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).     

On the robustness of finite element procedures based on Virtual Crack Closure Technique and fail release approach for delamination growth phenomena. Definition and assessment of a novel methodology

Numerical procedures based on the combined use of the Virtual Crack Closure Technique and of a fail release approach have been widely used to simulate delamination growth phenomena of composite material structures. This paper starts explaining why this kind of methodologies might not be robust due to mesh and load step size dependency and introduces a novel approach able to cope with the problems identified. Finally the effectiveness and robustness of the proposed procedure, implemented into a commercial finite element software by means of user subroutines, are assessed by comparing the obtained numerical results for a delamination growth phenomenon against literature experimental data on a stiffened panel with a circular embedded delamination under compressive load.     

Decohesion finite element with enriched basis functions for delamination

In order to address the stringent mesh size requirement of the cohesive element, currently 0.5 mm or less, the mixed-mode interface finite element is enriched with the analytical solution of an idealized beam on elastic foundation. Both the interface and the solid continuum elements are enriched; the partition of unity (PU) method is utilized to obtain the enhanced interpolation, implemented with two user elements (UEL) in the commercial package ABAQUS/Standard. The new formulation yields predictions in excellent agreement with theoretical and experimental results for a typical mode I delamination benchmark, with elements 5 mm in size.     

Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

Delamination modelling of GLARE using the extended finite element method

In this paper, an application of the Extended Finite Element Method (XFEM) for simulation of delamination in fibre metal laminates is presented. The study consider a double cantilever beam made of fibre metal laminate in which crack opening in mode I and crack propagation were studied. Comparison with the solution by standard Finite Element Method (FEM) as well as with experimental tests is provided. To the authors’ knowledge, this is the first time that XFEM is used in the fracture analysis of fibre metal laminates such as GLARE. The results indicated that XFEM could be a promising technique for the failure analysis of composite structures.     

Cohesive zone modelling of delamination response of a composite laminate with interleaved nylon 6,6 nanofibres

This work simulates numerically Double Cantilever Beam and End Notched Flexure experiments on Carbon Fibre Epoxy Resin specimens that have been performed by some of the authors in a previous work. Specimens have been nanomodified by interleaving plies with a layer of electrospun nanofibres in the delaminated interface. Eight different configurations of nanofibres have been used as interleave, for a total of 9 configurations (8 nanomodified plus the virgin one) to be simulated for both kind of tests to identify the cohesive zone parameters corresponding to the effect of nanofibre diameter, nanolayer thickness and nanofibre orientation on the delamination behaviour of the composite.Results showed that a bilinear damage law is necessary for almost all nanomodified configurations, and presented a clear relationship between nanomat layer parameters and the cohesive energy of the interface.     

Modeling delamination migration in cross-ply tape laminates

A novel modeling approach is proposed that combines the Floating Node Method (FNM) with the Virtual Crack Closure Technique (VCCT) to capture delamination migration in cross-ply tape laminates. Delamination migration is the damage process by which a delamination propagating at an interface relocates to a different interface via one or multiple matrix cracks. In the approach proposed, delamination, matrix cracking, and their interaction, are represented in a single element. The kinematics of both delamination and matrix cracks are represented explicitly. Migration onset location, and subsequent path, are determined as part of the solution, in a mesh-independent fashion. Delamination growth, matrix cracking, and migration onset, are all modeled using fracture mechanics based failure and migration criteria. The proposed approach is applied to the modeling of the Delamination Migration (DM) test, showing good qualitative and quantitative agreement with experiments.     

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.     

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.     

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.     

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.     

Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.     

Predicting microdroplet force response using a multiscale modeling approach

An axisymmetric microscale finite element model of a microdroplet test specimen is developed where the structural response of the fiber–droplet interface is accounted for by surface-based cohesive behavior. In this study, the interface cohesive response is estimated using a nanoscale interface finite element model that explicitly includes the effects of fiber surface topography and the interphase region. The interphase behavior in the nanoscale interface model is calibrated using indirect experimental data. Once calibrated, the fiber surface topography in the nanoscale interface model is modified in order to estimate the parameters defining the surface-based cohesive behavior of similar fiber–matrix systems with different fiber topography. The effect of altering the fiber topography on the force response of the microdroplet test can then be predicted by the microdroplet FE model. Comparing the simulation results with experimental data from the literature shows that this multiscale modeling approach gives accurate predictions for the interfacial shear stress.     

Interfacial damage in biopolymer composites reinforced using hemp fibres: Finite element simulation and experimental investigation

The present study aims at considering the effect of interfacial damage on the mechanical performance of a starchy composite reinforced using hemp fibres. Mechanical behaviour is approached experimentally using tensile testing coupled to digital image acquisition. Thermomoulded samples with single fibres are designed to allow sample testing perpendicularly to the direction of fibre alignment. Experimental evidence of localised damage is then highlighted in the elasticity stage. Finite element computation is attempted to explain the observed damage using an adequate mechanical model that considers weak adhesion between phases and dynamic evolution of damage. Predicted results show that the FE model is able to reproduce the observed behaviour suggesting that local damage evolution is a serious mechanism affecting the performance of the studied composite.     

A non-local criterion for modelling unbalanced woven ply laminates with stress concentrations

A non-local ply scale criterion [Hochard C, Lahellec N, Bordreuil C. A ply scale non-local fibre rupture criterion for CFRP woven ply laminated structures. Compos Struct 2007;80:321–26] was previously developed for predicting the failure of balanced woven ply structures with stress concentrations. This non-local criterion was based on the mean values determined over a Fracture Characteristic Volume (FCV) corresponding to a cylinder with a circular area and the same thickness as the ply. This non-local approach along with a ply scale continuum damage behavioural model was implemented in the ABAQUS Finite Element Code. The behavioural model was developed from a classical Continuum Damage Mechanics (CDM) model [Ladevèze P. A damage computational method for composite structures. Comput Struct 1992;44:79–87]. In the present study, this approach was extended to the case of unbalanced woven ply. The FCV approach and the CDM behavioural model are presented and comparisons are made between the experimental data and the modelling predictions obtained on plates with open holes, notches and saw cuts.     

Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis

Bridging by intact fibers in composite materials is one of the most important toughening mechanisms. However, a direct experimental assessment of its contribution is not easy to achieve. In this work a semi-experimental method is proposed to quantify its contribution to fracture of unidirectional carbon fiber/epoxy double cantilever beam (DCB) specimens in mode I delamination under monotonic and 1 Hz fatigue loads. In each specimen, an embedded optical fiber with an array of eight wavelength-multiplexed fiber Bragg gratings is used to measure local strains close to the crack plane. The measured strain distribution serves in an inverse identification procedure to determine the tractions in the bridging zone in monotonic and fatigue loads. These tractions are used to calculate the energy release rate (ERR) associated with bridging fibers. The results indicate that the ERR due to bridging is about 40% higher in fatigue. The bridging tractions are further included in a cohesive element model which allows to predict precisely the complete load displacement curve of monotonic DCB tests. Using the principle of superposition and the identified tractions, the total stress intensity factor (SIF) is calculated. The results show that the SIF, at initiation, is very close to the one calculated at crack propagation and bridging by intact fibers is responsible for the entire increase in toughness seen in the DCB specimens used herein.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

Identification of material parameters for modelling delamination in the presence of fibre bridging

Delamination processes often exhibit an increase in delamination resistance, or R-curve, with crack extension. It is shown that cohesive laws can represent the R-curves due to large-scale fibre bridging and that the shape of the cohesive laws can be derived from conventional experimental results. Two approaches are investigated for determining the shape parameters of cohesive laws. The first approach consists of extracting the cohesive parameters from experimental R-curves through the use of a new semi-analytical equation. The second approach consists of a numerical optimization procedure that identifies material parameters by reducing the error between a finite element model and the experimental load–deflection results. The second approach is advantageous when fibre bridging introduces inaccuracies in the experimental energy release rate measurements. In addition, the second approach can be extended to allow more complex approximations of cohesive laws.     

A cohesive zone model for predicting delamination suppression in z-pinned laminates

This paper presents a cohesive zone model based finite element analysis of delamination resistance of z-pin reinforced double cantilever beam (DCB). The main difference between this and existing cohesive zone models is that each z-pin bridging force is governed by a traction-separation law derived from a meso-mechanical model of the pin pullout process, which is independent of the fracture toughness of unreinforced laminate. Therefore, two different traction-separation laws are used: one representing the toughness of unreinforced laminate and the other the enhanced delamination toughness owing to the pin bridging action. This approach can account for the large scale bridging effect and avoid using concentrated pin forces, thus removing the mesh dependency and permitting more accurate analysis solution. Computations were performed using a simplified unit strip model. Predicted delamination growth and load vs. displacement relation are in excellent agreement with the prediction by a complete model, and both models are in good agreement with test measured load vs. displacement relation. For a pinned DCB specimen, the unit strip model can reduce the computing time by 85%.