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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 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]

Fatigue fracture of fiber-reinforced polymer composites (FRP) occurs when microcracks are induced by debonding, pull-out and delamination at the interface between the matrix and fiber. This microcrack area increases with increase in fatigue cycles and a damage region is formed. In our previous paper, fatigue life of a short fiber-reinforced polymer composite consisting of glass fibers and polycarbonate matrix was found to be related not to the main crack growth behavior but to the progression behavior of the damage region. In this paper, using our proposed real time observational system, we performed detailed observations on the behavior of fatigue damage and clarified the mechanism of damage progression. Furthermore, mechanical considerations were performed by finite-element elastic-plastic stress analysis. The results mentioned above indicate that control of short fiber alignment makes it possible to release the stress concentration caused in the matrix, and disperse fatigue damage. This results in an enormous improvement in fracture toughness. [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 (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]

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]

Interfacial delamination is a common failure mode in multilayered IC packages. In this paper, an experimental technique using Brazil-nut specimens is employed to determine the interfacial fracture toughness of an adhesively sandwiched joint with the introduction of edge interfacial crack. The design of experiments (DOE) is applied to study variations in strain rates and the thickness of the sandwich structure. In addition, the effects of moisture content and temperature on the interfacial adhesion are investigated. For the DOEs conducted, as the loading angle increases from 20° to 90°, the interfacial fracture toughness decreases. The fracture toughness and its corresponding mode mixity are determined from the measured critical load by finite element modeling computation. [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]

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]

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]

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]

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]

The paper presents a solution to a delamination problem of an infinite elastic film resting on a rigid substrate and loaded by a monotonically increasing in-plane point force. A rigid-slip contact is assumed between the film and the substrate, leading to the development of two regions at the interface: a damaged zone with a relative slip between the materials, and a region where the interface remains intact. Both film natural and essential boundary conditions are zero on the boundary between these two interfacial zones with the shape of the boundary being a part of the solution. Problem's self-similarity enables us to obtain an approximate distribution of interfacial traction within the delaminated zone and a shape of the zone itself. For film's Poisson's ratio ν=−1 the approximate solution becomes exact. It is argued that this can be treated as a special case of a rigid film sliding on a rigid substrate. The presented approach can be used to obtain approximate closed-form solutions to similar delamination problems. [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]

This paper describes an investigation into the low velocity impact response on complex geometry sections taken from a pultruded glass/polyester product. The empirical impact behaviour of the system was evaluated using instrumented falling weight impact testing (IFWI) in conjunction with ultrasonic C-Scan, optical microscopy and thermal deply techniques to detect delamination, matrix cracking, and fibre breakage. [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]

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]

The phenomenon of edge fractures is analyzed using a fracturing process approach. Such fractures often initiated from the free surface of layered materials, and often terminate at the interface that divides the fractured layer and the matrix layer, or continue to expand along the interface, or create a peel-crack. To understand better the pattern of fractures with different spacing and the fracture mechanism, a double-layer elastic model with the same material properties with a fractured overlying layer subjected to uniaxial tension is simulated firstly. The stress distribution between two adjacent fractures is periodically distributed as a function of the ratio of the fracture spacing to the thickness of the fractured layer (S/t ratio), and homogeneous and heterogeneous material properties are considered in the simulation. The simulation results show that both the stress distribution and the critical value of fracture spacing to layer thickness ratio are affected by material heterogeneity; the S/t ratio of heterogeneous material is much smaller and it is much easier to crack compared with the homogeneous materials. In particular, the fracture saturation mechanism is analyzed by stress state change. Then a numerical simulation is carried out to reveal the fracturing process from micro-fracture formation, propagation, coalescence, nucleation, fracture infilling, fracture saturation, termination, to interface delamination. A fitting curve of the relationship between strain and spacing to layer thickness radio is obtained. It is found that infilling fractures may grow near the bottom or the free surface of the fractured layer by coalescence of micro-fractures and flaws. We also find that fracture spacing in the case of interface delamination is greater than that without interface delamination. A study of stress transition between the two layers on fracture spacing in the fracture process is also carried out, with a focus on stress transfer mode. [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]

To realize the explosive separation of carbon-fiber-reinforced composites under a linear-shaped charge, the failure mode of the materials under a linear-shaped charge jet was obtained by combining numerical simulation with experiment. Results show that under the action of the shaped charge jet, the three main failure modes of composite materials are shear failure, delamination failure and tensile failure. Moreover, there are different failure modes of composite materials with different thicknesses. In the early stage of cutting, local fiber peeling occurs on the surface of laminates with different thicknesses under the action of initial jet and stress wave. The thin laminate is sheared directly under the energy of the high-speed jet while the thick laminate first suffers shear failure under the action of the jet. After the end of the jet action, tensile failure occurs under the action of stress wave and, at the same time, spalling occurs along the thickness direction. [ABSTRACT FROM AUTHOR]

This manuscript describes an experimental and numerical study conducted to investigate two representative cases of delamination in ultra-thin chopped carbon fiber tape-reinforced thermoplastics (UT-CTT): delamination in a double cantilever beam (DCB, mode I) and delamination in an end-notched flexure (ENF, mode II). In examples of mode I delamination, unstable crack growth resulted in sawtooth-like load–displacement curves after the initial stage of increasing load, while some specimens displaying mode II delamination exhibited stable crack propagation. The crack surfaces of DCB and ENF UT-CTT specimens were observed by a three-dimensional measurement macroscope and a scanning electron microscope. The values of mode I and mode II interlaminar fracture toughness were obtained based on linear elastic fracture mechanics and beam theory in reference to JIS K 7086 standard, respectively. Furthermore, numerical analysis utilizing the surface-based cohesive zone model based on the triangular traction–separation law was used to predict the delamination behavior in UT-CTT. The minimum and maximum values of critical strain energy release rate were used to define the range of load–displacement curves corresponding to unstable crack propagation under mode I, while the parameters including interlaminar shear strength and friction were taken into account for the predictions of delamination propagation under mode II. The numerically predicted load–displacement curves showed good correlation with the theoretical and experimental results. The research provides interlaminar mechanical properties for damage modeling and numerical simulation method to express fracture behaviors of UT-CTT structures. [ABSTRACT FROM AUTHOR]

Thermoelectric thin film/substrate structures have many practical applications such as in heat recovery systems. The general problem of thermally induced delamination between a thermoelectric thin film and a substrate is investigated. The temperature varies along the length direction but is constant along the thickness direction of the film. Analytical solutions of the temperature field in the film and the stress intensity factors (SIFs) at the delamination crack tips are obtained. The combined heat convection and heat radiation between the film surfaces and the surrounding medium (i.e., the air) are taken into account. Numerical results show that the SIFs sharply increase as the tips of the delamination crack approach the ends of the film. The combined heat convection and heat radiation can increase or decrease the SIFs. The mechanism for the delamination propagation in the thermoelectric film/substrate system is examined. The critical (permissible) temperature difference across the film governing the delamination propagation is identified. [ABSTRACT FROM AUTHOR]

A fracture mechanics analysis is conducted for a delamination problem of a multilayered thermoelectric material (TEM) that consists of an n-type layer and a p-type layer sandwiched by an insulating layer. A time-varying energy release rate is presented when the n-type layer delaminates from the insulating layer. Effects of the temperature difference across the system and the applied electric current on the energy release rate are identified. The influence of the thickness ratio of the insulating layer to the thermoelectric (TE) layer is also examined. Based on the energy release rate criterion, the critical temperature difference for delamination propagation is obtained. Some useful conclusions are given. [ABSTRACT FROM AUTHOR]

An analytical study of delamination in the crack lap shear beam is performed. It is assumed that the material is functionally graded along the width and height of the beam. Delamination is studied in terms of the total strain energy release rate by applying methods of linear-elastic fracture mechanics. An additional analysis of the total strain energy release rate is performed by considering the strain energies in the beam cross sections ahead of and behind the crack front for verification. The effects of the crack location and material gradient on delamination are evaluated. [ABSTRACT FROM AUTHOR]

The energetics controlling delamination versus echelon crack advance in a tape composite laminate subjected to anti-plane shear loading are studied. The finite element method is used to model both single and multiple echelon cracks that intersect the planar delamination front. Energy release rates are determined along the echelon crack peripheries and along the planar delamination front. Various echelon crack shapes are evaluated in order to represent progressive stages of growth. It is shown that the echelon cracks advance due to primarily mode I conditions, whereas a mode III criterion is appropriate for predicting advance of the planar delamination. It is further shown that mode I advance of the echelon crack and mode III advance of the delamination are competing yet coupled processes, and that the sequence of events predicted by this approach agrees with what has been observed experimentally. [ABSTRACT FROM AUTHOR]

Although superior in properties, composite materials still have problems in machining, such as delamination, cracking, burning, tool blockage, and cost and efficiency issues. These problems can prevent wide application of extraordinary composite materials. As an effective method in composite machining, rotary ultrasonic machining (RUM) process has been paid much attention to recently. The current studies on RUM tool design are mostly based on experiments. However, the insufficiency of RUM tool design theory would generally result in the tool blockage, which subsequently leads to the sharp increase in cutting force and poor machining quality in the engineer application. Besides, few investigations are made to combine tool design parameters with machining conditions to avoid tool blockage during RUM process. In this work, based on the RUM material removal mechanism, two models for the chip space and the chip length are built. Thus, the tool blockage condition in RUM is linked with the tool design parameters and the cutting parameters. Experimental study is performed for theoretical verification. Due to the differences in the modalities of the chip, two typical types of composites, C/SiC and CFRP T700, are selected to obtain their tool blockage conditions. The test results show that to prevent the occurrence of blockage, the chip space should be greater than the chip length in C/SiC milling, while in T700 milling, the chip space should be at least over 8 times greater than the chip length. [ABSTRACT FROM AUTHOR]

Delamination between the layers of smart composite beams is a possible failure type. The effectiveness of active vibration control, when delamination appears, is investigated in this article. In particular, optimized fuzzy controllers are developed and tested on partially delaminated piezocomposites. A finite element model based on layerwise theory, which incorporates the electromechanical coupling and the adhesive layer, is first developed. Delamination is considered by nonlinear structural analysis techniques and is used for the creation of realistic partially delaminated structures. Fuzzy controllers are built and applied to the smart structure. The fine-tuning of the parameters of control is done using genetic algorithms. Based on the results obtained from the numerical investigation, the applicability of fine-tuned fuzzy controllers, even in the case of partial delamination, is shown. According to different delamination scenarios, which were tested in this work, the design of adaptive fuzzy controllers, robust against delamination, is feasible. [ABSTRACT FROM AUTHOR]

The modeling of progressive delamination by means of a discrete damage zone model within the extended finite element method is investigated. This framework allows for both bulk and interface damages to be conveniently traced, regardless of the underlying mesh alignment. For discrete interfaces, a new mixed-mode force-separation relation, which accounts for the coupled interaction between opening and sliding modes, is proposed. The model is based on the concept of Continuum Damage Mechanics and is shown to be thermodynamically consistent. An integral-type nonlocal damage is adopted in the bulk to regularize the softening material response. The resulting nonlinear equations are solved using a Newton scheme with a dissipation-based arc-length constraint, for which an analytical Jacobian is derived. Several benchmark delamination studies, as well as failure analyses of a fiber/epoxy unit cell, are presented and discussed in detail. The proposed model is validated against available analytical/experimental data and is found to be robust and mesh insensitive. [ABSTRACT FROM AUTHOR]

A discrete damage zone model is developed to describe the mode-mix ratio and temperature dependent delamination of laminated composite materials under high cycle fatigue loading within the framework of the finite element method. In this approach, discrete nonlinear spring elements are placed at the finite element nodes of the laminate interface, and a combination of static and fatigue damage growth laws is used to define its constitutive behavior. The model is implemented in the commercial software Abaqus using the user element subroutine. The static damage model parameters are estimated from fracture mechanics principles, whereas the fatigue damage model parameters are calibrated by fitting the numerical results to published experimental data. A quadratic relation is proposed to describe the non-monotonic variation of fatigue damage model parameters with mode-mix ratio. Next, an Arrhenius relation is proposed for the temperature dependence of fatigue damage, in addition to the incorporation of the temperature dependence of critical fracture energy. The model is convergent upon mesh refinement; however, for accurate prediction the mesh size used for model calibration should be sufficiently small. The model predicted fatigue crack growth rates are in agreement with those obtained from a quadratic relation for the Paris law parameters for variable mode mix conditions, thus verifying the approach. While the model captures the temperature effects on delamination for mode I and 50 % mode II, our prediction deviates from experiments for pure mode II, since the corresponding damage mechanism entirely changes with temperature. [ABSTRACT FROM AUTHOR]

An incremental crack extension procedure is implemented for simulating the growth of an interface defect in an electronic flip-chip device subjected to fatigue temperature cycling. The distributions of fracture mechanics parameters including the strain energy release rate, the stress intensity factors and phase angles along the curvilinear front of an embedded corner defect on the interface of silicon die and underfill are estimated and substituted into a subcritical crack growth model to predict the evolution of the defect under cyclic loading condition. It is observed from the analysis that the corner defect is under crack faces contact condition during temperature cycling, and consequently, the delamination growth is under mode-II and mode-III driving forces. In addition, the crack growth rate is highest in the middle of the crack front, and the corner crack evolves from an initially concave front to a quarter-circular front under temperature cycling. [ABSTRACT FROM AUTHOR]

The rate of propagation of embedded delamination in the strap adherend of lap shear joint (LSJ) made of carbon/epoxy composites has been evaluated employing three-dimensional non-linear finite elements. The delamination has been presumed to pre-exist in the thin resin layer between the first and second plies of the strap adherend. The inter-laminar peel and shear stress distributions have been studied in details and are seen to be predominantly three-dimensional in nature. The components of strain energy release rate (SERR) corresponding to the opening, sliding and cross sliding modes of delamination are significantly different at the two fronts of the embedded delamination. The sequential release of multi-point constraint (MPC) finite elements in the vicinity of the delamination fronts enables to simulate the growth of the delamination at either ends. This simulation procedure can be utilized effectively for evaluation of the status of the structural integrity of the bonded joints. [ABSTRACT FROM AUTHOR]

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]

We present an analytical investigation of a test protocol recently developed to extract the fracture toughness of thin films used in microelectronics and other engineering applications. The testing method involves the dynamic delamination of patterned thin films initiated by a laser-induced pressure pulse applied on the backside of the substrate. The kinetic energy imparted by the pulse to a weakly bonded (pre-cracked) region of the film is converted into fracture energy as the thin film delaminates in a controlled fashion over multiple milimeters. To support these experiments and extract the interface fracture toughness values, we develop a numerical scheme based on the combination of a nonlinear beam model used to capture the elastodynamic response of the thin film and a cohesive failure model to simulate the spontaneous propagation of the delamination front. The accuracy of the beam model is assessed through a comparison with the results of a more complex 2D hybrid spectral/finite element scheme. Numerical results are compared with experimental measurements of the delamination length and the outcome of a parametric study of some of the key geometrical and loading quantities defining the delamination event is presented. [ABSTRACT FROM AUTHOR]

A double cantilever beam specimen loaded with uneven bending moments (DCB-UBM) is proposed for mixed mode fracture mechanics characterisation of adhesive joints, laminates and multilayers. A linear elastic fracture mechanics analysis gives the energy release rate and mode mixity analytically for both isotropic and orthotropic materials. By varying the ratio between the two applied moments, the crack tip stress state can be varied from pure mode I to pure mode II for the same specimen geometry. The specimen allows stable crack growth. A special test fixture is developed to create uneven bending moments. As a preliminary example, the DCB-UBM specimen was used for characterising fracture of adhesive joints between two laminates of thermoset glass fibre reinforced plastic. [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]

Two distinct cohesive layer models are developed for numerical simulation of delamination growth in composite layered specimens tested under static loading. One of these designated as the UMAT (user supplied material) model has a small, but finite thickness and the other designated as the UEL (user element) model has zero initial thickness. Crack growth in double cantilever beam specimens as well as in two test configurations of a composite plate carrying some discontinuities subjected to lateral load are studied using the models. It turns out that UEL model, though slightly more involved, is able to predict both crack initiation and large crack growth with sufficient accuracy. The UMAT model too consistently predicts crack initiation, but is unable to predict the crack growth accurately. It gives consistently higher loads for given crack extensions and predicts that the crack growth shuts off prematurely. Careful examination of the stresses in the cohesive layer of the UMAT model, in the upstream of the crack tip indicates that a ‘neck’ develops due to compressive stresses at some distance from the crack tip. Apparently it is the formation of this neck that ‘locks’ the crack from growing and is the cause of the inaccurate results given by the model. [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]

Temperature- and moisture- induced delamination leading to popcorn package cracking is a major package reliability issue for surface-mount plastic encapsulated microcircuits (PEM). Crack propagation along one of the interfaces of a ductile adhesive joining two elastic substrates is modeled to study interface delamination and toughness of PEMs. The polymeric adhesive is stressed by remote loading and residual stress. Along the crack front, the film-substrate interface is modeled by a strip of cells that incorporates vapor pressure effects on void growth and coalescence through a Gurson porous material relation. Results show that under high levels of vapor pressure, increasing film thickness will produce smaller enhancement on the steady-state fracture resistance of the interface, also referred to as the joint toughness. Across all mode mixity levels, vapor pressure effects dominate over residual stress. The adverse effects of vapor pressure are greatest in highly porous adhesives subjected to a strong mode II component. The latter is representative of the likely state of loading in IC packages since residual stress, resulting from the film-substrate thermal mismatch, induces a predominantly mode II component. [ABSTRACT FROM AUTHOR]

Steady-state tunneling and plane-strain delamination of an H-shape crack are examined for elastic, isotropic multi-layers. Both tunneling and delamination are analysed by employing linear elastic fracture mechanics within a 2D finite element framework. Failure maps are produced to reveal the sensitivity of cracking path to the relative toughness of layer and interface, and to the stiffness mismatch of layers. Closed-form expressions are derived for the critical stress level for steady-state plane-strain delamination. By means of a comparison with experimental results taken from the literature, it is demonstrated that these expressions serve as useful design criteria for elastic multilayers. [ABSTRACT FROM AUTHOR]

In this investigation, the conservative M-integral is extended to treat thermal-elastic, mixed mode problems. With it, stress intensity factors are obtained for cracks in homogeneous, isotropic materials, as well as isotropic and anisotropic, bimaterials. Excellent agreement is found between results determined in this study and those found in the literature. In addition, new results are obtained for interface cracks for a wide range of material properties and for a delamination in a composite material. [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]

Length scales are essential to the understanding of small volume deformation and fracture in emerging technologies. Recent analysis by two groups at the atomistic (Horstmeyer and Baskes, 1999) and mesoscopic (Gerberich et al., 2002) levels have shown the importance of the volume to surface ratio to the indentation size effect (ISE) at small depths of penetration. We have interpreted this in terms of the plastic work under the contact and the surface work associated with the creation of new surface or the excess surface stress. Treating this as a modified Griffith criterion the case is made that this same length scale should apply to the delamination of thin films. By making this simple equivalency in length scales, an R-curve analysis for crack growth resistance, GR, in thin film delamination emerges. This recovers the classic σ2ysh/E term as well as the fact that interfacial toughness should scale with the square root of incremental crack growth. Here σys is yield strength, h is thickness and E is modulus of the film. As applied to thin Cu and Au films bonded to silicon substrates, the model is in good agreement. [ABSTRACT FROM AUTHOR]