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The focus of the present paper is on the mode-II (shear mode) interlaminar fracture of laminated composite materials with randomly distributed defects such as those generated due to the manufacturing process. The study is conducted using cohesive-zone Finite Element (FE) models of the Interlaminar Shear (ILS) and the End Notch Flexure (ENF) geometries with explicit inclusion of defects on a representative interlaminar plane. The effective interlaminar shear strength and the effective mode-II fracture energy are obtained by comparing the FE analysis with explicit defects against corresponding homogeneous models. Based on the parametric FE results it was found that the effective ILS strength and the mode-II fracture energy are significantly affected by the defects present on the critical interlaminar fracture plane, and when the defects are small, they follow a linear scaling with the defect area fraction. Simulations with various defect sizes reveal that for defects larger than the size of the delamination process-zone, the concept of the effective ILS strength and effective mode-II fracture energy is not valid, and defects must be represented explicitly in the models. [ABSTRACT FROM AUTHOR]

In this paper, the recently-developed floating node method is extended for damage analysis of laminated composites with large deformations. Strong discontinuities including interfacial delamination and matrix cracks are explicitly represented by geometrically nonlinear kinematics. Interactions between these two kinds of failure patterns are enabled through enriched elements equipped with floating nodes. A cohesive zone model is utilized for the damage process zone. A general implicit procedure with user-defined elements is developed for both quasi-static and dynamic analysis. The performance of this formulation is verified with two benchmark simulations, involving buckling-induced delamination and low-velocity impact damage. The results presented show good quantitative and qualitative agreements with results from literature. [ABSTRACT FROM AUTHOR]

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations. [ABSTRACT FROM AUTHOR]

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on Isogeometric Analysis (IGA), where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum Damage Mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations. [ABSTRACT FROM AUTHOR]

Large residual stress in the micro electroforming layer has been considered to be the main reason for causing warpage, delamination and micro cracking of the microdevice. These undesirable phenomena dramatically influence the productivity, dimensional accuracy and service life of the microdevice. Reasonable control of the residual stress is a direct and efficient way to improve the production rate of microdevice and expand the application of microdevice. In this paper, the residual stress finite element analysis (FEA) simulation model for Ni micro electroforming layer was established by the method of 'Equivalent Reference Temperature (ERT)'. The simulation result shows that the ERT for Ni micro electroforming layer is 238.15 K. The error of residual stress value is 0.37% between the simulation result and the experimental result. This error value proves the accuracy of the FEA model. [ABSTRACT FROM AUTHOR]

This paper is a continuation of Survey I [], where the historical background and general remarks on the problem formulation and solution methods were outlined and results related to plane-strain problems were reviewed. In the present paper, a review of axisymmetric and 3D buckling delamination problems is presented. [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]

In this paper, the extended layerwise method (XLWM), which was developed for laminated composite beams with multiple delaminations and transverse cracks (Li et al. in Int J Numer Methods Eng 101:407-434, 2015), is extended to laminated composite plates. The strong and weak discontinuous functions along the thickness direction are adopted to simulate multiple delaminations and interlaminar interfaces, respectively, whilst transverse cracks are modeled by the extended finite element method (XFEM). The interaction integral method and maximum circumferential tensile criterion are used to calculate the stress intensity factor (SIF) and crack growth angle, respectively. The XLWM for laminated composite plates can accurately predicts the displacement and stress fields near the crack tips and delamination fronts. The thickness distribution of SIF and thus the crack growth angles in different layers can be obtained. These information cannot be predicted by using other existing shell elements enriched by XFEM. Several numerical examples are studied to demonstrate the capabilities of the XLWM in static response analyses, SIF calculations and crack growth predictions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the impact behaviour and damage characterization of carbon fibre reinforced aluminium hybrid laminates (Al/CFRP) in comparison to classic carbon fibre reinforced polymer (CFRP) at low-velocity and low-energy impact. Impact damage characteristic with damage initiation and progression, internal failure modes and understanding of the role of the metal layers in the impact behaviour under low-energy were examined and discussed. The damage mechanism of the tested laminates is very complex. There is an internal degradation of the material, with the plastic deformation in case of fibre metal laminates. Characteristic matrix cracks (bending and shearing cracks) running at the fibre–matrix interface in composite layers are the first damage mode. The critical damage mode is delaminations observed between composite layers with different orientation as well as delaminations at the metal–composite interface in fibre metal laminates. For the tested materials, particularly carbon fibre reinforced composites, the absorbed impact energy is mainly connected with elastic response and damage of the laminate. In case of fibre metal laminates the absorbed energy is also connected with plastic deformation of the laminate, occurring especially in the metal layers. High impact resistance of fibre metal laminates indicates that metal (aluminium) layers may prevent delamination propagation and impactor penetration. [ABSTRACT FROM AUTHOR]

In the field of cultural objects conservation efficient stabilisation of fragile and failing, multilayered decorative coatings is a complex and challenging task. This paper introduces a new application of the standardised double-cantilever beam (DCB) test method to improve the understanding of the mechanical properties of failing material and to determine the effect of polymeric agents (consolidants) added for their stabilisation. The adapted DCB method was used to measure the fracture energy, G, and the fracture behaviour of brittle, protein-bound (gesso-type) foundation layers on wooden substrates that typically suffer from delamination and flaking. Wooden DCB specimens containing a brittle layer of protein glue mixed with finely ground clay powder were prepared, fractured, then consolidated with a range of commonly used polymer formulations and finally re-fractured to provide measurements for direct comparison. Consolidants tested included gelatine-based glues (bovine hide glue, isinglass; both pre-stained with Fast Green dye), acrylics (Lascaux Medium for Consolidation, Paraloid B-72/B-48N), poly(vinyl acetates) (Mowilith 50, Mowilith DMC2) and poly(vinyl alcohol) (Mowiol 3-83). Before second-phase fracture cross-sections were taken from the DCB specimens for determining penetration depth and gap-filling ability. For better visibility, the specimens containing acrylics were stained with Solvent blue G dye; iodine-potassium iodide was used for staining the other synthetic consolidants. The resulting data showed that the test method could determine measurable differences between initial G (47 ± 22 J/m) and post-consolidation G values. Also, penetration behaviour could be well characterised and valuable, and detailed information on the type and location of crack path propagation was gained. [ABSTRACT FROM AUTHOR]

Carbon-epoxy (C-epoxy) laminated composites having different fibre volume fractions (40, 50, 60 and 70) were fabricated with and without the addition of aminofunctionalized carbon nanofibres (A-CNF). Flexural strength, interlaminar shear strength (ILSS) and tensile strength of the composite laminates were determined. It was observed that, the ability of A-CNF to enhance the mechanical properties of C-epoxy diminished significantly as the fibre volume fraction ( V) of the C-epoxy increased from 40 to 60. At 70 V, the mechanical properties of the A-CNF reinforced C-epoxy were found to be lower compared to the C-epoxy composite made without the addition of A-CNF. In this paper suitable mechanisms for the observed trends are proposed on the basis of the fracture modes of the composite. [ABSTRACT FROM AUTHOR]

This paper investigates edge delamination in an orthotropic layered structure composed of a thin film and a substrate under a temperature change. An edge interface crack is analyzed for two configurations in which it emerges from an interior or corner edge of the film. Special attention is paid to the effects of orthotropic material constants on delamination cracking. The necessary material parameters involved in the energy release rate and mode mixity for the interface crack are found based on a modified Stroh formalism. The explicit dependence of the energy release rate and mode mixity on one orthotropic parameter for the film is discovered using an orthotropy rescaling technique. The effects of other material parameters on the energy release rate and mode mixity are examined numerically, and the growth and arrest of edge interface cracks are discussed based on an energy criterion. [ABSTRACT FROM AUTHOR]

Delamination is often identified as an important failure mechanism in structures with a high interface density, such as modern microelectronic systems and advanced composite materials. Delamination tests performed on different interface structures reveal complex failure mechanisms (crack bridging, fibre pull out, micro-void coalescence, fibrilation, crack meandering, etc.) in the fracture process zone that lead to an irreversible unloading response of the interface, ranging from full damage to full plasticity. Modeling the unloading response of an interface is important for predicting phenomena such as crack branching and crack propagation at multiple interfaces. This paper presents a 2D irreversible combined plasticity-damage unloading model, which can be used to extend the cohesive zone (loading) models with a proper unloading description that is suitable for modeling the entire loading-unloading response in the process zone. The presented model is able to capture changes in unloading behavior as a function of mode mixity, whereas it introduced only two additional model parameters that can be determined from dedicated delamination experiments. As a demonstration, the improved Xu–Needleman cohesive zone law has been extended with the proposed combined damage-plasticity unloading formulation. Numerical simulations with this extended model are performed for a glue interface system, recovering the typical observed behavior in delamination experiments. Finally, a complete procedure to extract all CZ model parameters is presented and illustrated for the glue interface system. [ABSTRACT FROM AUTHOR]

Telescopic front fork tube of the bike is manufactured by electrical resistance welding of pickled hot rolled strip followed by cold drawing. The fork undergoes cyclic loading during operation and is prone to crack along the weld. This paper presents the investigation of such a failure of fork at field. The investigation consists of visual inspection, chemical analysis, characterization of microstructure, and energy dispersive spectroscopy. The result of the analysis revealed that there was a pre-existing crack, known as hook crack, which lead to the cracking of the tube. The hook crack was slightly offset from the bond line, i.e., weld line between the edges of the cold drawn electrically welded seam. Metallographic examination exhibited that during field operation the pre-existing hook crack was surfaced out leading to crack in the pipe. Parallel separation/delamination due to upsetting of pipe edges during welding caused the 'hook crack' formation. [ABSTRACT FROM AUTHOR]

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]

In this paper nonlinear cohesive fracture models with cohesive parameters and laminar elasticity typical of polymer composites are used to study the initiation and propagation of a transverse intra-ply crack that is coupled to possible delaminations at the ply interfaces in a [0/90/0°] laminate. The evolution of the transverse crack is found to be more complex than previously described, involving initial growth, growth along the ply in a tunneling mode, and expansion across the thickness of the ply in a plane strain mode. For the coupled crack system, two failure modes are distinguished: (1) complete tunneling propagation of the transverse crack before any delamination occurs, followed by delamination initiation and propagation; and (2) simultaneous propagation of the transverse and delaminations cracks. The former process is always stable, is favored by large values of the mode II to mode I toughness ratio and low values of the cohesive strength, and is predicted to be the prevalent failure sequence for polymer composites. The latter process is often unstable, because it tends to occur when the cohesive strength is so high that the stress for initiating the transverse crack exceeds the stress required for its tunneling propagation. The nonlinear fracture models provide a unified description of the entire process of initiation and crack propagation. If the delamination cracks are modeled by linear elastic fracture mechanics, substantially inaccurate predictions result for the onset of delamination cracking and for the tunneling crack initiation from a pre-existing flaw. [ABSTRACT FROM AUTHOR]

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]

In this paper, the durability of the bondline between concrete and FRP reinforcement was characterized at various temperature and humidity levels. The linear and nonlinear viscoelastic constitutive behavior of the epoxy bondline was characterized and used for a nonlinear viscoelastic fracture analysis of delamination. A hygrothermal nonlinear viscoelastic pseudo-stress model was developed and calibrated in order to compute a generalized J integral. Driven wedge tests were conducted for examining the fracture behavior of the interface. A finite element analysis was developed for determining the cohesive zone size and the generalized J integral at various temperature and humidity levels. The fracture energy obtained from these parameters greatly depended upon crack growth rate, temperature and humidity. [ABSTRACT FROM AUTHOR]

ERRATUM: This paper is an identical reprint of an article published in Engineering Fracture Mechanics, Vol. 61, 163–171 (1998). Due to unforeseen circumstances this article was published again in a special issue of the International Journal of Fracture. The Editor-in-Chief and the publisher regret this unfortunate turn of events. The publication in Engineering Fracture Mechanics is to be regarded as the initial one and therefore the only valid publication of the article. [ABSTRACT FROM AUTHOR]