Magd Abdel Wahab

Modelling the Environmental Degradation of the Interface in Adhesively Bonded Joints using a Cohesive Zone Approach

The use of a cohesive zone model (CZM) to predict the long-term durability of adhesively bonded structures exposed to humid environments has been investigated. The joints were exposed to high relative humidity (RH) environments and immersion in both tap and deionised water for up to a year before quasi-static testing to failure. Both stressed and unstressed conditions during aging were considered. The degradation was faster for the stressed joints and for those joints immersed in the more corrosive environments. Two mechanisms were suggested to explain this behaviour: cathodic delamination and stress-enhanced degradation. In the model, the cohesive zone parameters determine the residual strength of the joints. The degradation of these parameters was, in the first instance, related directly to the moisture concentration. The model was then extended to include degradation due to stress and more corrosive environments. Good correlation between the numerical modelling and the experimental results was obtained.

Modelling Environmental Degradation in EA9321-Bonded Joints using a Progressive Damage Failure Model

ABSTRACT A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic–plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.

On the use of fracture mechanics in designing a single lap adhesive joint

The design of adhesively bonded joints is a quite difficult task, due to the stress singularity that arises at the edges of the adhesive adjacent to the loaded substrate. This stress singularity makes any design approach based on elastic stress analysis inconvenient. A more convenient design tool for an adhesive joint should be based on its mode of failure. Most of the adhesive joints fail at the adhesive/adherend interface or very close to it in the adhesive layer. Therefore, a fracture theory such as linear elastic fracture mechanics (LEFM) can be used to analyse the failure of an adhesive joint. In this paper, the design of a single lap joint using a fracture mechanics parameter, i.e. the strain energy release rate (SERR), is discussed. The SERR is extracted from a finite element model using Irwins virtual crack closure integral. A design equation relating the lap length to the adherend thickness through some design parameters is derived.

The effect of residual strains on the progressive damage modelling of environmentally degraded adhesive joints

This work is concerned with developing numerical modelling techniques for predicting the environmental degradation of adhesively-bonded joints. Associated experimental data are also reported. The moisture-dependent mechanical properties of the adhesive were obtained by testing bulk specimens also exposed to various moisture contents. The diffusion parameters for moisture in the adhesive were determined by carrying out gravimetric experiments on bulk adhesive samples. The moisture-dependent interfacial bond strength of the adhesive system investigated has been determined by testing a mixed mode flexure (MMF) specimen, exposed to obtain various levels of moisture content at the interface. Progressive damage in the joints was modelled with a two-parameter cohesive zone model (CZM). The CZM parameters were determined by correlating the experimental data obtained from the MMF test with results from the numerical simulation. The parameters were then used to predict the response of another configuration, the notched coating adhesion (NCA) specimen. When the residual stresses were neglected in the modelling, the predicted NCA response was seen to be in good agreement with the experimental data. However, initial simulations that included the residual stresses resulted in poor predictions of the NCA response. Creep tests on the saturated adhesive, at the ageing temperature, showed large viscoplastic deformations at low loads. Coupled diffusion-stress modelling, including viscoplastic material properties for the adhesive continuum, showed that the residual stresses for the aged specimens decreased significantly and thus did not contribute strongly to the environmental weakening. Good predictions were then obtained for the NCA tests.

Continuum damage modelling of environmental degradation in joints bonded with E32 epoxy adhesive

A mesh-independent continuum damage model has been proposed to predict the residual strength of adhesively-bonded joints by introducing a displacement-based damage parameter into the constitutive equation of the damaged materials. This approach was originally developed for EA9321-bonded single-lap joints and this paper extends it to butt joints bonded with a different ductile adhesive (E32). This involves not only a different adhesive and joint configuration but the high hydrostatic stress requires a more realistic yielding model. A dry and a partially saturated steel joint were used to calibrate the moisture dependent damage parameters of the adhesive E32, and then these parameters were used without further modification to predict the failure of the other environmentally degraded steel butt joints and the aluminum butt joints. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. A von Mises yield model was used initially. Then, a linear Drucker–Prager plasticity model was used, as this could incorporate the hydrostatic stress dependency found in the adhesive. The predicted joint residual strengths agreed well with the corresponding experimental data, which exhibited a significant reduction in strength on exposure to moisture but still retained a cohesive failure mode in the adhesive. The mesh independence of the model was also demonstrated.

Brush Dynamics: Models and Characteristics

This paper reviews investigations into the dynamics and modelling of brushes. They include brushes for surface finishing operations, removal of fouling, post-CMP brushing processes, air duct cleaning, and street sweeping. The methods that have been proposed to model brush dynamics are described, and the results of the research into brush mechanics are presented and discussed. Some conclusions of the paper are as follows: brush dynamics is very complex, as it depends on the interaction among many phenomena and variables. The bristle oscillations that occur in some brushes constitute a complexity for modelling brush behaviour and are not normally addressed. Additionally, the literature reveals that the coefficient of friction is not a constant value that depends only on the materials and surface roughness of the two contacting bodies. Frictional behaviour strongly depends on many variables, such as brush setup angles and rotational speed, which play a part in the development of stick-slip friction cycles. Finally, it is concluded that brush behaviour and the phenomena involved in brushing have not been fully studied or understood and more research into this field is needed.Copyright

Fatigue Crack Propagation in Adhesively Bonded Joints

Adhesive bonding has become a powerful joining technique during the last few decades. It has many applications in aerospace, automotive and other industries. One of the major advantages of adhesive bonding, compared to riveting or welding, lies in its superior fatigue resistance. In this paper, fatigue crack propagation in adhesively bonded joints is analysed and discussed. Three different bonded joints are considered in this study, namely Double Cantilever Beams, Single Lap Joints and Double Lap Joints. Experimental samples were made from carbon fibre composite substrates bonded with an epoxy adhesive. The joints were tested in constant amplitude fatigue at different loads and plots of load against number of cycles to failure were obtained. A crack propagation law was then derived from the experimental results of the Double Cantilever Beam and implemented in a finite element based predictive tool in order to predict the number of cycles to failure for Single Lap and Double Lap joints subjected to cyclic fatigue loading. The prediction technique is based on numerically integrating the crack growth law along the bonding line from an initial crack length to a final crack length. A comparison of mode I strain energy release (G(I)) and total strain energy release rate (G(T)) as failure criteria in the prediction procedures is presented.

On the analytical determination of strain energy release rate in bonded DCB joints

A comparison of the different methods used to calculate strain energy release rate in bonded DCB joints has been made. The standard beam theory method has been shown to be in error and models with a compliant crack front have been evaluated in search of a more reliable analytical method. It is found that in fatigue testing, a beam on elastic foundation (BEF) model gives excellent results and a simple form of the BEF equation is proposed.

Theoretical model for the dynamics of an unconstrained cutting brush of a street sweeper

A theoretical model for the free-flight behaviour of an oscillatory cutting brush-of a street sweeper is developed. The bristles are modelled as cantilever beams, and the equation of motion for the transverse vibrations is derived based on the theory of vibrations and small deflection beam theory. Two angular velocity functions are studied: a sinusoidal function and a function that provides small shaft accelerations and whose exact shape depends on a parameter b. The model is applied for a range of frequencies of oscillation that contains the first and second natural frequency of the bristle. The effects of the alternating component of the rotational speed, the type of function, and the value of b are also studied. The results are compared with those obtained in a previous work for a flicking brush. The findings suggest that the bending moment and bristle deflection tend to depend fairly linearly on the altemating velocity. In contrast to the bristles of a flicking brush, in the cutting brush resonance tends to occur only near the natural frequencies of the bristle. Additionally, the behaviour of the cutting brush is similar for both functions and for different values of b.

Qualitative Experimental Behavior of Oscillatory Gutter Brushes

Cutting and flicking128 brushes are two types of gutter brushes that sweep the debris that lies in the gutter towards the main sweeping mechanism of a street sweeper. As most of the debris is commonly found in the gutter, the operation of gutter brushes is important. In this work, the concept of oscillatory gutter brushes is studied. Qualitative experimental tests are carried out to determine frequencies at which enhanced vibration patterns of the bristles of cutting and flicking128 brushes are obtained. The brushes are rotated at variable angular speed, first in free rotation, and then against a concrete test bed. The findings are analyzed in the light of previous theoretical results. The results suggest that bristle vibrations may be excited at the first natural frequency of the bristles for both brush types. Notably, the trends indicate that when the frequency is a third of the first natural frequency, a resonant condition seems to occur. The results also indicate that an equivalent length for bristle vibration has to be calculated, due to the way in which the bristles are clamped into the mounting board. This equivalent length is necessary for the comparison between the experimental and analytical results. These tests are useful in the determination of frequencies that may be potentially helpful during sweeping.Copyright