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.     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

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.     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part II: Modelling

Fatigue propagation of a through-the-thickness crack in thin woven glass laminates is difficult to model when using homogeneous material assumption. Crack growth depends on both the fatigue behaviour of the fibres and of the matrix, these two phenomena occurring at different time and space scales. The developed finite element model is based on the architecture of the fabric and on the fatigue behaviours of the matrix and the fibre, even if the pure resin and fibre behaviours are not used. That thus limits the physical meaning of this model. Basically, the objective of this simulation is to illustrate and to confirm proposed crack growth mechanism. The fatigue damage matrix is introduced with user spring elements that link the two fibre directions of the fabric. Fibre fatigue behaviour is based on the S-N curves. Numerical results are compared to experimental crack growth rates and observed damage in the crack tip. Relatively good agreement between predictions and experiments was found.     

Numerical experimental analysis of hybrid double lap aluminum-CFRP joints

Due to their reliability and ease of assembly, both the adhesively bonded and the mechanical joints are commonly used in different fields of modern industrial design and manufacturing, to joint composite materials or composites with metals.As it is well known, adhesively bonded joints are characterized by high stiffness and good fatigue life, although delamination phenomena localized near the free edges may limit their use, especially for applications where corrosive environments and/or moisture can lead to premature failure of the bonding. In these cases, a possible alternative is given by the well-known mechanical joints. On the contrary, these last joints (bolted, riveted) require a preliminary drilling of the elements to be joined, that may cause localized material damage and stress concentration, especially for anisotropic laminates characterized by high stress concentration factors and easy drilling damaging, with significant decrease of the load-carrying capacity of the joined elements. In order to exploit the advantages of the bonded joints and those of the mechanical joints, both industrial manufacturing and research activity have been focused recently on the so called hybrid joints, obtained by the superposition of a mechanical joint to a simple adhesively bonded joint.In order to give a contribution to the knowledge of the mechanical behavior of hybrid bonded/riveted joints, in the present work a numerical–experimental study of bonded/riveted double-lap joints between aluminum and carbon fiber reinforced polymer (CFRP) laminates, has been carried out. It has permitted to highlight both the static and the fatigue performance of such joints obtained by using aluminum and steel rivets, as well as to known the particular damage mechanisms related also to the premature localized delamination of the CFRP laminate due to the riveting process.     

Analysis of adhesively bonded CFRE composite scarf joints modified with MWCNTs

The main objective of the present work is to improve the performance of bonded joints in carbon fiber composite structures through introducing Multi-Walled Carbon Nanotubes (MWCNTs) into Epocast 50-A1/946 epoxy, which was primarily developed for joining and repairing of composite aircraft structures. Results from tension characterizations of structural adhesive joints (SAJs) with different scarf angles (5–45°) showed improvement up to 40% compared to neat epoxy (NE)–SAJs. Special attention was considered to investigate the performance of SAJs with 5° scarf angle under different environments. The tensile strength and stiffness of both NE-SAJs and MWCNT/E-SAJs were dramatically decreased at elevated temperature. Water absorption showed a marginal drop of about 2.0% in the tensile strength of the moist SAJs compared to the dry one. Cracks initiation and propagation were detected effectively using instrumented-SAJs with eight strain gauges. The experimental results agree well with the predicted using three-dimensional finite element analysis model.     

Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2 + Ni) functionally graded bolted joint

Ceramic–metal functionally graded materials (FGMs) have been extensively used in aerospace engineering where high strength and excellent heat insulation materials are desired. In this paper, the thermodynamic behavior of the Thermal Protection System (TPS) used bolted joints made up of porous ZrO₂/(ZrO₂ + Ni) FGMs is investigated by finite-element (FE) modeling. The bolted joint is subjected to reentry heating corresponding to the Access to Space Vehicle. Thermodynamic simulations are carried out to yield the transient response of the porous ZrO₂/(ZrO₂ + Ni) functionally graded bolted joint (FGBJ). The effects of the preload on the thermomechanical behavior and service reliability of the bolted joint are numerically analyzed in detail by ABAQUS codes. It is found that the preload relaxation of the bolted joint occurs at elevated temperature, and the preload has significant influence on service reliability of the bolted joint under transient thermomechanical circumstances. With the increase of the preload, stress concentration which occurs at the root of the first thread of the bolt increases rapidly and predominates in service reliability. Proper preload is thus defined to balance the service reliability and tightness of the bolted joint. Further studies show that the shape of the nut has a great effect on the stress concentration of the thread, the optimized nut is designed to reduce the stress concentration of the thread, and thus the reliability of the bolted joint is also improved.     

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.     

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.     

Mechanical characterization of rubberized concrete using an image-processing/XFEM coupled procedure

A coupled (two-step) numerical procedure to characterize the mechanical behaviour of Rubberized Concrete (RuC) is proposed and validated in this paper. In particular, the splitting tensile strength test is described in detail. In the first step, MATLAB Image Processing is used to obtain the model geometry and the RuC heterogeneous configuration (distribution of rubber particles within the concrete matrix). In the second step, the Extended Finite Element Method (XFEM) included in ABAQUS software is used to simulate the inelastic behaviour of the concrete matrix and allow the nucleation and development of cracks, as well as the damage evolution and ultimate strength of the RuC specimen cross-section. Additionally, a set of experimental results on mechanical behaviour of RuC is presented. This shows that RuC has both lower strength and stiffness but higher ductility (less brittle behaviour) than normal concrete (NC). Finally, a good agreement between the two-step procedure results and the experimental results (in terms of indirect tensile strength, stiffness and failure mode) is observed.     

Failure analysis of quasi-isotropic CFRP laminates under high strain rate compression loading

Dynamic compressive strength of quasi-isotropic fiber composite is investigated experimentally and also numerically simulated. In-plane compression tests at strain rates around 400/s quasi-isotropic laminates were performed using the Split Hopkinson Pressure Bar (SHPB). The material system used was Texipreg^® HS160 REM, comprising high strength unidirectional carbon fiber and epoxy resin. The dynamic strength of quasi-isotropic laminates exhibits a considerable increase when compared to the static values. The finite-element model used ABAQUS™ three-dimensional solid elements C3D8I with 8 nodes and user-defined interface finite elements with 8 nodes [Gonçalves JPM, de Moura MFSF, de Castro PMST, Marques AT. Interface element including point-to-surface constraints for three-dimensional problems with damage propagation. Eng Comp: Int J Comput Aided Eng Software 2000;17(1):28–47; de Moura MFSF, Pereira AB, de Morais AB. Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross-ply laminates. Fatigue Fract Eng Mater Struct 2004;27(9):759–66.]. These interface elements which connect the three-dimensional solid elements modeling the composite layers, include a cohesive damage model allowing the simulation of delamination initiation and propagation. Hence the present model assumes that the phenomenon of failure under these conditions is mainly dictated by interface delamination. This is supported by experimental tests which showed that all quasi-isotropic laminates split into several almost intact sublaminates. The model compares very well with experimental results, confirming the formulated hypothesis that the internal layer damage does not markedly contribute to the quasi-isotropic laminate failure.     

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.     

Subcritical damage mechanisms of bolted joints in CFRP composite laminates

A detailed experimental programme is presented that was conducted in order to establish a data base for strength and subcritical damage mechanisms of bolted joints in CFRP composite laminates. Single fastener double-shear tensile tests for various joint geometries were performed for a range of cross-ply and quasi-isotropic lay-ups of HTS40/977-2 CFRP material system. Penetrant enhanced X-ray radiography was used to define the subcritical damage locations which are of great importance when modelling the failure response of the joints. It is suggested that the subcritical damage planes can be modelled using cohesive zone elements (CZEs) in order to develop physically based strength prediction methods for bolted joints in CFRP laminates.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

Numerical optimization of strengthening disturbed regions of dapped-end beams using NSM and EBR CFRP

This paper presents a parametric investigation, based on non-linear finite element modeling, to identify the most effective configuration of carbon fiber-reinforced polymers (CFRP) for strengthening reinforced concrete (RC) dapped-end beams. Following a field application and laboratory tests, it focuses on effects of 24 externally bonded (EBR) and near surface mounted reinforcement (NSMR) configurations on yield strain in steel and the capacity and failure mode of dapped-end beams. The investigated parameters were the mechanical properties of the CFRP, the strengthening procedure and the inclination of the fibers with respect to the longitudinal axis. Two failure scenarios were considered: rupture and debonding of the FRP. The results indicate that high-strength NSM FRPs can considerably increase the capacity of dapped-end beams and the yielding strains in reinforcement can be substantially reduced by using high modulus fibers.     

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.     

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.     

Post buckling analysis of the shape memory polymer composite laminate bonded with alloy film

As a new kind of smart materials, shape memory polymer composites (SMPCs) are being used in large in-space deployable structures. However, the recovery force of pure SMPC laminate is very weak. In order to increase the recovery force of a SMPC laminate, an alloy film was bonded on the surface of the laminate. This paper describes the post bulking behavior of the alloy film reinforced SMPC laminate. The energy term associate with this in-plane post buckling have been given .Based on the theorems of minimum energy, a mathematical model is derived to describe the relation between the strain energy and the material and geometry parameters of the alloy film reinforced SMPC laminate. The finite element model (FEM) is also conducted to demonstrate the validity of the theoretical method. The relation between the recovery force and the material geometry parameters were also investigated. The presented analysis shows great potential in the engineering application such as deployment of space structures.     

Determination of cohesive laws of composite bonded joints under mode II loading

In this work, mode II cohesive laws of carbon–epoxy composite bonded joints were obtained using the direct method applied to the end notched flexure (ENF) test. The direct method is based on the differentiation of the relation between the evolution of the fracture energy (J_II) and the crack tip opening displacement in mode II (CTOD_II) during the test. A data reduction scheme based on equivalent crack length concept was used to obtain the evolution of the fracture energy during the test. The method allows overcoming problems related to identification of crack tip in mode II tests and the presence of a non-negligible fracture process zone (FPZ), which both difficult the right estimate of J_II. The digital image correlation technique (DIC) was used to monitor the CTOD_II, which was synchronized with the load–displacement data. A trapezoidal cohesive law was fitted to the experimental one in order to perform numerical simulations using finite element analysis. The main goal was to validate all the procedure used to get the cohesive laws. The good agreement obtained between the numerical and experimental load-CTOD_II curves and between the cohesive laws demonstrates the adequacy of the proposed procedure concerning the evaluation of the composite bonded joints cohesive laws under mode II loading.     

Resistance to delamination of 3D woven textile composites evaluated using End Notch Flexure (ENF) tests: Cohesive zone based computational results

The flexural response of 3D woven textile composite panels containing an edge crack is evaluated using the End Notch Flexure (ENF) test. In doing so, the effectiveness of 3D reinforcement in increasing and/or eliminating delamination is demonstrated. A finite element model of the ENF configuration using the Discrete Cohesive Zone Model (DCZM) was used to evaluate the deformation response and fracture properties corresponding to the experimental results presented in Pankow et al. (2011) [1]. A modified trapezoidal traction law was used in the DCZM to computationally evaluate the ENF test results. Good agreement between experimental results and predictions are reported, up to the point at which the crack reaches under the loading roller and damage begins to occur locally under the roller.