Failure prediction for a glass/epoxy cruciform specimen under static biaxial loading

Material models were developed to predict the mechanical behavior of glass/epoxy multidirectional laminates under complex stress states. An incremental plane stress analysis was performed, taking into account the anisotropic material non-linearity, separate damage onset conditions and distinct post-failure stiffness degradation rules. Theoretical formulations were implemented in a shell element of the 1st order shear deformation theory. Numerical results were validated via comparison with test data from cruciform specimens subjected to static biaxial tensile loading. Local strain gauge and full-field strain measurements, obtained using the Digital Image Correlation (DIC) technique, corroborated numerical predictions. Improved strength and failure mode results were derived when, in addition to stiffness reduction, compressive strength degradation in the fiber direction was also considered.     

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.     

Electrical resistance change and crack behavior in carbon nanotube/polymer composites under tensile loading

This paper studies the electrical and mechanical responses of cracked carbon nanotube (CNT)-based polymer composites. Tensile tests were performed on single-edge cracked plate specimens of the nanocomposites at room temperature and liquid nitrogen temperature (77 K), and the electrical resistance change of the specimens was monitored. An analytical model based on the electrical conduction mechanism of CNT-based composites was also developed to predict the resistance change resulted from crack propagation. The crack induced resistance change was calculated, and a comparison of the analytical predictions against the experimental data was made to validate the applicability of the model. In addition, the fracture properties of the nanocomposites were assessed in terms of the J-integrals using an elastic-plastic finite element analysis.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part I: Material constitutive model

A life prediction algorithm and its implementation for a thick-shell finite element formulation for GFRP composites under constant or variable amplitude loading is introduced in this work. It is a distributed damage model in the sense that constitutive material response is defined in terms of meso-mechanics for the unidirectional ply. The algorithm modules for non-linear material behaviour, pseudo-static loading-unloading-reloading response, Constant Life Diagrams and strength and stiffness degradation due to cyclic loading were implemented on a robust and comprehensive experimental database for a unidirectional glass/epoxy ply. The model, based on property definition in the principal coordinate system of the constitutive ply, can be used, besides life prediction, to assess strength and stiffness of any multidirectional laminate after arbitrary, constant or variable amplitude multi-axial cyclic loading. Numerical predictions were corroborated satisfactorily by test data from constant amplitude fatigue of glass/epoxy laminates of various stacking sequences.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.     

Finite element modeling of post-fire flexural modulus of fiber reinforced polymer composites under constant heat flux

In this study, a simple 1D finite element model was developed to predict the temperature evolution and post-fire mechanical degradation of glass fiber reinforced polymers (FRPs) subjected to constant heat fluxes, including 35 kW/m², 50 kW/m², 75 kW/m², and 100 kW/m². A temperature-dependent post-fire mechanical property model was proposed and implemented. The calculated temperature and residual mechanical moduli showed good agreement with the experimental data. By properly selecting the parameters of the model, an effective strategy was demonstrated to design FRP structure with enhanced durability.     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part I: Experimental

Helicopter blades are made of composite materials mainly loaded in fatigue and have normally relatively thin skins. A through-the-thickness crack could appear in these skins. The aim of this study is to characterize the through-the-thickness crack propagation due to fatigue in thin woven glass fabric laminates. A technological test specimen is developed to get closer to the real loading conditions acting on these structures. An experimental campaign is undertaken which allows evaluating crack growth rates in several laminates. The crack path is linked through microscopic investigations to specify damage in woven plies. Crack initiation duration influence on experimental results is also underlined.     

Modeling damage and load redistribution in composites under tension–tension fatigue loading

A fatigue model developed for composite laminates and based on the cycle-by-cycle probability of failure has been modified to account for damage creation and evolution and its effect on cycles to failure. The residual strength of different parts of the laminate is determined during cyclic loading and damage such as matrix cracking is quantified along with its effect on load redistribution and cycles to failure of different parts of the laminate. The model does not require any curve fitting or experimentally measured data other than basic material static strength values and their associated experimental scatter. The model is applied to uni-directional and cross-ply laminates. A stress-based approach using energy minimization and calculus of variations is used. The model predictions range from fair to excellent.     

Behaviour of ±45° glass/epoxy filament wound composite tubes under quasi-static equal biaxial tension–compression loading: experimental results

The primary aim of this paper is to present results describing in detail the behaviour of ±45° E-glass/MY750 (GRP) tubes, of various wall thicknesses, subjected to equal biaxial tension–compression loading, generated under combined internal pressure and axial compression. The role played by the non-linear lamina shear has also been assessed by comparing various shear stress–strain curves for embedded laminae (extracted from tests on ±45° tubes subjected to circumferential: axial stress ratios SR=1:0, 1:−1 and 2.3:−1) with that of an ‘isolated’ lamina (measured from torsion of 90° tubes). Extracted shear failure strains, for embedded laminae, were more than four fold larger than those measured at ultimate failure for an ‘isolated’ lamina. Soft characteristics were observed in the embedded lamina and these were believed to be due to interaction between early matrix damage initiation (and propagation) and shear. Factors affecting the behaviour of the tubes, such as bulging, scissoring, thermal stresses and stress variation through the thickness are discussed.     

A parametric study of fiber volume fraction distribution on the failure initiation location in open hole off-axis tensile specimen

We present a model to study the effect of the spatial distributions in fiber volume fraction on the failure initiation location in the open hole off-axis tensile. These variations are introduced with a micromechanical enhancement dehomogenization process. Good agreement is obtained between our predicted failure locations and experimental results by considering a failure criterion based on the effective shear strain in the matrix. The predicted failure angle distribution is in good agreement with the experimental results when the variability in the fiber volume fraction is included in the simulations.     

Multi-scale ballistic material modeling of cross-plied compliant composites

The open-literature material properties for fiber and polymeric matrix, unit-cell microstructural characteristics, atomic-level simulations and unit-cell based finite-element analyses are all used to construct a new continuum-type ballistic material model for 0°/90° cross-plied highly-oriented polyethylene fiber-based armor-grade composite laminates. The material model is formulated in such a way that it can be readily implemented into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User Documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc. (2007)] and ABAQUS/Explicit [ABAQUS version 6.7, User Documentation, Dessault Systems, 2007] as a User Material Subroutine. Model validation included a series of transient non-linear dynamics simulations of the transverse impact of armor-grade composite laminates with two types of projectiles, which are next compared with their experimental counterparts. This comparison revealed that a reasonably good agreement is obtained between the experimental and the computational analyses with respect to: (a) the composite laminates’ capability, at different areal densities, to defeat the bullets with different impact velocities; (b) post-mortem spatial distribution of damage within the laminates; (c) the temporal evolution of composite armor laminate back-face bulging and delamination; and (d) the existence of three distinct penetration stages (i.e. an initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix de-bonding/decohesion and the final stage associated with the extensive back-face delamination and bulging of the armor panel).     

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.     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

Co-cured in-line joints for natural fibre composites

Little attention has been paid to joining unidirectionally-reinforced high strength natural fibre composites in the manufacture of engineered structures. Therefore the main objective of the paper is to investigate the effect of joint geometry on the strength of natural fibre composite joints. Epoxy-bonded single lap shear joints (SLJs) between henequen and sisal fibre composite elements were manufactured and tested in tension to assess the shear strength of the structural bonds. The performance of co-cured joints, termed “intermingled fibre joints” (IFJs) and “laminated fibre joints” (LFJs) was also evaluated. These IFJ and LFJ configurations possess much higher lap shear strengths than the single lap shear joints and the failure modes of the three joint configurations are compared. SLJ and LFJ joints have been modelled using finite element analysis, allowing interpretation of the experimental observations.     

Predicting dynamic in-plane compressive properties of multi-axial multi-layer warp-knitted composites with a meso-model

Proper prediction of material microstructure from known processing conditions and constituent material properties is a critical step to determine the bulk properties of the composite. This paper reports a meso-structure model of multi-axial multi-layer warp-knitted (MMWK) composites from an elastic–plastic material model considering the strain rate effect for the components of the MMWK composite. The representative unit cell (RUC) of fiber tow is created to obtain the elastic–plastic parameters of the fiber tow. The 3D meso-structure model of the MMWK composite is based on an idealized geometrical model according to the preform structure of the MMWK fabric. The model is used to investigate the effect of the volume fraction of the knitting yarn on the dynamic in-plane compressive properties. The results show that the fiber tow failure at large extent is mainly caused by the micro cracking of the matrix, and the effects of the knitting yarn on the mechanical properties of MMWK composite are very limited. Particularly, MMWK composites could be considered as laminates when the volume fraction of the knitting yarn is low, such as below 1.5%. Experiments were also conducted to validate the results from the simplified meso-structure model of the MMWK composite. The material is found to be strain rate sensitive, and the experimental and predicted results agree well with respect to the compressive strength and modulus of the composite. This confirms that the meso-structure MMWK composite model proposed is capable of capturing the essential features for the response of the composite under different strain rate conditions at the meso-level.     

A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis

A simple model based on experimental observations of the yarn-parallel biaxial extension of PVC-coated polyester fabric cruciform specimens is proposed. In situ loading conditions are considered. The material behaviour is assumed to be plane stress orthotropic for a particular load ratio, while the elastic properties can vary with the load ratio in order to represent the complex interaction between warp and fill yarns. A linear relationship is experimentally found between elastic moduli and normalized load ratios for a wide range of PVC-coated polyester (Type I to Type IV). Two new parameters corresponding to the moduli variations are introduced to complement the existing plane stress orthotropic model. Theoretical results show that only five biaxial tests are required to accurately describe the material response with the proposed material model. Finally, the model was integrated in a commercial finite element software. It is shown that the proposed material model significantly increases the accuracy of the finite element predictions compared to the standard orthotropic linear material model with almost identical computation times.     

Dynamic response of full-scale sandwich composite structures subject to air-blast loading

Glass-fibre reinforced polymer (GFRP) sandwich structures (1.6 m × 1.3 m) were subject to 30 kg charges of C4 explosive at stand-off distances 8–14 m. Experiments provide detailed data for sandwich panel response, which are often used in civil and military structures, where air-blast loading represents a serious threat. High-speed photography, with digital image correlation (DIC), was employed to monitor the deformation of these structures during the blasts. Failure mechanisms were revealed in the DIC data, confirmed in post-test sectioning. The experimental data provides for the development of analytical and computational models. Moreover, it underlines the importance of support boundary conditions with regards to blast mitigation. These findings were analysed further in finite element simulations, where boundary stiffness was, as expected, shown to strongly influence the panel deformation. In-depth parametric studies are ongoing to establish the hierarchy of the various factors that influence the blast response of sandwich composite structures.     

Compressive damage mechanism of GFRP composites under off-axis loading: Experimental and numerical investigations

Experimental and computational studies of the microscale mechanisms of damage formation and evolution in unidirectional glass fiber reinforced polymer composites (GFRP) under axial and off-axis compressive loading are carried out. A series of compressive testing of the composites with different angles between the loading vector and fiber direction were carried out under scanning electron microscopy (SEM) in situ observation. The damage mechanisms as well as stress strain curves were obtained in the experiments. It was shown that the compressive strength of composites drastically reduces when the angle between the fiber direction and the loading vector goes from 0° to 45° (by 2.3–2.6 times), and then slightly increases (when the angle approaches 80–90°). At the low angles between the fiber and the loading vector, fiber buckling and kinking are the main mechanisms of fiber failure. With increasing the angle between the fiber and applied loading, failure of glass fibers is mainly controlled by shear cracking. For the computational analysis of the damage mechanisms, 3D multifiber unit cell models of GFRP composites and X-FEM approach to the fracture modeling were used. The computational results correspond well to the experimental observations.     

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.     

Establishing a new Forming Limit Curve for a flax fibre reinforced polypropylene composite through stretch forming experiments

In developing an understanding of the failure in natural fibre reinforced polymer composites, the failure limits of this class of the material system are required. It is found that the conventional Forming Limit Curve is not suitable to predict the failure initiated in the natural fibre composite as principal strains cannot differentiate the strain on the flax fibres and the polypropylene matrix. This study proposes a new Forming Limit Curve for the composite which expresses limiting fibre strain as a function of forming mode depicted by the ratio of minor strain to major strain. The new Forming Limit Curve, along with the Maximum Strain failure criterion have been successfully implemented in FEA simulations, and numerical simulations suggest that the former is more accurate. The current work provides an innovative method to predict the onset of failure in natural fibre composites, which can be applied in composite forming and structural design.