VIBRATIONAL ANALYSIS OF ADHESIVE BONDING

Transcription

1 lean VIBRATIONAL ANALYSIS OF ADHESIVE BONDING Literature overview for Adhesive Bonding ABSTRACT There are many joints used in aerospace structures such as lap joint, double-strap joint etc. In this work Vibration analysis of adhesively bonded lap joint is done by means of ANSYS software and comparison is done by means of experimental analysis. Rubber is used as viscoelastic material. By changing the thickness of rubber & overlap ratio different natural frequencies are obtained. Experimental analysis is done by preparing lap joint with aluminum and rubber material. Locktite 407 is used as an adhesive. Analysis is done by using FFT analyzer. The effect of thickness of rubber and overlap ratio on natural frequency is also carried out. Keywords: - Adhesive, Viscoelastic material, Passive damping, Composites BABASAHEB YAWALKAR Mechanical Design Engineer yawalkarb@leanmaestro.in

2 Introduction In recent years, adhesives have been widely used to bond dissimilar material members particularly in aircraft and automobile structures. In many applications adhesively bonded joints are more suitable than traditional joining techniques such as mechanical fastening, especially for components made from composite or polymeric materials, because they can provide uniform distribution of load, resulting in better damage tolerance and excellent fatigue life. Because of the involvements of many geometric, material and fabrication variables, and complex failure modes and mechanics present in the joints, a deep understanding of the failure behaviour of adhesively bonded joints, particularly under combined loading conditions, is needed in order to fully achieve the benefits of adhesive bonding. There are several typical failure modes associated with adherents and adhesive in adhesively bonded composite repairs including substrate yielding, patch fibre breaking in tension, fibre failing in compression, adhesive shearing, substrate-adhesive peeling, patch-adhesive peeling, patch interlaminar peeling, and patch interlaminar shearing. Since substrate yield is not a catastrophic failure mode, an optimal design will focus on other failure modes associated with the patch and adhesive. The failures in adhesively bonded joints are mainly of two types, adhesive and cohesive; occurring mainly due to interfacial (adhesive) cracking, also called debonding, at geometric boundaries due to stress concentrations, or resulting from faulty joining in fabrication. Well-bonded joints should fail within the adhesive (cohesive) or within the adherents (interlaminar failure) when broken apart. Failure at the adherent-adhesive interface (interfacial failure) generally indicates that the bond was not performed properly. Adhesive bonding usually requires curing of adhesive at temperature higher than applied condition. Joints and fasteners often have a significant effect on the dynamical behaviour of assembled mechanical structures and the analytical prediction of structural responses therefore depends upon the accuracy of joint modelling. Detailed constitutive models that fully describe the behaviour of frictional interfaces are often unduly complicated; in which case simpler phenomenological models having parameters identified from vibration tests may be preferable. Unfortunately the direct measurement of forces transmitted between two contacting surfaces and their relative displacements are not possible in practice and it is therefore necessary to rely on measurements remote from joints. In this paper, the parameters of an assumed nonlinear joint model are identified by force-state mapping from time-domain acceleration records in response to singlefrequency excitation close to the first natural frequency. The problem of lack of accessibility for measurement at the joint is overcome by casting the governing equation of the system in modal coordinates so that modal parameters are identified to represent the nonlinear behaviour of the joint.

3 A particular result from the experimental program is the identification of viscous damping coefficients dependent upon displacement amplitude. The significance of this result is that the complex phenomenon of energy dissipation in lap joints can be represented by a simple analytical model capable of producing accurate results. Bolted lap joints have significant influence on the dynamical behaviour of the assembled structures due to creation of strong local flexibility and damping. In modelling the dynamical behaviour of assembled structures the joint interface model must be represented accurately. A nonlinear model for bolted lap joints and interfaces is proposed capable of representing the dominant physics involved in the joint such as micro/macro-slip. The joint interface is modelled using a combination of linear and nonlinear springs and a damper to simulate the damping effects of the joint. An estimate of the response of the structure with a nonlinear model for the bolted joint under external excitations is obtained using the method of multiple scales. The parameters of the model, i.e. the spring constants and the damper coefficient, are functions of normal and tangential stresses at the joint interface and are identified by minimizing the difference between the model predictions and the experimentally measured data. Various types of single-lap specimens with different overlap lengths and adhesive thicknesses were used in the experimental program to investigate the effect of bonding dimensions on fatigue strength. Experimental results indicate that under the fixed average shear stress condition, the larger adhesive thickness detrimentally affects fatigue strength. Similarly, the fatigue resistance decreases as the overlap increases except for the specimens with an adhesive thickness of 0.5 mm. The finite element method was adopted herein to obtain the local stress states at the interface between the adhesive and the adhered. Three selected parameters based on the simulated interfacial stresses were considered to correlate with the fatigue life data of all specimens with various adhesive dimensions. These parameters are maximum interfacial peeling stress, maximum interfacial shear stress and a linear combination of interfacial peeling stress and shear stress. These three interfacial parameters yield much better correlation results than the bulk average stress parameter. The evaluation results demonstrate that peeling stress and the linear combination of interfacial peeling stress and shear stress provide better correlation results than the interfacial shear parameters, revealing that the interfacial peeling Stress is the main driving force of the fatigue failure of the single-lap joints. Boeing 747 aircraft has 62% of its surface area constructed with adhesive bonding, while Lockheed C-5A aircraft has 3250 m 2 of bonded structure. In many structures such as those for flight and space vehicles etc adhesively bonded structures have often been used recently, because of great advances in adhesive bonding techniques. Many aerospace

4 structures such as truss system of space telescope & space station are constructed using predominantly composites beams, plates & bonded joints. These structures should possess sufficient inherent damping capacity to keep vibration & acoustics response caused by external disturbances within acceptable limits. The current trend is to use viscoelastic material in the joints for passive vibration control in the structures subjected to dynamic loading. Features which make adhesive bonding attractive include improved appearance, good sealing high strength to weight ratio, low stress concentration, low cost, corrosion resistance and fatigue resistance. The rapid development of structural adhesives has led to the widespread use of adhesive joining technique in defence, aerospace, rail, ground transportation applications. In these applications the joints are designed to carry in plane roads, although they are also prone to transverse loading from crashes, bullets, fragments, tool drops, or flying debris. The usage of bonded joints in primary load bearing structures, especially aerospace and military applications, makes it important to understand their failure mechanisms under transverse and in plane loading. Fig.1. Lap Joint

5 Literature Review The literature review here focuses upon books, edited volumes and journal articles, previous research thesis and dissertations available on Vibrational analysis of adhesive bonding of lap joint and T-joint. The research has been traced out from The classic works in the area of static analysis of a simple lap joint is done by Goland and Reisner [1] (1944). They studied the stresses in bonded and single lap joints for two different cases. In first case, the bond layer was very thin, in the second case, the bond layer was so thick that it was the primary contributor to joint flexibility. In both case, they derived equations to evaluate the shearing and normal stresses in the bond layer as well as those in the jointed plates. In the Goland and Reisner analysis, the peel and shear stresses were assumed to be constants across the adhesive thickness. In later works by Ojalvo and Eidinoff (1978) [2], attempts are made to incorporate a linear variation of these stresses across the thickness of the adhesive. Delale and Erdogan (1981)[3] have carried out the stress analysis of a bonded tap joint system assuming that the adherents are elastic and the adhesive is linearly viscoelastic. Renton and Vinson (1977) [5] and Delate, Erdogan etc, (1981) [4] have attempted to include an isotropic adherents in the mathematical model. Hart smith (1973, 1974) [6] was the first investigator to extensively use continuum mechanics approach in the analysis of bonded joints. Smith has analyzed double-lap single- lap, scarf, stepped,-lap, and tapered-lap configurations. Tensile, compressive and in-plane shear stresses in the system were considered based on-an elastic-plastic analysis of the configurations. Saito and Tani (1984) [7] have derived equations for predicting the modal parameters of the coupled longitudinal and flexural vibrations of a system consisting of pair of elastic beams lap jointed over a certain length by an adhesive. Numerical results are presented for the case of fixed boundary conditions at the ends. No experimental verification was undertaken in their effort. Prucz (1985) [8] has developed a model for the quasi-static analysis of double-lap bonded joint. The model is an extension of the one-dimensional model of Hart-smith (1973) for the analysis of a fully elastic double lap joint. Prucz has incorporated the viscoelastic behaviour of the adhesive layers in the joint and catalyzed a quasi-static analysis of constrained layer damping treatment to evaluate the joint damping properties.

6 Miles and Reihall (1986) [9] have presented a comprehensive model for the vibration of sandwich beams by including the effects of both shear and thickness deformation in the adhesive layer. This analysis is an extension of the previous sixth order theory of DiTaranto (1965) and Mead and Marks (1969) [10]. The equations of motion were derived using Hamition's principle and solutions were obtained by Ritz Method. Mead,Marks et.all have shown that the use of a light-weight constraining layers which is stiff in bending will result in a design which is considerably more damped than a conventional configuration in which the adhesive is undergoing predominant shear deformation. Efforts to model the vibration of joints using coulomb friction damping model have been reported in several publications in recent years (Beards 1979). In this type of model, the friction force at the interface is assumed to be proportional to the normal force holding the surface together. Menq (1989) [11] has cocently presented a more general micro slip model for the Vibration analysis of friction joint. The technique includes the use of very accurate instrumentation to measure force transmission properties of a joint as a function of the full mechanical state of the joint. Rao and Crocker (1990) [12] has done analytical model. It is used to predict the natural frequency & mode shapes of a Lap joint system. Passive Damping Vibration and noise suppression are becoming more important in our society. Noise suppression of office machines, home appliances, and aircraft automobile makes environment more pleasant. Vibration suppression allows more precise medical instrument, faster and more compact disc drives, more precise image in ground space based telescopes, safer building in the event of an earthquake and lower stresses in products generally leading to longer life and lighter weight. Passive damping is now the major means of suppressing unwanted vibrations. The primary effect of increased damping in a structure is a reduction of vibration amplitudes at resonances with corresponding decrease in stresses, displacement, fatigue and sound radiation. However, damping is one of the more difficult issues to deal with in structural damping. To achieve a substantial increase in passive damping a structural dynamist must have a good working knowledge of many factors passive damping technologies, materials, concepts and implementations in addition to design analysis and prediction methods for passive damping systems.

7 Benefits of Applied Damping Treatments: When the natural damping in a system is inadequate for its intended function then an applied damping treatment may provide the following benefits: a. Control of Vibration Amplitude at Resonance: Damping can be used to control excessive resonance vibrations which may cause high stresses, leading to premature failure. It should be in conjunction with other appropriate measures to achieve the most satisfactory approach. For random excitation it is not possible to detune a system and design to keep random stresses within acceptable limits without ensuring that the damping in each mode at least exceeds a minimum specified value. This is the case for sonic fatigue of aircraft fuselage, wing and control surface panels when they are excited by jet noise or boundary layer turbulence induced excitation. In these cases, structural designs have evolved toward semi empirical procedures, but damping levels are a controlling factor and must be increased if too low. b. Noise control: Damping is very useful for the control of noise radiation from vibrating surfaces or the control of noise transmission through a vibrating surface. The noise is not reduced by sound absorption as in the case of an applied acoustical material but by decreasing the amplitudes of the vibrating surface. For example in a diesel engine many parts of the surface contribute to the overall noise level and the contribution of each part can be measured by the use of acoustic intensity technique or by blanketing off in turn all parts except that of interest. If many parts of an engine contribute more or less equally to the noise significant amplitude reductions of only one or two parts (whether by damping or other means) leads to only very small reductions of the overall noise typically 1 or 2 db. c. Product Acceptance: Damping can often contribute to product acceptance not only by reducing the incidence of excessive noise, vibration or resonance induced failure but also by changing the feel of the product. The use of mastic damping treatment in car doors is a case in point. While the treatment may achieve some noise reduction it may be the subjective evaluation by the customer of the solidity of the door which carries the greater weight. d. Simplified Maintenance: A useful by product from reduction of resonance induced fatigue by increased damping or by other means can be the reduction of maintenance costs.

8 Finite Element Modelling: Ansys is an integrated package of mechanical engineering software tools. Ansys mechanical family of products differs a full depth of analysis from concept simulation to advanced analysis. The software provides simulation tools used widely across industry by designers to advanced analysis, providing a full complement of nonlinear and linear elements laws ranging from metal to rubber and the most comprehensive set of solvers available. Element Used: For Finite Element Analysis of adhesively bonded lap joint 4 noded Solid Brick element is used. The analysis of the joint is done by using fixed- fixed boundary condition. Fig.2. Meshing of Lap joint

9 Fig.3. Zoom view of Meshing Experimental Modal Analysis Experimental modal analysis also known as modal analysis or model testing deals with determination of natural frequencies, damping ratio and mode shapes through vibration testing. Two basic ideas are involved 1) When a structure, machine or any system is excited its response exhibits a sharp peak at resonance when the forcing frequency is equal to its natural frequency when damping is not large. 2) The phase of response changes by 180 degree as the forcing frequency crosses the natural frequency of the structure or machine and the phase will be 90 degree at resonance.

10 Fig.4. Experimental Setup Result and Discussion: The specimens were prepared by bonding two similar beams over the desired using an adhesive much care was taken to obtain a good bond by properly curing the joint system in an oven. The dimensions of the unbounded beams are having length 15 cm width 3.6 cm and thickness 0.5 cm. These dimensions and material properties were input to software to predict the natural frequencies and mode shapes. The supports to simulate fixed supported boundaries at the ends were especially fabricated. An impact hammer with an attached force transducer was used to excite the specimen and the response was measured by accelerometer. The frequency response was immediately computed and recorded on FFT analyzer. From table it is seen that there is good agreement between the predicted values of natural frequency and experimental data. The percentage difference between the two results is in the range of three to nine percent.