Adhesive non-linearity

Additionally, analyses which allow for adhesive non-linear behaviour will need data on ductility, e.g. ... 

The effect of adhesive non-linearity on the behaviour of FRP adhesively bonded joints was adequately addressed in Section 10.3. However, it is useful to recall that considering adhesive non-linear representation in FEM has a negligible effect on the predicted shear and peel stresses at service load levels of the FRP composite joint, because their distribution along the whole bondlength is mainly linear-elastic. Interfacial adhesive non-linearity has a substantial effect on the accuracy of quantitative FEM predictions of both stresses, and thus joint capacity, only at loads nearing joint failure where all practical adhesives, even brittle ones, exhibit non-linear behaviour. 

FE mesh refinement, model representability, dimensionahty and adhesive non-linearity are the main influential factors that determine the accuracy of stress predictions to be anticipated from any FEM anaEysis. 

So what are we looking for All the theoretical methods for predicting joint strength need the elastic moduli such as E (Young s) and G (shear). In addition, those theories which allow for adhesive non-linear behaviour will need data such as the yield stress (strain) and the ultimate stress (strain). More sophisticated analyses, e.g. Adams et al. 

Finite-element techniques can cope with large, highly non-linear deformations, making it possible to model soft tissues such as skin. When relatively large areas of skin are replaced during plastic surgery, there is a problem that excessive distortion of the apphed skin will prevent adequate adhesion. Finite-element models can be used to determine, either by rapid trial-and-error modelhng or by mathematical optimisation, the best way of... 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

A tapping mode (also called intermittent contact mode) it is a non linear resonance mode. In this case, the oscillation amplitude is larger and the mean position of the tip is closer to the surface. The tip almost touches the surface at each oscillation. In this mode, friction can be avoided as well as the sample deformation and wear. Adhesion is also avoided thanks to the extremely short time of contact . The height of the sample is generally controlled so that the oscillation amplitude remains constant. The phase shift of the oscillation is then characteristic of the system dissipation, which is very useful for characterizing viscoelastic materials. 

The correlation is quite good for the SRI500 resin, while for the more ductile adhesive resin the predictions overestimate the measured failure loads. However, in the latter case an extensive damage zone develops before final failure and the non-linear elastic fracture model is no longer appropriate. It is interesting to note however, that when a fillet is left at the end of the overlap the test values are much closer to the predictions. 

The results above suggest that it may be possible to apply fracture mechanics data to determine failure loads of more complex structures, provided that (i) the adhesives used are not too ductile, (ii) bondline thickness is known and controlled, (iii) non-linear behaviour due to adherend and interface damage is limited, and (iv) the specimens employed to determine... 

Fig. 11 Non linear deformations in the wood adhesive joint loaded in shear at the critical experimental conditions.

The design analysis of a scarf may be considered similar to a single lap bonded joint, detailed analysis of which can be found in MIL-HDBK 17-3E 3. The analysis of a bonded joint is made complex, however, by the modulus difference of the adhesive compared to the adherends and the relative thicknesses of both which causes a non-linear distribution of the shear forces in a lap joint with peak stresses at the ends [1]. Scarf repairs provide a more uniform stress distribution however, to achieve this an adequate scarf angle is required [24] shown in Eigure 14.6. 

The methods developed over the last decade or so to predict failure employ in-bondline non-linear adhesive characterisation. This in turn requires some fairly sophisticated experimental techniques, carefully conducted for a range of test conditions and environments. Hart-Smith concluded that a precise representation of the adhesive stress-strain characteristic is not important. He maintains that the... 

A number of analysts (e.g. 5, 19) maintain that non-linear analysis is the key to being able to predict failure of bonded joints. It is also apparent that the strength of bonded joints, however loaded, is determined largely by the ultimate stress or the ultimate strain capability of the adhesive in tension. 

A number of cruciform joints of rectangular hollow section were fabricated with adhesive gusset plates (Fig. 8.15). Hollow sections of two different sizes were used, and some of the specimens were subjected to accelerated ageing prior to testing in tension. The structural behaviour of these joints was also predicted by non-linear, three-dimensional, finite-element analysis. Very good agreement was obtained between the experimental and predicted load-displacement behaviour. 

Where non-linear behaviour of adherends or adhesive is expected, the strains (deformations) should also be considered. 

Adhesives, as all plastics, are viscoelastic materials combining characteristics of both solid materials like metals and viscose substrates like liquids. Typically, the adhesive shear stress vs. shear strain curve is non-linear. This behaviour is characteristic especially for thermoplastic adhesives and modified thermosetting adhesives. Thermosetting adhesives are, by their basic nature, more brittle than thermoplastic adhesives but, as discussed earlier, are often modified for more ductile material behaviour. 

The rigorous design method is based on generally accepted closed-form models. The adhesive behaviour in the models is assumed to be linearly elastic. Only the formulae used in the calculation of the temporary maximum joint resistance require the complete shear stress—shear strain curve or the elastic—plastic model of the adhesive to be known. As adhesives typically have a non-linear shear behaviour, using only the linear part of the stress—strain curve brings added conservatism to the models with respect to the actual joint resistance. 

The ESDU/Grant method (references 5.32 and 5.33) uses a non-linear model for the adhesive shear behaviour in double-lap joints. The analysis is available in the form of a computer program and on ESDU (Engineering Science Data Unit) data sheets. 

Russell (reference 5.35) has presented a method to analyse adhesively bonded joints under generalised in-plane loading. His approach is based on the Hart-Smith method using a non-linear adhesive model. 

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