF technique for quantitative damage identification.     

Delamination growth in long composite tubes under external pressure

Delamination growth is a phenomenon known to reduce the integrity of laminated composite structural elements and may lead to premature failures. In the present study, state of the art procedures of delamination growth analysis are overviewed. The energy release rate calculation is formulated for composite delaminated tubular cross sections and specialized to a finite element model for delamination buckling and growth analysis of long laminated composite tubes taking into account initial geometric imperfections, large deformations, contact between delamination faces and material degradation. It is, then, used to study the potential of delamination growth in a hybrid composite tube. Parametric studies are conducted to assess the effects of delamination length, location and geometric imperfection on growth.     

Delamination tolerance studies in laminated composite panels

Determination of levels of tolerance in delaminated composite panels is an important issue in composite structures technology. The primary intention is to analyse delaminated composite panels and estimate Strain Energy Release Rate (SERR) parameters at the delamination front to feed into acceptability criteria. Large deformation analysis is necessary to cater for excessive rotational deformations in the delaminated sublaminate. Modified Virtual Crack Closure Integral (MVCCI) is used to estimate all the three SERR components at the delamination front from the finite element output containing displacements, strains and stresses. The applied loading conditions are particularly critical and compressive loading on the panel could lead to buckling of the delaminated sublaminate and consequent growth of delamination. Numerical results are presented for circular delamination of various sizes and delamination at various interfaces (varying depth-wise location) between the base- and the sub-laminates. Numerical data are also presented on the effect of bi-axial loading and in particular on compressive loading in both directions. The results can be used to estimate delamination tolerance at various depths (or at various interfaces) in the laminate.     

Optimization of laminated composites subject to uncertain buckling loads

Optimal design of composite laminates under buckling load uncertainty is presented. The laminates are subjected to biaxial compressive loads and the buckling load is maximized under worst case in-plane loading which is computed using an anti-optimization approach. The magnitudes of the in-plane loads are not known a priori resulting in load uncertainty subject to the only constraint that the loads belong to a given uncertainty domain. Results are given for continuous and discrete fibre orientations which constitute the optimization problem coupled to load anti-optimization problem leading to a nested solution method. It is observed that the stacking sequence of a laminate designed for a deterministic load case only differs considerably from that of a robust laminate designed taking load uncertainties into account. Consequently the buckling load carried by a deterministic design is considerably less than the one carried by a robust design when both are subjected to uncertain loads.     

Finite element buckling analysis of rotationally periodic laminated composite shells

A finite element (FE) buckling analysis of rotationally periodic laminated composite shells is performed in this paper. Because the buckling mode of such structures is characterized as rotationally periodic, a corresponding FE buckling analysis scheme is proposed to reduce the computational expenses. Moreover, a new kind of relative degrees‐of‐freedom element is developed, which can be connected to other solid elements with ease and can yield satisfactory results with a relatively coarse FE mesh. Numerical results of two laminated cylindrical shells subjected to lateral pressure are compared with theoretical ones. The good agreement of them shows the validity of this new computational strategy. Finally, a practical structure is analysed to demonstrate the advantage of this method. Copyright © 2001 John Wiley & Sons, Ltd.     

Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method

An isogeometric finite element method based on non-uniform rational B-splines (NURBS) basis functions is developed for natural frequencies and buckling analysis of thin symmetrically laminated composite plates based upon the classical plate theory (CPT). The approximation of the solution space for the deflection field of the plate and the parameterization of the geometry are performed using NURBS-based approach. The essential boundary conditions are formulated separately from the discrete system equations by the aid of Lagrange multiplier method, while an orthogonal transformation technique is also applied to impose the essential boundary conditions in the discrete eigen-value equation. The accuracy and the efficiency of the proposed method are thus demonstrated through a series of numerical experiments of laminated composite plates with different boundary conditions, fiber orientations, lay-up number, eigen-modes, etc. The obtained numerical results are then compared with either the analytical solutions or other available numerical methods, and excellent agreements are found.     

Analysis of critical buckling load of laminated composites plate with different boundary conditions using FEM and analytical methods

In this study, the critical buckling load of fiber reinforced composite plate was calculated by analytical and finite element methods. The critical buckling loads and composite deformations were obtained on the basis of plate dimensions ratio (L_x/L_y). The deformation behaviour of the plate is shown for modes i = 1,2 and different values of orientation angles [0/θ]₂. As a result of the analysis, for the composite plates with symmetric and antisymmetric layup the critical buckling loads were obtained for different support conditions. It was observed that difference between results increased depending on θ angle, although critical buckling load values obtained by using numerical and finite element methods were nearly same in [0/θ]₂ orientation angles.     

Modeling of the dynamic delamination of L-shaped unidirectional laminated composites

One of the widely used geometrically complex parts in advanced commercial aircraft is the L-shaped composite. Due to the sharp curved geometry, interlaminar opening stresses are induced and delamination occurs under considerable mode-mixities in L-shaped beams. Dynamic phenomena during delamination initiation and propagation of L-shaped beams are investigated using dynamic (explicit) finite element analysis in conjunction with cohesive zone methods. The 2-D model consists of 24 plies of unidirectional CFRP laminate with an initial 1 mm crack at the center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading type yields different traction fields and mode-mixities in the two sides of the crack in which delamination occurs under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed of the delamination under shear dominated loading at one side is 800 m/s and under normal stress dominated loading is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, a different failure mode is observed in which a secondary crack nucleates at the arm and propagates towards the center crack.     

Numerical analysis of delamination buckling and growth in slender laminated composite using cohesive element method

In this article, the finite element method (FEM) using cohesive element is applied to predict the delamination buckling and growth in slender laminated composite with embedded delamination under compressive load. In particular, the study is focused on the significant effects of delamination buckling for various parameters in slender composite laminate, such as model length–width ratio, delamination shape, delamination size, and delamination depth position. Furthermore, the delamination growth is assessed to investigate the influence of some key parameters (delamination size and delamination depth position) on the delamination growth load, growth shape and direction.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

Delamination identification and response prediction in composites using bivariate Gamma function-based microgenetic algorithms

This study deals with an identification of stiffness reduction and response predictions occurred by the delamination damage in laminated composite plates under impact loads. Combined bivariate Gamma function and microgenetic algorithms are developed to determine the crack region due to the delamination and predict future responses. The validity of the proposed method was verified using impact-induced data obtained from a two-dimensional delamination finite element model. Examples indicated that the proposed approach is a feasible and advantageous method through which future dynamic responses can be predicted and the distribution of the degraded stiffness of laminated composite structures can be inspected for different measuring locations and fibre angles.     

Flutter of delaminated cross-ply laminated cylindrical shells

In this study, the instability of delaminated cross-ply thin laminated cylindrical shells and panels when subjected to supersonic flow parallel to its length edge is investigated. The delamination is parallel to the shell reference and it extends along the entire length of the cylindrical shell. The Love’s shell theory and Von-Karman–Donnell type of kinematic relations along with first-order potential theory have been employed to construct the aeroelastic equations of motion. The effects of several parameters such as length to radius ratio, delamination position, size and thickness on the critical values are discussed in the details. The results indicate that the presence of delamination reduced the overall stiffness of the structure and thereby decreases the flutter critical boundaries.     

飞机典型薄壁复合材料夹层结构整体屈曲

为了研究飞机机身无筋无框复合材料典型薄壁夹层结构在型号上应用的可行性,本文采用解析方法、有限元方法和试验方法对蜂窝夹层复合材料结构的面内压缩和剪切整体屈曲开展系统研究。基于经典层合板理论和工程解析方法推导蜂窝夹层复合材料的压缩和剪切屈曲载荷随试验件尺寸的变化规律。依据某型飞机机身典型结构分别设计压缩和剪切试验件尺寸大小、边界条件和加载方式。利用有限元商用软件ABAQUS对试验设计建立虚拟试验分析,对比验证解析方法和有限元方法的一致性。最后通过真实试验方法确定解析方法和有限元方法的有效性,并验证典型薄壁夹层结构的承载能力和破坏模式。结果显示,压缩试验结果失效模式与理论预测一致,故3种方法得到的结构整体失稳载荷相近,验证了理论方法的有效性;剪切试验结果发生局部破坏,故试验结果偏低,但有限元方法与解析方法所得结果一致,解析方法相对保守。     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.