Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

On the non-linear elastic stresses in an adhesively bonded T-joint with double support

Structures consisting of single or more materials, such as adhesive joints, may undergo large displacements and rotations under reasonably high loads, although all materials are still elastic. The linear elasticity theory cannot predict correctly the deformation and stress states of these structures, since it ignores the squares and products of partial derivatives of the displacement components with respect to the material coordinates. When these derivatives are not small, these terms result in a non-linear effect called geometrical non-linearity. In this study, the geometrically non-linear stress analysis of an adhesively bonded T-joint with double support was carried out using the incremental finite element method. Different T-joint configurations bonded to a rigid base and to a flexible base were considered. For each configuration, linear and geometrically non-linear stress analyses of the T-joint were carried out and their results were compared for different horizontal and vertical plate end conditions. The geometrically non-linear analysis showed that the large displacements had a considerable effect on the deformation and stress states of both adherends and the adhesive layer. High stress concentrations were observed around the adhesive free ends and the peak adhesive stresses occurred inside the adhesive fillets. The adherend regions corresponding to the free ends of the adhesive–plate interfaces also experienced stress concentrations. In addition, the effects of the support length on the peak adhesive and adherend stresses were investigated; increasing the support length had a considerable effect in reducing the peak adhesive and adherend stresses.     

Damping characteristics of machine structures assembled by bonding: a beam in which two steel strips are partially joined by an adhesive

Machine structures assembled by adhesive bonding are expected to possess a high damping capacity because of the high damping capacity of the adhesive. In this study, the damping characteristics of a beam in which two steel strips were partially joined by an adhesive have been investigated. The primary aim of this study was to clarify the damping characteristics of adhesively bonded structures and to establish an estimation method for the damping capacity. In the analysis, strain energy distributions in the adhesively bonded beam in motion are analyzed by the finite element method. Then the damping capacity of the beam is derived using the strain energies and damping ratios of the two materials, i.e. the steel strips and the adhesive, which were obtained beforehand in independent experiments. The validity of the proposed estimation method for the damping capacity and the effects of the thickness of the adhesive and vibration modes on the damping capacity were confirmed by experiments. Satisfactory agreement was shown by comparing the estimated values of the damping capacity of the beam with the experimental results. Furthermore, the temperature dependence of the damping capacity was examined.     

The effects of overlap length and adherend thickness on the strength of adhesively bonded joints subjected to bending moment

In this work, elasto-plastic stress analysis of a Single Lap Joint (SLJ) subjected to bending moment was investigated using 2D non-linear Finite Element Analysis (FEA). The SLJs, consisting of hardened steel as the adherend bonded by two adhesives, one stiff and one flexible, with very different mechanical behaviors were analyzed. In order to determine the effect of geometrical parameters on the performance of the SLJs, four different adherend thicknesses and overlap lengths for each adhesive were used. For verification of the analysis, the FEA results were compared with experimental results. It was observed that there was a significant effect of adherend thickness on the strength of the joint with both adhesives. However, the load carried by the SLJ with the flexible adhesive increased with increasing overlap length.     

Geometrical range of microscopic stress distribution change due to fibre array irregularities for thermally and transversely loaded CF/epoxy composites

Abstract

A detailed numerical investigation has been carried out to investigate the effect of local fibre array irregularities on microscopic interfacial normal stress for transversely loaded unidirectional carbon fibre/epoxy composites with random fibre arrangement. Linear elastic finite element analyses were carried out for a two-dimensional image based model composed of 70 fibres. One fibre in this image based model is replaced with resin as the resin equivalent fibre, and the resulting change in microscopic interfacial normal stress distribution is investigated. Three fibres are selected for the resin equivalent fibres to clarify the individual local geometrical irregularity. Calculations were carried out for three loading conditions: case A, cooling of –155 K from the curing temperature; case B, transverse loading of 75 MPa chosen as an example of macroscopic transverse fracture strength and case C, both cooling from the curing temperature and transverse loading of 75 MPa. The effect of fibre array irregularities on the interfacial stress state is limited to the region between the resin equivalent fibre and its first neighbouring fibres. The contribution of the second neighbouring fibre is small and that of further fibres is negligible.     

Experimental and Numerical Analysis of T-peel Joints for the Automotive Industry

The T-peel joint is commonly used in the automotive industry, especially in the panels of the load compartment in vans. In order to determine the effect of using a structural adhesive instead of spot-welding, a detailed series of tests and finite element analyses were conducted. The adhesive was a toughened epoxy and the adherend was mild steel used in the manufacture of the car bodyshell. Various parameters were investigated such as the bondline thickness and adherend radius. The spew fillet was maintained flush in all cases. Contrary to the case of lap joints, there are no stress concentrations around the fillet area and, therefore, it is possible to use the maximum uniaxial tensile stress as a failure criterion for these joints. The bending moment at failure was found to be constant across the different geometries modelled, and it was also similar to that found in lap shear joints in previous studies.     

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.     

A novel mathematical procedure to evaluate the effects of surface topography on the interfacial state of stress. Part I: Verification of the method for flat surfaces

A mathematical procedure is developed to utilize the complementary energy method, by minimization, in order to obtain an approximate analytical solution to the 3D stress distributions in bonded interfaces of dissimilar materials. The stress solutions obtained predict the stress jumps at the interfaces, which cannot be captured by current FEA methods. As a novel method, the penalty function is used to enforce the displacement boundary conditions at the interfaces. Furthermore, the mathematical procedure developed enables the integration of different interfacial topographies into the solution procedure. In order to incorporate the effects of surface topography, the interface is expressed as a general surface in Cartesian coordinates, i.e. F (x, y, z) = 0. In this paper, the flat interface problem, i.e. y = 0 surface is considered for verification of the method by comparison with the FEA method. A comparison of the results reveals our new mathematical procedure to be a promising and efficient method for optimizing interface topographies.     

Comparative Study of the Results of Various Experimental Tests Used for the Analysis of the Mechanical Behaviour of an Adhesive in a Bonded Joint

The use of adhesively bonded joints is often limited by a lack of reliable models able to accurately predict their behaviour in industrial applications, in which the stress distribution is often complex. The mechanical behaviour of an adhesive in a bonded joint is often heavily dependent on its stress state (i.e., the tensile–shear combinations). Thus, a large experimental database is required to accurately represent the complex behaviour of an adhesive in a bonded joint. On the one hand, the initial yield surface (initial elastic limit) often has to be described taking into account the two stress invariants, hydrostatic stress and von Mises equivalent stress, and on the other hand the non-linear behaviour of the adhesive is also quite complex to model. However, the mechanical response of adhesively bonded joints often presents quite large stress concentrations; thus, the analysis of experimental tests is made particularly difficult. Obtaining reliable experimental results makes it possible to contribute to optimization of an adhesive in a bonded joint. This paper presents comparisons between results of different experimental tests (with bulk and bonded joints), some of them are designed to greatly limit the edge effects. Results are presented for two adhesives under proportional monotonic loadings. The two adhesives have very different behaviours (a ductile adhesive and a brittle adhesive) and two different surface preparations of aluminium substrates (a mechanical preparation and a chemical preparation recommended by the adhesive manufacturer) were studied.     

A novel mathematical procedure to evaluate the effects of surface topography on the interfacial state of stress. Part II. Verification of the method for scarf interfaces

A mathematical procedure was developed to utilize the complementary energy method, by minimization, in order to obtain an approximate analytical solution to the 3D stress distributions in bonded interfaces of dissimilar materials. The stress solutions obtained predict the stress jumps at the interfaces, which cannot be captured by the current FEA methods. As a novel method, the penalty function is used to enforce the displacement boundary conditions at the interfaces. Furthermore, the mathematical procedure developed enables the integration of different interfacial topographies into the solution procedure. In order to incorporate the effects of surface topography, the interface is expressed as a general surface in Cartesian coordinates, i.e. F(x, y, z) = 0. In this paper, the scarf interface problem, i.e. y = x/2 surface is considered for verification of the method by comparison with finite element analysis (FEA) results. Comparison of the results reveals our new mathematical procedure to be a promising and efficient method for optimizing interface topographies.     

A unified K-BKZ model for residual stress analysis of injection molded three-dimensional thin shapes

The flow-induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post-filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K-BKZ viscoelastic constitutive model, capable of modeling both the fluid-rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow-induced residual stress predictions of the filling stage, a quasi-steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post-filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post-filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post-filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow-induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow-induced residual stress by one to two orders of magnitude.     

A simple approach for characterizing the performance of metallic tubular adhesively-bonded joints under torsion loading

Adhesive bonding of joints is one of the most commonly and widely used joining methods in piping systems. This work is concerned with the investigation of the influence of the non-linear behavior of the adhesive used in such bonded joints on their performance. The parametric analysis module of ABAQUS was used to model the joint. The model facilitated the analysis of different geometric, loading and material characteristics of the system, in particular the adhesive nonlinearity, which is of prime interest in this work. By using the Ramberg–Osgood plasticity model, the failure threshold of the adhesive for various joint lengths (hereafter referred to overlap length) was characterized. The plasticity model used in this study was fine-tuned using only a limited number of known parameters, through comparison with the results of the finite element (FE) simulation. The results obtained from the FE analysis were verified by experimental results. The FE strategy is demonstrated to be an effective means for predicting the capacity of such joints, where conducting a pure shear test is either impossible or difficult to accomplish. Contrary to the findings based on the elastic finite element analysis, the plasticity analysis revealed that the overlap length affects the ultimate strength of the joint.     

A numerical study of parallel slot in adherend on the stress distribution in adhesively bonded aluminum single lap joint

The effect of the length and depth of a parallel slot as well as the elastic modulus of the adhesive on the stress distribution at the mid-bondline and in the adherend was investigated using the elastic finite element method. The results showed that the peak stress in mid-bondline decreased markedly when there were two of parallel slots located in the outside of the adherend, corresponding to the middle part of the lap zone and the original low stress in this zone of the joint increases. The peak stress decreased at first, and then increased again as the length of the parallel slot was increased. The stress distribution in the mid-bondline at the position corresponding to the parallel slot decreased significantly as the depth of the parallel slot was increased. The high peak stresses caused by the tensile load occurred close to the edge of the parallel slot in the adherend. Almost all the peak values of stresses at the mid-bondline increased when the elastic modulus of the adhesive was increased. The effect of the parallel slot on the peak stress at the mid-bondline with a low elastic modulus adhesive was negligible, but the peak stress decreased markedly for adhesives with a high elastic modulus.     

A unified model for the structure of polymers in semidilute solution

A model is developed to analyse the concentration dependence of the range ξ_? of the monomer pair correlation function. In semidilute solution, three concentration regimes are found for semiflexible molecules and the crossover points between the various regimes are predicted in terms of the characteristic ratio of the chains in dilute solution and in terms of the Flory interaction parameter χ. A simple physical interpretation is given which explains the concentration dependence of ξ_? based on binary contacts initially and then ternary contacts at higher concentration. Temperature-concentration diagrams are developed for several common polymer-solvent systems.     

A model for the oxidation of carbon silicon carbide composite structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.     

Sequence divergence analysis for the prediction of seven-helix membrane protein structures: II. A 3-D model of human rhodopsin

A three-dimensional (3-D) model of the transmembrane domainof human rhodopsin was predicted from the sequence divergenceanalysis of 42 sequences of rhodopsins and visual pigments withouta template. The prediction steps include multiple sequence alignment,calculation of a variability profile of the aligned sequences,use of the variability profile to identify the boundaries oftransmembrane regions, their secondary structure and packingshape in a helix bundle, prediction of side-chain conformationsand structure refinement. The identification of the retinalbinding site was assisted by its known covalent linkage withK296. The structural features of the predicted 3-D model arein good agreement with a low resolution electron density mapof bovine rhodopsin and with residues in contact with retinalas determined experimentally.     

A model analysis on the reasons for unstable operation of jet-pulsed filters

Various physically based models are available to describe an uneven distribution of the filter cake on the filter area of jet-pulsed bag filters. Such an uneven distribution is intrinsically present, when only segments of the filter are cleaned at a time but not the entire filter. Moreover, also patchy cleaning causes an uneven filter cake loading, since only a fraction of a filter cake is removed by a jet pulse while the other fraction remains basically intact on the filter cloth. Unstable filter operation can be defined by a continuous or periodic reduction of the filtration time per cleaning pulse. The operation of a jet-pulsed filter was mathematically simulated and, by systematically altering model parameters, unstable operation was obtained. Three situations were investigated: a continuous increase of the filter cake resistance parameter, a continuous increase of the filter cloth resistance parameter, and a particular cake detachment function where, after a filter cake survived some filter cycles, it can hardly be removed. The transient pressure difference simulation results reveal characteristic patterns: Taking normal stable operation as a reference, an increase of the filter cake resistance leads to shorter filtration and somewhat longer cleaning intervals (i.e., more cleaning pulses). An increase of the filter cloth resistance causes longer filtration and also considerably more cleaning pulses. Deficient filter cleaning gives shorter filtration periods and extremely long cleaning intervals. A comparison between model simulations and pilot plant results shows that there, the experimentally observed unstable operation can most likely be attributed to problems with cake detachment. Hence appropriate measures for avoiding unstable operation were successfully introduced.     

A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures

The mechanical response of solid amorphous polymers is strongly dependent on the temperature and strain rate. More specifically, the yield stress increases dramatically for the low temperatures as well as for the high strain rates. To describe this behavior, we propose a new formulation of the cooperative model of Fotheringham and Cherry where the final mathematical form of the model is derived according to the strain rate/temperature superposition principle of the yield stress. According to our development, the yield behavior can be correlated to the secondary relaxation and we propose an extension of the model to temperatures above the glass transition temperature. For a wide range of temperatures and strain rates (including the impact strain rates), the predicted compressive yield stresses obtained for the polycarbonate (PC) and the polymethylmethacrylate (PMMA) are in excellent agreement with the experimental data found in the literature.     

A hybridized snapshot proper orthogonal decomposition-discrete wavelet transform technique for the analysis of flow structures and their time evolution

A novel hybrid technique has been proposed in order to reveal in a greater detail the turbulent flow structures and their time evolution, and to address the issues and limitations related to the application of snapshot proper orthogonal decomposition (POD) and wavelet transform technique. The proposed hybrid technique combines the inherent abilities of the snapshot proper orthogonal decomposition and the two-dimensional discrete wavelet transform technique. The POD gives us the overall view of the most energetic flow pattern in an ensemble by decomposing the flow field into spatial and temporal modes, while two-dimensional wavelet transform gives us the localized spatial information through scale wise decomposition of the flow field. In this work, we apply the wavelet transform on the POD spatial modes. This enables us to understand the space scale structure of the flow events captured by the spatial POD modes, and the scale wise selectivity of these spatial POD modes. Thus, we are able to relate the most energetic flow events over a period of time (as obtained in spatial modes of snapshot POD) with the localized dominant scales that are contributing to it. Further, this information is utilized in the selection of those pod spatial modes that can effectively reconstruct a flow structure and its time evolution. The proposed technique has also been able to address the issues in the literature concerning the application of POD when the flow is less deterministic, as then a single POD mode may not reveal the flow structure and combination of modes is required to reconstruct it. In the present work, this hybrid methodology has been used to reveal the near wall intermittent events in channel flow: the ascending streaks and the bursts and their time evolution, the vortex tube and leading edge vortices in jet and the Taylor-Couette and irregular small chaotic vortices in Taylor-Couette flow. The planar dataset used for such an analysis has been obtained from particle image velocimetry and large eddy simulation studies.     

Study of the rheological behaviour of monomodal quartz particle beds under stress. A model for the shear yield functions of powders

A model is proposed that describes the yield locus of powders. The model is based on the adhesive contact of elastic spheres theory developed by Johnson, Kendall, and Roberts (JKR model). The proposed model improves the results by applying the Warren Spring Laboratory (WSL) equation and the Coulomb model. Only two parameters are needed in the present model to describe the yield locus of a powder: powder cohesion (C) and the coefficient of friction (μ) of the powder bed. The study verifies the validity of the new equation to describe the yield locus of different powders.The proposed model was used to calculate the cohesion and coefficient of friction of monomodal quartz particle beds with different average particle sizes. The study examines the influence of average particle size (d_s) and bed compactness (?) on these parameters. Cohesion was observed to increase by the sixth power of compactness and inverse of the particle Sauter diameter. The bed coefficient of friction increased asymptotically with bed compactness, this relationship depending on particle size.