Design of composite structures including delamination studies

Composite materials are increasing their use in structures used for road transportation vehicles. From car bodies to trucks, these materials are being more popular. This use is obliging designers to take care of topics different to the traditional ones already studied for aerospace applications. Design must be simplified and, what is even more important, commercial codes should be used to continue with the extension of the use of composite materials in non aerospace industry. One of the most important problems arising when dealing with finite element design of composite materials including delamination is the requirement of using huge computer resources to solve the three dimensional stress field in the vicinity of free edges, holes, changes of number of layers and similar discontinuities.

To solve this problem, there are some well known techniques as global-local approaches that can be used for designing with good results. From an engineering point of view, the problem is that they are not usually implemented in commercial finite element codes so that engineers can not use them for everyday calculations.     

Cohesive zone length in numerical simulations of composite delamination

Accurate analysis of composite delamination using interface elements relies on having sufficient elements within a softening region known as the cohesive zone ahead of a crack tip. The present study highlights the limitations of existing formulae used to predict numerical cohesive zone length and demonstrates modifications necessary for improved accuracy. Clarification is also provided regarding the minimum number of interface elements within the cohesive zone. Finally, appropriate values of numerical interfacial strength are examined. The results presented will aid the application of mesh design techniques that both preserve numerical accuracy, whilst minimising computational expense.     

Charpy impact damage behaviour of single and multi-delaminated hybrid composite beam structures

The ply delamination which is known as a principle mode of failure of layered composites due to separation along the interfaces of the layers is one of the main concerns in designing of composite material structures. In this regard, the effect of hybrid laminate lay-up with different delamination positions in composite beam was investigated. The Charpy impact test was chosen to study the energy absorbing capability of delaminated composite beam. Hybrid composite beams were fabricated from combination of glass/epoxy and carbon/epoxy composites. It was shown that composite beams with closer position of delamination to impacted surface are able to absorb more energy in comparison with other delamination positions in hybrid and non-hybrid ones. The Charpy impact test of delaminated composite beams was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental results.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

An interface element for the simulation of delamination in unidirectional fiber-reinforced composite laminates

Unidirectional fiber-reinforced composite laminates are widely used in aerospace industry for a great variety of structural parts. In order to enhance the exploitation of material reserves, there is a need for the integration of progressive damage scenarios in the design phase. Due to their hazardous effects on the load-carrying capacity of composite structures, this work focusses on the simulation of delaminations. A finite element based on a cohesive zone approach is developed. Two constitutive laws are proposed. One is characterized by linear degradation after delamination onset, the other is governed by exponential softening response. The damage process is history-dependent leading to an irreversible stiffness degradation in damaged zones. The practicability of the proposed model and the assets and drawbacks of the two material laws are shown by some numerical examples.     

A novel approach based on ALE and delamination fracture mechanics for multilayered composite beams

A novel approach able to predict debonding or fracture phenomena in multilayered composite beams is proposed. The structural model is based on the first-order shear deformable laminated beam theory and moving mesh strategy developed in the framework of Arbitrary Lagrangian–Eulerian (ALE) formulation. The former is utilized to evaluate fracture parameters by using a multilayer approach, in which a low number of interface elements are introduced along the thickness, whereas the latter is utilized to reproduce crack tip motion due to the crack extension produced by moving boundaries. The model is able to avoid computational complexities introduced by an explicit crack representation in bi-dimensional structures, in which typically high computational efforts are expected for handling moving boundaries. To this aim, a moving mesh strategy is proposed for the first time in the context of beam modeling based on a multilayered configuration. Such an approach, essentially based on ALE formulation, is able to reproduce interfacial crack paths by using a low number of computational elements. The numerical method is proposed in the framework of the finite element formulation for a quasi-static or dynamic evolution of the crack tip front. In order to investigate the accuracy and to validate the proposed methodology, comparisons with experimental data and existing formulations available from the literature are developed. Moreover, a parametric study in the framework of dynamic fracture is developed to investigate the capability of the proposed model to reproduce more complex loading cases.     

Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams

This paper presents a new finite element formulation, referred to as reference surface element (RSE) model, for numerical prediction of dynamic behaviour of delaminated composite beams and plates using the finite element method. The RSE formulation can be readily incorporated into all elements based on the Timoshenko beam theory and the Reissner–Mindlin plate theory taking into account the transverse shear deformations. The ‘free model' and ‘constrained model' for dynamic analysis of delaminated composite beams and/or plates have been unified in this RSE formulation. The RSE formulation has been applied to an existing 2-node Timoshenko beam element taking into account the transverse shear deformations and the bending–extension coupling. Frequencies and vibration mode shapes are determined through solving an eigenvalue problem. Numerical results show that the present RSE model is reliable and practical when used to predict frequencies and mode shapes of delaminated composite beams. The RSE formulation has also been used to investigate the effects of the number, size and interfacial loci of delaminations on frequencies and mode shapes of composite beams.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

Drilling of composite structures

Structural parts made of composites have frequently to be drilled in the aircraft industry. However, little is know about the interacting conditions between the drilling tool and the material, which may be multi-type and multi-size. This study proposes a model which links the axial penetration of the drill bit to the conditions of delamination (crack opening mode I) of the last few plies. Several types of tool/material contact conditions were analyzed and were compared with experimental measurements, and with a model taken from the literature. Our study shows a close correlation between experiment and calculation when the thrust force of the drill is modeled by taking into account the geometrical nature of the contact between the tool and a laminate composite material.     

Investigating the quasi-static axial crushing behavior of polymeric foam-filled composite pultrusion square tubes

The capability of structures to absorb large amounts of energy is a crucial factor, particularly for structural components of vehicles, in reducing injury in case of collision. In this study, an experimental investigation was conducted to study the crashworthiness of polymeric foam-filled structures to the pultruded square cross-section E-Glass fiber-reinforced polyester composite tube profiles. Quasi-static compression was applied axially to composite tubes to determine the response of the quasi-static load displacement curve during progressive damage. Three pultruded composite tube wall thicknesses at different sizes were examined, and the effects of crushing behavior and failure modes were analyzed and discussed. Experimental results indicated that the foam-filled profile is superior to the non-filled foam composite tube profile in terms of the capacity to absorb specific energy.     

Separation of delamination modes in composite beams with symmetric delaminations

Delaminated composite beam under general edge loading conditions is studied. Based on a technical engineering theory an analytical procedure for calculation of strain energy release rate and its separation into modes I and II of delamination is presented. By choosing a suitable displacement field based on second-order shear-thickness deformation theory and using the principle of minimum total potential energy, the equations of equilibrium are obtained along with the appropriate boundary conditions. The J integral and its definition for different modes of fracture is used for calculation of strain energy release rate and its separation into different modes. Double cantilever beam (DCB) problem is a special case of this general problem in which loading is in mode I of fracture. The results of this method shows good agreement with FEM (i.e., finite element method) results and experimental data.     

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

Computational and experimental investigation of delamination in L-shaped laminated composite components

Formation of initial delaminations and growth of existing delaminations in L-shaped laminates made of plies of a unidirectional carbon fiber reinforced epoxy resin is investigated computationally and experimentally. For this purpose an experimental test is designed which allows to realize load states for which delamination is the dominant failure mechanism. Two types of test specimens, with and without initial delaminations, are investigated and good agreement is obtained between the computational predictions and the experimental results concerning delamination emergence, delamination growth, growth stability, the structural response, and the maximum principal strains.     

Numerical investigation of a crash test of a composite helicopter subfloor structure

Composite energy-absorbing aircraft structures are being studied within a European Commission research programme (CRASURV – Design for Crash Survivability). One of the aims of the project is to evaluate the current capabilities of crashworthiness simulation codes for modelling future composite primary structures. In this paper, a detailed analysis is presented of a generic module of a composite helicopter subfloor structure, subjected to crash loading. The analysis is performed with the explicit finite element code PAM-CRASH and is compared with the results of a drop test. It has been found that pre-test simulations with only coupon data as input are capable of providing a reasonable overall representation, but to closely match the behaviour of the test, a significant amount of post-test work is required. The calibration of the post-failure material properties proved to be more crucial than the behaviour up to initial failure. The representation of fabric materials was found to be inadequate and a new fabric material model is under development as a result. The importance of modelling frictional effects was highlighted, and a mesh density study showed the model to be robust over a range of mesh densities.     

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM).A finite element model considering solid elements of the ABAQUS^® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.     

Formulation and assessment of an enhanced finite element procedure for the analysis of delamination growth phenomena in composite structures

An existing procedure based on the combined use of the Virtual Crack Closure Technique and of a fail release approach for the analysis of delamination growth phenomena in composite structures has been enhanced with a front-tracing algorithm and suitable expressions for the evaluation of the Strain Energy Release Rate when dealing with non-smoothed delamination fronts. The enhanced procedure has been implemented into a commercial finite element software by means of user subroutines and applied to the analysis of a composite stiffened panel with an embedded delamination under compressive load. The effectiveness and robustness of the enhanced procedure have been assessed by comparing literature experimental data and numerical results obtained by using different mesh densities in the damaged area (global/local approach).