Fastener pull-through in a carbon fibre epoxy composite joint

This paper considers the capability of finite element (FE) modelling to accurately predict fastener pull-through failure of composite laminates. Such failures are dominated by inter-ply delamination and through-thickness shear failure of the laminate and the common modelling approach is to use computationally expensive, detailed three-dimensional models that include delamination for every ply interface, fastener contact and prestress. This paper considers a simplified FE modelling strategy achieved through judicious use of symmetry boundary conditions, hybrid shell/solid modelling and reduced numbers of interfaces for delamination. The LS-DYNA FE software was used for this study using the available composite material and cohesive failure models. The conclusion drawn from this work is that the use of simplified FE models does have merit in modelling fastener pull-through provided the material is quasi-isotropic and the boundary conditions are uniform around a circular perimeter. Additional work is however required to determine suitable cohesive properties and progressive shear failure parameters.     

Delamination modelling in a double cantilever beam

The simulation of the delamination process in composite structures is quite complex, and requires advanced FE modelling techniques. Failure analysis tools must be able to predict initiation, size and propagation of delamination process. The objective of the paper is to present modelling techniques able to predict a delamination in composite structures. Four different ways of modelling delamination growth of a double cantilever beam test (DCB) are proposed. The first two approaches were based on a cohesive zone model: the interface being represented either by using delamination elements or non-linear springs. The idea of the third approach was to use a fracture mechanics criterion, but to avoid the complex moving mesh techniques it often implies. The interface between the two layers was simulated with solid elements representing the matrix, which were eliminated when their energy release rate exceeded the critical value. The energy release rate was computed using the virtual crack closure technique (VCCT). In the last approach, the interface behaviour was modelled by a tiebreak contact. Coincident nodes were tied together with a constraint relation and remained joined, until when the maximum interlaminar stresses was reached. Once this value was exceeded, the nodes associated with that constraint were released to simulate the initiation of delamination. The comparison of the results of the first three modelling techniques with experimental data showed that very good correlation was achieved. Poor results were obtained using tiebreak contact. It was due to the criterion used, since when the critical interlaminar stress was reached, the delamination was experienced before the critical energy release rate was reached.     

Numerical prediction of damage in composite structures from soft body impacts

The paper summarises recent progress on materials modelling and numerical simulation of soft body impact damage in fibre reinforced composite aircraft structures. The work is based on the application of finite element (FE) analysis codes to simulate damage in composite shell structures under impact loads. Composites ply damage models and interply delamination models have been developed and implemented in commercial explicit FE codes. Models are discussed for predicting impact loads on aircraft structures arising from deformable soft bodies such as gelatine (synthetic bird) and ice (hailstone). The composites failure models and code developments are briefly summarised and applied in the paper to numerical simulation of synthetic bird impact on idealised composite aircraft structures.     

A generic approach to constitutive modelling of composite delamination under mixed-mode loading conditions

A generic approach to constitutive modelling of composite delamination under mixed mode loading conditions is developed. The proposed approach is thermodynamically consistent and takes into account two major dissipative mechanisms in composite delamination: debonding (creation of new surfaces) and plastic/frictional deformation (plastic deformation of resin and/or friction between crack surfaces). The coupling between these two mechanisms, experimentally observed at the macro scales through the stiffness reduction and permanent crack openings, is usually not considered in depth in many cohesive models in the literature. All model parameters are shown to be identifiable and measurable from experiments. The model prediction of mixed-mode delamination is in good agreement with benchmarked mixed-mode bending experiments. It is further shown that accounting for all major dissipative mechanisms in the modelling of delamination is the key to the accurate prediction of both resistance and damage of the interface.     

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.     

Prediction of initiation and growth of single level delaminations in a transversely loaded composite specimen using fracture mechanics

The behaviour of a composite test specimen with an embedded delamination subjected to transverse tension has been investigated through experimental testing and finite element (FE) analyses. The testing program consisted of specimens in two geometrical configurations; square and rectangular delamination. The initiation and growth of the delamination was numerically predicted by fracture mechanics. FE models were analysed with both MSC.Nastran and Abaqus FE codes. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. Both approaches accurately predicted failure initiation locations as observed in the test specimens. Failure loads were also well predicted. The mode mix at the crack tip in the proposed specimen was found to be similar to the mode mix expected in a conventional in-plane compression specimen.     

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.     

Fracture simulation of CFRP laminates in mixed mode bending

This paper analyses the progressive mixed mode delamination failure in unidirectional and multidirectional composite laminates using fracture experiments, finite element (FE) simulations and an analytical solution. The numerical model of the laminate is described as an assembly of damageable layers and bilinear interface elements subjected to mixed mode bending. The analytical approach is used to estimate the total mixed mode and decomposed fracture energies for laminates with different stacking sequences, which is also validated through experiments. It is concluded that the interlaminar fracture toughness of multidirectional laminates is considerably higher than that of the unidirectional ones. The effect of initial interfacial stiffness and element size is studied and it is also shown that their value must not exceed a definite limit for the numerical simulations to converge. The model can also be further extended to simulate the mixed mode fracture in hybrid fiber metal laminates.     

An Experimental Method for Dynamic Delamination Analysis of Composite Materials by Impact Bending

An improved experimental method for characterizing dynamic delamination growth in composite structures has been developed and verified using high speed photography and explicit finite element simulation. The method is based on a three-point bending device. End notch flexure carbon fiber composite beam specimens were subjected to both quasi-static and impact rates of Mode II loading. The experimental results showed no significant strain rate dependency of the delamination fracture toughness. This important result complements the scarce and conflicting data available in the literature, and serves as a reference for calibration of numerical modeling strategies.     

Experimental testing and phenomenological modelling of the fragmentation process of braided carbon/epoxy composite tubes under axial and oblique impact

A new simulation technique is presented for the phenomenological modelling of stable fragmentation in fibre reinforced composite structures under dynamic compressive loading. An explicit crash code is used for implementation of a hybrid modelling technique, in which two distinct material models act simultaneously. The first model is implemented in a multi-layered shell element and uses a unidirectional composites fracture criterion to predict potential ply fracture mechanisms on a macroscopic scale. This model is, however, unable to represent the complex localised fracture mechanisms that occur on a meso (sub-ply) scale under compression fragmentation loading. Therefore, a second constitutive model is added to capture the energy absorbing process within the fragmentation zone, utilising an Energy Absorbing Contact (EAC) formulation between the composite structure and the impacting body. The essential benefits of the procedure are that it requires minimal input data that can be obtained from simple fragmentation tests, and that the procedure is computationally efficient enabling application to large scale industrial structures. The EAC theory is discussed, together with the required material model parameters. A series of dynamic axial and oblique impact tests and simulations of cylindrical continuous carbon fibre reinforced composite tubes have been performed to validate the approach. Furthermore, the application to more complex load cases including combinations of fragmentation and global structural fracture have also shown a good correlation with test results.     

Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach

A geometrically and physically nonlinear finite element approach is presented for the analysis of mode-I and mixed-mode free edge delamination in composite laminates which properly accounts for the effects of initial thermal and hygroscopic stresses. A constitutive model based on nonlinear fracture mechanics is used to describe delamination. An orthotropic softening plasticity model is used to determine the initiation and propagation of delamination. Although the orthotropic yield surface is based on stresses, it is proved, that, in combination with a softening type of post-failure response controlled by the fracture toughness, the approach results in a unique and physically realistic solution upon mesh refinement. The results from the nonlinear finite element computations, including predictive analysis, are compared with mode-I and mixed-mode free edge delamination experiments. This comparison shows that the numerical results are within 10% of the experimental data.     

Simulation of delamination by means of cohesive elements using an explicit finite element code

This paper presents the formulation of a tri-dimensional cohesive element implemented in a user-written material subroutine for explicit finite element analysis. The cohesive element simulates the onset and propagation of the delamination in advanced composite materials. The delamination model is formulated by using a rigorous thermodynamic framework which takes into account the changes of mixed-mode loading conditions. The model is validated by comparing the finite element predictions with experimental data obtained in interlaminar fracture tests under quasi-static loading conditions.     

Finite Element Analysis of Delamination inWoven Composites under Quasi-Static Indentation

Delamination initiation and propagation in plain woven laminates and 3D orthogonal woven composites during short beam shear (SBS) test were analyzed using finite element (FE) analyses. Two kinds of 3D woven composites, containing single z-yarns and double z-yarns, were considered. The FE models were guided by experimental observations from SBS tests for the same material systems. A series of mechanisms including creation and evolution of matrix cracks and delaminations were modeled discretely. The force-displacement curves obtained from the FE simulations were compared with those from experiments. Further parametric studies were conducted to investigate the effects of z-yarns and interlaminar fracture toughness on delamination in woven composites. The results from the FE simulations revealed that z-yarns in 3D woven composites can play a major role in impeding propagation of interlaminar cracks. On the other hand 2D plain woven laminates without any z-reinforcement demonstrated higher interlaminar fracture toughness due to undulation in yarns. 3D woven composites with double yarns showed better damage tolerance than single yarn 3D woven composites and their behavior was very similar to composite laminates with high interlaminar fracture toughness.     

Numerical analysis of size effects on open-hole tensile composite laminates

The tensile strength of open-hole fibre reinforced composite laminates depends on in-plane, thickness and ply lay-up scaling. Translaminar (fibre direction) mode I fracture toughness has recently been experimentally determined to be thickness dependent. This paper presents a computational study of the tensile strength prediction of open-hole laminates using a cohesive zone model. To the authors’ knowledge, it is for the first time in the literature that the thickness-dependence of translaminar fracture toughness is accounted for in the numerical modelling of composites. The thickness size effect in the strength of open-hole composite laminates failed by pull-out is accurately predicted for the first time by a deterministic model. It is found that neglecting delamination in the numerical models will lead to mesh-dependency and over-estimation on the predicted strength. Smeared crack model with cohesive elements to model delamination is able to predict the correct failure mode; but it is found not suitable for accurate strength predictions for laminates failed by delamination.     

Modeling delamination growth in composites under fatigue loadings of varying amplitudes

A numerical model was developed to simulate the progressive delamination of a composite subjected to mode I fatigue loading regimes of varying amplitude. The model employs a cohesive zone approach, which combines damage mechanics and fracture mechanics, and requires only standard material data as input, namely the delamination toughness and the fatigue delamination growth curve. The proposed model was validated against delamination growth data obtained from a fatigue test conducted on a DCB specimen. The model predictions agree very well with the experimental results. This model is an initial step toward life prediction of composite structures subjected to complex fatigue regimes.     

Numerical simulation of delamination in laminated composite components – A combination of a strength criterion and fracture mechanics

An approach for the numerical treatment of delamination in laminated composite components is presented. A first ply failure criterion is employed to predict delamination initiation, while delamination propagation is analyzed using linear elastic fracture mechanics. The combination of initiation and propagation criteria yields a conservative estimation of the load earring capacity of a structure. Furthermore, the growth stability, the sensitivity of the results with respect to a change in the interface properties, and the non-linear structural response caused by the delamination growth process are determined. Two structures are investigated, which show the capability of the proposed approach, a curved laminate and a double lap shear test specimen.     

Prediction of Delamination Onset and Critical Force in Carbon/Epoxy Panels Impacted by Ice Spheres

Polymer matrix composite structures are exposed to a variety of impact threats including hail ice. Internal delamination damage created by these impacts can exist in a form that is visually undetectable. This paper establishes an analysis methodology for predicting the onset of delamination damage in toughened carbon/epoxy composite laminates when impacted by high velocity ice spheres (hailstones). Experiments and analytical work focused on ice sphere impact onto composite panels have determined the failure threshold energy as a function of varying ice diameter and panel thickness, and have established the ability to predict the onset of delamination using cohesive elements in explicit dynamic finite element analysis. A critical force associated with damage onset was found to be independent of the ice diameter and thus can be expressed as a function of basic panel-describing parameters, namely bending rigidity and interlaminar fracture energy. Critical force can be used as a failure criterion in simpler models (e.g., shell elements) when predicting the onset of delamination by high speed spherical ice impact.     

基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测

基于连续损伤力学,建立了同时考虑复合材料剪切非线性效应和损伤累积导致材料属性退化的三维损伤本构模型。模型能够区分纤维损伤、基体损伤和分层损伤不同的失效模式,并定义了相应损伤模式的损伤变量。复合材料层合板层内纤维初始损伤采用最大应力准则判定,基体初始损伤采用三维Puck准则中的基体失效准则判定,分层初始损伤采用三维Hou准则中的分层破坏准则判定,为了计算Puck失效理论中的基体失效断裂面角度,本文提出了分区抛物线法,通过Matlab软件编写计算程序并进行分析。结果表明,与Puck遍历法和分区黄金分割法对比,本文提出的分区抛物线法有效地降低了求解断裂面角度的计算次数,提高了计算效率和计算精度。推导了本构模型的应变驱动显式积分算法以更新应力和解答相关的状态变量,开发了包含数值积分算法的用户自定义子程序VUMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著非线性效应的AS4碳纤维/3501-6环氧树脂复合材料层合板进行渐进失效分析,验证了本文提出的材料本构模型的有效性。结果显示,已提出的模型能够较准确地预测此类复合材料层合板的力学行为及其失效强度,为复合材料构件及其结构设计提供一种有效的分析方法。      

Delamination buckling of FRP layer in laminated wood beams

An analytical solution for predicting delamination buckling and growth of a thin fiber reinforced-plastic (FRP) layer in laminated wood beams under bending is presented. Based on a strength-of-materials approach, displacement functions for a delaminated beam under four-point bending are derived. Using force and displacement compatibility conditions, an explicit form relating the applied transverse load with the delamination buckling load is established. An explicit form of the strain-energy release rate is presented to study the delamination growth in beams under bending. The analytical solution is evaluated using experimental data for glued-laminated timber (glulam) beams reinforced with a thin fiber-reinforced plastic composite on the compression face. The delamination growth in bending is shown to behave differently to that of the in-plane loading case.     

Structural design of single lap joints with delaminated FRP composite adherends

This paper deals with the structural design of single lap joints (SLJs) with delaminated adherends using fracture mechanics principles. The interlaminar stresses and Strain Energy Release Rate (SERR) are considered as damage characterizing parameters used for designing the SLJ when delamination damages are pre-embedded in both the adherends at similar positions. Three dimensional geometrically non-linear finite element analyses (FEAs) of SLJ with delaminated adherends have been performed to determine the interlaminar and SERR values along the delamination fronts by simulating the simultaneous interaction delamination damages when pre-embedded at similar positions in both the adherends. SERR values are evaluated using Modified Crack Closure Technique (MCCI) which is based on energy principle. The delaminations are assumed to be of linear front, and have been considered to be embedded in both the laminated FRP composite adherends beneath the surface ply of the adhesively bonded SLJ. The delamination damages are presumed either to pre-exist or get evolved at the interlaminar locations. Such delaminations have been modelled using the sublaminate technique. The critical issues of modelling pre-embedded delamination damages are discussed in detail. The numerical results presented in this paper are based on the validated FE model compared with the available literature. Based on the present analyses, the structural design recommendations have been made for the SLJ when pre-embedded delamination damages are present in both the adherends. It is observed from the stress based design that the delamination damage when present in the bottom adherend is more detrimental for failure of SLJ compared to that for the case when it is present in the top adherend. Also, SERR based design reveals that the opening mode predominantly governs the propagation of delamination damage for all positions of the pre-embedded delaminations in both the adherends of the SLJ.