Tensile failure of laminates containing an embedded wrinkle; numerical and experimental study

The failure of a quasi-isotropic composite laminate containing an embedded out-of-plane fibre wrinkle defect was investigated under tension loading. Laboratory test specimens with controlled severity of fibre waviness were manufactured. Along with recording load–displacement data, high resolution camera images were taken at regular intervals which monitored the initiation and interaction of different damage mechanisms during test. Three-dimensional FE models were built following the geometry of actual test specimens. The information obtained from the tests was used to develop user material subroutines, implemented in Abaqus/Explicit as continuum damage and cohesive zone models for intra- and inter-ply failure respectively. The results of the simulations showed very good correlation with test observations in terms of failure load, location of damage initiation and interaction between different damage mechanisms for a range of waviness cases tested.     

Micro-mechanical modelling of shear-driven fibre compressive failure and of fibre kinking for failure envelope generation in CFRP laminates

A micro-mechanical Finite Element (FE) model is used to investigate the failure mechanisms and generate failure envelopes for fibre reinforced composites under combined in-plane shear and longitudinal compressive loading. The results show that the failure envelopes are defined by two regions corresponding to different failure mechanisms: (i) shear-driven fibre compressive failure and (ii) kinking/splitting. The FE model is also used to reproduce and give insight into different experimental trends typically reported in the literature.     

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length (a_e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy (G_Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength (σ_u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.     

An experimental and finite element study of the transverse bending behaviour of CFRP composite T-joints in vehicle structures

The behaviour of a woven fabric carbon/epoxy composite T-joint (representing a simplified version the T-joint located at the connection between the B-pillar and the longitudinal rocker in a car body structure) is investigated using experimental and numerical methods. Details of the manufacturing process and experimental design factors are considered to understand their influence on the performance of the T-joint structure. The experimental results reveal the influence of manufacturing process and experimental setup on the load-carrying capacity and failure mode of the T-joint. Numerical simulation accurately predicts the stress distribution and load-carrying capacity of the T-joint obtained from experimental tests. The FEM model, which includes the adhesive interface layers at the edges, convincingly represents the experimentally found stiffness: the error is less than 3%. According to Hashin matrix tension criteria, the first ply failure occurs at 3.746 kN when the Hashin failure index (R) becomes equal to 1. Whereas, in the case of experimental tests, the first ply failure occurs around 3.4 kN, at which force the first load drop is observed.     

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.     

Modelling of the bond behaviour of tuff elements externally bonded with FRP sheets

The performance of fibre reinforced plastic (FRP) materials used for external strengthening depends strongly on the bond behaviour at the FRP-substrate interface. In this paper, the results of an analytical model and of two Finite Element (FE) models (bi-and three-dimensional) for simulating bond behaviour in FRP-strengthened masonry elements using zero-thickness interface elements are presented. The primary parameters of bilinear and nonlinear bond-slip laws were determined from experimental results of single shear bond tests that the authors conducted on masonry blocks of yellow tuff bonded with FRP carbon and glass fabrics. Several parametric analyses were conducted to estimate the effect of the primary bond law parameters on the global behaviour of the specimens and to determine the effective bonded length for the investigated masonry support.     

Mixed-mode quasi-static failure criteria for adhesively-bonded pultruded GFRP joints

The strain energy release rates of adhesively-bonded pultruded GFRP joints were determined experimentally. The crack propagated in the adherend along paths outside the symmetry plane accompanied by fiber bridging. A new method, designated the “extended global method”, was introduced to facilitate mode partitioning in the mixed-mode experiments. Non-linear finite element models were developed in order to quantify the effect of the observed fiber bridging on crack propagation. An exponential traction-separation cohesive law was used to model the fiber bridging zone and calculate the energy release rate due to the fiber bridging, while the virtual crack closure technique was used for calculation of the fracture components at the crack tip. Experimental, analytical and numerical analyses were used to establish quasi-static mixed-mode failure criteria for crack initiation and propagation. The derived mixed-mode failure criteria can be used for simulating progressive crack propagation in other joint configurations comprising the same adhesive and adherends.     

Determination of material parameters for discrete damage mechanics analysis of carbon-epoxy laminates

Discrete damage mechanics (DDM) refers to micromechanics of damage constitutive models that, when incorporated into commercial finite element software via user material subroutines, are able to predict intralaminar transverse and shear damage initiation and evolution in terms of the fracture toughness of the composite. A methodology for determination of the fracture toughness is presented, based on fitting DDM model results to available experimental data. The applicability of the DDM model is studied by comparison to available experimental data for Carbon Epoxy laminates. Sensitivity of the DDM model to h- and p-refinement is studied. Also, prediction of modulus vs. applied strain is contrasted with ply discount results and the effect of in situ correction of strength is highlighted.     

Numerical and experimental study on morphing bi-stable composite laminates actuated by a heating method

This paper presents a new heating actuation method to induce the snap-through phenomenon of bi-stable laminates by manipulating the residual stress in laminates. The mechanism of the heating actuation method is analyzed, and the snap-through process is simulated by the finite element method. The heating actuation experiments on two types of laminates with different stacking sequences are performed. Good agreement is obtained between the experimental data and the finite element analysis (FEA). Subsequently, the heating actuation method is applied to several different bi-stable laminates and investigated by FEA. The FEA results show that this heating actuation method is an effective way to induce the snap-through phenomenon of bi-stable laminates of different thicknesses, sizes and shapes.     

Optimum shapes of scarf repairs

Adhesively bonded scarf repairs are the preferred method for repairing composite structures, limited mainly by the amount of material removal associated with scarfing. In addition to the high strength restoration, scarf repairs also enable recovery of the original external surface as required by aerodynamic and/or external mould line considerations. However, scarf repairs almost inevitably result in the removal of undamaged material to make way for the scarf insert. This can be a particularly significant issue for thick structures, because the scarf length can vary between 20 and 100 times the thicknesses of the parent structure. In this investigation, an optimisation method has been developed for determining the optimum repair shapes for a given biaxial loading condition. The optimum scarf shape is determined by numerically solving the resulting non-linear differential equation governing the scarf angle. The optimum and near-optimum shapes are presented and discussed with respect to computational modelling using the finite element method.     

Representative volume elements for discontinuous carbon fibre composites – Part 1: Boundary conditions

In part 1 of this 2 part paper a method is presented for generating RVE analyses of discontinuous fibre planar distributions of random discontinuous carbon fibre bundles, with no limitation to the fibre volume fraction. An embedded element approach is used to simplify mesh generation for the matrix phase. This approach is shown to yield errors of 1% compared with a more conventional unstructured mesh, whilst offering significant reductions in model size. Periodic boundary conditions are adopted, applying Saint-Venant’s principle to provide an approximation of the effective material properties within an inner RVE region, some distance away from the outer boundary of the model. The critical decay length of prescribing such boundary conditions is shown to be approximately two times the fibre length in all cases, when a heterogeneous material (rather than homogeneous material) is used to model the outer region.     

Compressive failure of laminates containing an embedded wrinkle; experimental and numerical study

An experimental and numerical study has been carried out to understand and predict the compressive failure performance of quasi-isotropic carbon–epoxy laminates with out-of-plane wrinkle defects. Test coupons with artificially induced fibre-wrinkling of varied severity were manufactured and tested. The wrinkles were seen to significantly reduce the pristine compressive strength of the laminates. High-speed video of the gauge section was taken during the test, which showed extensive damage localisation in the wrinkle region. 3D finite element (FE) simulations were carried out in Abaqus/Explicit with continuum damage and cohesive zone models incorporated to predict failure. The FE analyses captured the locations of damage and failure stress levels very well for a range of different wrinkle configurations. At lower wrinkle severities, the analyses predicted a failure mode of compressive fibre-failure, which changed to delamination at higher wrinkle angles. This was confirmed by the tests.     

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.     

Bending strength of adhesive joints in microelectronic components: Comparison of edge-bonding and underfilling

The bending strength of underfilled and edge-bonded ball grid array (BGA) microelectronic packages assembled on printed circuit boards (PCBs) was compared using double cantilever beam (DCB) specimens. All specimens with fillets of the same size and shape failed at the same load, with cracks initiating and propagating within the PCB. This was consistent with measurements of the crack initiation strain energy release rate for PCB interfacial failure, which was significantly smaller than that of cohesive failure within the adhesives. Finite element analysis (FEA) indicated that the stress state in the PCB near the PCB-fillet interface in both underfilled and edge-bonded specimens was only a function of the adhesive fillet size and shape, and independent of the extent of the adhesive layer between the PCB and the BGA, and independent of the adhesive mechanical and thermal properties over the broad range of properties of the tested adhesives. This explained why decreasing the fillet curvature in edge-bonded specimens produced a significant increase in the joint strength. The crack path in the PCB of the edge-bonded specimens was found to change with the adhesive cure temperature; however, this had a negligible effect on the failure load.     

Design of copper filled fibreglass moulds for manufacturing a customized product using linear programming optimization and finite element analysis

This paper presents a design procedure and cost analysis for a mould made of glass fibre reinforced polyester filled with copper particles (GRP/copper). It also describes their potential use in rotational moulding as an alternative to steel and aluminium moulds operating at high temperatures up to 250 °C. The thermal conductivity of glass reinforced polyester (GRP) was improved by incorporating copper particles acting as fillers in the composite. An optimum composite structure consisting of 25% glass fibres, 45% polyester, and 30% copper was achieved by linear programming search optimization methods. Then a finite element analysis (FEA) of a typical GRP/copper mould made of the optimized composite structure under thermal loading was conducted. The induced thermal stresses obtained from FEA were used to check the failure condition of the mould using the Tsai–Hill failure criterion. The FEA design procedure was also used to determine the mould thickness with a safety factor of at least four. Scheduling and cost analysis showed that 76% reduction in production time and 64% reduction in manufacturing costs have been achieved with the developed method.     

Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element

We present new numerical results in buckling failure analysis of cracked composite functionally graded plates subjected to uniaxial and biaxial compression loads. An accurate extended 3-node triangular plate element in the context of the extended finite element method (XFEM) is developed, integrating the discrete shear gap method (DSG) to eliminate shear-locking. The plate kinematics is based on the Reissner–Mindlin theory, and material properties are assumed to vary through thickness direction, obeying a power law distribution. The developed DSG-XFEM is found to be effective and accurate as it owns many desirable advantages: conveniently representing crack geometry which is independent of the mesh; shear-locking effect is no longer valid; mesh distortion is insensitive and controllable; thin plates is possible; triangular elements are easily generated for problems even with complex geometries; and high accuracy. All these arisen features are demonstrated through numerical examples and the effects of crack-length, material gradation, mesh distortion, inclined angles of cracks, boundary conditions, width-to-thickness ratio, length ratio, etc. on the critical buckling coefficient (CBC) are analyzed. Numerical results reveal that the material gradation, crack-length, thickness, length ratios, etc. have a strong effect on the behavior of CBC. This phenomenon is mainly attributed to the plate stiffness degradation due to the presence of local defects and material composition. Also, the boundary conditions greatly alter the CBC whereas the inclination of cracked angle is found to be insignificant.     

Effect of adhesive fillet geometry on bond strength between microelectronic components and composite circuit boards

Printed circuit boards (PCBs) assembled with ball grid array (BGA) microelectronics packages were tested in a double cantilever beam (DCB) configuration. The results were compared for a filled and an unfilled underfill epoxy adhesive as well as a cyanoacrylate adhesive. The original fillet, formed in the underfilling process, was modified to create fillets of different sizes. Regardless of the underfill thermal and mechanical properties as well as its curing profile, the crack initiation load and the failure mode were solely a function of the size of the underfill fillet, and the failure always initiated within the PCB. Moreover, the strength of the underfilled solder joints was increased significantly (approximately 100%) by the presence of a relatively large fillet. This effect of the underfill fillet on the crack path and the fracture load was then examined in terms of differences in the stress states using a finite element model.     

High resolution tomographic imaging and modelling of notch tip damage in a laminated composite

Synchrotron radiation computed tomography (SRCT) has been used to observe in situ damage growth and enable micromechanical damage characterization in [90/0]_S carbon fibre–epoxy composite samples loaded in uniaxial tension to stresses ranging from 30% to 90% of the nominal failure stress. A 3-D finite element model has been constructed to predict crack opening displacements and shear displacements in the 0° plies resulting from thermal residual stress imposed during autoclave cure and from the application of mechanical load. Of particular interest is the demonstration of SRCT as a technique to enable direct, in situ, 3-D, non-destructive damage quantification to assist model development and provide model validation. In addition it has been identified that SRCT has the potential for full field analysis of strain re-distributions during damage growth.     

Pull out of FRP reinforcement from masonry pillars: Experimental and numerical results

In this paper, debonding phenomena between carbon fiber reinforced polymer (CFRP) strips and masonry support were investigated on the basis of single-lap shear tests, considering different dimensions of the bond length. To capture the post-peak response of the CFRP–masonry joint, the slip between the support and the reinforcement strip was controlled using a clip gauge positioned at the end of the reinforcement. The tests were simulated by means of a finite element model able to capture the post-peak snap-back behavior due to the failure process. The numerical model is based on zero-thickness interface elements and on a proper non-linear cohesive law. The comparison between experimental and numerical results was performed in terms of overall response, measured by both the machine stroke and the clip gauge positioned at the free end of the reinforcement. The cases of effective bond length greater and lesser than the minimum anchorage length, suggested by the CNR Italian recommendation, were considered.