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Abstract: In nonlinear fracture mechanics testing of thin-sheet short-fiber composites, special problems occur that do not appear in other engineering materials, such as steels. The most important problem is the formation of a long process zone, where fiber pull-out, realignment and breakage occur, making an optical crack length measurement impossible. This impedes the determination of a reproducible value of the fracture toughness and the construction of a crack growth resistance curve. Two new approaches are presented to overcome this problem. In the first one, a procedure is presented to determine experimentally the cohesive zone relation on deeply-notched double-edge notch tension specimens. The cohesive zone relation enables us, together with the mechanical properties, to simulate numerically a fracture mechanics test on an arbitrary geometry and to determine a crack growth resistance curve. In the second approach, the displacements and strains around the process zone are measured during in situ experiments under an optical microscope using digital image analysis. With this local deformation analysis, a critical local strain is determined where the load bearing capacity of the material decreases to zero. The knowledge of this critical strain is used to find the location of the crack tip and to determine a crack growth resistance curve. The application of the two approaches is demonstrated on commercial printing paper as model material. It is shown that reproducible fracture toughness parameters can be determined with both procedures. [Copyright &y& Elsevier]

This paper proposes a three-dimensional failure criterion model for unidirectional fiber-reinforced composites. In contrast to previous models that only accounted for the effect of fiber misalignment in the presence of longitudinal compressive stress, the proposed failure criterion model comprehensively considers the effect of localized misaligned regions on the failure under any stress state. Another key contribution of this study is the introduction of the effective misalignment angle. Considering effective misalignment angles, the proposed failure criterion model can reasonably reveal the effect of localized misaligned regions on the failure behavior under different stress states. The agreement between the predicted results and the experimental data proves that the proposed model has good applicability. Furthermore, the influence of initial misalignment angles on failure is analyzed under varying stress conditions. The results indicate that even under longitudinal tensile stress, the initial misalignment angle still plays an important role in the failure behavior of materials. [Display omitted] • A three-dimensional failure model considering fiber misalignment is proposed. • The traditional method for determining the misalignment angle is corrected. • Fiber misalignment has an effect on material failure under longitudinal tensile stress. • The influence of the initial misalignment angle on failure is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the coupled Finite Fracture Mechanics criterion is extended to assess the finite fatigue life of orthotropic notched laminated composites. The approach is validated through a comprehensive experimental program conducted on laminated composites under tension-tension cyclic loading conditions with two distinct lay-ups. For a given loading ratio, fatigue tests on plain and cracked specimens are first performed to provide the model inputs, the critical cyclic stress and stress intensity factor amplitudes. Fatigue tests on samples weakened by circular holes of two different radii are then used for blind predictions. Accurate predictions of the number of cycles to failure are achieved without the need for inverse calibration of material properties or deviation from standard testing procedures. Finally, a parametric study is performed to investigate the hole radius effect. It is worth mentioning that the proposed approach is general and can be applied to any notched geometry. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with impact damage and permanent indentation modeling. A numerical model has been elaborated in order to simulate the different impact damage types developing during low velocity/low energy impact. The three current damage types: matrix cracking, fiber failure and delamination, are simulated. Inter-laminar damage, i.e. interface delamination, is conventionally simulated using interface elements based on fracture mechanics. Intra-laminar damage, i.e. matrix cracks, is simulated using interface elements based on failure criterion. Fiber failure is simulated using degradation in the volume elements. The originality of this model is to simulate permanent indentation after impact with a “plastic-like” model introduced in the matrix cracking elements. This model type is based on experimental observations showing matrix cracking debris which block crack closure. Lastly, experimental validation is performed, which demonstrates the model’s satisfactory relevance in simulating impact damage. This acceptable match between experiment and modeling confirms the interest of the novel approach proposed in this paper to describe the physics behind permanent indentation. [Copyright &y& Elsevier]

Abstract: Detecting impact damage is an important factor in maintaining the structural integrity of aerospace composite structures. Since impacts can cause severe reductions in stiffness and strength of composite structures, there is a need to investigate the material’s stiffness and strength after an impact event. The work discussed in this paper is concerned with one overall goal, which is to determine if an impact has caused damage and then to determine the extent of that damage using only the structural responses that are acquired from low-profile surface-mounted transducers. The work presented in this paper demonstrates that responses recorded from these sensors can provide sufficient information to infer impact damage. Previous work by various authors has established that it is possible to distinguish between damaging and non-damaging impacts if the impact force time-history is available. Therefore, it is the requirement that only response data be used here that distinguishes this work from the previous studies. Following a systematic series of experiments, on the induction of impact damage in Carbon Fibre Reinforced Polymer (CFRP) laminates, a damage model was proposed from this work which can provide preliminary information on the type and extent of damages through observations made from Scanning Electron Microscopy (SEM) and X-ray radiography. The model can be used to provide a general understanding on the prediction of damage and failure progression in CFRP as a function of the number of layers and impact energies. To accommodate the results from SEM and X-ray, discussions on outlier analysis and visualisation, which emphasise the idea of discordancy from the discipline of statistics, are presented. Results from discordancy tests, for both univariate and multivariate data, can be used to clearly separate the data (non-damaging and damaging impacts as well as the separation of the type of failure modes) by a calculated threshold value. Both of these features (univariate and multivariate) can be used as damage indicators and proxies for determining the extent of damage. [Copyright &y& Elsevier]

Abstract: An original, ply-level, computationally efficient, three-dimensional (3D) composite damage model is presented in this paper, which is applicable to predicting the low velocity impact response of unidirectional (UD) PMC laminates. The proposed model is implemented into the Finite Element (FE) code ABAQUS/Explicit for one-integration point solid elements and validated against low velocity impact experimental results. Mesh-regularisation of the impact results is one of the greatest challenges in impact damage modelling of composite targets. Currently published mesh-regularisation strategies can produce mesh-size-independent impact results for a very limited range of mesh-sizes. The originality of the model presented in this paper is based on a novel mesh-regularisation strategy, which is applicable to predicting mesh-size-independent impact results for any target discretisation. Accurate modelling of composites’ impact damage using a relatively coarse mesh, and thus at a much reduced computational cost when compared to existing techniques, can be achieved with the proposed method. [Copyright &y& Elsevier]

Abstract: This paper describes fractographic observations from the detailed examination of delamination fracture surfaces and offers an interpretation of the key growth mechanisms. Firstly, the relationship between toughness, delamination failure criteria and fracture morphology is presented and the influence of cusp formation and deformation on toughness is discussed. Observations regarding delaminations migrating through the lamina at multidirectional ply interfaces are then discussed. It is demonstrated how this migration process can be avoided in fracture toughness coupons and consequently the toughness of multidirectional ply interfaces can be characterised. The influence of migration on delamination growth from embedded defects in laminates under compression is presented, and these results are extended to demonstrate how migration influences damage growth in structures. The paper concludes by making recommendations for realistic modelling of migration, and suggests how it can be exploited in damage tolerant structural design. [Copyright &y& Elsevier]

Abstract: This paper relates to a newly developed peel stopper concept for sandwich structures. The proposed concept is a specially designed core insert, which has the ability to confine face sheet debonding/delamination (peeling) by deflecting a delamination crack front away from the face/core interface into the bulk of the sandwich core, and thereby constraining the debonding/delamination to a limited prescribed area. In this paper various peel stopper designs are analysed for their ability to deflect cracks away from propagating along a face–core interface. The crack deflection ability of the studied peel stopper designs leads to design guidelines, which describes the minimum requirements regarding the relation between the two interface toughnesses. The analysis further reveals that compliant peel stopper wedges are preferred because they lead to the lowest interface toughness ratio requirement. This has been confirmed through an experiment with a sandwich beam subjected to three-point bending loading. The experiment has shown that the ability of a peel stopper to deflect cracks is highly dependent on the stiffness of the wedge. [Copyright &y& Elsevier]

Abstract: Degradations initiated near the edges of a laminate can have a significant effect on its state of degradation, even at the core. Indeed, results from the literature show that laminates which have the same stress state at the core can have completely different states of degradation, even far away from the edges. The paper discusses the influence of the edge effect on damage initiation and propagation for a specific example. A computational micromechanical approach to the degradation of laminated composites was developed recently at LMT-Cachan. This is a hybrid approach in which, depending on the scale, the mechanisms are described using continuous damage mechanics or finite fracture mechanics. Initially developed for static loading, this technique is being extended to fatigue and environmental effects. The aim of this paper is to illustrate the capability of such an approach to take into account major observations during cyclic loading in an oxidizing atmosphere, even when edge effects are significant. [Copyright &y& Elsevier]

Abstract: The high quality of a lamina-by-lamina failure analysis of FRP laminates depends on both realistic failure criteria and a correct stress–strain analysis. This paper presents some advances in the non-linear stress–strain analysis of UD laminae with non-flexibilized thermoset matrix as they are used in structural applications. In addition to the well-known non-linearity of the stress–strain curve in pure longitudinal shear τ 21 and uniaxial transverse compression σ 2 there is an influence under combined (σ 2, τ 21)-stress of the normal stress σ 2 on the shear strain γ 21 and an influence of the shear stress τ 21 on the transverse strain ε 2. Although this strain-interaction is already known for a rather long period none of the participants of the Worldwide Failure Exercise (WWFE) has included this effect in the stress–strain analysis. In this paper, a new computational model on a physical basis is presented by which these problems can be handled very easily. The variable of decisive importance for this procedure is the stress exposure ratio f E, which is a measure for the ‘risk of inter-fibre fracture’. In the numerical examples f E is calculated from the new realistic action plane fracture criteria for brittle inter-fibre fracture. [Copyright &y& Elsevier]

Abstract: This paper deals with the dynamic behaviour up to fracture of a three-dimensional carbon/carbon composite (3D C/C). This study is conducted jointly by the LMT and the Centre d’Études de Gramat facilities, a research centre of the French weaponry administration. In the first part, a one and a half dimensional (11/2D) mesomodel dedicated to normal impact is described and used successfully. This model is build through the analysis of the one-dimensional wave propagation in the longitudinal yarns of fibres and the equivalent matrix, the two entities being linked by an interface. For more general impacts, a full three-dimensional mesomodel is needed. This model is presented and identified. The computation of such a model using a classical approach leads to considerable computation costs. In this paper are presented the first results obtained with a dedicated mesoscale computational strategy that is briefly described herein. [Copyright &y& Elsevier]

The vast majority of the fatigue models for fibre-reinforced composites is limited to one-dimensional loading conditions. Due to the heterogeneous and anisotropic nature of composites, the extension of these models towards multi-axial fatigue loading conditions is not straightforward. This paper presents a phenomenological residual stiffness model that predicts the stiffness degradation and (possible) permanent strain in fibre-reinforced polymers under in-plane fatigue loading. The model takes into account the actual stress state in each material point and does not make any assumptions about geometry or boundary conditions of the fatigue loaded specimen. As the presented model has been developed within a larger research programme, the emphasis in this paper lies on the theoretical modelling framework, rather than on an in-depth validation of the model which would require much more detail about the close feedback between experimental data and finite element simulations. Therefore the development of the stress–strain-damage relationships and the damage growth rate equations is explained thoroughly and a few finite element results are presented for plain woven glass/epoxy composites. [Copyright &y& Elsevier]

The attainment of both strength and toughness is a vital requirement for most structural materials. Unfortunately, these properties are generally mutually exclusive in synthetic materials. Natural structural materials defeat the conflict of strength versus toughness, and provide design motifs for the high-performance materials. However, there still lacks a deep understanding of the toughening mechanisms in bioinspired composites. This paper presents a microstructure-based nonlinear fracture mechanics model for staggered composites, to investigate the toughening effect of the nonlinear deformation in the process zone. Firstly, a nonlinear stress–strain relationship of staggered composites is derived, to capture the plastic deformation of the matrix. Then, a multiscale nonlinear fracture mechanics model incorporating the effect of crack bridging and process zone is established based on the above constitutive relation and HRR theory. Finally, the model is used to reveal the influence of geometric and constitutive parameters. The results demonstrate that the process zone leads to a tremendous contribution to the overall toughness. And the crack resistance curve is rising with crack extension due to the increase of the process zone. What is more, there still exists an optimal balance between toughness, stiffness, and strength in biological materials. These results can provide guidelines for the design of high-performance composites. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper addresses the fracture behaviour of bonded composite plates featuring a kissing bond along the crack growth path. Double cantilever beam (DCB) experiments are carried out under a displacement controlled loading condition to acquire the load response. The experimental data are collected and analysed analytically for specimens with and without kissing bond. The following aspects are observed and discussed: effect of the adhesive carrier film, non-smooth crack growth and rising R curve. An analytical model taking into account the aforementioned effects is proposed. The kissing bond leads to unstable crack growth resulting in a loss of the load carrying capacity. The presence of the knit carrier in the adhesive film results in the crack growth process characteristic for the stick-slip phenomena and a significant increase of the resistance to fracture of the bondline by triggering a bridging phenomenon. The model shows a very good agreement with the experimental data. A sound understanding of the fracture process is gained enabling analysis and prediction of the effects of kissing bonds and supporting carrier. [ABSTRACT FROM AUTHOR]

High-performance biological structural materials such as bone and spider silk have evolved soft and stiff components to optimize the load transfer path. This inspired many researchers to achieve engineering composites with significantly improved properties. In this paper, we designed a class of 2D elastomer filled composites with periodic units. The designs of these composites were realized by 3D printing of a soft elastomer and a stiff plastic. The plastic constructed a honeycomb-like mesh, in which the soft elastomer formed isolated inclusions. Variation of the mesh geometries, the elastomer content, and the constituent material properties could tune the in-plane dynamic responses and fracture behaviors. Dynamic mechanical analysis measurements showed two tan δ peaks, corresponding to the elastomer and the plastic. By changing the geometry, a very wide range of storage modulus values (about three orders of magnitudes) could be achieved at room temperature. The fracture strain of the composites was found to increase with the elastomer content, and an obvious brittle-ductile transition was observed. Tough samples showed several stress plateaus and a trumpet-shaped crack profile. Increasing the vertex angles of the rhombus filler geometry was found to result in a brittle-ductile transition. In both experiments and simulations, a forward-backward crack propagation mode was observed, indicating that soft elastomer inclusions stabilize the crack propagation. Compared to staggered composites with stiff inclusions, the current design with soft inclusions showed higher modulus, tensile strength and toughness. [ABSTRACT FROM AUTHOR]

In this paper, experimental results for rate dependence of interlaminar mode I fracture of a polymer matrix composite laminate are presented. A modified wedge-insert fracture (MWIF) method for conducting mode I fracture testing at elevated loading rates is used. A correction factor has been introduced to the modified beam theory method for measuring the mode I interlaminar fracture toughness using the MWIF method. The experimental method was successfully verified against the most widely used standardized method at quasi-static loading rates. Mode I interlaminar fracture testing was conducted at loading rates ranging from 0.01 mm/s to 3600 mm/s. A reduction in fracture toughness with rate was seen. The fracture behavior at elevated rates differed from the lower rates. The effect of bridging (and process zone) lengths on the fracture toughness were seen decreasing drastically with increased loading rate. [ABSTRACT FROM AUTHOR]

This paper reports on the damage mechanisms of 3D circular braided composite tubes under transverse impact, applied by a Split Hopkinson Pressure Bar (SHPB) system. X-ray computed tomography (XCT) was employed to obtain 3D images of the 3D braided composite tubes after the impact test. Effects of impact velocity, braiding angle and the number of braiding layers on the damage mechanisms were researched, using the XCT data. For low impact velocity, it was found that cracks nucleate in weak areas and propagate along the path of least resistance between yarns, which give rise to matrix cracking and debonding between yarns. For high impact velocities, cracks develop along a relatively straight path with fiber breakage under high shear and tensile stresses. The orientation of yarns in the tubes showed a great effect on crack propagation. [ABSTRACT FROM AUTHOR]

Thin ply laminates are a new class of composite materials with great potential for application in the design of thinner and highly optimized components, resulting in potential weight savings and improved mechanical performance. These new composites can stir the development of lighter structures, overcoming current design limitations as well as notably reducing the onset and development of matrix cracking and delamination events. This paper presents the application of two recent modeling methods for the failure analysis and strength prediction of open-hole thin ply laminates under tensile loading, which exhibit a brittle response upon failure: (i) the analytical coupled energy-stress Finite Fracture Mechanics (FFMs) technique, and (ii) the FE-based Phase Field (PF) approach for fracture that is incorporated into an enhanced assumed solid shell element. The predictions obtained using both strategies are compared with experimental data. These correlations exhibit a very satisfactory level of agreement, proving the robustness and reliability of both methods under consideration. [ABSTRACT FROM AUTHOR]

This paper presents a study on the Mode I fracture behavior and crack monitoring of bonded carbon fiber reinforced polymer (CFRP) composite joints with carbon nanotube (CNT)-based polymer adhesive layer. Bonded joints were fabricated using woven carbon/epoxy composite substrates and CNT-based epoxy adhesives. Mode I fracture tests were carried out with double cantilever beam (DCB) bonded joint specimens, and the dependence of the critical energy release rate at the onset of crack growth, i.e., fracture toughness, on the nanotube content in the adhesive layer and the adhesive layer thickness was examined. The electrical resistance of the bonded joint specimens was monitored during the tests. An analytical model based on the electrical conduction mechanism of CNT-based polymers was also employed to describe the electrical resistance change due to crack propagation in the bonded joint specimens, and a good correlation was obtained between the predicted and measured results. The electrical resistance change is found to result in quantitative assessment of crack length based on resistance measurement. It is demonstrated that the bonded CFRP composite joints with CNT-based polymer adhesive layer have improved fracture properties together with crack sensing capability. [ABSTRACT FROM AUTHOR]

This paper describes experimental and numerical studies addressing mixed-mode I+II fracture characterization of a carbon-epoxy/cork hybrid laminate using the Single-Leg Bending test. An equivalent crack length based data reduction scheme applied to the hybrid specimen was developed to evaluate the fracture energy. The proposed method does not require crack length monitoring during the test which is difficult to perform accurately in a tough material, as is the case of cork. It was observed that hybridization is quite effective since stable crack growth occurred even for unstable specimen configurations. Moreover, the more efficient quadratic energetic criterion was found to be representative of the hybrid material fracture, instead of the linear one characterizing the monolithic carbon-epoxy material. The proposed procedure was validated by means of finite element analysis including a new trapezoidal cohesive zone model based on incremental calculation of energy dissipation during fracture. [ABSTRACT FROM AUTHOR]

In this paper an energy-based failure envelope for unidirectional fiber reinforced polymers (FRP) has been developed. It is based on the stress and the damage energy release rate (DERR) components, which makes it suitable for being used as a damage surface in continuum damage mechanics (CDM), when a thermodynamically consistent evolution rule is intended to be used. The proposed failure surface is an interactive quadratic function of the DERR components accompanying with linear stress components in the form of an invariant. The mathematical formulation of the criterion is originated from the fully interactive Tsai-Wu criterion. The failure locus of the two criteria were compared with each other for several unidirectional FRP composites under several combined stress states. The two criteria were found to be in a reasonably good agreement for investigated composites with Eglass and carbon fibers, especially where the experimental data were available. [ABSTRACT FROM AUTHOR]

In this paper a multiscale method for modelling damage evolution at meso and macro scales with application to plain woven composites is presented for the first time. The method couples the macro and micro-scale simulations using an averaging theorem in which the computations in the two scales are performed simultaneously. Unlike the local–global approach, the developed multiscale analysis is carried out over the entire macro domain rather than a predefined segment. To address the computational challenges in multiscale damage analysis, the proposed method a) employs a non-local approach in constructing the macro–micro interface to avoid the pathological localisation effect introduced by microdamage at the macro continuum; b) reduces the considerable computing effort incurred by the non-linear behaviours in multiscale damage analysis by the introduction of machine learning meta-models. Experimental tensile tests conducted are shown to be in good agreement with the proposed method for both on-axis and off-axis load directions. The biaxial loading cases are also investigated with the results illustrated by the failure envelopes and compared with the existing damage criteria. Finally, an example of open-hole tension test is presented to demonstrate an application of the proposed method to model progressive damage and crack propagation in composite plates. [Display omitted] • A novel multiscale modelling strategy for material damage evolution is proposed. • Meta-modelling method and non-local approach are applied in the interface between meso and macro scales. • The application to plain woven composites is investigated. • Open-hole tensile simulations are conducted for composite plates. [ABSTRACT FROM AUTHOR]

Thermoplastic composites are likely to emerge as the preferred solution for meeting the high-volume production demands of passenger road vehicles. Substantial effort is currently being directed towards the development of new modelling techniques to reduce the extent of costly and time consuming physical testing. Developing a high-fidelity numerical model to predict the crush behaviour of composite laminates is dependent on the accurate measurement of material properties as well as a thorough understanding of damage mechanisms associated with crush events. This paper details the manufacture, testing and modelling of self-supporting corrugated-shaped thermoplastic composite specimens for crashworthiness assessment. These specimens demonstrated a 57.3% higher specific energy absorption compared to identical specimen made from thermoset composites. The corresponding damage mechanisms were investigated in-situ using digital microscopy and post analysed using Scanning Electron Microscopy (SEM). Splaying and fragmentation modes were the primary failure modes involving fibre breakage, matrix cracking and delamination. A mesoscale composite damage model, with new non-linear shear constitutive laws, which combines a range of novel techniques to accurately capture the material response under crushing, is presented. The force-displacement curves, damage parameter maps and dissipated energy, obtained from the numerical analysis, are shown to be in a good qualitative and quantitative agreement with experimental results. The proposed approach could significantly reduce the extent of physical testing required in the development of crashworthy structures. [ABSTRACT FROM AUTHOR]

The paper deals with the experimental determination of material properties required as model parameters in Cuntze's invariant-based Failure-Mode-Concept, applied to transversely-isotropic UD materials. For the envisaged 3D strength failure conditions (criteria) of this material, 5 strengths and 2 friction values must be determined. So far, no concept for the determination of the physically necessary internal friction values has been agreed to. In this publication bi-axial ARCAN tests are performed to obtain the friction values from data points on the inter-fiber failure fracture curve. The initiation of inter fiber failure is identified through sudden strain changes, recorded with strain gauges and digital image correlation. Further, the strength values for one specific material (M21/T700GC) are determined. To obtain the necessary shear strength three different shear test setups are investigated: the ±45°-Tension, the IOSIPESCU and the ARCAN test. They are compared considering the smoothness quality of their stress field distribution. The presented methodology enables to determine the two internal friction values. [ABSTRACT FROM AUTHOR]

This paper presents detailed experimental information on mode-II delamination development in fibre/epoxy composite materials and provides observations about the process zone in the vicinity of the crack tip. It is shown that the energy dissipated in delamination propagation is spent on two ways (i) creating new fracture surfaces (delamination) and (ii) nonlinear shear deformation in the composite plies adjacent to the delaminating interface. Therefore, the nonlinear process zone is not restricted to the resin-rich interface between the layers, but also extends into the fibre/epoxy composite layers. This is different from the conventional assumption in modelling delamination using cohesive elements where the fibre/epoxy layers are fully linear-elastic and the process zone is lumped at the plane of fracture. Based on the accurately measured displacement field around the crack tip, the experimental traction-separation relation at the interface is found to be trapezoidal which is again different from the conventional bilinear cohesive law. [ABSTRACT FROM AUTHOR]

This paper describes the results related to the crack growth rate measurement on double cantilever beam (DCB) specimens made of a carbon-fibre fabric-reinforced multifunctional epoxy composite. Two plates were evaluated where the resin was enhanced using a combination of 0.5% carbon nanotubes (CNTs) and Glycidyl POSS (GPOSS) flame retardant for one of the plates. Loading in mode I was displacement-controlled with R = 0.1, f = 4 Hz and a constant maximum strain energy release rate ( G I ) max during the cycle. The value of ( G I ) max was defined to be from 20% up to 60% of the mode I interlaminar fracture toughness. The specimens enhanced by CNTs and GPOSS highlighted a significant decrease in the fatigue crack growth rate of approximately 80%. The crack growth rate was also observed to be significantly related to the interface of the weft and warp tows of the plain weave. [ABSTRACT FROM AUTHOR]

In this paper, a reliable progressive fatigue damage model (PFDM) for predicting the fatigue life of composite laminates is proposed by combining the normalized fatigue life model, nonlinear residual degradation models and fatigue-improved Puck criterion. To balance the accuracy of life predictions and computational efficiency, an adaptive cyclic jump algorithm is developed and implemented within the PFDM. The sensitivity of life prediction to cyclic jump parameter has been greatly reduced by correlating the cyclic jump with the increment time and viscous coefficient. Therefore, the cyclic jump parameter can be arbitrarily selected within a relatively large range to obtain convergent results. When incorporating the adaptive cyclic jump algorithm, there is no need to define a standard for determining the material failure in numerical calculations, which effectively eliminates an artificially induced uncertainty in life predictions. Two sets of experiments are conducted to validate the proposed PFDM. The numerical predictions including static failure strength and fatigue life correlate reasonably well with the available experimental data. [Display omitted] [ABSTRACT FROM AUTHOR]

Thin ply laminates have shown much promise in recent times in terms of their exciting damage suppression characteristics. Utilisation of this damage suppression in carbon–epoxy angle-ply laminates has been shown experimentally to yield a highly non-linear stress–strain response. This paper presents an analytical modelling method that incorporates matrix plasticity and reorientation of the fibres into a classical laminate analysis for the prediction of the in-plane response of thin ply angle-ply laminates. It is shown that the method can successfully predict the non-linear behaviour of [ ± θ 5 ] s laminates with values of θ between 15° and 45°. The main characteristics of the stress–strain curve, such as the initial largely linear region, yield point and stiffening before final failure, are all well captured. The modelling has allowed straightforward identification of a particular fibre angle that exhibits strength in excess of 900 MPa, strain to failure of more than 3.5% and a promising pseudo-ductile strain of 1.2%. [ABSTRACT FROM AUTHOR]

Predictive models have struggled to accurately simulate progressive delamination growth in composite structures, often due to the challenges associated with modelling delamination migration phenomenon. This paper presents a methodology with which to model such migration. Firstly, the interlaminar shear at a delamination front were partitioned into axial and transverse modes, the mode-mixity of which was controlled by the mismatch between this front and the ply directions. An element formulation was presented which utilised this mismatch. Consequently, delamination migration was shown to have ensued when the transverse mode exceeded a critical mode-mixity G iii /G T = 0.22. This approach was verified against experimental studies on width tapered end loaded split coupons by correlating the fracture morphology against mode-mixity. In particular, the orientation of the cusps on the delamination surface were shown to be controlled by the relative dominance of the axial and transverse modes. This methodology provides a means to accurately and robustly model progressive delamination growth processes in composite structures. [ABSTRACT FROM AUTHOR]

Abstract: Fibre-reinforced composites are being used more and more widely in many fields. However, the theoretical prediction of the failure of these composites is still a challenging task. In this paper, the physically-based failure theory developed by Puck and co-workers is combined with the fracture mechanics based in situ strength theory developed by Wang and Karihaloo. The latter considers the influence of both the thickness of the lamina itself and the ply angles of its neighbouring laminae. This combined failure theory also incorporates a new final failure mode. It is able to predict accurately the initial failure stress, thus overcoming one of the weaknesses of Puck’s theory which significantly underestimates this stress. Also, it explains why the number of non-fatal failure modes predicted by Puck’s theory is different from those observed in experiments under certain loads. Finally, it is able to overcome the problem of discontinuities in the failure envelope under some load combinations predicted by Puck’s original theory. [Copyright &y& Elsevier]

Abstract: Analysis methods to predict the open-hole tensile and compressive response of thin-ply non-crimp fabric laminates are investigated in this paper. The point- and average-stress models and the Finite Fracture Mechanics model are used. It is shown that all models predict with reasonable accuracy the observed size effects in both tension and compression. The Finite Fracture Mechanics model, which requires two material properties (the unnotched strength and the fracture toughness) and does not need calibration from a baseline specimen, is used to predict the notched response of thin-ply non-crimp fabric laminates and of typical aerospace grade laminates based on unidirectional pre-impregnated plies. No substantial differences in notch sensitivity and inherent material/geometry brittleness is predicted. [Copyright &y& Elsevier]

Abstract: CFRP (Carbon Fibre Reinforced Polymer) composite consists of two materials characterised by different electric properties i.e., carbon fibres – the high strength component with conductive features as well as polymer fillers with insulating properties. For this reason, any structural damage will result in changes in electrical properties of the whole composite. This paper presents a mathematical FEM-based model allowing for simulation of damage in monolayer symmetric laminate structure. The dependences of electrical responses on the size and location of damage as well as the sensitivity of the method for accurate placement of electrodes supplying electric current were investigated. The effectiveness of this method for determining the approximate size and location of the damage and the usefulness of the FEM for modelling the changes in electrical properties of the composite were demonstrated. [Copyright &y& Elsevier]

A novel micromechanics-based multiscale progressive damage model, employing minimal material parameters, is proposed in this paper to simulate the compressive failure behaviours of 3D woven composites (3DWC). The highly realistic constructions of microscopic and mesoscopic representative volume cells are accomplished, and a set of strain amplification factor is employed to bridge the meso-scale and micro-scale numerical calculations. Considering that the multiple failure mechanisms of 3DWC under compression are all caused by the matrix failure from the microscopic perspective, a new method incorporating the micromechanics of failure (MMF) theory and 3D kinking model is developed to identify the micro matrix failure associated with the kinking of yarns, inter-fiber fracture and pure matrix failure. As a result, only the matrix parameters are required for the failure simulation of 3DWC, eliminating the necessity of using other material parameters such as the fracture toughness and failure strengths of fiber yarns, which are generally difficult to accurately obtain through experiments. The newly proposed damage model is numerically integrated into ABAQUS with a user-defined subroutine UMAT. The numerical predictions and the experimental results exhibit good agreement, verifying the feasibility and accuracy of the novel damage model. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The incorporation of particles into polymer matrix causes local stresses in their neighbourhood when the composite is loaded. High multiaxial stress fields are created in front of a crack which leads to various fracture processes in a region close to the crack tip. These processes contribute to the energy dissipation of the moving crack, increasing the crack resistance of the material. One of these processes is matrix yielding around particles after debonding of the particles and that is considered in this paper. At first the crack resistance for this mechanism was obtained by integration over the stress field within the dissipation zone. At second the mechanical problem of a spherical particle within a spherical elastic/perfectly plastic matrix under uniform radial tensile stress was solved. After particle debonding, the yielding energy of the matrix shell was calculated. Finally an analytical equation for the composite crack resistance for this mechanism was obtained, which is a function of mechanical properties of the components, particle volume fraction in the composite and local particle fraction. Debonding energy, matrix yield stress and particle size come only into play if the debonding stress is larger than the minimum uniform stress for yielding initiation. [Copyright &y& Elsevier]

Abstract: A new finite element to seamlessly model the transition from a continuum to a non-continuum (through fracture) is introduced in this paper, motivated by the variational multi-scale cohesive (VMCM) method. In-plane fiber–matrix fracture (also referred to as splitting) is frequently observed in tensile failure of fiber reinforced polymer matrix composites (FRPCs). By considering a single lamina, this mechanism is modeled through the development of a continuum-decohesive finite element (CDFE). In the CDFE method, the transition from a continuum to a non-continuum is modeled directly (physically) without resorting to enrichment of the shape functions of the element, as is done in other methods, such as the VMCM or through nodal enrichment, as is done with the extended finite element method (XFEM). The CDFE is a natural merger between cohesive elements and continuum elements. The predictions of the CDFE method were found to be in very good agreement with corresponding experimental data. [Copyright &y& Elsevier]

Abstract: Linear elastic fracture mechanics (LEFM) implies that crack-like flaws would intensify stress in brittle materials with stress intensity scaling up with the square root of the crack size. Therefore, the apparent strength of materials tends to be much smaller than the theoretical value. In this paper, we examine the stress state in nacreous composites and find that in such materials the crack-induced stress intensification and its dependence on crack size can be suppressed greatly. This feature of nacreous composites can be attributed to the unique “brick-and-mortar” (B-and-M) structure and a synergistic match of the mechanical properties between “brick” (e.g. minerals) and “mortar” (e.g. proteins) phases. Our findings not only provide a fundamental insight into the origin of the excellent mechanical properties of nacreous composites such as high strength, high toughness and flaw tolerance, but also will be of great value to the design and synthesis of new structural materials for superior mechanical properties. [Copyright &y& Elsevier]

Abstract: The application of Weibull theory to the analysis of experimental data obtained from the tensile testing of reinforcement fibres is widespread in composites research and development. One basic assumption implicit in the use of Weibull analysis is that all values of fibre strength described by any set of unimodal or multimodal Weibull parameters are accessible experimentally. However, this is not the case, as a minimum level of fibre strength is necessary in order to be able to isolate, prepare and test any fibre. In this paper the consequences of this experimental limitation are explored in terms of the commonly applied Weibull graphical analysis method. It is demonstrated that this can result in significant curvature in a standard Weibull plot at the low strength end of the data. Furthermore, at low sampling numbers this effect can be misinterpreted as evidence of multiple defect populations. The phenomenon significantly affects the values of the Weibull parameters obtained from the graphical analysis and also from the average strength versus gauge length analysis. The presence of this lower limit presents a serious challenge to those wishing to support conclusions on the physics and mechanics of fibre fracture from Weibull analysis of single fibre tensile data. [Copyright &y& Elsevier]

Abstract: In this paper, the damage progression and failure characteristics of stitched composites under out-of-plane loading are experimentally investigated. Test specimens, stitched with various stitch densities and stitch thread thicknesses, are studied using quasi-static indentation test. Test specimens are loaded and unloaded in 0.5mm incremental indentation displacement to examine for damage phenomena using non-destructive inspection techniques namely ultrasonic C-scan, X-ray radiography and X-ray micro-computed tomography to elucidate complex damage mechanisms and fracture behavior. Recorded test history of load–displacement curves indicate that damage progression can be characterized into three stages: damage initiation, damage propagation and final damage failure. Results show that damage initiation occurs at a lower load in stitched composites due to the presence of resin-rich regions which act as crack initiation sites. X-ray radiography convincingly shows that stitch-induced matrix crack lines are joined between stitch loops, being particularly evident in densely stitched composites. During damage propagation, stitching becomes highly effective in suppressing delamination growth, resulting in stitched laminates having much smaller delamination area compared to unstitched laminates, and the rate of delamination growth being inversely related to stitch density. It is found out that final failure is distinguished by a sharp load drop in the load–displacement curve. It is revealed that the final failure load increases with increasing stitch fiber volume fraction. The final failure mechanism in unstitched and moderately stitched composite is mainly delamination failure; while densely stitched composite failed by indenter penetration comprising of in-plane fiber fracture and matrix crushing. Energy absorption throughout the quasi-static indentation process is presented and discussed. This work provides novel insight to the damage progression and damage penetration of stitched composites. [Copyright &y& Elsevier]

Abstract: This paper experimentally and theoretically investigates the influence of creep of the concrete and the adhesive on the edge debonding failure load of reinforced concrete beams strengthened with externally bonded composite materials. The theoretical study includes a stress analysis phase and a fracture analysis phase. In the stress analysis phase, the strengthened beam is modeled as a layered structure and creep of the different materials involved, as well as cracking and material nonlinearity of the concrete are considered using rheological generalized Maxwell models. The theoretical model also accounts for the development of shear and vertical normal stresses through the thickness of the adhesive layer. The failure criterion for edge debonding is based on a fracture mechanics model that uses the concept of the energy release rate through the J-integral and accounts for the creep deformations. An experimental study is conducted, which includes testing of three strengthened beams and one control under short-term loading for evaluation of their failure loads, and long-term testing of another set of beams under different levels of sustained loads for a period of one year. After the sustained loading period, the beams are further loaded to failure without releasing the existing load, in order to estimate the influence of creep deformations on the residual load carrying capacity. In both sets of tests, the failure mode is characterized by interfacial edge debonding. The experimental and theoretical results show that, depending on the material properties, creep can increase or decrease the maximum load that leads to edge debonding failures in FRP strengthened members. [Copyright &y& Elsevier]

Abstract: This paper presents a finite element model (FEM) to analyse the structural deformation, strength properties and delamination fracture behaviour of composite T-joints reinforced with z-pins. The FE modelling involves multi-level analysis of a pinned joint using unit cell and macro-scale structural models. Unit cell model is used to calculate the crack bridging traction loads generated by the elastic and interfacial friction (pull-out) stresses of a single pin within a representative unit cell of the joint. Macro-scale analysis involves modelling delamination crack growth in the pinned joint using a cohesive zone model, which is based on the traction load analysis of a single pin. The FE model was validated using experimental results for a pinned carbon fibre/epoxy T-joint subjected to tensile (stiffener pull-off) loading. The model accurately calculated the crack initiation load, ultimate load, and fracture mode of the pinned joint. [Copyright &y& Elsevier]

Abstract: For fiber-reinforced plastics exists a big number of different criteria for the failure prediction. The intention of this paper is to compare the TSAI-HIL-, the LaRC04- and PUCK’s criterion in terms of their fracture curves for a unidirectional glass-fiber reinforced composite layer. Therefore after the implementation of these three criteria, the two-dimensional fracture curves for all possible stress combinations, which can be derived from a general spatial stress tensor, are computed. In this way, the characteristics of the criteria, similarities and differences and possible weak points become obvious. [Copyright &y& Elsevier]

Abstract: This paper addresses the issue of using energy balance methods and crack closure concepts to predict the growth of delaminations associated with ply cracks during the progressive loading of cross-ply laminates subject to a combination of in-plane biaxial stresses and thermal residual stresses. When the effective applied stresses and the temperature are held fixed during delamination growth, and there is negligible interaction of the delamination tips with the ply cracks, very simple analytical formulae for the energy release rate can be derived for unconstrained and generalised plane strain conditions, which are exact when the ply crack separation tends to infinity. In some practical applications, such as for wide plates, delamination growth is constrained transversely by surrounding undamaged laminate and this has an effect on energy release rates. An analytical method is described that determines the energy release rate for delamination growth under such constrained conditions. This result is also exact in the limit of ply crack separations tending to infinity. The boundary element method (BEM) has been used to investigate energy release rates for constrained conditions for a range of ply crack densities, both in the presence and absence of thermal residual stresses, for a special case where the delamination tips are mid-way between neighbouring ply cracks. BEM results show a slight dependence of the energy release rate on ply crack separation, and predictions for the maximum ply crack separation considered are within 1.6% of the exact limiting analytical predictions valid for infinite separation. This agreement indicates the validity of both the analytical methods used, and the numerical analysis based on the BEM. [Copyright &y& Elsevier]

Abstract: This paper presents a new approach to numerically investigate the lap shear fracture of a hybrid laminate made of Carbon Fibre Reinforced Plastic (CFRP) and metal foil plies (e.g. aluminium), validated by corresponding experiments. The numerical Finite Element (FE) model of the hybrid laminate, subjected to lap shear fracture, is composed of five laminas with alternating metal/CFRP layers with cohesive elements lying within Al/CFRP interface. In the FE model, individual CFRP laminas are assumed as an orthotropic homogenized continuum under plane stress, and aluminium facesheets are modelled as an elastic–plastic continuum. The Al/CFRP interface is represented via quadratic cohesive elements, the constitutive law of which is an exponentially decaying law representing the degrading behaviour of the interface (implemented as user element in ABAQUS). The numerical model captures the experimentally obtained results with minimal error, and predicts the failure modes successfully. The influence of specimen geometry (e.g. overlap length, total length, and total width) on lap shear fracture response is analyzed in detail in this study, too, in order to confirm the specimen design for the test, as there is still no corresponding test standard for hybrid laminates. [Copyright &y& Elsevier]

Abstract: This paper presents experimental fatigue results for GFRP face sheet/balsa core sandwich beams with face sheet wrinkle defects, subjected to fully reversed in-plane fatigue loading. An estimate of the fatigue design limit is presented, based on static test results, finite element analyses and application of the Northwestern University failure criteria. The presence of a wrinkle defect reduced the fatigue life by approximately 66%, compared to that of an unnotched reference laminate. Furthermore, the results from the fatigue tests revealed that the design limit was initially overestimated, as the specimens loaded close to the predicted design limit typically failed before reaching the target life, or reached test run-out with visible face sheet damage indicating imminent final failure in the worst case. It was found that specimens would reach target life with no visible or otherwise detectable damage by lowering the fatigue load amplitude below 80% of the predicted design limit. By extrapolating the test results it appears that the undamaged specimens would reach a fatigue life of 107–108 load cycles and would thus be safe for design of wind turbine blades. [Copyright &y& Elsevier]

Abstract: This paper presents an experimental study into a new type of stitched fibre–polymer laminate that combines high interlaminar toughness with self-healing repair of delamination damage. Poly(ethylene-co-methacrylic acid) (EMAA) filaments were stitched into carbon fibre/epoxy laminate to create a three-dimensional self-healing fibre system that also provides high fracture toughness. Double cantilever beam testing revealed that the stitched EMAA fibres increased the mode I interlaminar fracture toughness (by ∼120%) of the laminate, and this reduced the amount of delamination damage that must subsequently be repaired by the self-healing stitches. The 3D stitched network was effective in delivering self-healing EMAA material extracted from the stitches into the damaged region, and this resulted in high recovery in the delamination fracture toughness (∼150% compared to the original material). The new self-healing stitching method provides high toughness which resists delamination growth while also having the functionality to repeatedly repair multiple layers of damage in epoxy matrix laminates. [Copyright &y& Elsevier]

Abstract: The relation between the nominal strength of open hole specimens manufactured with quasi-brittle isotropic materials with respect to the specimen size and the shape of the cohesive law is examined in the present paper. The obtained results can be used by engineers as design charts or to obtain valuable information on the failure characteristics of quasi-brittle materials. [Copyright &y& Elsevier]

Abstract: Fracture experiments were carried out on continuous fiber polymer matrix laminated composite panels to investigate cohesive, through-the-thickness crack propagation. The experiments were designed to examine curved cracks, resulting from either eccentric loading or non-symmetric specimen geometry with respect to the starter crack. The constitutive description of the observed complex diffused damage zone, which from a continuum viewpoint may be considered a macroscopic crack, involves complex/evolving traction–separation relations and mode-mixity conditions. This paper presents some relevant experimental investigations and their numerical modeling using the variational multiscale cohesive method developed by Rudraraju et al. which is an effective framework for simulating cohesive crack evolution and thereby predicting the residual strength of cracked composite panels. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: In polymer layered silicate nanocomposites, significant differences have been reported between the effects of the nano-reinforcement on rigid and elastomeric nanocomposites. In this paper, we have studied elastomeric nanocomposites based upon DGEBA epoxy resin filled with montmorillonite (MMT) and cured with a long-chain polyoxypropylene diamine, for comparison with analogous rigid nanocomposites. Ultrasonic mixing was used to disperse the MMT in the matrix to improve homogeneity and decrease the agglomerate size. Two different methods of nanocomposite preparation were used in which the MMT was first swollen with either the curing agent or the epoxy before the addition of, respectively, DGEBA or diamine. A better dispersion of the nanoclay in the matrix and a greater amount of intercalation occurred when the MMT was first swollen with the diamine. The effect of MMT concentrations up to 8wt.% on the mechanical behaviour of the epoxy/MMT nanocomposites was investigated. It was found that the addition of MMT increased the tensile strength and modulus, although SAXS and TEM indicated that a significant fraction of the clay layers were not exfoliated. Nevertheless, the addition of the clay resulted in changes in the fracture surfaces, as indicated by SEM, consistent with the tensile results and indicative of toughening. [Copyright &y& Elsevier]

Abstract: In this paper we present the biaxial failure curve of a chopped glass-reinforced polyester composite. The curve has been obtained combining the results of experimental tests with the results of numerical simulations developed by means of the Finite Element Method. The experimental tests have been performed applying perpendicular loads to cruciform specimens. Then, taking into account the numerical results, we have constructed the failure envelope in the tensile–tensile quadrant. Moreover we propose to modify the cruciform geometry to obtain, varying the widths of the loaded arms and the tapered central zone, points of the failure curve in which the two components of the plane stress tensor are different. [Copyright &y& Elsevier]