Impact Fracture of Thermally Tempered Glass Helicopter Windshields

In-service fracture of helicopter windshields was studied. Simulated catastrophic fracture tests were conducted by firing alumina and steel spheres onto stationary tempered and as-received glass panels. The results were studied by Hertzian analysis and modified Auerbach's relations. Thermally tempered glass shows much higher impact resistance than that estimated from superposition of residual stresses. Subcritical impact sites exhibit slow crack growth in tempered plates, eventually leading to fracture of the entire plate.     

Stress analysis of a finite plate adhesively bonded to an elastic half-space

An analysis is performed of finite plates bonded to an elastic half-space through an adhesive layer. Parametric studies of the effects of plate dimensions adhesive and plate material properties, and thickness of the adhesive, on bond strength are obtained. A higher order plate theory, which accounts for transverse normal stresses, is used to obtain the stress state in the plate and the adhesive for various normal and shear loadings applied to the top surface of the plate. The governing partial differential equations are generated by means of variational principle and then solved numerically. Specific numerical results for stresses as a function of the parameter variations are presented. The results are significant for the optimum design of adhesive joints.     

On the Effect of Time-Dependent Deformations on the Interface Behaviour of RC Beams Strengthened by FRP Plates

In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between a concrete beam and a fibre reinforced polymer plate is presented. The analysis given here involves a closed-form solution for such stresses and includes creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of both concrete beam and fibre reinforced polymer panel. Contrary to some existing studies, the assumption that both the concrete beam and the fibre reinforced polymer panel have the same curvature is not used in this investigation. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical examples of a typical concrete beam strengthened with an externally bonded fibre reinforced polymer plate are discussed with the emphasis on the shear and normal stresses at the edge of the plate.     

Geometrically non-linear analysis of adhesively bonded corner joints

When adhesively bonded joints are subjected to large displacements, the small strain-small displacement (linear elasticity) theory may not predict the adhesive or adherend stresses and deformations accurately. In this study, a geometricaly non-linear analysis of three adhesively bonded corner joints was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The first one, a corner joint with a single support, consisted of a vertical plate and a horizontal plate whose left end was bent at right angles and bonded to the vertical plate. The second corner joint, with a double support, had two plates whose ends were bent at right angles and bonded to each other. The final corner joint, with a single support plus angled reinforcement, was a modification of the first corner joint. The analysis method assumes that the joint members, such as the support, plates, and adhesive layers, have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have a considerable effect on the peak adhesive stresses, they were taken into account. The joints were analyzed for two different loading conditions: one loading normal to the horizontal plate plane P_y and the other horizontal loading at the horizontal plate free edge P_x. In addition, three corner joints were analyzed using the finite clement method based on the small strain-small displacement (SSSD) theory. In predicting the effect of the large displacements on the stress and deformation states of the joint members, the capabilities of both analyses were compared. Both analyses showed that the adhesive free ends and the outer fibres of the horizontal and vertical plates were subjected to stress concentrations. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the locations where the horizontal and vertical adhesive fillets finished. The SSLD analysis predicted that the displacement components and the peak adhesive and plate stress components would show a non-linear variation for the loading condition P_x, whereas the SSSD analysis showed smaller stress variations proportional to the applied load. However, both the SSLD and the SSSD analyses predicted similar displacement and stress variations for the loading condition P_y. Therefore, the stress and deformation states of the joint members are dependent on the loading conditions, and in the case of large displacements, the SSSD analysis can be misleading in predicting the stresses and deformations. The SSLD analysis also showed that the vertical and horizontal support lengths and the angled reinforcement length played an important role in reducing the peak adhesive and plate stresses.     

Analysis and design of adhesively bonded corner joints

In this study, the stress and stiffness analyses of corner joints with a single corner support, consisting of two plates, one of which plain and the other bent at right angles, have been carried out using the finite element method. It was assume that the plates and adhesive had linear elastic properties. Corner joints without a fillet at the free ends of the adhesive layer were considered. The joint support was analysed under three loading conditions, two linear and one bending moment. In the stress analysis, it was found that for loading in the y-direction and by bending moment, the maximum stresses occurred around the lower end of the vertical adhesive layer/ vertical plate interface; for loading in the x-direction, the maximum stresses occurred around the right free end of the horizontal adhesive layer/vertical plate interface. The effects of upper support length, support taper length and adhesive thickness on the maximum stresses have been investigated. Since the peel stresses are critical for this type of joint, a second corner joint with double corner support (i.e., one in which the horizontal plate is reinforced by a support that is an extension of the vertical plate) was investigated which showed considerable decreases in the stresses, particularly peel stresses. A third type of corner joint with single corner support plus an angled reinforcement member was investigated as an alternative to the previous two configurations. It was found that increasing the length and particularly the thickness of the angled reinforcement reduced the high peel stresses around the lower free end of the adhesive/vertical plate interface, but resulted in higher compressive stresses. In the stiffness analysis, the effects of the geometry of the joints, relative stiffness of adhesive/adherends and adhesive thickness were investigated under three loading conditions. For three types of corner joint, results were compared and recommended designs were determined based on the overall static stiffness of the joints and on the stress analysis.     

Large-Deflection Solution of the Coaxial-Ring-Circular-Glass-Plate Flexure Problem

Nonlinear deflections and radial surface stresses in thin elastic circular plates laterally deformed into symmetrical concave shapes are analyzed. The deformations are induced by loading each plate with a small center ring while the plate is resting on a ring of nearly the same diameter as the plate. The rings and plate are coaxial, i.e. concentric. Center deflections up to 3 and 4.5 times the plate thickness were predicted for ring-diameter ratios of 0.5 and 0.2, respectively. The predicted deflection profiles at various loads agreed quite well with those which were determined experimentally on a chemically strengthened glass plate. This analysis provides a new criterion for using the coaxial-ring loading method for flexural strength testing of brittle materials.     

Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre reinforced polymer (FRP) plates to their tensile faces. An important failure mode of such plated beams is the debonding of the FRP plates from the concrete due to high level of stress concentration in the adhesive at the ends of the FRP plate. This paper presents an improved solution for interfacial stresses in a concrete beam bonded with the FRP plate by including the effect of the adherend shear deformations. The analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the concrete beam and the bonded plate. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions.     

Geometrically non-linear analysis of adhesively bonded double containment cantilever j oints

Under an increasing load, the adhesively bonded joints may undergo large rotations and displacements while strains are still small and even all joint members are elastic. In this case, the linear elasticity theory cannot predict correctly the nature of stress and deformation in the adhesive joints. In this study, an attempt was made to develop an analysis method considering the large displacements and rotations in the adhesive joints, assuming all joint members to be still elastic. An incremental finite element method was used in the application of the small strain-large displacement theory to the adhesively bonded joints. An adhesively bonded double containment cantilever (DCC) joint was analysed using this incremental finite element method under two different loadings: a tensile loading at the horizontal plate free end, P_x. and one normal to the horizontal plate plane, P_y. The adhesive and plates were assumed to have elastic properties, and some amount of adhesive, called spew fillet, that accumulated at the adhesive free ends was also taken into account. The analysis showed that the geometrical non-linear behaviour of adhesively bonded joints was strictly dependent on the loading and boundary conditions. Thus, a DCC joint exhibits a high non-linearity in the displacements, stresses, and strains in the critical sections of the adhesive and horizontal plate under a tensile loading at the free end of the horizontal plate, P_x, while a similar behaviour in these regions was not observed for a loading normal to the horizontal plate plane, P_y. However, an increasing non-linear variation in the stresses and deformations of the horizontal plate appeared from the free ends of the adhesive-horizontal plate interfaces to the free end of the horizontal plate for both loading conditions. Consequently, joint regions with a low stiffness always undergo high rotations and displacements, and if these regions include any adhesive layer, the non-linear effects will play an important role in predicting correctly the stresses and deformations in the joint members, especially at the adhesive free ends at which high stress concentrations occurred. In addition, the DCC joint exhibited a higher stiffness and lower stress and strain levels in the joint region in which the support and horizontal plate are bonded than those in the horizontal plate.     

Stress analyses of composite tee joints at elevated temperature

Thermal–structural coupling nonlinear finite element analyses are conducted in this paper to determine three-dimensional stresses of a composite tee joint, which is formed when a right angled plate is adhesively bonded to a base plate at elevated temperature. The von-Mises stresses of the adhesive layer of the tee joint with three different laminate stacking sequences viz. unidirectional [0]₈, cross-ply [(0/90)_s]₂, and angle-ply [(+45/?45)_s]₂ laminates have been evaluated when the tee joint is subjected to an out-of-plane loading through the right angled plate in addition to an elevated temperature applied at the undersurface of the base plate. The effects of laminate stacking sequence and temperature on von-Mises stresses have been investigated in this paper. The effects of the coefficient of thermal expansion and thermal conduction of the adhesive layer on von-Mises stresses have also been studied. Conclusions about the stresses of the composite tee joint with different stacking sequence, different coefficient of thermal expansion, and different thermal conduction of the adhesive layer are drawn.     

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, I: Convective Cooling at Rear Surface

An analysis is presented of the thermal stresses in a partially absorbing brittle ceramic flat plate asymmetrically heated by radiation on the front surface and cooled by convection on the rear surface with a heat transfer coefficient, h , being finite or zero. For finite A, the transient thermal stresses are a function of h , whereas the steady-state thermal stresses are independent of h . The maximum value of tensile thermal stresses occurs at an optical thickness μ a = 2 and equals zero for μ a = 0 or ∞. For an optical thickness μ a <10.7, the steady-state thermal stresses exceed the transient stresses, with the converse being true for μ10.7. The maximum tensile thermal stresses occur in the front surface where the temperatures are highest. For h =0, the tensile thermal stresses increase with increasing value of optical thickness. The role of the material properties which control the thermal stress resistance under conditions of combined radiation heating and convection cooling are discussed. Appropriate thermal stress resistance parameters are proposed.     

Thermal non-linear elastic stress analysis of an adhesively bonded T-joint

Adhesive joints consist of adherends and an adhesive layer having different thermal and mechanical properties. When they are exposed to uniform thermal loads the mechanical-thermal mismatches of the adherends and adhesive layer result in uniform but different thermal strain distributions in the adhesive and adherends. The thermal stresses arise near and along the adherend-adhesive interfaces. The present thermal stress analyses of adhesively bonded joints assume a uniform temperature distribution or a constant temperature imposed along the outer boundaries of adhesive lap joints. This paper outlines the thermal analysis and geometrically non-linear stress analysis of adhesive joints subjected to different plate edge conditions and varying thermal boundary conditions causing large displacements and rotations. In addition, the geometrically non-linear thermal stress analysis of an adhesively bonded T-joint with single support plus angled reinforcement was carried out using the incremental finite element method, which was subjected to variable thermal boundary conditions, i.e. air streams with different temperatures and velocities parallel and perpendicular to its outer surfaces. The steady state heat transfer analysis showed that the temperature distribution through the joint members was non-uniform and high heat fluxes occurred inside the adhesive fillets at the adhesive free ends. Based on the geometrically non-linear stress analysis of the T-joint bonded to both rigid and flexible bases for different plate edge conditions, stress concentrations were observed at the free ends of adhesive-adherend interfaces and inside the adhesive fillets around the adhesive free ends, and the horizontal and vertical plates also experienced considerable stress distributions along outer surfaces. In addition, the effect of support length on the peak thermal adhesive stresses was found to be dependent on the plate edge conditions, when a support length allowing moderate adhesive stresses was present.     

夹套管端板强度分析探讨

通过对夹套管结构进行分析,建立了端板力学模型,用板理论求解与内管连接处的应力,给出中心点作用力的求解方程,建立了一套各种应力的评判方法,使得端板的强度分析更加方便、科学。     

STRESSES IN VISCOELASTIC PLATE DRIED CONVECTIVELY

The deformations and drying-induced stresses in a saturated porous plate insulated on one side and dried convectively on the others were analysedPlate material is assumed to be elastic and viscoelastic. A rigorous solution of the problem is presented using Laplace transformations and the method of variable separation. The results are presented in the form of a series resulting from the solution of a Sturm-Liouville problem. The shrinkage stresses in the plate are caused by non-uniform distribution of the moisture content. The thermal stresses are not included as the consideration were confined to only constant rate drying period.     

Analysis of Effectiveness and Stress Development during Convective and Microwave Drying

The aim of the article is to study the effectiveness of convective and microwave drying with respect to drying time and stress generation in clay-like dried bodies. The theoretical analysis of stresses was confined to the constant drying rate period because clay shrinks and the stresses are generated mainly in this period. The theoretical prediction of stress development was validated using an acoustic emission method by monitoring the micro- and macrocracks formation caused by the stresses. Apart from the stress analysis, the combined convective-microwave drying was examined experimentally during whole process in order to show that the volumetric heat supply due to microwave heating enhances convective drying and, apart from this, such a combined drying process develops less stress in dried material. The theoretical and experimental studies were performed on a kaolin sample in the form of a thin plate.     

Analysis of Effectiveness and Stress Development during Convective and Microwave Drying

The aim of the article is to study the effectiveness of convective and microwave drying with respect to drying time and stress generation in clay-like dried bodies. The theoretical analysis of stresses was confined to the constant drying rate period because clay shrinks and the stresses are generated mainly in this period. The theoretical prediction of stress development was validated using an acoustic emission method by monitoring the micro- and macrocracks formation caused by the stresses. Apart from the stress analysis, the combined convective-microwave drying was examined experimentally during whole process in order to show that the volumetric heat supply due to microwave heating enhances convective drying and, apart from this, such a combined drying process develops less stress in dried material. The theoretical and experimental studies were performed on a kaolin sample in the form of a thin plate.     

A New Coupled Solution for Interfacial Stresses Analysis in a Repaired Beam with an Adhesively Bonded Prestressed FRP Plate

This paper focuses on a new coupling solution for determining the elastic interfacial shear and normal stresses in an adhesive joint between a strengthening plate and a simply supported beam. The mismatch of the curvatures in the beam and plate is considered by including both the effect of the adherend shear deformations and the prestressed laminates model. This new method leads to the coupling of governing differential equations for the interfacial shear and normal stresses. Most of the other solutions in the literature assume that the beam and plate have an equal curvature to uncouple this effect. In this paper, however, a solution is presented to calculate the interfacial stresses of beams strengthened with a prestressed composite plate having a new rigidity model coupled with the shear lag effect, which are neglected by the previous studies. It is found that the present method can predict accurately stresses in the interior and near the ends of the adhesive layer, where the stress fields can be significantly influenced by the edge effects. A parametric study was carried out to show how the stress concentration and distribution are influenced by the dimensions of the adherends and the material properties of the strengthened beam.     

An improved four-parameter model on stress analysis of adhesive layer in plated beam

The prediction of stresses in an adhesive layer is helpful in revealing the mechanism of debonding failure in plated beams. This study proposes an improved analytical model for the stress analysis of an adhesive layer in a plated beam. The beam and the soffit plate are individually modelled as a single Timoshenko sub-beam with separate rotations, while the adhesive layer is modelled as a two-dimensional elastic continuum in plane stress, which considers different adherend-adhesive interface stresses. The internal forces of the adhesive layer are assumed to satisfy the Timoshenko beam theory, and the shear deformation and bending moment of the adhesive layer can be considered. The internal forces and displacements of the adhesive layer are fully considered in the displacement compatibility equations, and deformable interfaces are assembled so that the effect of interface stresses on local deformation is captured. Based on equilibrium equations and displacement continuity, the governing differential equations of beam forces are derived, and then the analytical solutions of interface stresses and stresses along the thickness of the adhesive layer are obtained. Comparisons of the results of the finite-element analysis and the existing four-parameter model solutions show that the present model is reasonable. The influence of adhesive thickness on stress distributions in adhesive layers is also investigated.     

Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate

The paper presents the results of an analytical and numerical solution for interfacial stresses in carbon fiber reinforced plastic (CFRP)–reinforced concrete (RC) hybrid beams studied by the finite element method. The analytical analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the concrete beam and the bonded plate. In numerical analysis, the mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions. We can conclude that this research is helpful for the understanding the mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, II: Convective Cooling at Front Surface

Thermal stresses in a partially absorbing brittle ceramic plate asymmetrically heated by radiation and cooled by convection on the same surface with finite and infinite heat transfer coefficients are analyzed. Comparison of the results from this study with those obtained in Part I, where the plate is subjected to radiation heating in the front surface and cooled by convection at the rear surface, indicates that the magnitudes of the maximum steady-state tensile thermal stresses are nearly identical. Significant differences are found in the transient thermal stresses and the temperature distribution. The relative temperature levels in the present case are found to be significantly lower than those obtained in Part I. Implications of these results to the design and operation of engineering structures such as concentrated solar receivers are discussed.     

STRESSES IN VISCOELASTIC PLATE DRIED CONVECTIVELY

ABSTRACT

The deformations and drying-induced stresses in a saturated porous plate insulated on one side and dried convectively on the others were analysedPlate material is assumed to be elastic and viscoelastic. A rigorous solution of the problem is presented using Laplace transformations and the method of variable separation. The results are presented in the form of a series resulting from the solution of a Sturm-Liouville problem. The shrinkage stresses in the plate are caused by non-uniform distribution of the moisture content. The thermal stresses are not included as the consideration were confined to only constant rate drying period.