Bending strength of adhesive joints in microelectronic components: Comparison of edge-bonding and underfilling

The bending strength of underfilled and edge-bonded ball grid array (BGA) microelectronic packages assembled on printed circuit boards (PCBs) was compared using double cantilever beam (DCB) specimens. All specimens with fillets of the same size and shape failed at the same load, with cracks initiating and propagating within the PCB. This was consistent with measurements of the crack initiation strain energy release rate for PCB interfacial failure, which was significantly smaller than that of cohesive failure within the adhesives. Finite element analysis (FEA) indicated that the stress state in the PCB near the PCB-fillet interface in both underfilled and edge-bonded specimens was only a function of the adhesive fillet size and shape, and independent of the extent of the adhesive layer between the PCB and the BGA, and independent of the adhesive mechanical and thermal properties over the broad range of properties of the tested adhesives. This explained why decreasing the fillet curvature in edge-bonded specimens produced a significant increase in the joint strength. The crack path in the PCB of the edge-bonded specimens was found to change with the adhesive cure temperature; however, this had a negligible effect on the failure load.     

Acoustic emission analysis of composite pressure vessels under constant and cyclic pressure

The use of acoustic emission (AE) for the detection of damage in carbon fibre composite pressure vessels was evaluated for constant and cyclic internal gas pressure loading conditions. AE was capable of monitoring the initiation and accumulation of damage events in a composite pressure vessel (CPVs), although it was not possible to reliably distinguish carbon fibre breakage from other microscopic damage events (e.g. matrix cracks, fibre/matrix interfacial cracks). AE tests performed on the carbon fibre laminate used as the skin of pressure vessels revealed that the development of damage is highly variable under constant pressure, with large differences in the rupture life and acoustic emission events at final failure. Numerical analysis of the skin laminate under constant tensile stress revealed that the high variability in the stress rupture life is due mainly to the stochastic behaviour of the carbon fibre rupture process.     

Experimental and finite element studies on hot sizing process for L-shaped composite beams

This work aims at developing a hot sizing process on composite materials to correct the profiles of composite structures during manufacture. Hot sizing experiments were carried out at 150 °C with different sizing loads and hot sizing periods for L-shaped composite beams made of carbon fiber plain-weave fabric and epoxy resin. To predict the springback in hot sizing process, a corresponding finite element simulation method was developed using stress relaxation equations determined at the same temperature. Excellent agreements between the predicted and observed results were obtained. The effects of the component thickness and 45° ply percentage on the springback rate were investigated by simulation. Springback rate in hot sizing process on composite materials ranges from 60% to 95%. In conclusion hot sizing process is proved to be a valid method for compensation for the process-induced deformation (PID) of L-shaped composite beams.     

Numerical method for optimizing design variables of carbon-fiber-reinforced epoxy composite coil springs

To successfully reduce a vehicle's weight by replacing steel with composite materials, it is essential to optimize the material parameters and design variables of the structure. In this study, we investigated numerical and experimental methods for determining the ply angles and wire diameters of carbon fiber/epoxy composite coil springs to attain a spring rate equal to that of an equivalent steel component. First, the shear modulus ratio for two materials was calculated as a function of the ply angles and compared with the experimental results. Then, by using the equation of the spring rate with respect to the shear modulus and design variables, normalized spring rates were obtained for specific ply angles and wire diameters. Finally, a finite element model for an optimal composite coil spring was constructed and analyzed to obtain the static spring rate, which was then compared with the experimental results.     

Effect of an interphase region on debonding of a CNT reinforced polymer composite

The effect on stiffness and debonding of an interphase zone of altered polymer properties surrounding each carbon nanotube (CNT) in a CNT reinforced polymer composite is investigated. The interphase zone has position dependent material properties that merge with those of the polymer at a sufficiently large distance from the inclusion. There is evidence that such an interphase zone must be included in models in order to represent the overall composite properties. The analyses are based on an axisymmetric unit cell model of the composite. An elastic–viscoplastic conventional continuum constitutive relation (a size-independent relation between stress, strain and strain rate) is taken to characterize the bulk polymer material and the interphase, with the material properties being position dependent in the interphase. The interface between the polymer and the CNT is modeled by a phenomenological cohesive relation that allows for complete separation and the creation of new free surface. The effect of varying interface strength on the composite stress–strain response and on debonding is analyzed both with and without an interphase. The presence of an interphase increases the composite stiffness but promotes debonding which ultimately reduces composite stress carrying capacity. The compliance of the interface also affects the stress–strain response prior to debonding and leads to stress redistributions within both the fiber and the matrix (and/or interphase) which can affect the fracture mode that occurs.     

Effect of fibre wrinkling to the spring-in behaviour of L-shaped composite materials

To determine the amount of deformation resulting from fibre wrinkling at corner regions, a set of experiments have been conducted. As known in the conventional lay-up method, the prepregs are laid sequentially layer by layer on the mould surface. At the corner region of a female tool the radius decreases at the inner surface and the amount of wrinkles increase towards the top layer as the layers are laid up. In order to determine how much these wrinkles influence the dimensional stability of the manufactured parts, an alternative lay-up method is used. The amount of the wrinkles can be increased for the parts of same geometry by first stacking prepregs on a flat plate and then bending the whole stack to conform to the surface of the L-shaped mould. In this method, more wrinkling occurs on the inner surface of the corner regions as compared to the conventional lay-up procedure. It was found that fibre wrinkling decreases the spring-in values. The mechanism behind that observation is discussed with the help of a heuristic Finite Element Analysis (FEA). The conformation of the stacked prepregs on the mould was simulated by using FEA.     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures

This paper presents the development of a highly efficient user-defined finite element for modelling the bolt-load distribution in large-scale composite structures. The method is a combined analytical/numerical approach and is capable of representing the full non-linear load-displacement behaviour of bolted composite joints both up to, and including, joint failure. In the elastic range, the method is generic and is a numerical extension of a closed-form method capable of modelling the load distribution in single-column joints. A semi-empirical approach is used to model failure initiation and energy absorption in the joint and this has been successfully applied in models of single-bolt, single-lap joints. In terms of large-scale applications, the method is validated against an experimental study of complex load distributions in multi-row, multi-column joints. The method is robust, accurate and highly efficient, thus demonstrating its potential as a time/cost saving design tool for the aerospace industry and indeed other industries utilising bolted composite structures.     

Establishing a new Forming Limit Curve for a flax fibre reinforced polypropylene composite through stretch forming experiments

In developing an understanding of the failure in natural fibre reinforced polymer composites, the failure limits of this class of the material system are required. It is found that the conventional Forming Limit Curve is not suitable to predict the failure initiated in the natural fibre composite as principal strains cannot differentiate the strain on the flax fibres and the polypropylene matrix. This study proposes a new Forming Limit Curve for the composite which expresses limiting fibre strain as a function of forming mode depicted by the ratio of minor strain to major strain. The new Forming Limit Curve, along with the Maximum Strain failure criterion have been successfully implemented in FEA simulations, and numerical simulations suggest that the former is more accurate. The current work provides an innovative method to predict the onset of failure in natural fibre composites, which can be applied in composite forming and structural design.     

Cohesive zone modelling of delamination response of a composite laminate with interleaved nylon 6,6 nanofibres

This work simulates numerically Double Cantilever Beam and End Notched Flexure experiments on Carbon Fibre Epoxy Resin specimens that have been performed by some of the authors in a previous work. Specimens have been nanomodified by interleaving plies with a layer of electrospun nanofibres in the delaminated interface. Eight different configurations of nanofibres have been used as interleave, for a total of 9 configurations (8 nanomodified plus the virgin one) to be simulated for both kind of tests to identify the cohesive zone parameters corresponding to the effect of nanofibre diameter, nanolayer thickness and nanofibre orientation on the delamination behaviour of the composite.Results showed that a bilinear damage law is necessary for almost all nanomodified configurations, and presented a clear relationship between nanomat layer parameters and the cohesive energy of the interface.     

Mode-I,mode-II and mixed-mode I+II fracture behavior of composite bonded joints: Experimental characterization and numerical simulation

The fracture behavior of composite bonded joints subjected to mode-I, mode-II and mixed-mode I + II loading conditions was characterized by mechanical testing and numerical simulation. The composite adherents were bonded using two different epoxy adhesives; namely, the EA 9695 film adhesive and the mixed EA 9395-EA 9396 paste adhesive. The fracture toughness of the joints was evaluated in terms of the critical energy release rate. Mode-I tests were conducted using the double-cantilever beam specimen, mode-II tests using the end-notch flexure specimen and mixed-mode tests (three mixity ratios) using a combination of the two aforementioned specimens. The fracture behavior of the bonded joints was also simulated using the cohesive zone modeling method aiming to evaluate the method and point out its strengths and weaknesses. The simulations were performed using the explicit FE code LS-DYNA. The experimental results show a considerable scatter which is common for fracture toughness tests. The joints attained with the film adhesive have much larger fracture toughness (by 30–60%) than the joints with the paste adhesive, which exhibited a rather brittle behavior. The simulation results revealed that the cohesive zone modeling method performs well for mode-I load-cases while for mode-II and mixed-mode load-cases, modifications of the input parameters and the traction-separation law are needed in order for the method to effectively simulate the fracture behavior of the joints.     

Dynamic response of full-scale sandwich composite structures subject to air-blast loading

Glass-fibre reinforced polymer (GFRP) sandwich structures (1.6 m × 1.3 m) were subject to 30 kg charges of C4 explosive at stand-off distances 8–14 m. Experiments provide detailed data for sandwich panel response, which are often used in civil and military structures, where air-blast loading represents a serious threat. High-speed photography, with digital image correlation (DIC), was employed to monitor the deformation of these structures during the blasts. Failure mechanisms were revealed in the DIC data, confirmed in post-test sectioning. The experimental data provides for the development of analytical and computational models. Moreover, it underlines the importance of support boundary conditions with regards to blast mitigation. These findings were analysed further in finite element simulations, where boundary stiffness was, as expected, shown to strongly influence the panel deformation. In-depth parametric studies are ongoing to establish the hierarchy of the various factors that influence the blast response of sandwich composite structures.     

A parametric study of fiber volume fraction distribution on the failure initiation location in open hole off-axis tensile specimen

We present a model to study the effect of the spatial distributions in fiber volume fraction on the failure initiation location in the open hole off-axis tensile. These variations are introduced with a micromechanical enhancement dehomogenization process. Good agreement is obtained between our predicted failure locations and experimental results by considering a failure criterion based on the effective shear strain in the matrix. The predicted failure angle distribution is in good agreement with the experimental results when the variability in the fiber volume fraction is included in the simulations.     

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.     

Analysis of adhesively bonded CFRE composite scarf joints modified with MWCNTs

The main objective of the present work is to improve the performance of bonded joints in carbon fiber composite structures through introducing Multi-Walled Carbon Nanotubes (MWCNTs) into Epocast 50-A1/946 epoxy, which was primarily developed for joining and repairing of composite aircraft structures. Results from tension characterizations of structural adhesive joints (SAJs) with different scarf angles (5–45°) showed improvement up to 40% compared to neat epoxy (NE)–SAJs. Special attention was considered to investigate the performance of SAJs with 5° scarf angle under different environments. The tensile strength and stiffness of both NE-SAJs and MWCNT/E-SAJs were dramatically decreased at elevated temperature. Water absorption showed a marginal drop of about 2.0% in the tensile strength of the moist SAJs compared to the dry one. Cracks initiation and propagation were detected effectively using instrumented-SAJs with eight strain gauges. The experimental results agree well with the predicted using three-dimensional finite element analysis model.     

Effect of excessive bending on residual tensile strength of hybrid composite rods

Excessive bending has been identified as a concern for the hybrid composite core that is currently being used as the structural member for the Aluminum Conductor Composite Core Trapezoidal Wire (ACCC/TW™) transmission line. In this work the flexure strength of the ACCC core was measured in a series of four point bend tests while monitoring acoustic emissions. To quantify the stress state within the rods and to evaluate its flexure strength, an analytic solution for the bending stress was derived and numerically verified using the finite element method. In the second part of the study several specimens that had been subjected to excessive bending were subsequently tested for their residual tensile strength. It was found that wrapping the ACCC core around a 1 m mandrel, which is a common loading condition in practice, will not generate significant structural damage in the composite core. It was determined that the diameter of the mandrel that would cause failure of the composite core is 467 mm. From this work it was found that excessive bending, up to 90% of the flexural strength of the ACCC core, had no detrimental effect on the residual tensile strength of the hybrid composite. It was observed that the majority of the micro-structural damage that was accrued during the excessive bending of the cores presented itself in the form of matrix damage without any significant fiber kinking.     

Simulation of curing process of carbon/epoxy composite during autoclave degassing molding by considering phase changes of epoxy resin

Strain monitoring of a carbon/epoxy composite cross-ply laminate ([0₅/90₅]_s) during thermoforming was conducted by using fiber Bragg grating (FBG) sensors. The entire process was simulated by employing finite element analysis (FEA) by taking into consideration the phase changes of the epoxy resin. For the precise simulation of the curing process, a dielectrometry sensor was used to detect the epoxy-resin dissipation factor, which in turn was used to identify the curing point. To investigate the phase changes and consolidation of the composite laminate by employing FEA, modulus changes with temperature were measured by dynamic mechanical analysis (DMA), and the permeability was estimated by measuring the fiber volume fraction according to the curing temperature. As the epoxy resin changed from a liquid to solid phase, the strain generated along the carbon fibers dynamically changed, and the analysis results generally predicted the strain variation quite well. To apply this simulation technique to practical structures, a composite-aluminum hybrid wheel was analyzed and experimentally verified.     

Finite element modeling of post-fire flexural modulus of fiber reinforced polymer composites under constant heat flux

In this study, a simple 1D finite element model was developed to predict the temperature evolution and post-fire mechanical degradation of glass fiber reinforced polymers (FRPs) subjected to constant heat fluxes, including 35 kW/m², 50 kW/m², 75 kW/m², and 100 kW/m². A temperature-dependent post-fire mechanical property model was proposed and implemented. The calculated temperature and residual mechanical moduli showed good agreement with the experimental data. By properly selecting the parameters of the model, an effective strategy was demonstrated to design FRP structure with enhanced durability.     

Multi-scale ballistic material modeling of cross-plied compliant composites

The open-literature material properties for fiber and polymeric matrix, unit-cell microstructural characteristics, atomic-level simulations and unit-cell based finite-element analyses are all used to construct a new continuum-type ballistic material model for 0°/90° cross-plied highly-oriented polyethylene fiber-based armor-grade composite laminates. The material model is formulated in such a way that it can be readily implemented into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User Documentation, Century Dynamics Inc. a subsidiary of ANSYS Inc. (2007)] and ABAQUS/Explicit [ABAQUS version 6.7, User Documentation, Dessault Systems, 2007] as a User Material Subroutine. Model validation included a series of transient non-linear dynamics simulations of the transverse impact of armor-grade composite laminates with two types of projectiles, which are next compared with their experimental counterparts. This comparison revealed that a reasonably good agreement is obtained between the experimental and the computational analyses with respect to: (a) the composite laminates’ capability, at different areal densities, to defeat the bullets with different impact velocities; (b) post-mortem spatial distribution of damage within the laminates; (c) the temporal evolution of composite armor laminate back-face bulging and delamination; and (d) the existence of three distinct penetration stages (i.e. an initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix de-bonding/decohesion and the final stage associated with the extensive back-face delamination and bulging of the armor panel).     

Real-time inference of stochastic damage in composite materials

This study describes a control system designed for real-time monitoring of damage in materials that employs methods and models that account for uncertainties in experimental data and parameters in continuum damage mechanics models. The methodology involves (1) developing an experimental set-up for direct and indirect measurements of damage in materials; (2) modeling damage mechanics based constitutive equations for continuum models; and (3) implementation of a Bayesian framework for statistical calibration of model with quantification of uncertainties. To provide information for real-time monitoring of damage, indirect measurement of damage is made feasible using an embedded carbon nanotube (CNT) network to perform as sensor for detecting the local damage. A software infrastructure is developed and implemented in order to integrate the various constituents, such as finite element approximation of the continuum damage models, generated experimental data, and Bayesian-based methods for model calibration and validation. The outcomes of the statistical calibration and dynamic validation of damage models are presented. The experimental program designed to provide observational data is discussed.