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In this Thesis, the problems of the Free Flexural (or Bending) Vibrations of Composite, Orthotropic Plates and/or Panels with Various Bonded Joints are formulated and investigated in detail. The composite bonded plate system is composed of Plate Adherends adhesively bonded by relatively very thin adhesive layers. The general problem is considered in terms of the three Main PROBLEMS, namely Main PROBLEM I, Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on Mindlin Plate Theory which is a First Order Shear Deformation Plate Theory (FSDPT). Thus, the transverse shear deformations, the transverse and the rotary moments of inertia of the plates are included in the formulation. Very thin, elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The entire composite bonded joint assembly is assumed to be simple supported along the two opposite edges, so that the Classical Levy&amp / #8217 / s Solutions can be applied in this direction. The dynamic equations of the Bonded Joint System which combines together the Mindlin Plate dynamic equations with the adhesive layer equations are reduced to a system of First Order Ordinary Differential Equations in the state vector form. This special form of the Governing System of the First Order Ordinary Differential Equations are numerically integrated by means of the Modified Transfer Matrix Method which is a combination of the Classical Levy&amp / #8217 / s Method, the Transfer Matrix Method and the Integrating Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials). The Main PROBLEMS are investigated and presented in terms of the mode shapes and the corresponding natural frequencies for various sets of boundary conditions. The significant effects of the hard and the soft adhesive layer elastic constants on the mode shapes and on the natural frequencies are demonstrated. Some important parametric studies such as the influences of the Joint Length Ratio, the Joint Position Ratio, the Bending Stiffness Ratio, etc. on the natural frequencies are computed and plotted for the hard and soft adhesive cases for several support conditions.

Water-assisted crack growth at an epoxy/glass interface was measured as a function of applied strain energy release rate, G, and temperature using a wedge test geometry. The specimens consist of two glass plates bonded with a thin layer of proprietary epoxy adhesive. The crack fronts along the epoxy/glass interfaces were measured using an optical stereomicroscope. The relationship between G and the debonding rate, v, can be measured using this method, and the threshold value of strain energy release rate, Gth, can be determined from the measured data. Two types of testing procedures were conducted in this study: ex situ, i.e., pre-conditioned wedge tests and in situ ones, in which wedges were applied before the specimens were submerged into water. A preliminary model was developed based on the thermal activation barrier concept, and allows the prediction of Gth for the temperatures beyond the testing region. Changes in interfacial strain energy release rate caused by thermal residual stresses in a triple-layered specimen were analyzed in Chapter Three. The method is based on linear elastic fracture mechanics and simple beam theory. The curvature of a bimaterial strip was chosen to characterize the residual stress in the specimen, and the strain energy release rate, caused by both tensile and compressive residual stresses in the adhesive, was derived for an asymmetric double cantilever beam (ADCB) geometry. The contribution of the thermal residual and mechanical stress to the global energy release rate was analyzed. The thermally induced energy release rate, GT, is found to be independent of crack length, but is a function of residual stress level and geometric and material parameters of the specimen. The adhesion of films and coatings to rigid substrates is often measured using blister geometries, which are loaded either by an applied pressure or a central shaft. The measurement will be affected if there are residual stresses that make a contribution to the energy release rate. This effect is investigated using analytical solutions based on the principle of virtual displacements. A geometrically nonlinear finite element analysis is conducted for comparison. Furthermore, the relationships among strain energy release rate, load, deflection, and fracture radius are discussed in detail in Chapter Four. Both analytical solutions and numerical results reveal that uniform tensile residual stresses reduce a specimen's deflection if it experiences plate behavior under small loads. However, this effect diminishes when membrane behavior is dominant. The mechanics of a single-lap joint with different boundary conditions subjected to tensile loading are investigated. Closed-form solutions are obtained for a specimen configuration considering different clamping methods. Based on the approach pioneered by Goland and Reissner, the solutions reported in this paper provide a simple but useful way to understand the effects of boundary conditions on this test geometry. The solutions in this study suggest that different grip configurations mainly affect the response of the specimens if the grip position is close to the joint edge or the loads are small. Generally, the influence caused by different gripping methods is only limited to the boundary region, and the behavior of the joint part subjected to tensile loading is almost the same as that for a simply-supported case. / Ph. D.

Fiber-reinforced composites comprise an important class of lightweight materials which are finding increasing applications in engineering structures including body components of automobiles and aircraft. Traditionally, synthetic fibers made of glass, carbon, etc. along with a polymeric resin have constituted the most common composites. However, due to environmental concern, occupational health safety considerations, higher cost, etc., research has been focused on substituting synthetic fibers, especially glass fibers with safer, economic and biodegradable natural fibers. Due to the ease of availability and affordability in terms of cost, woven jute mats, among a wide variety of natural fiber-based reinforcements, offer a good choice in combination with a suitable resin such as polyester or epoxy for fabrication of composite laminates. In structural applications, joining of parts made of jute fiber-reinforced composites (JFRCs) would be a natural requirement. Alternatives to joining processes for metals such as welding, riveting, etc. are required for composites. A joining process of high potential is adhesive bonding which has the advantages of reducing stress concentration, permitting fastening of dissimilar materials, etc. In the present study, adhesively bonded joints of JFRCs and their mechanical behavior are investigated under quasi-static and cyclic loading conditions. Initially, characterization of substrates is carried out under monotonic loading. This is followed by determination of stress- Strain curves, failure load and mean shear strength of bonded joints as functions of joint curing temperature and overlap length using a two-part structural epoxy adhesive. All tests are carried out according to relevant ASTM standards. It has been observed that higher curing temperatures give rise to only marginally high failure load and mean shear stress at failure compared to curing at room temperature. For a given curing temperature, failure load increases while mean shear strength decreases with respect to overlap length in both types of joints. As fatigue failure is a crucial consideration in design, the behavior of adhesively bonded JFRC joints is studied for the first time under cyclic loading conditions leading to the commonly-used S-N curve for characterization of failure of materials at different loading-unloading cycles. Interestingly, the fatigue strength for infinite life of adhesively bonded JFRC joints turns out to be approximately 30% of the quasi-static strength, a correlation which usually applies to materials in general. The effect of joint overlap length on fatigue life is studied and it is observed that the above relation between fatigue and quasi static strength is retained for different overlap lengths. Additionally, insights are provided into failure modes of joints under different loading conditions and for varying overlap lengths. Various empirical predictors such as exponent, power and hybrid models fitting the S-N curve are obtained and their relative efficacy (in terms of Coefficient of Determination R2, Adjusted-R2, Akaike’s Information Criterion and Residual Sum of Squares) enumerated in prediction of failure load including quasi-static failure load. As numerical simulation is an indispensable tool in designing geometrically complex structures under nonlinear conditions including failure and contact, finite element modeling of JFRC substrates, bulk adhesive and adhesively bonded joints has been investigated using implicit and explicit LS-DYNA solvers. In this context, the effects of various modeling parameters (mesh size and loading rate) and details of constitutive models capable of capturing plasticity and failure in an orthotropic composite and isotropic adhesive are discussed. Mesh size has been found to be an important parameter affecting computed results. Finally, a good correlation within ~(4% - 7%) was found between the predicted and experimental results for JFRC substrates, bulk adhesive and adhesively bonded single lap joints.

Adhesive bonding which has been in use for long as a traditional joining method has gained ground in the last couple of decades due to the introduction of advanced composite materials into the aerospace industry. Bonded structures have advantages such as high corrosion and fatigue resistance, ability to join dissimilar materials, reduced stress concentration, uniform stress distribution, good damping characteristics etc. They also have certain limitations like environmental degradation, existence of defects like pores, voids and disbonds, difficulty in maintenance and repair etc. A serious drawback in the use of adhesively bonded structures has been that there are no established comprehensive non-destructive testing (NDT) techniques for their evaluation. Further, a reliable evaluation of the effect of the existing defects on strength and durability of adhesive joints is yet to be achieved. This has been a challenge for the research and development community over several decades and hence, been the motivation behind this piece of research work. Under the scope of the work carried out in the thesis, some of the primary factors such as the existence of defects, degradation of the adhesive, stress and strain distribution in the bonded region etc., have been considered to study the bond integrity in composite to composite lap shear joints. The problem becomes complex if all the parameters affecting the adhesive joint are varied simultaneously. Taking this into consideration, one of the key parameters affecting the bond quality, viz., the adhesive layer degradation was chosen to study its effect on the bonded joint. The epoxy layer was added with different, definite amount of Poly vinyl alcohol (PVA) to arrive at sets of bonded joint specimens with varied adhesive layer properties. A thorough review of different non destructive testing methods applied to this particular problem showed that ultrasonic wave based techniques could be the right choice. To start with, preliminary experimental investigations were carried on unidirectional glass fiber reinforced plastic (GFRP-epoxy) lap joints. The adhesive joints were subjected to non destructive evaluation (NDE) using ultrasonic through transmission and pulse echo techniques as also low energy digital X-ray techniques. The results obtained showed a variation in reflected and transmitted ultrasonic pulse amplitude with bond quality. Digital X-Ray radiography technique showed a variation in the intensity of transmitted x-rays due to variation in the density of adhesive. Standard mechanical tests revealed that the addition of PVA decreased the bond strength. A plot of coefficient of reflection from the first interface and the bond strength showed a linear correlation between them. After obtaining a cursory feel and understanding of the parameters involved with the preliminary experiments on GFRP adhesive joints which yielded interesting and encouraging results, further work was carried on specimens made out of autoclave cured carbon fiber reinforced plastic (CFRP)-epoxy bonded joints. Normal incidence ultrasound showed a similar trend. Analyses of the Acoustic Emission (AE) signals generated indicate early AE activity for degraded joints compared to healthy joints. Literary evidences suggest that the ultrasonic shear waves are more sensitive to interfacial degradation. An attempt was made to use oblique incidence ultrasonic interrogation using shear waves. The amplitude of reflected shear waves from the interface increased with an increase in degradation. Further, a signal analysis approach in the frequency domain revealed a shift in the frequency minimum towards lower range in degraded samples. This phenomenon was verified using analytical models. An inversion algorithm was used to determine the interfacial transverse stiffness which decreased significantly due to increase in degradation. Conventional ultrasonic evaluation methods are rendered ineffective when a direct access to the test region is not possible; a different approach with guided wave techniques can be explored in this scenario. Investigations on CFRP-epoxy adhesive joints using Lamb waves showed a decrease in the amplitude of ‘So’ mode in degraded samples. Theoretical dispersion curves exhibited a similar trend. Frequency domain studies on the received modes using Gabor wavelet transform showed a negative shift in frequency with increased degradation. It was also observed that the maximum transmission loss for the most degraded sample with 40 percent PVA occurred in the range of 650 – 800 kHz. Non linear ultrasonic (NLU) evaluation revealed that the nonlinearity parameter (β) increased with increased degradation. Kissing bonds are most commonly occurring type of defects in adhesive joints and are very difficult to characterize. A recent non-contact imaging technique called digital image correlation (DIC) was tried to evaluate composite adhesive joints with varied percentage of inserted kissing bond defects. The results obtained indicate that DIC can detect the kissing bonds even at 50 percent of the failure load. In addition, to different experimental approaches to evaluate the bonded joint discussed above, the effect of degradation on the stresses in the bond line region was studied using analytical and numerical approach. A linear adhesive beam model based on Euler beam theory and a nonlinear adhesive beam model based on Timoshenko beam theory were used to determine the adhesive peel and shear stress in the joint. Digital image correlation technique was used to experimentally obtain the bond line strains and corresponding stresses were computed assuming a plane strain condition. It was found that the experimental stresses followed a similar trend to that predicted by the two analytical models. A maximum peel stress failure criterion was used to predict failure loads. A failure mechanism was proposed based on the observations made during the experimental work. It was further shown that the critical strain energy release rate for crack initiation in a healthy joint is much higher compared to a degraded joint. The analytical models become cumbersome if a larger number of factors have to be taken into account. Numerical methods like finite element analysis are found to be promising in overcoming these hurdles. Numerical investigation using 3D finite element analysis was carried out on CFRP-epoxy adhesive joints. The adherend – adhesive interface was modeled using connector elements whose stiffness properties as well as the bulk adhesive properties for joints with different amounts of PVA were determined using ultrasonic inspection method. The peel and shear stress variation along the adhesive bond line showed a similar trend as observed with the experimental stress distribution (DIC) but with a lesser magnitude. A parametric study using finite element based Monte-Carlo simulation was carried out to assess the effect of variation in various joint parameters like adhesive modulus, bondline thickness, adherend geometrical and material properties on peel and shear stress in the joint. It was found that the adhesive modulus and bond line thickness had a significant influence on the magnitude of stresses developed in the bond line. Thus, to summarize, an attempt has been made to study the bond line integrity of a composite epoxy adhesive lap joint using experimental, analytical and numerical approaches. Advanced NDE tools like oblique incidence ultrasound, non linear ultrasound, Lamb wave inspection and digital image correlation have been used to extract parameters which can be used to evaluate composite bonded joints. The results obtained and reported in the thesis have been encouraging and indicate that in specific cases where the bond line thickness and other relevant parameters if can be maintained or presumed reasonably non variant, it is possible to effectively evaluate the integrity of a composite bonded joint.