A framework for cohesive element enrichment

It was shown in a previous work by the same authors that the stringent mesh size requirement on cohesive, interface elements, can be alleviated through enrichment of the finite element basis functions. In this paper, some limitations of the enriched formulation are discussed and a new maximum mesh size requirement is established. The enriched formulation is also applied here to the simulation of mixed-mode delamination for the first time.     

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).     

Composite delamination modelling using a multi-layered solid element

This paper focuses on the latest development of a solid hexahedron element for composite delamination analysis. The 8-node solid is derived from a 20-node hexahedron. It is transformed into two physical independent 4-node shell elements according to the propagation of delamination process within the element.     

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.     

Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite

An investigation of the effects of moisture on mixed-mode I/II delamination growth in a carbon/epoxy composite is presented. Experimental quasi-static and fatigue delamination tests were carried out on composite specimens. The quasi-static fracture test results showed that exposure to moisture led to a decrease in mode II and mixed-mode delamination toughness while mode I toughness was enhanced. The fatigue tests revealed an adverse effect of moisture on delamination growth under mixed-mode loadings. Existing delamination criteria and growth rate models were evaluated to determine which ones best predict delamination toughness and growth, respectively, at any given mixed-mode ratio. Quasi-static and fatigue simulations with a cohesive zone-based finite element model that incorporated the selected mixed-mode delamination models were performed and good agreement between experimental and numerical data was shown for dry and moisture-exposed specimens.     

A critical plane-based fracture criterion for mixed-mode delamination in composite materials

A new critical plane-based mixed-mode delamination failure criterion is proposed in this study. First, many existing models are reviewed and their capability to handle the mixed-mode fracture of general anisotropic materials are discussed. Following this, a previously developed critical plane approach is extended to analyze the interfacial fracture of composite materials by considering the anisotropic fracture resistance under mixed-mode loadings. Next, comparison with extensive experimental data available in the literature is performed to demonstrate the validity of the proposed criterion. A general good agreement is observed between the model's predictions and experimental observations. Finally, some conclusions and future work are drawn based on the proposed study.     

Compressive static strength model for impact damaged laminates

A simple analytical model for the prediction of the compressive strength of composite structures with Barely Visible Impact Damage (BVID) subject to static loading is presented. The model represents the complex damage morphology using circular approximations of the damage area and determines a critical interface for propagation of BVID. Results are compared with experimental values for static strength of a variety of examples reported in the literature. For impacts on the skin under a stiffener the model is accurate to within 5% of the reported experimental result. It is demonstrated how the model can be manipulated for use in laminate optimisation for improved damage tolerance.     

Modelling complex progressive failure in notched composite laminates with varying sizes and stacking sequences

The emergence of advanced computational methods and theoretical models for damage progression in composites has heralded the promise of virtual testing of composite structures with orthotropic lay-ups, complex geometries and multiple material systems. Recent studies have revealed that specimen size and material orthotropy has a major effect on the open hole tension (OHT) strength of composite laminates. The aim of this investigation is develop a progressive failure model for orthotropic composite laminates, employing stepwise discretization of the traction–separation relationship, to predict the effect of specimen size and laminate orthotropy on the OHT strength. The results show that a significant interaction exists between delamination and in-plane damage, so that models without considering delamination would over-predict strength. Furthermore, it is found that the increase in fracture toughness of blocked plies must be incorporated in the model to achieve good correlation with experimental results.     

Occurrence and propagation of delamination during the machining of carbon fibre reinforced plastics (CFRPs) - An experimental study

The machining of carbon fibre reinforced plastics (CFRPs) is often accompanied by delamination of the top layers of the machined edges. Such damage necessitates time-consuming and costly post-machining and in some cases leads to rejection of components. The work described in this paper systematically investigates the occurrence of delamination of the top layers during the machining of CFRP tape, with the focus being on the process of contour milling. The occurrence and propagation of delamination were studied by milling slots in unidirectional CFRP specimens having different fibre orientations and mainly analysing the slot tip. This allowed the key mechanisms to be clarified. The results show that delamination is highly dependent on the fibre orientation and the tool sharpness. The experiments allow derivation of a novel system for describing the occurrence and propagation of delamination during milling. Furthermore, the principles also apply for drilling. The results allow customisation of the machining procedure to reduce and in some cases totally avoid delamination, leading to a significant increase in the quality of components.     

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.     

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.     

Micromodel-based simulations for laminated composites

We develop a calculation strategy for the simulation of a complete microscopic model. This strategy enables one to account for damage mechanisms in laminated composites. The model mixes discrete and continuous approaches by introducing potential rupture surfaces and a damageable continuous medium. This approach requires suitable calculation tools unavailable in industrial analysis codes. The strategy presented is multiscale in space and is based on a decomposition of the domain into substructures and interfaces. This strategy enables one to simulate complex problems with multiple cracks. In practice, to use such a model, the strategy must be improved in order to handle very large numbers of substructures and interfaces and to estimate the rupture criteria for the surfaces introduced into the model. We provide simple examples which demonstrate the capabilities of the microscopic model.     

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.     

Delamination growth in Fibre Metal Laminates under variable amplitude loading

This paper presents the experimental and analytical investigation of the effect of variable amplitude (VA) load sequences on delamination behavior in Fibre Metal Laminates (FMLs). Delamination tests were performed and results are compared with linear damage accumulation predictions. Scanning Electronic Microscopy (SEM) was used to analyse the delaminated surfaces to study the delamination growth rate under VA loading in more detail. The correlation between test results and predictions highlighted the absence of load sequence and interaction effects in delamination growth rate under VA loading. This correlation is supported by the SEM observations.     

Parametric study of failure mechanisms and optimal configurations of pseudo-ductile thin-ply UD hybrid composites

The effect of different parameters on the gradual failure and pseudo-ductility of thin UD hybrids is studied using an analytical method developed recently. Damage mode maps are proposed to show the effect of different geometric parameters for a specific material combination. This type of map is a novel and efficient method to find the optimum configuration of UD hybrids and also indicates the importance of thin layers to achieve the optimum geometric parameters in practice. The material parametric study reveals that there is always a trade-off between the “yield stress” and the amount of pseudo-ductility; higher yield stresses leads to lower pseudo-ductility and vice versa. However, application of high-stiffness fibres with high strengths as the low strain material can provide both better pseudo-ductility and yield stress.     

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

A numerical model for delamination growth simulation in non-crimp fabric composites

In this paper, a novel finite-element tool, for the simulation of delamination growth in non-crimp fabric (NCF) composite materials, is presented. The proposed finite-element tool is based on the stiffness averaging method (SAM), on the modified virtual crack closure technique (MVCCT) and on the penalty method (PM); all these methods have been implemented in the research oriented B2000 finite-element code. The stiffness averaging method allows taking into account the effects of the processing variables, which characterize the representative volume element (RVE) of the non-crimp fiber composites (NCF) on their mechanical performances; while the modified virtual crack closure technique is used to determine the strain energy release rate (SERR) for the delamination growth. Already available experimental data on Mode I fracture toughness, obtained by using double cantilever beam (DCB) tests have been employed for validation purpose of numerical procedure. The modeling of DCB tests, considering different geometrical cases, has been performed by means of non-linear analyses. Excellent results in terms of deformed shapes and load–displacement curve, compared with experimental data, are reported to support the validity and the accuracy of the presented computational procedure. Moreover, the ability of the developed tool to take account for the NCF performances variability with processing parameters along with the delamination growth has been assessed and critically discussed.     

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.     

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.     

Investigation of the response to low velocity impact and quasi-static indentation loading of particle-toughened carbon-fibre composite materials

This work investigates damage caused by low velocity impact and quasi-static indentation loading in four different particle-toughened composite systems, and one untoughened system. For impact tests, a range of energies were used between 25 and 50 J. For QSI, coupons were interrupted at increasing loading point displacement levels from 2 to 5 mm to allow for monitoring of damage initiation and propagation. In both loading cases, non-destructive inspection techniques were used, consisting of ultrasonic C-scan and X-ray micro-focus computed tomography. These techniques are complemented with instrumentation to capture force–displacement data, whereby load-drops are associated with observed damage modes. Key results from this work highlight particular issues regarding strain-rate sensitivity of delamination development and an earlier onset of fibre fracture associated with particle-toughened systems. These issues, in addition to observations on the role of micro-scale events on damage morphology, are discussed with a focus on material development and material testing practices.