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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]

Bilinear delamination failure criteria proposed by Reeder for mixed-mode (I–II) fracture of composite laminates has four limitations: require mixed-mode (I–II) fracture data by the more complex MMB test; determination of bilinear constants by two independent curve fits; failure of bilinear equations to intersect at G I m / G II m = 1 ; and the data representation by G I m versus G II m instead of the conventional G c m versus G II m / G T . Some of these limitations were overcome by limited input bilinear criteria (LIBC) proposed by Davidson and Zhao by replacing the MMB test data by DCB, ENF, and SLB (single leg beam) test data. But the LIBC retained the two discontinuous forms of the equations for no specific reason in a continuous material system. This paper eliminates the two equations by a single power law equation that covers the whole domain of fracture as in Benzeggagh and Kenane's empirical equation. This simplified mixed-mode delamination fracture criterion we call "Limited Input B–K (LIBK) criterion in recognition of the works of Davidson and Zhao, and Benzeggagh and Kenane. The criterion was validated by a large number of test data in the literature. [ABSTRACT FROM AUTHOR]

The delamination of a circular thin film at micro/nanoscale is studied using the Kirchhoff plate theory incorporating surface effects in this paper. Bending of a clamped circular nanoplate subjected to a concentrated force at the center or a uniformly distributed force over a lateral surface is solved. The bending deflection is derived in closed form. The adhesion energy and its release rate for delamination are determined when surface effects are taken into account. The influences of surface residual stress and surface elasticity along with the film’s size on the energy release rate of debonding advance or interfacial adhesion of a thin film bonded to an elastic substrate are analyzed for applied loading or given displacements. Analytic results are compared with experimental data and satisfactory agreement is confirmed. [ABSTRACT FROM AUTHOR]

This paper originally proposes a nonlinear cohesive/frictional contact coupled model for the mode-II shear delamination of adhesive composite joint based on a modified Xu and Needleman's exponential cohesive model. First, the friction is assumed to increase nonlinearly at the delamination interface when the tangential cohesive softening appears. Second, a non-associative plasticity model based on the Mohr-Coulomb frictional contact law is proposed, which includes a frictional slip criterion and a slip potential function. Third, a return mapping algorithm based on the non-associative plasticity theory is proposed to solve the updated normal and tangential tractions and stiffnesses. It is shown the tangential cohesive traction and stiffness depend on the friction and dilatancy of the delamination interface. Finally, the proposed theoretical model is implemented using three-dimensional finite element analysis by ABAQUS-UEL (user element subroutine) and demonstrated by comparing the finite element results with the analytical results for the $$[0^{\circ }]_{6}$$ , $$[\pm 30^{\circ }]_{5}$$ , $$[\pm 45^{\circ }]_{5}$$ end-notched flexure adhesive composite joints with the mode-II shear delamination. The effects of the friction coefficient, cohesive strength, normal contact stiffness and mesh size on the load-displacement curves and delamination mechanisms of composites are studied. Numerical results show the shear delamination growth is governed by the transition from the decreased tangential cohesive traction to the increased tangential friction, and the frictional effect becomes distinct after unstable delamination for angle-ply laminates. [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]

Interfacial delamination is a key reliability challenge in composites and micro-electronic systems due to (high density) integration of dissimilar materials. Predictive finite element models require the input of interface properties, often determined with an interface delamination growth experiment with (nearly) constant process zone, relying on the assumption of no permanent deformation in the sample structure layers. However, much evidence in the literature exists that plasticity often does occur in the sample structure during delamination experiments, which should be adequately dealt with to obtain the real interface fracture toughness that is independent of the thickness of the two sample arms. This paper presents a practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment on a double-cantilever beam specimen involving only small-scale plasticity at the interface. The procedure does not require knowledge of the constitutive behavior of the adherent layers. It only deals with the separation of structural plasticity in the adherents, whereas small-scale plasticity in connection with ductile interface fracture is lumped into the interface fracture toughness. The proposed approach was numerically verified for one set of parameters. Experimental assessment of the approach on industrially-relevant copper lead frame-molding compound epoxy interface structures showed a correction of the interface fracture toughness of more than a factor of two, demonstrating the potentially significant errors induced by plastic deformation of the sample structure during delamination experiments. [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]

This paper addresses the question of rate effects in the propagation of delamination cracks in Composite Fiber-Reinforced Plastics (CFRPs). In order to make use of a simple loading device, a mode-II case is used as the basis of the experimental study. The position of the crack is recorded quantitatively by means of a high-speed camera and dedicated image processing techniques. The delamination process is modeled by means of an interfacial Continuum Damage Model (CDM), similar to Cohesive Zone Model (CZM) approaches. In order to make suitable comparison between test and explicit finite element simulation of the test, criterai of proper temporal and spatial discretization have been derived. They ensure a fine description of the process zone and a proper description of the degradation evolution of the interface. Using such simulations and direct comparisons with the tests results, it is shown that the experimental results cannot be reproduced numerically without introducing rate effects. Then, it is proposed and identified by means of comparison between experiments and numerical simulation a bounded-damage-rate interfacial model. The main consequence of the proposed rate-dependent model is that it introduces a maximum crack velocity which is a function of the maximum damage rate. The dependence of the critical energy release rate on the crack’s velocity is analyzed, which leads to the identification of an equivalent rate-dependent fracture mechanics criterion. [ABSTRACT FROM AUTHOR]

Channeling cracks in brittle thin films have been observed to be a key reliability issue for advanced interconnects and other integrated structures. Most theoretical studies to date have assumed no delamination at the interface, while experiments have observed channel cracks both with and without interfacial delamination. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that, depending on the elastic mismatch and interface toughness, a channel crack may grow with no delamination, with a stable delamination, or with unstable delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value, while stable delamination along with the channel crack is possible only in a small range of interface toughness for a specific elastic mismatch. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. [ABSTRACT FROM AUTHOR]

Three-dimensional non-linear finite ele- ment analyses have been carried out to evaluate the out-of-plane stresses in the adhesive layer existing between the lap and the strap adherends of the Lap Shear Joint (LSJ) in laminated FRP composites for varied delamination lengths. The delaminations are presumed to be pre-embedded in the thin resin rich layer existing between the first and second plies of the strap adherend. Sublaminate technique has been used to model the LSJ with the delamination. Contact finite element analyses have been performed in order to avoid interpenetration of delaminated surfaces. The effects of varied delamination lengths on the peel and interlaminar shear stresses and the individual modes of Energy Release Rate (ERR) in the delamination zones are highlighted in this paper. It is seen that three-dimensional effects exist near the free edges of the overlap end of the joint. The delamination propagation significantly affects the stress distributions in the adhesive layer existing between the lap and the strap adherends of the LSJ. The variations of interlaminar stresses and ERRs on both the delamination fronts are found to be significantly different and thus, indicate that the propagation of delamination does not occur at same rate at the two delamination fronts. This may throw some light to the evaluation of structural integrity of the LSJ in the presence of pre-embedded delaminations. [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]

The shrinkage cracking processes in a cement-based composite, which include crack initiation, propagation and coalescence, as well as diffusion-damage coupling, are numerically studied using a mesomechanical numerical model to better understand the shrinkage cracking growth mechanisms and the effects of cracks on moisture diffusion. This study analyzes the shrinkage crack initiation and growth processes in a repair layer of mortar, which is cast on the top of an old concrete substrate and initially saturated with water. The potential shrinkage crack development is driven by the associated drying process. The results illustrate the fracture infilling, saturation and delamination processes in the concrete repair system by decreasing the bond strength between the repair mortar and the substrate from 4 to 1 MPa. Large concrete repair system bond strengths cause cracks to initiate on the surface of the repaired mortar and propagate to the interface. However, debonding is observed at lower bond strengths. The numerical model is shown to be a viable tool for damage analyses under both mechanical loads and hygral gradients. [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]

Previous numerical work on crack tunnelling and plane-strain delamination in layered solids is evaluated with static and fatigue experiments and analysis. It is concluded that the translation of the theory derived for static fracture to fatigue loading is not as straightforward as initially assumed. Details such as delamination location, stress state, plasticity and mode-mixity need further consideration to obtain a theory that is sufficiently adequate to describe the static and fatigue phenomena observed in practice. [ABSTRACT FROM AUTHOR]

Mixed-mode fracture toughness tests were carried out on a multi-directional laminate making use of a Brazilian disk specimen. The composite laminate consisted of plain, balanced woven plies with tows in the 0 ∘ / 90 ∘ -directions and the + 45 ∘ / - 45 ∘ -directions. The delamination was placed between two of these plies by means of a polytetrafluoroethylene (PTFE) film. Tests at various loading angles were performed in order to obtain a wide range of mode mixities. Each ply was homogenized by means of a micro-mechanical model to obtain its effective properties. The specimens were analyzed by means of the finite element method. An interaction energy or M-integral was extended for this interface to obtain the stress intensity factors. The latter were used to determine the critical interface energy release rate and two phase angles. Employing this information, a three-dimensional failure criterion proposed elsewhere was presented. The criterion may be used to predict failure of a composite structure containing a delamination along the interface and material studied here. [ABSTRACT FROM AUTHOR]

Dynamic fracture analysis for the crack arrest phenomenon is performed by ordinary state-based peridynamics formulation and discretization employing transition bond concept. Double cantilever beam specimen is chosen for our numerical evidence purpose. The analysis consists of two main phases namely, generation and application (prediction) phases. In the generation phase, the dynamic stress intensity factors of propagating and arrested cracks are estimated by the present formulation for given crack path histories, and a good agreement is achieved. As for the application phase, dynamic stress intensity factors as well as total crack lengths after crack arrests are in good agreement with the experiments. Moreover, the influence of transition bond concept on the crack arrest behavior is investigated and it is found that the transition bond is very efficient in the simulation of the crack arrest problem such that premature arrests of cracks are observed without transition bond cases. [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]

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]

Two hierarchical approaches, the $$s$$ -method and the extended finite element method (XFEM), are compared to the classical ply-by-ply discretization approach in terms of their effectiveness in modeling delamination in laminated composites. In the two hierarchical approaches, a smooth approximation field based on the mesh made of through-the-thickness solid laminated elements is first introduced to resolve a delamination-free response of the composite structure. The initiation and propagation of delamination is modeled by either superposition of element patches (s-method) or by enrichment functions (XFEM). A cohesive zone model is employed to model decohesion at the inter-ply interfaces. In terms of representing strong discontinuities, the two hierarchical methods have been shown to represent an identical approximation space as the classical ply-by-ply discretization approach, even though the s-method gives rise to sparser matrix structure. In terms of representing weak discontinuities, the s-method has been shown to be equivalent to the ply-by-ply discretization approach and provides a seamless transition from weak to strong discontinuity. [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]

Four-point bending experiments are conceptually the method of choice when investigating the delamination strength of multi-layered components, which are of particular interest for semiconductor applications. However, experimental studies have shown that the crack continues as mode-I crack in most cases while delamination is rarely observed, thus making the four-point bending method useless. This study uses the finite element method with cohesive zones to study crack propagation and the likelihood of turning the initial mode-I crack into a delamination crack in a multi-layered structure. We close with a conclusion which can help to increase the delamination probability and thereby help to determine the delamination strengths of layered structures. [ABSTRACT FROM AUTHOR]

This work explores the effects of grain orientation and T-stress on crack-front shielding and delamination cracking in modern aluminum-lithium alloys. In the crack-arrestor configuration of interest here, a primary crack extends through the grain thickness while triggering delaminations over susceptible grain boundaries that lie normal to the plane of the primary crack. A three-dimensional, small-scale-yielding framework that employs a gradient-enhanced, crystal plasticity material model reveals key features of the strain/stress fields in a simulation of pancake-shaped grains with alternating orientation near a primary crack front. The alternating grain configurations exhibit a soft/stiff behavior and alternating out-of-plane, L-T shear stress-effects observed in recently-published experiments completed by the authors and others on various Al-Li alloys. Both texture effects contribute to highly localized driving forces for delamination cracking while concurrently shielding the primary crack. Moreover, texture does not act to shield the arrestor delamination planes, thereby favoring arrestor delamination development over primary crack growth. A compressive T-stress further enhances shielding of the primary crack-a result which aids in understanding marked differences in observed fracture behavior of tested M(T) and C(T) specimens of Al-Li alloys. [ABSTRACT FROM AUTHOR]

Bimaterial interfaces in microelectronics packages are the most common regions of failure under thermo-mechanical excursions. In this work, we report experimentally observed role of heating rate on the delamination initiation and propagation across a metal-polymer interface in a microelectronic package. We observe that the rate of delamination propagation increases with increasing heating rate. When the heating rate increases, in addition to the higher amount of delamination growth per unit time, experimental results suggests that higher growth will also incur per unit temperature (loading). Correspondingly, the temperature at which complete delamination occur decreases. Using finite element modeling with cohesive interfaces, we provide a plausible explanation to this observed phenomenon. The analyses indicate that the mechanical behavior of the bimaterial interface is sensitive to both temperature and thermal rate. [ABSTRACT FROM AUTHOR]

Four split-beam-type tests are proposed for determining the mode III delamination toughness of laminated composite materials. Each test is first assessed via three dimensional finite element analysis. Experimental evaluations are then conducted, for which two different unidirectional carbon/epoxy materials are considered. For either material, it is shown that the same mode III toughness is obtained by the four different tests, provided that specimens with the same delamination length are tested. However, when a single test configuration is utilized to investigate the effect of delamination length, the apparent mode III toughness is observed to decrease with increasing delamination length. In order to understand the mechanisms behind this, transverse section cuts were taken at the delamination front of tested specimens. Photomicroscopic examinations of these cross sections revealed matrix cracks at the delamination front that were oriented at an inclination of $$45^{\circ }$$ 45 ∘ to the plane of the delamination. Based on previous observations of mode III crack initiation in homogeneous materials, it is hypothesized that these matrix cracks initiate prior to or concurrent with delamination advance, and therefore are responsible for the observed geometry-dependence of the mode III delamination toughness in laminated polymeric composites. [ABSTRACT FROM AUTHOR]

An axisymmetric thermo-mechanical model is developed for laser-driven non-contact transfer printing, which involves laser-induced impulsive heating to initiate separation at the interface between a soft, elastomeric stamp and hard micro/nanomaterials (i.e., inks) on its surface, due to a large mismatch in coefficients of thermal expansion. The result is the active ejection of the inks from the stamp, to a spatially separated receiving substrate, thereby representing the printing step. The model gives analytically the temperature field, and also a scaling law for the energy release rate for delamination at the interface between the stamp and an ink in the form of a rigid plate. The normalized critical laser pulse time for interfacial delamination depends only on the normalized absorbed laser power and width of the ink structure, and has been verified by experiments. [ABSTRACT FROM AUTHOR]

For a variety of modern industries, interfacial delamination is a critical issue for the design and application of laminated composite structures. Numerous global experimental studies have been conducted to characterize the toughness of adhesively bonded composite structures. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions. The local interfacial traction-separation laws as the fundamental input are crucial for the successful applications of CZMs. Several local tests have also been conducted to determine the interfacial traction-separation laws in adhesively bonded joints. However, very few tests have been employed to investigate the dependency of the local interfacial traction-separation laws on the bondline thickness, particularly, for the laminated composite joints under Mode-II loading conditions. In this work, the effects of bondline thickness on the interfacial behavior have been systematically investigated at various typical bondline thicknesses (from 0.1 to 0.8 mm). The effects of adhesive thickness on the interfacial toughness, interfacial strength, and shapes of the local interfacial traction-separation laws have also been evaluated. The test results indicated that the measured Mode-II (shear test) interfacial shear strength of the composite joints increases as the adhesive layer becomes thicker. It was found a significant dependency of the measured shapes of the Mode-II interfacial laws on the bondline thickness. Several other interesting issues were also reported in this work. This work may provide valuable baseline test data for analytical and numerical modeling of fracture and failure of laminated composite structures. [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 penny-shaped delamination is modeled as a flat octahedral shaped crack between layers of a cross-ply laminate. The fibers of the laminate intersect the edges of the delamination at angles of 0°/90°, +45°/−45°, 90°/0° and −45°/+45° as one proceeds along the delamination edge. Two lay-ups are considered, a cross-ply consisting of two layers, and a symmetric composite, consisting of three layers. The delamination is always between two of the layers. Both tension and shear are applied to the outer boundary of the body. Stress intensity factors about the delamination edge are calculated by means of a conservative M-integral. These are employed to calculate the interface energy release rate and corresponding phase angles. Use is made of existing experimental results to predict the location of propagation along the edge of the delamination. It was found that the most dangerous regions along the delamination front occurred for the 0°/90° or 90°/0° interfaces. [ABSTRACT FROM AUTHOR]

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation. [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, G R, in thin film delamination emerges. This recovers the classic σ2 ys h/ 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]