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This paper deals with a basic methodology for the application of the finite element (FE) simulation and linear elastic fracture mechanics (LEFM) to predict the onset of delamination growth. The first step of the proposed methodology is the experimental characterisation of material interlaminar fracture in pure mode I (DCB test), pure mode II (ENF test) and mixed mode I+II (MMB test). In the second step, the results of the interlaminar fracture tests are translated from load/displacement data to strain energy release rates by means of test FE simulations; thus, the critical strain energy release rate (Gc), or fracture toughness are obtained as a function of mode ratio. The third step of the methodology consists of applying FE simulations to determine the strain energy release rate (G) and mode ratio for the delamination and then comparing the result to the values of the Gc curve. The main innovative aspect of the paper is that FE simulation is used as a part of the material characterisation process; in fact, data reduction of interlaminar fracture tests is carried out by means of FE simulations. In addition, regarding the practical details of FE application to the proposed methodology, some innovative aspects are introduced, such as the analysis is carried out as a non-linear geometric problem (taken into account large displacements) and considering inside each simulation different elastic properties for the material depending on whether it is under tension or compression. These aspects and the rest of the proposed methodology are validated by the experimental results presented in the paper. [ABSTRACT FROM AUTHOR]

Thin bonded cement-based overlays include surface repairs, toppings, and linings, especially on slabs, slabs on soil, concrete pavements, and tunnel walls. The aim of this paper is to show that, contrary to a widely held belief, debonding of cement-based overlays is governed not by the shear stress along the overlaybase interface but by the built-in tensile stress perpendicular to this interface. After a brief comparison with laminated composite materials and with beams reinforced by bonded strips (made of metal or of composite), the specific case of thin cement-based overlays is presented. Different conditions of debonding of an overlay are investigated. In all cases, the tensile stress perpendicular to the base-overlay interface is confirmed as the designing parameter. In terms of fracture mechanics, debonding of cement-based overlays is governed by a mixed mode in which mode I is widely dominant. There is a lack of appropriate tests to accurately characterize the mechanical behavior of the interface. Nevertheless, finite-element calculation relying on the mean values of the shear and tensile strength of the interfacial bond (calculation was performed with CESAR code) provides a good approximation of debonding initiation and propagation. [ABSTRACT FROM AUTHOR]

Abstract: A method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated beam structures is presented. The novelty of this method is the use of one-dimensional finite elements to discretize the geometry of the beam. The key property of this beam element, named LRZ [1], is the possibility to capture the relative displacement between consecutive layers which occurs during delamination. The fracture mode that the LRZ element is capable to predict is mode II. In order to capture the relative displacement using the LRZ element it is necessary to adapt the RZT theory as presented in this paper. The mechanical properties of the layers are modeled using a continuum isotropic damage model [2]. The modified Newton–Raphson method is used for solving the non-linear problem. The RZT theory, the LRZ finite element and the isotropic damage model are described in the paper. Also, the implicit integrations algorithm is presented. The performance of the LRZ element is analyzed by studying the delamination in a beam for two different laminates, using the plane stress solution as a reference. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Results related to the buckling delamination of elastic and viscoelastic composite plates are reviewed and analyzed. They have been obtained during the last fifteen years by the author and his students. The plates contain cracks whose faces have initial infinitesimal imperfections. The evolution of the imperfections under compression of the plates is studied, and the values of critical parameters are determined from a criterion of initial imperfection. The study is performed with the use of 3D geometrically nonlinear field equations. In the present paper, the historical background of the problems is outlined considered, general remarks about the field equations and solution method are made, and problems related to the plane strain state are reviewed. [ABSTRACT FROM AUTHOR]

Design and manufacture of composite test specimens with two embedded delaminations subjected to transverse tension is described in this paper. The behaviour of the specimens has been investigated through experimental testing and finite element analyses. Fracture mechanics approaches were applied to predict the initiation and growth of delaminations and the degradation of the load carrying capacity of the specimens. Models were generated in the FE software programs MSC.Nastran and Abaqus. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. The accuracy of numerical solutions was established by qualitative and quantitative comparisons with the experimental measurements, the results obtained from the ultrasonic non-destructive inspections and microscopic examination. It was shown that fracture mechanics can be used to accurately predict the failure initiation locations and failure loads of composite specimens containing multi-level delaminations. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes a 2D FE modelling technique for predicting fatigue crack growth life of integral structures reinforced by bonded straps. This kind of design offers a solution to the intrinsic lack of damage tolerance of integral structures. Due to the multiple and complex failure mechanisms of bonded structures, a comprehensive modelling technique is needed to evaluate important design parameters. In this Part I of a two-part paper, the actions and mechanisms involved in a bonded structure are discussed first, followed by presenting the modelling approaches to simulate each mechanism. Delamination or disbond of the strap from the substrate is modelled by computing the strain energy release rate on the disbond front and applying a fracture mechanics criterion. Thermal residual stresses arising from the adhesive curing process and their redistribution with the substrate crack growth are calculated and taken into account in the crack growth analysis. Secondary bending effect caused by the un-symmetric geometry of one-sided strap is also modelled. In the classic linear elastic fracture mechanics, a non-dimensional stress intensity factor, i.e. the geometry factor , depends only on the sample’s geometry. This factor cannot be found for this kind of bonded structures, since the magnitude of disbond is related to the applied stress and the disbond size modifies the geometry of the structure. Moreover, secondary bending effect is geometric nonlinear thus the stress intensity factor cannot be normalised by the applied stress. For these reasons an alternative technique has been developed, which requires calculating the stress intensity factors at both the maximum and minimum applied stresses for each crack length. This analysis technique is implemented in a computer program that interfaces with the NASTRAN commercial code to compute the fatigue crack growth life of strap reinforced structures. [Copyright &y& Elsevier]

A high fidelity assessment of accumulative damage of woven fabric composite structures subjected to aggressive loadings is strongly reliant on the accurate characterization of the inherent multi-scale microstructures and the underlying deformation phenomena. Damage in composite sandwich and joint structures is characterized by the coexistence of discrete (delamination) and continuum damage (matrix cracking and intralaminar damage). A purely fracture mechanics-based or a purely continuum damage mechanics-based tool alone cannot effectively characterize the interaction between the discrete and continuum damage and their compounding effect that leads to the final rupture. In this paper, a hybrid discrete and continuum damage model is developed and numerically implemented within the LS-DYNA environment via a user-defined material model. The continuum damage progression and its associated stiffness degradation are predicted based on the constituent stress/strain and their associated failure criteria while the discrete delamination damage is captured via a cohesive interface model. A multi-scale computational framework is established to bridge the response and failure predictions at constituent, ply, and laminated composite level. The calculated constituent stress and strain are used in a mechanism-driven failure criterion to predict the failure mode, failure sequence, and the synergistic interaction that leads to global stiffness degradation and the final rupture. The use of the cohesive interface model can capture the complicated delamination zone without posing the self-similar crack growth condition. The unified depiction of the continuum and discrete damage via the damage mechanics theory provides a rational way to study the coupling effects between the in-plane and the out-of-plane failure modes. The applicability and accuracy of the damage models used in the hybrid dynamic failure prediction tool are demonstrated via its application to a circular plate and a composite hat stiffener subjected to shock and low velocity impact loading. The synergistic interaction between the continuum and discrete damage is explored via its application to a sandwich beam subjected to a low velocity impact. [ABSTRACT FROM AUTHOR]

The successful design of anisotropic conductive adhesive (ACA) assemblies depends mainly on the accurate prediction of their electrical contact resistance. Among the parameters that influence this resistance, the bonding force used to compress the conductive particles against the conductive tracks during the assembly process is very important. This paper investigates how the contact resistance changes as the bonding force is removed at the end of the assembly process when the epoxy resin used to bond the surfaces has cured. The final contact resistance is determined by examining, through theoretical, experimental and numerical analyzes, the evolution of the residual stress as the elastic recovery of the compressed conductive particles and tracks takes place when the bonding force is removed. An iterative algorithm derived from methods found in fracture mechanics analysis is used to determine the relationship between the contact resistance, the adhesive strength and the stiffness of the cured resin. It is shown that smaller values of adhesive strength yield higher contact resistance values; and similarly, smaller values of modulus of elasticity of the resin lead to higher contact resistance values. [ABSTRACT FROM AUTHOR]

Laminated composites are prone to delamination failure due to the lack of reinforcement through the thickness. Therefore, during the design process the initiation and propagation of delaminations should be accounted for as early as possible. This paper presents computationally efficient nine degree-of-freedom (dof) and eight-dof shear locking-free beam elements using the mixed form of the refined zigzag theory (RZT ( m ) ). The corresponding nine-dof and eight-dof elements use the anisoparametric and constrained anisoparametric interpolation schemes, respectively, to eliminate shear locking in slender beams. The advantage of the present element over previous RZT beam elements is that no post-processing is required to accurately model the transverse shear stress while maintaining the computational efficiency of a low-order beam element. Comparisons with high-fidelity finite element models and three-dimensional elasticity solutions show that the elements can robustly and accurately predict the displacement field, axial stress and transverse shear stress through the thickness of a sandwich beam or a composite laminate with an embedded delamination. In fact, the accuracy and computational efficiency of predicting stresses in laminates with embedded delaminations make the present elements attractive choices for RZT-based delamination initiation and propagation methodologies available in the literature. [ABSTRACT FROM AUTHOR]

The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress-strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity. [ABSTRACT FROM AUTHOR]

• An interface is an independent object for fracture mechanics. • The interface strength criterion cannot be written in the terms of the "intrinsic" interface deformations only. • In the general case, it is impossible to obtain the interface strength criterion in an explicit analytical form, but it is possible to construct this criterion in the form of a computer program. • The phenomena discussed in the paper have an asymptotic nature and are valid as the thickness of the joint tends to zero. In the limit, the individual elastic and geometrical properties of the joint influence the strength properties of the interface. • The macroscopic strength criterion may be used in practice as an approximation. We deal with a layered composite formed from "thick" layers of unidirectional fibers (layers containing many unidirectional fibers), which are product the so called "prepreg" technology widely used in the industry. It is demonstrated that the local stress–strain state in such composite consists of local stress–strain states in "thick" (thick a compared with the fiber diameter, i.e. containing a large number of the fiber) layers and local stress–strain states at the layer interfaces. We theoretically predict and numerically confirm the presence of a boundary layer at the junction of adjacent fiber layers. This asymptotic phenomenon, to the best of our knowledge, has not been described earlier. Since the boundary layer is a specific region, different from the other regions of the composite, there arises a specific strength criterion in this region – the interface strength criterion. The interface strength criterion is a phenomenon of the asymptotic nature. From the mechanical point of view, the interface strength criterion is associated with the delamination in laminated composite material. [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]

Delamination is one of the most important defects in fiber reinforced composite laminates. This paper presents the delamination resistance of thick woven glass fiber reinforced polyester specimens and experimentally examines the effect of ply orientations in terms of the critical strain energy release rate. Specimens with different ply orientations (0°, 30°, 45° and 70°) are fabricated with plain woven (taffetas) fabrics. The tests used for the experiments are Double Cantilever Beam (DCB) for pure mode I, End Load Split (ELS) for pure mode II and Mixed Mode Flexure (MMF) for mixed mode I/II under static conditions. The experimental results have been expressed in terms of total strain energy release rate and R -curves. Results show that fiber bridging for woven fabrics occurred due to non-midplane crack propagation. The fracture toughness results show that the delamination resistance increase with ply angle until 45° then it decrease. [ABSTRACT FROM AUTHOR]

Fibre bridging plays an important role in fatigue delamination growth in composite materials. It decreases the crack growth rate significantly with the increase of delamination length. In this paper, it is demonstrated how the Paris relation depends on the amount of fibre bridging. For this purpose, both parameters n and C in the Paris relation, are described as function of the crack extension a − a 0 , as a measure to quantify the contribution of fibre bridging. It appears that the parameter n only depends on the stress ratio and remains independent on the amount of fibre bridging. The parameter C depends on both the stress ratio and crack extension. The obvious difference in trends between both stress ratios indicates that a method incorporating the contribution of fibre bridging in the Paris relation requires extensive data sets. [ABSTRACT FROM AUTHOR]

High values for the work of separation have been reported in peel tests on fibrillating interfacial systems. The exact origin of these high values is not properly understood, since it remains unclear which dissipative mechanisms related to fibrillation cause a significant increase in the work of separation. In this paper, the contribution of fibril mechanics to the work of separation is quantified. To this end, a micromechanical model of a single fibril is used, in which the growth of a nucleated fibril up to the moment of fracture is described. The initial geometry is varied to reflect the variability in the substrate profile. It is observed that the stresses and strains that occur in the model are well beyond typical bulk values. Given the large variation in measured stress–strain curves for rubber materials reported in literature, a small scale single fibril experiment is performed to assess the applicability of reported bulk material parameters to this problem. The obtained experimental response falls well within the model bandwidth for the range of material parameters from literature. Furthermore, the fibril fracture stress, which serves as the failure criterion in the model, is extracted from the experiment. From the micromechanical model results, it appears that, for the considered range of material properties, the work of separation is mainly influenced by the fracture stress. Furthermore the initial geometry has a profound influence on the obtained work of separation. It is concluded that the work of separation determined from the micro-model is significantly larger than the intrinsic adhesion energy, yet it remains still an order of magnitude smaller than the values reported in literature. For the considered system this indicates that, although it has a significant contribution, fibril deformation is not the only contribution to the high work of separation. [ABSTRACT FROM AUTHOR]

The studies reported in the literature on the effect of stress ratio or mean stress on fatigue delamination growth in composites are critically reviewed in this paper. These studies are classified according to their mode of fracture. Majority of the studies lack a mechanistic approach to the delamination growth characterization and the effect of stress ratio. The researchers are divided in the use of a unified correlating parameter for the delamination growth. The mechanisms of fatigue crack growth in metals are often extended to the delamination growth characterization. [ABSTRACT FROM AUTHOR]

This paper presents a study on quantifying the effective properties of spray-applied fire-resistive material (SFRM) to mitigate delamination of fire insulation from steel structures. The crack development in SFRM, its propagation and then delamination is investigated for two types of structural elements; a flimsy steel truss chord, and a beam-column assembly in a moment-resisting frame insulated with three types of SFRM widely utilized in steel construction. In the truss chord, the strain ductility of steel at which delamination initiates and propagates is studied, while in the beam-column assembly, the extent of delamination over the plastic hinge region developed on the beam is monitored. A fracture mechanics-based numerical model is employed to undertake parametric studies to determine effective parameters of SFRM for minimizing delamination. In the sensitivity study, the material properties of SFRM applied on steel members are varied over a wide range. Results from the sensitivity study indicate that the elastic modulus of fire insulation ( E ), thickness of insulation ( t ) and interfacial fracture energy ( G c ) are the crucial factors that govern the delamination of SFRM from the steel surface. Subsequently, results from an additional set of parametric studies, carried out on a beam-column assembly, also infer that delamination of SFRM occurs over the plastic hinge region and is mainly governed by the critical factors of E , t and G c . Results from these studies indicate that all three governing factors play a critical role in determining the extent of delamination and such delamination can be overcome if the interface fracture energy in normal mode is enhanced to 350 J/m 2 . [ABSTRACT FROM AUTHOR]

Abstract: In the first part (Saeedi et al., 2011) of this two-part paper, a layerwise stress model, called the LS1 model, has been extended to the analysis of delaminated multilayered plates subjected to uniaxial extension. The LS1 analytical solutions of general delaminated multilayered plates have been derived and compared to three-dimensional finite element method (3D-FEM) solutions. It has been proved that there is a good agreement between the LS1 and 3D-FEM models except very near singularities (free edges, crack tips,…). In order to overcome the drawback of the LS1 model in the vicinity of singularities, a refinement approach, called the refined LS1 is proposed in this part. Based on an irregular layerwise mesh, the refined LS1 model is applied to the prediction of the delamination onset in angle-ply composite laminates. The comparison between the refined LS1 and 3D-FE models reveals an excellent agreement in terms of interlaminar stresses and strain energy release rate, even very close to singularities. The proposed refined LS1 model can be used as an accurate and very efficient model for the prediction of initiation and propagation of delamination in multilayered plates under uniaxial extension using stress based or energy release rate based criteria. [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: The effect of delamination resistance on fatigue crack growth behavior of composite laminates is studied. The strain energy release rate normalized to fatigue delamination resistance (G cf) is proposed as a controlling parameter to evaluate the fatigue crack growth rates and thresholds. Compared to previously developed G cf determination method, the compliance approach presented in this paper shows obvious advantages, such as no interruption to the fatigue crack growth and independence on the specimen dimensions. Based on this approach, the fatigue delamination growth rates and thresholds of carbon/bismaleimide composite laminates under mixed I/II mode loadings are determined experimentally. [Copyright &y& Elsevier]

Abstract: This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress–strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained. [Copyright &y& Elsevier]

Abstract: This paper addresses a new method based on the combination of mechanical behavior and acoustic emission (AE) information of composite materials during mode I delamination. The method is based on a special purpose function, called sentry function, which is defined as the logarithm of the ratio between mechanical energy and acoustic energy (f =Ln(Es /Ea )). The sentry function is used to study the delamination process and to evaluate the delamination fracture toughness in mode I. The relationship between cumulative fracture toughness energy release rate (G I) and the integral of the sentry function during crack propagation showed a transition point with two sensitive regions below and above it. This behavior can be followed to obtain the critical strain energy release rate value (G I c ). Results obtained by means of the sentry function are compared with results obtained by a methodology proposed by other authors. [ABSTRACT FROM AUTHOR]

Abstract: The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90] s , [45/−45] s , [30/−30] s and [90/45/0/−45] s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed. [Copyright &y& Elsevier]

Abstract: This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface. [Copyright &y& Elsevier]

Abstract: In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements. [Copyright &y& Elsevier]

An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model. [ABSTRACT FROM AUTHOR]

The model of quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e. distinguishing opening (Mode I) from shearing (Mode II), devised in [Delamination and adhesive contact models and their mathematical analysis and numerical treatment, Chap. 9, in Mathematical Methods and Models in Composites, ed. V. Mantič (Imperial College Press, 2014), pp. 349-400; and in Quasistatic mixed-mode delamination model, Discrete Contin. Dynam. Syst. Ser. S 6 (2013) 591-610], is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the one-homogeneous potential of dissipative forces driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretization in time is shown to converge to (specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretization, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial two-dimensional example. [ABSTRACT FROM AUTHOR]

An experimental investigation aimed at identifying the presence and onset of an asymptotic stable fracture region in the mode II fatigue delamination growth behaviour of composites is presented. The study is motivated by the possibility that experimental data sets, particularly those obtained at high R-ratios, may unknowingly contain data points within the asymptotic stable fracture region that influence its perceived log-linear behaviour and the fit of various log-linear delamination growth models. Results from the experimental investigation indicate that the asymptotic stable fracture region can extend to GIImax values as low as 0.7GIIc. The implications of this result on characterizing and fitting of various delamination growth models (including models assuming log-linear behaviour) to delamination growth behaviour are discussed. [ABSTRACT FROM PUBLISHER]

The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer surface are studied. The energy amounts dissipated in fracture Mode I (opening) and Mode II (shear) at an interface may be different. A concept of internal parameters is used here on the delaminating interfaces, involving a couple of scalar damage variable and a plastic tangential slip with kinematic-type hardening. The so-called energetic solution concept is employed. An inelastic process at an interface is devised in such a way that the dissipated energy depends only on the rates of internal parameters and therefore the model is associative. A fully implicit time discretization is combined with a spatial discretization of elastic bodies by the BEM to solve the delamination problem. The BEM is used in the solution of the respective boundary value problems, for each subdomain separately, to compute the corresponding total potential energy. Sample problems are analysed by a collocation BEM code to illustrate the capabilities of the numerical procedure developed. [ABSTRACT FROM AUTHOR]

The effect of z‐pin reinforcement on the structural properties and damage tolerance of composite joints is experimentally studied in this article. The ultimate load, failure strain, and absorbed energy capacity of carbon fiber‐epoxy T‐joints and single lap joints increased rapidly with the volume content of z‐pins. The improvement to these properties was due to the capacity of z‐pins to resist unstable (rapid) delamination growth along the bonded region to the T‐joints (induced by interlaminar mode I stress) and lap joints (induced by interlaminar mode II stress) by forming a crack bridging traction zone. Large increases to the damage tolerance of T‐joints and lap joints containing pre‐existing bond‐line cracks were also achieved by z‐pins. The z‐pins formed a bridging traction zone across the delaminated bond‐line which retained high strength in the joints, even in the presence of very long cracks which severely weakened conventional joints. [ABSTRACT FROM AUTHOR]

Multilayer woven reinforcements are increasingly employed in the domain of composite materials. Delamination occurrence and resultant failure of a laminated composite piece subjected to high vibrations, is an issue of much concern in aeronautics. The situation becomes more complex in case of bended/curved pieces. In order to improve through the thickness mechanical properties, 3D-woven multilayer interlock fabric is used as composite reinforcement. Structural changes, i.e. thickness change, relative slippage of layers, change in tow aspect ratio and change of orientation of the tows columns, etc. occur in such fabrics during the forming process. These changes may lead to the gradient of the resin amount in composite, internal stresses and variations of mechanical properties in the piece. No significant research has been conducted on this aspect. Lack of knowledge or neglecting these changes may lead to prejudicial estimations of ultimate mechanical properties and fracture analysis. In the present article, the changes that occurred in 5-layer and 13-layer 3D-woven multilayer interlock fabrics have been studied, when moulded at five different angles and two different bending radii. A significant change in thickness, tow aspect ratio, tow orientation and relative layer slippage is observed. [ABSTRACT FROM AUTHOR]

In this work, stress-based and fracture mechanics criteria were developed to predict initiation and evolution, respectively, of intra- and inter-laminar cracking developed in composite laminates subjected to low velocity impact. The Soutis shear stress-strain semi-empirical model was used to describe the nonlinear shear behaviour of the composite. The damage model was implemented in the finite element (FE) code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Delamination (or inter-laminar cracking) was modelled using interface cohesive elements and the splitting and transverse matrix cracks that appeared within individual plies were also simulated by inserting cohesive elements between neighbouring elements parallel to the fibre direction in each single layer. A good agreement was obtained when compared the numerically predicted results to experimentally obtained curves of impact force and absorbed energy versus time. A nondestructive technique (NDT), penetrant enhanced X-ray radiography, was used to observe the various damage mechanisms induced by impact. It has been shown that the proposed damage model can successfully capture the internal damage pattern and the extent to which it was developed in these carbon fibre/epoxy composite laminates. [ABSTRACT FROM AUTHOR]

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This study shows that a simple approach to stiffness tailoring of composite face sheets can improve the performance of sandwich panels under compressive loading when delaminations are present. The simple stiffness tailoring concept used here is to reposition of all 0° material (aligned with the loading direction) into regions of certain width near the edges of the sandwich panel. This concept has been shown to improve the buckling and postbuckling performance of solid plates and to offer control of delamination growth. To evaluate this tailoring design concept in sandwich panels, numerical simulations of onset and propagation of the delamination growth were conducted with uniform face sheets and tailored face sheets. The delamination front tracing method previously developed by the authors was used to perform the delamination growth analysis. The interfacial elements, which allow the growth of the delamination front to be traced, are placed at the interface between the top face sheet and the core in the undelaminated region. They enable calculation of the strain energy release rates and application of a fracture mechanics delamination growth criterion. Gap elements were used to avoid interfacial overlap. Based on the numerical study, the improvement in the ultimate load provided by the simple stiffness tailoring concept ranges from 80% to 100%, depending on the extent of tailoring. Substantial improvements in the residual strength and stiffness, after significant delamination growth, can also be observed. Therefore, this article provides a potential design concept that can improve the damage tolerance of sandwich panels without adding weight. [ABSTRACT FROM AUTHOR]

The Mode III interlaminar fracture toughness, GIIIc, of composite materials based on both thermoplastic and thermosetting-matrices have been investigated using the edge crack torsion (ECT) test geometry. Tests were undertaken at room temperature and over a range of crosshead displacement rates to study the influence of strain rate on the interlaminar fracture properties of these materials. Further information concerning the crack tip loading conditions was obtained by undertaking a finite element analysis of the ECT specimen geometry. The experimental results show that the value of GIIIc depends on initial crack length, increasing steadily with increasing crack length for both types of material. It has been shown that the interlaminar fracture toughness of the glass fiber/epoxy-based system was superior to that offered by its thermoplastic counterpart, an effect that may be due to the fact that the glass fiber-reinforced polypropylene composite was slow-cooled from its processing temperature. The interlaminar fracture toughness of both types of composite remained roughly constant over the range of crosshead displacement rates considered here suggesting that they do not exhibit any rate-sensitive fracture behavior. The finite element analysis of the ECT specimens showed that the specimen is subjected to pure Mode III loading over the central part of the test specimen whereas regions of locally-high Mode II loading were observed over the region in which the load was applied. The Mode III strain energy release rate profile does not depend on specimen thickness or the displacement of the ECT test geometry. [ABSTRACT FROM AUTHOR]

Experiments are carried out to determine the delamination toughness for a crack along the interface between two transversely isotropic materials. The material chosen for study consists of carbon fibers embedded within an epoxy matrix. A crack is introduced between two layers of this material, with fibers in the upper layer along the + 45°-direction and those in the lower layer along the − 45°-direction both with respect to the crack plane. The Brazilian disk specimen is employed in the testing. To calibrate the specimens, stress intensity factors are obtained which result from the applied load, as well as residual curing stresses. It may be noted that all three modes are coupled, leading to a three-dimensional problem. The finite element method and a mechanical M-integral are employed to determine the stress intensity factors arising from the applied load. For the residual stresses, a three-dimensional conservative thermal M-integral is presented for stress intensity factor determination. The stress intensity factors found for the applied load and residual stresses are superposed to obtain a local energy release rate, together with two phase angles. From the load at fracture, the critical interface energy release rate or interface toughness $${{\mathcal G}_{ic}}$$ as a function of phase angles ψ and ϕ is determined. Results are compared to a fracture criterion. [ABSTRACT FROM AUTHOR]

A direct energy balance approach has been developed and used to determine energy release rates in three and four point bend end notched flexure tests. This study was performed in the context of the larger goal of understanding the wide variation in mode II toughnesses that have been obtained by the two tests when used on the same material. The primary motivation for developing the direct energy balance approach was to fully account for the effects of friction, large deformations, and other geometric nonlinearities that occur during these tests. The direct energy balance approach simulates crack advance as it occurs in physical testing. Most significantly, this approach accounts for frictional dissipation that occurs during crack advance, which is an effect that has been neglected in previous analyses of these tests. The direct energy balance approach is used to show that, for most cases of practical interest, the virtual crack closure technique is quite accurate, and predictions by this latter approach are only in error when moderately large geometric nonlinearities occur prior to crack advance. Based on these results, a “cut-off value,” expressed in terms of the maximum slope in the specimen as predicted by classical beam theory, is suggested for the upper limit of applicability of the virtual crack closure technique. [ABSTRACT FROM AUTHOR]

A fracture energy approach for modelling mixed-mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post-failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E-glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included. [ABSTRACT FROM AUTHOR]

Carbon fiducial marks are formed during thin film local delamination processes induced either by superlayer indentation forming circular blisters, or by residual stress relief through telephone cord blister formations. Hydrocarbons are sucked into the crack tip during the delamination process, outlining the crack tip opening angle (CTOA), which can be used to back calculate thin film adhesion using either elastic or plastic analyses presented here. Fiducial marks have been observed in two different thin films systems, namely Cu/SiO2 and TiWXNY/GaAs. TiWXNY/GaAs system also exhibited biaxial compressive stress-induced phone cord buckling delaminations. Surface AFM CTOA measurement approach is used to estimate the strain energy release rate increase along these phone cords delaminations. [ABSTRACT FROM AUTHOR]