Stress wave propagation in a functionally graded adhesive layer between two identical cylinders

This study investigates the stress wave propagation in circular aluminum cylinders bonded with a functionally graded adhesive layer subjected to an axial impulsive load. The adhesive joint consists of two identical (aluminum) cylinders and a functionally graded adhesive layer. The volume fractions of the two constituents: aluminum and epoxy in the adhesive layer were functionally tailored through the adhesive thickness by obeying a power-law. Therefore, the effective material properties at any point in the adhesive layer were predicted by the Mori-Tanaka homogenization scheme. The governing equations of the wave propagation in the joint were discretized by means of the finite difference method. The influence of the compositional gradient exponent on the displacement and stress distributions of the joint was examined. It was observed that changing the material composition of the adhesive layer had an evident effect on the displacement and stress levels, especially in the lower cylinder. On the contrary, the influence of the compositional gradient exponent was found to be minor on the displacement and stress distributions. The displacement and stress distributions were also investigated along the upper and lower cylinder-adhesive interfaces. Accordingly, with increasing the ductility of the adhesive layer the waves transmitted to the lower cylinder caused lower displacement levels. The normal stresses become peak at the bottom corners of the upper and lower cylinder-adhesive interfaces whereas the shear stresses concentrate in the middle region of the interfaces. In addition, the temporal variations of the displacement and stress components were evaluated at some critical points of the adhesive and lower cylinder. The compositional gradient exponent played an important role on the displacement and stress levels as well as the wave speeds in the adhesive and lower cylinder rather than in the upper cylinder. The stresses in the joints were observed to be alleviated by employing a functionally graded adhesive layer.     

Stress wave propagation in a through-thickness functionally graded adhesive layer

In this study, an improved mathematical model is presented to investigate the stress wave propagation in two circular cylinders bonded with a functionally graded adhesive layer. In the proposed model, the spatial derivatives of mechanical properties are included in the governing equations of the wave propagation. Also, the finite-difference method was used for the solution of the governing equations and boundary conditions. The Mori-Tanaka homogenization scheme was employed to evaluate the through-thickness mechanical properties of the adhesive layer. The effects of the spatial derivatives of the local mechanical properties and the through-thickness material composition variation in the adhesive layer were examined in detail. The presence of the material spatial derivatives in the governing equations mitigated the stress and displacement levels as well as axial and radial wave speeds.     

Thermal Residual Stresses in Adhesively Bonded In-plane Functionally Graded Clamped Plates Subjected to an Edge Heat Flux

In this study we have carried out the thermal residual stress analyses of adhesively bonded functionally graded clamped plates for different edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The plate material properties near the interfaces played an important role in the interfacial adhesive stresses. The compositional gradient affected considerably both in-plane temperature distributions and heat transfer periods. The type of in-plane heat flux had only a minor effect on the temperature profiles but affected both the temperature levels and heat transfer period. Both plates undergo considerable compressive normal strains and stresses, but shear strains were more effective. Peak equivalent strains were observed for a constant heat flux and plates with a metal-rich composition. The compositional gradient and direction played important role in the profiles and levels of normal, shear and equivalent stresses as well as strains. The equivalent stress and strains concentrated along the free edges of the adhesive layer. The adhesive layer experienced a considerable distortional deformation rather than volumetric deformation. The equivalent stress exhibited small changes through the adhesive thickness and along the overlap length. The equivalent stress remained uniform in a large region of the overlap length and increased to a peak level around the free edges of the first plate–adhesive interface, whereas it increased to a peak level in a large region of the overlap length from a minimum level around the free edges of the second plate–adhesive interface. The strains and equivalent strains were higher for a metal-rich material composition. The direction of the material composition of the plates affected both stress and strain levels; thus, the CM–CM and CM–MC plates exhibited lower strain and stress levels than those in the MC–CM and MC–MC plates. However, only the adhesively bonded CM–MC plate configuration could achieve the lowest deformations and stresses in both plates and adhesive layer.     

Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plates

This study investigates the effects of in-plane compositional gradient exponent and direction on the thermal residual stress and deformations in adhesively bonded functionally graded clamped circular plates. The material composition was assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations in polar coordinates describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo-singular-value method. The material composition direction is designed as Ceramic-Metal (CM)–CM, CM–Metal-Ceramic (MC), MC–CM, and MC–MC for the inner and outer plates. The temperature decreased radially along the plates, but exhibited a sharp decrease across the adhesive layer. The compositional gradient exponent and direction affected evidently temperature levels and heat transfer period. The compressive radial and shear strains are more effective on the deformation in the adhesive layer and the plate regions near the plate–adhesive interfaces. The adhesive layer is subjected to considerable shear deformations. The equivalent strain and stresses are very low in a large region of the plates but exhibit sharp peaks on the plate regions near the plate–adhesive interfaces, and decrease towards the adhesive interfaces. These stress and strain peaks in the plates and adhesive layer are affected by the compositional gradient and direction. For an outer edge flux, the largest equivalent strain and stresses are observed in the CM–MC joint but the lowest levels occur in the MC–CM or secondly CM–CM joint. In addition, an inner edge flux results in the lowest and highest peak strains and stresses in the MC–CM and CM–MC joints, respectively. The MC–MC and CM–CM joints result in lower temperature, stress and strain levels around the adhesive layer and along the adhesive interfaces for outer and inner edge fluxes, respectively.     

FEM stress analysis and strength of adhesive butt joints of similar hollow cylinders under static and impact tensile loadings

The stress wave propagations in butt adhesive joints of similar hollow cylinders subjected to static and impact tensile loadings are analyzed in elastic and elasto-plastic deformation ranges using the finite-element method (FEM). The impact loading is applied to the joint by dropping a weight. The upper end of the upper adherend is fixed and the lower adherend of which the lower end is connected to a guide bar is subjected to the impact loading. The FEM code employed is DYNA3D. The effects of the adhesive thickness and Young's modulus of the adhesive on the stress wave propagation at the interfaces are examined. In addition, the characteristics of the joints subjected to impact loadings are compared with those of the joints under static loadings and the joint strengths are estimated by using the interface stress distributions. It is found that the maximum value of the maximum principal stress, σ₁ occurs at the outside edge of the interface of the lower adherend to which the impact loading is applied. The maximum value of the maximum principal stress, σ₁ increases as Young's modulus of the adhesive increases when the joints are subjected to impact loadings. It is found that the characteristics of the joints subjected to impact loadings are opposite to those subjected to static loadings. In addition, experiments were carried out to measure the strain response of the butt adhesive joints subjected to impact and static tensile loadings using strain gauges and the joint strengths were also measured. Fairy good agreements are observed between the numerical and the measured results.     

Axisymmetric pull-off test for a cracked adhesive layer

This paper is concerned with the elastostatic axisymmetric problem for an elastic incompressible adhesive layer bonded to a rigid substrate along its lower surface. An upward tensile force is applied to the upper surface of the adhesive layer through a rigid cylinder. The adhesive layer contains a penny-shaped crack parallel to its lateral surfaces. Solution of the governing equations of linear elasticity is obtained through the use of Hankel transforms. Due to the presence of the crack, the adhesive layer is treated as being composed of two sublayers for which the solutions are matched at the plane of the crack. The mixed boundary conditions of the problem lead the analysis to a system of four singular integral equations for cylinder-layer interface stresses and crack surface displacement derivatives. These integral equestions are solved numerically and the interface stress distributions, stress intensity factors at the crack tip and around the edge of the cylinder, probable cleavage angle, and the strain energy release rate for the crack are calculated for various geometries. Numerical results are presented in graphical form.     

Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Independent Material Properties

We have presented a numerical technique for analyzing one-dimensional transient temperature distributions in a circular hollow cylinder that was composed of functionally graded ceramic–metal-based materials, without considering the temperature-dependent material properties. The functionally graded material (FGM) cylinder was assumed to be initially in a steady state of gradient temperature; the ceramic inner surface was exposed to high temperature, and the metallic outer surface, which was associated with its in-service performance, was exposed to low temperature. Then, the FGM cylinder was cooled rapidly on the ceramic surface of the cylinder, using a cold medium. The transient temperature and related thermal stresses in the FGM cylinder were analyzed numerically for a model of the mullite–molybdenum FGM system. The technique for analyzing the temperature distribution is quite simple and widely applicable for various boundary conditions of FGMs, in comparison with methods that have been proposed recently by other researchers.     

Thermal residual stresses in an adhesively-bonded functionally graded single-lap joint

This study investigates three-dimensional thermal residual stresses occurring in an adhesively-bonded functionally graded single-lap joint subjected to a uniform cooling. The adherends are composed of a through-the-thickness functionally graded region between Al₂O₃ ceramic and Ni metal layers. Their mechanical properties were calculated using a power law for the volume fraction of the metal phase and a 3D layered finite element was implemented. In a free single-lap joint the normal stress σ_xx was dominant through the overlap region of the upper and lower adherends and along the adhesive free edges, whereas the transverse shear stress σ_xy concentrations appeared only along the free edges. The peel stress σ_yy and the transverse shear stress σ_xy became dominant along the free edges of the adhesive layer. In addition, the von Mises stress decreased uniformly through the adherend thickness from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer. In addition, the layer number had only a minor effect on the through-the-thickness stress profiles after a layer number of 50, except for the peak stress values in the ceramic layer. In a single-lap joint fixed at two edges both adherends underwent considerable normal stress σ_xx concentrations varying from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer along the free edges of both adherend–adhesive interfaces, whereas the peel stress σ_yy and transverse shear stress σ_xy reached peak levels along the left and right free edges of the adhesive layer. The layer number and the compositional gradient exponent had only minor effects on the through-the-thickness von Mises stress profiles but considerably affected the peak stress levels. The free edges of adhesive–adherend interfaces and the corresponding adherend regions are the most critical regions, and the adherend edge conditions play more important role in the critical adherend and adhesive stresses. Therefore, the first initiation of the joint failure can be expected along the left and right free edges of the upper and lower adherend–adhesive interfaces.     

Finite element stress analysis and strength evaluation of epoxy-steel cylinders subjected to impact push-off loads

The stress wave propagations and stress distributions in epoxy-steel cylinders in which the outside surface of a solid cylinder (steel) is adhered to the inside surface of a hollow cylinder (epoxy resin) subjected to impact push-off loads were analyzed using the finite element method (FEM). The impact push-off loads were applied to epoxy-steel cylinders on a solid cylinder by dropping a weight. The FEM code employed was ANSYS/LS-DYNA. It was found that the maximum principal stress occurs at the upper edge of the interface, where the rupture initiates in epoxy-steel cylinders under the impact push-off loads. Besides, it was also found that the normal stress near the upper edge of the interface increases as the rigidity and the initial impact velocity increase; meanwhile it decreases as the diameter and the height of the solid cylinder increase. The strength of epoxy-steel cylinders increases as the rigidity of the solid cylinder increases, and the diameter and the height of the solid cylinder decrease. In addition, it was observed that the characteristics of the joints subjected to the impact push-off loads are opposite to those of the joints subjected to the static push-off loads. Furthermore, experiments were carried out to measure the strain response of epoxy-steel cylinders subjected to impact and static push-off loads. Fairly good agreements were observed between the numerical and the measured results.     

Free Vibration Analysis of an Adhesively Bonded Functionally Graded Tubular Single Lap Joint

In this study, the three-dimensional free vibration analysis of an adhesively bonded functionally graded tubular single lap joint was carried out using the finite element method. The functionally graded tubes of the adhesive joint are composed of ceramic (Al₂O₃) and metal (Ni) phases varying through the tube thickness. The adhesive material properties, such as modulus of elasticity, Poisson's ratio, and density were found to have negligible effect on the first ten natural frequencies and mode shapes of the adhesive joint. The optimal design parameters of the adhesive joint, such as overlap length, inner radius of the inner tube, outer and inner tube thicknesses, and the through-the-thickness material composition variation were searched using both the artificial neural networks (ANNs) and the genetic algorithms (GAs). For this purpose, the natural frequencies and modal strain energy values were calculated for an adhesive joint with random geometrical properties and material compositions through the tube thicknesses, and were used for training the proposed artificial neural network models. The outer tube thickness, the inner tube-inner radius, and the compositional gradient exponent had considerable effect on the natural frequencies, mode shapes, and modal strain energies of the functionally graded tubular single lap joint, whereas the overlap length and the inner tube thickness had a minor effect. The GAs integrated with ANNs was employed to determine optimal design parameters satisfying both maximum natural frequency and minimum modal strain energy conditions for each natural mode of the tubular adhesive joint.     

An efficient analysis model for functionally graded adhesive single lap joints

Employing a functionally graded adhesive the efficiency of adhesively bonded lap joints can be improved significantly. However, up to now, analysis approaches for planar functionally graded adhesive joints are still not addressed well. With this work, an efficient model for the stress analysis of functionally graded adhesive single lap joints which considers peel as well as shear stresses in the adhesive is proposed. Two differential equations of the displacements are derived for the case of an axially loaded adhesive single lap joint. The differential equations are solved using a power series approach. The model incorporates the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young׳s modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young׳s modulus distributions and their impact on the peel and shear stresses as well as the influence of the adhesive thickness are studied and discussed in detail.     

Three-dimensional finite element analysis of single-lap adhesive joints subjected to impact bending moments

This paper deals with the stress wave propagations and stress distributions in single-lap adhesive joints subjected to impact bending moments with small strain rate. The elastic stress wave propagation and the stress distribution in single-lap adhesive joints of similar adherends subjected to impact bending moments are analyzed using three-dimensional finite-element method (FEM). A three-point impact bending moment is applied to the joint by dropping a weight. FEM code employed is DYNA3D. The effects of Young's modulus of the adherends, the lap length, the adherend thickness and the adhesive thickness on the stress wave propagation at the interfaces are examined. It is found that the maximum value of the maximum principal stress, σ₁, appears at the interface between the adhesive and the upper surface of upper adherend which is impacted. The maximum stress, σ₁, increases as Young's modulus of adherends, the lap length and the adhered thickness increase. It is also found that the maximum stress, σ₁ increases with decreasing adhesive thickness. In addition, experiments were carried out to measure the strain response of single-lap joints subjected to impact bending moments using strain gauges. A fairy good agreement was observed between the numerical and experimental results.     

功能梯度材料单参数反演分析(英文)

功能梯度材料的材料参数随位置变化,以目前的实验手段来看,逐一测定各个材料参数的分布曲线工作量很大,有些材料常数的测定十分困难(特别是沿厚度材料常数梯度分布).本文利用细观元法探讨功能梯度材料参数的反演识别问题,即在获知实测位移或固有频率的情况下,对功能梯度材料的内部参数及其分布进行反演识别.显然,这可大大简化功能梯度材料的基本力学性能测试工作,为功能梯度材料的进一步研究奠定基础.     

Strain energy release rate based damage analysis of functionally graded adhesively bonded tubular lap joint of laminated FRP composites

Strain energy release rate (SERR) based damage analyses of functionally graded adhesively bonded tubular lap joints of laminated fiber reinforced plastic (FRP) composites under varied loadings have been studied using three-dimensional geometrically non-linear finite element (FE) analyses. FE simulations have been carried out when a tubular joint is subjected to axial and pressure loadings. SERR is utilized as the characterizing and governing parameter for assessing damages emanating from the critical location. Individual and total SERR over the damage front have been computed using modified crack closure integral (MCCI) based on the concept of linear elastic fracture mechanics. Results reveal that damage initiation locations in tubular joints subjected to axial and pressure loadings are entirely different. Furthermore, modes responsible for propagation of such damages in tubular joints under axial and pressure loadings are also different. Based on the FE simulations, tubular joints under pressure loading are found to be more vulnerable for damage initiation and its propagation. Furthermore, the damage propagation behavior of tubular joints with pre-embedded damages at the critical location has been compared between conventional mono-modulus adhesives and functionally graded adhesives with appropriate material gradation profile. Results indicate that material gradient profile of the adhesive layer offers excellent reduction in SERR for shorter interfacial failure lengths in tubular joints under axial loading which is desired to delay the damage growth. Improved crack growth resistance in the joint enhances the structural integrity and service life of the tubular joint structure. However, considerable reduction in SERR has not been noticed in the said joint when subjected to pressure loading. Hence, the use of functionally graded adhesive along the bond layer is recommended for the designer/technologist while designing tubular joint under general loading condition.     

Finite Element Analysis of Functionally Graded Bond-Lines for Metal/Composite Joints

Failure in adhesive joints is usually the result of the non-uniform distribution of stresses that generally appears along the bond-lines, with peak values near the ends of the overlaps and inner zones where the adhesive essentially does not work. For joints comprised of dissimilar materials, the stress fields are also affected by the absence of symmetry. The present work is focused on “functionally graded adhesive joints” to avoid this phenomenon and to improve the strength of aluminum/composite joints under shear loads. Looking for the most favorable grading of properties, a search/optimization procedure is implemented based on finite element calculations and considering continuous variations of the material responses within the adhesive layer. After this, a comparative analysis of the continuous distributions obtained against discrete/“banded” approximations is performed, as these configurations are more feasible for manufacturing and therefore more suitable for industrialization. In order to avoid singularities appearing in the “banded” solutions simulations, a numerical strategy is proposed to model the transitions between the different adhesive phases.     

Thermomechanical Analysis of Functionally Graded Thermal Barrier Coatings with Different Microstructural Scales

The recently developed two-dimensional version of the higher-order theory for functionally graded materials (denoted as HOTFGM-2D in previous communications) has been used to investigate the effects of microstructural architectures in graded thermal barrier coatings (TBCs) on stress distributions in the presence of a through-thickness temperature gradient. In particular, the response of TBCs with different levels of functionally graded microstructural refinement and different arrangements has been investigated, and the results for the through-thickness stress distributions are compared with those based on the standard micromechanical homogenization scheme. The examples presented illustrate the shortcomings of the standard micromechanics-based approach that is applied to the analysis of functionally graded TBCs, particularly if the presence of creep effects is included in the analysis.     

Interfacial failure analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates

This paper deals with three-dimensional non-linear finite element analyses to assess the structural behavior of adhesively-bonded double supported tee joint of laminated FRP composites having embedded interfacial failures. The onset of interfacial failures is predicted by using Tsai–Wu coupled stress failure criterion with pre-determined stress values. The concept of fracture mechanics principle is utilized to study the sustainability of the tee joint having interfacial failures pre-existed at the critical locations. Individual modes of the strain energy release rates (SERR) G_I, G_II and G_III, are considered as the damage growth parameters and, are evaluated using the Modified crack closure integral (MCCI) technique based on the concept of linear elastic fracture mechanics (LEFM). Based on the stress analyses, it has been observed that the interfacial failures in tee joint structure trigger at the interface of base plate and adhesive layer from both ends of base plate. Depending on the SERR magnitudes, it has been noticed that the interfacial failure propagates under mixed mode condition. Therefore total SERR (G_T) is considered as the governing parameter for damage propagation. Furthermore, efforts have been made to retard damage propagation rate by employing functionally graded adhesive (FGA) instead of monolithic adhesive material. Series of numerical simulations have been performed for varied interfacial failure length in functionally graded adhesively bonded double supported tee joint structure in order to achieve the significant effect of FGA with various modulus ratios on SERR. Material gradation of adhesive indicates significant SERR reduction at the incipient stage of failure which necessitates the use of functionally graded adhesive for the tee joint and prolong the service life of the structure.     

Effect of macroscopic heterogeneity of the medium on the solid-state combustion wave characteristics in thermally and chemically heterogeneous media

A macroscopically heterogeneous medium is modeled by a set of cylinders (rods) pressed from a mixture of solid reagents, which have coaxial cylindrical cores made from an inert material. A three-dimensional mathematical model describing propagation of combustion waves over one cylinder is studied by numerical methods. The influence of the distance between the centerlines of the neighboring cylinders and transverse sizes of the cylinders on characteristics of combustion waves propagating over a heterogeneous medium is considered. It is demonstrated that there exists an optimal distance between the inert rods, which ensures a much higher velocity of the combustion wave along the specimen than the theoretically predicted velocity of the classical combustion wave propagating over a solid specimen. New types of spinning waves are described, whose motion makes the high-temperature spot move inside the charge mixture. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 3, pp. 39–49, May–June, 2008.     

CNG-2环向缠绕气瓶纤维缠绕残余预应力的优化设计

复合材料气瓶压力容器的纤维缠绕预应力对容器的性能有很大的影响,合理设计纤维预应力可提高复合材料容器的综合性能。借助ANSYS有限元软件,建立了带有纤维缠绕残余预应力的环向缠绕气瓶的有限元参数化模型。在模型中,将纤维缠绕层视为复合材料层合板。按照GB 24160—2009《车用压缩天然气钢质内胆环向缠绕气瓶》的规定,并结合各工况下应力水平的要求建立数学模型,对环向缠绕气瓶的纤维缠绕残余预应力进行优化,得到纤维缠绕残余预应力的最优值,使内胆在工作压力下有较低的应力水平,提高了气瓶的可靠性。