Development of a smart composite pipe joint integrated with piezoelectric layers under tensile loading

To actively reduce the stress concentration effect in adhesive layers, a novel smart adhesively bonded composite pipe joint system was developed by integrating piezoelectric layers as sensor/actuator in the connection coupler. In the presently developed smart pipe joint system, the mechanical loading induced structural deformation can be detected and monitored by integrated sensing piezoelectric layers, and then the signal is fed back to the integrated actuating piezoelectric layers to adaptively produce additional forces and moments so as to decrease the maximum peel and shear stresses in the adhesive layer. In order to theoretically predict the efficiency of the developed smart pipe joint system, an electro-mechanical theoretical analytical model was established to investigate the characteristics of the joint system under end tension load in terms of first-order shear deformation theory. Simultaneously, the state-space method was utilized to deduce the final analytical solutions, including the peel and shear stress distributions in the adhesive layer. Finally, some detailed numerical results were obtained to demonstrate the optimal design method of such smart pipe joint system and further validate the integrity of this joint system.     

Design and analysis of a smart composite pipe joint system integrated with piezoelectric layers under bending

Incorporating with the high electro-mechanical coupling performance of piezoelectric materials, design and analysis of an adhesively bonded smart composite pipe joint system were conducted. In this joint system, piezoelectric layers were integrated into the joint coupler in order to reduce stress concentration in the joint adhesive layer. To theoretically verify the composite action and efficiency of the integrated piezoelectric layers, an electro-mechanical model based on the first-order shear deformation theory was established. This model was able to clarify the energetic characteristics of the proposed joint system on the improvement in the joint strength, which was under the action of a bending moment at the joint ends. The state-space method was utilized to obtain the final analytical solutions, including the peel and shear stress distributions in the adhesive layer. Finally, some numerical examples were calculated to evaluate the effect of the detailed stacking sequence and size of the integrated piezoelectric layers on reducing the stress concentration in the adhesive layer as well as the applied electric fields. These numerical results validated the integrity of the developed adhesively bonded smart composite pipe joint system.     

Embedded piezoelectric sensors to measure peel stresses in adhesive joints

Although peel stresses are believed to be responsible for failure in many adhesive joint geometries, the measurement of these peel stresses has been elusive. In this work, embedded poly(vinylidene fluoride) piezoelectric sensors were used to measure peel stresses in adhesively bonded joints. Piezoelectric KYNAR^® film was etched to produce multi-area stress sensors which were bonded into adhesive joints. Calibration results and results for single-lap and elastomeric butt joints are presented. The elastomeric butt joint was compared to an analytical solution for the bond-normal stresses, and the single-lap joint results were compared to finite-element analysis. Promising features and liminations of this technique are discussed.     

Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.     

Analysis of an adhesively bonded single-strap joint integrated with shape memory alloy (SMA) reinforced layers

Shape memory alloys (SMAs) are increasingly becoming a topic of research in the area of smart materials. In this study, the design and analysis of a SMA reinforced joint is presented to elucidate the contribution of the active composite layer to the reduction of stress concentrations in the adhesive layer. Basic thermo-mechanical properties of the SMA are obtained by micromechanics. The forces and moments at the joint edges are obtained by incorporating the thermo-mechanical effect of the active composite layer within the joint. Further, an analytic model based on the first-order shear deformation theory was employed to conduct stress analyses of this joint system. The state-space method was utilized to obtain the final analytic solutions, including the peel and shear stresses in the adhesive layer. Detailed numerical analyses are conducted. The results confirm that the active composite layer significantly reduces stress concentrations at the joint edges.     

Progressive fracture of adhesively bonded composite structures

Progressive damage and fracture of adhesively bonded graphite/epoxy composite structures are evaluated via computational simulation. Load induced damage in both the adhesive bond and the adjoining laminate is considered. An integrated computer code is used for the simulation of structural degradation under loading. Damage initiation, growth, accumulation, and propagation to fracture are included in the simulations. Results show in detail the damage progression sequence and structural fracture resistance during different degradation stages. Design implications with regard to damage tolerance of adhesively bonded joints are examined. Influence of the type of loading as well as adhesive thickness on damage initiation and progression for an adhesively bonded composite structure are investigated.     

Exact static solutions to piezoelectric smart beams including peel stresses. II. Numerical results,comparison and discussion

This part presents the numerical results, comparisons and discussion for the exact static solutions of smart beams with piezoelectric (PZT) actuators and sensors including peel stresses presented in Part I. (International Journal of Solids and Structures, 39, 4677–4695) The actuated stress distributions in the adhesive and the adhesive edge stresses varying with the thickness ratios are firstly obtained and presented. The actuated internal stress resultants and displacements in the host beam are then calculated and compared with those predicted by using the shear lag model. The stresses in the adhesive caused by an applied axial force, bending moment and shear force are calculated, and then used to compute the sensing electric charges for comparison with those predicted using the shear lag model. The numerical results are given for the smart beam with (a) one bonded PZT and (b) two symmetrically bonded PZTs, with a comparison to those predicted using the shear lag model. Novel, simple and more accurate formulas for the equivalent force and bending moment induced by applied electric field are also derived for the host beam with one PZT or two symmetrically bonded PZTs. The symmetric shear stress and the anti-symmetric peel stress components caused by a shear force are discussed. In addition, in the case of PZT edge debonding, the stress redistribution in the adhesive and the self-arresting mechanism are also investigated.     

压电智能复合材料层合梁的力电耦合模型及层间应力分析

由于非凡的物理性能,石墨烯纳米片(GPL)被认为是最有吸引力的复合材料增强材料之一.GPL增强材料可以明显提高聚偏氟乙烯(PVDF)压电性能和力学性能.在力电载荷作用下,对含均匀石墨烯薄片增强(GSR)智能压电复合材料层合梁层间应力预测至关重要.若对受到力电耦合作用且层与层之间材料性能突变的压电层合梁层间剪切变形预测有误,则其层间应力过大可能导致层间失效.因此,论文提出一种适于分析此类问题且满足层与层之间相容性条件的有效力电耦合模型,用于含GSR致动器的复合材料层合梁层间应力分析.应用Reissner混合变分原理(RMVT),可以提高考虑力电耦合效应的横向剪应力预测精度.三维(3D)弹性理论和所选模型计算结果将用于评估所提梁模型性能.此外,还从力电载荷、压电层厚度、石墨烯体积分数和长厚比等方面对含GSR致动器复合材料层合梁力学响应特性进行了系统的研究.     

单搭接胶接接头拉伸剪切性能的数值模拟与实验研究

采用数值模拟和光测技术对单向拉伸载荷作用下单搭接胶接接头中的剪切性能进行分析,研究了不同厚度胶层中切应力的变化规律。用有限元方法(FEM)对不同胶层厚度的试件进行建模,得到了拉伸载荷下胶粘剂中的切应力分布及其统计参数。利用数字图像相关(digitalimage correlation,DIC)方法对试件的变形场进行测量。结果表明,当胶粘剂的厚度较小时,胶粘剂中的切应力的分布统计参数随着其厚度的增加会有显著的变化,但是当厚度超过一定的数值时,统计参数对厚度的变化不再敏感。     

Exact dynamic solutions to piezoelectric smart beams including peel stresses Part II: Numerical results,comparison and approximate solution

This work presents numerical results for the exact dynamic solution of piezoelectric (PZT) smart beams including peel stresses, which was developed in Part I. Numerical results are presented in details for frequency spectra, natural frequencies, normal mode shapes, harmonic responses of the shear and peel stresses, and sensing electric charges for a cantilever beam with a bonded PZT patch to the clamped end. The exact dynamic solution can provide useful data for benchmarking other methods. The numerical results of the present model including peel stresses (PSM) are also compared with those obtained using the shear lag beam model and the shear lag rod model. On the basis of the equivalent forces derived in the static analysis, simple approximate dynamic solutions are obtained and compared with the exact solutions, and then the application and limitation of the simple approximate solutions are investigated. By comparing numerical results predicted by the present PSM model with the shear lag models and the approximate solutions based on the static equivalent forces, effects of the dynamic shear and peel stresses on natural frequencies and dynamic responses of the smart structures are examined.     

A theoretical analysis of piezoelectric/composite anisotropic laminate with larger-amplitude deflection effect,Part I: Fundamental equations

Considering the effects of both the different material properties of composite layers and the poling directions of piezoelectric layers, we utilized the assumption of the simple-higher-order shear deformation theory to model and analyze the laminated composite plate integrated with the random poled piezoelectric layers. Further, the generalized Hamilton’s variation principle for electro-elasticity was employed to deduce the fundamental equations of piezoelectric/composite anisotropic laminate, i.e. the governing equations and boundary conditions. For the special requirement of the larger-amplitude deflection of smart structures, the Von Karman strains were used to account for the geometric nonlinear effect of the practical larger-amplitude deflection on the electro-elastic behavior of smart composite structures. Moreover, the sensor equations were also carried out with considering the large-amplitude deflection effect of smart composite structures.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

A smart single-lap adhesive joint integrated with partially distributed piezoelectric patches

The powerful electro-mechanical coupling attribute of piezoelectric materials enables these materials to act as effective actuators. Using this attribute, a smart single-lap adhesive joint was developed by anti-symmetrically surface bonding piezoelectric patches onto a typical single-lap joint. The forces and bending moments at the edges of the developed smart joint can be adaptively controlled by adjusting the applied electric field in the piezoelectric patches, thus reducing the stress concentration in the joint edges. In order to further verify the effect of surface bonding of the piezoelectric patches, a first-order shear deformation theory based analytical model was developed to evaluate the stress distribution in the adhesive layer. It was established that the piezoelectric patched joint could significantly reduce the stress concentration in the joint edges. The influence of location and size of the piezoelectric patches was also investigated. Furthermore, the state-space method was used to obtain the analytical solution. A series of finite element analyses were also carried out to verify the integrity of the developed solution. Results from the computational analyses were in good agreement with those obtained from the proposed results, thus validating the solutions.     

复合材料层合板单搭胶接力学性能检测技术与分析

胶接工艺缺陷对单搭胶接接头的拉伸剪切性能有着重要的影响。为了研究不同单搭接胶接层厚度对不同材质复合材料层合板胶接性能的影响规律,通过喷水穿透法超声C扫描对试样的剪切区域进行无损检测,并分别采用1mm、2mm、4mm的胶层厚度,以碳纤维/玻璃纤维复合材料层合板为被粘物,进行单搭胶接拉伸剪切性能试验。检测及试验结果表明:当胶层厚度h1mm时,对于相同材料的被粘物,胶层厚度越大,试件胶接接头剪切强度越小;相同的粘接剂厚度,以碳纤维增强复合材料板为被粘物的试件胶接接头剪切强度大于以玻纤增强复合材料板为被粘物的试件胶接接头强度;胶粘剂与碳纤维被粘物表面的润湿效果要优于胶粘剂与玻纤被粘物表面的润湿效果。     

Nonlinear proportionality of shear-bond stress to shear force in partially plastic regions of asymmetric FRC-laminated steel members

This paper focuses on the elastic–plastic flexural characteristics of hybrid members comprising I-section steel beams with adhesively bonded fiber reinforced composite (FRC) laminates. Specifically, predictive models are presented for the shear-bond stresses developed within the adhesive layer. The asymmetry of the hybrid section, due to the presence of the laminate, is shown to have two important consequencies, namely that two parameters are required to fully define the elastic–plastic behavior, and that there is a progressive migration of the neutral axis towards the laminate as elastic–plastic flexure of the section increases. Five different phases of elastic–plastic flexure are identified. Analytically exact two-parameter predictive models, which incorporate the nomadic tendencies of the neutral axis, are derived for the shear-bond stresses associated with each phase. The models reveal that, in contrast to fully elastic flexure, shear-bond stress is nonlinearly proportional to shear force during elastic–plastic behavior. Predictions from the models are compared with test data from the laboratory and with predictions from a finite element program, for FRC-laminated I-section steel beams under both distributed loads and point loads. These comparisons show that two elastic–plastic phases, each defined by axial stress redistribution within the tension steel flange, stimulate rapidly varying shear-bond stresses in the adhesive. The capabilities of the models are highlighted, and areas open for further work are discussed.     

Linear and higher order displacement theories for adhesively bonded lap joints

This work presents an adhesive model for stress analysis of bonded lap joints, which can be applied to model thin and thick adhesive layers. In this theory, linear variations of displacement components along the adhesive thickness are firstly assumed, and the longitudinal strain and the Poisson's effect of the adhesive are modeled. A differential form of the equilibrium equations for the adherends is analytically solved by means of compatible relations of the adhesive deformation. The derived shear and peel stresses are compared with the classical adhesive model of continuous springs with constant shear and peel stresses, and validated with two-dimensional finite element results of the geometrically nonlinear analysis using a commercial package. The numerical results show that the present linear displacement theory can be applied to both thin and moderately thick adhesive layers. The present formulation of the linear displacement theory is then extended to the higher order displacement theory for stress analysis of a thick adhesive, whose numerical results are also compared with those of the finite element computation.     

Exact dynamic solutions to piezoelectric smart beams including peel stresses I: Theory and application

This work presents exact dynamic solutions to piezoelectric (PZT) smart beams including peel stresses. The governing equations of partial differential forms are firstly derived for a PZT smart beam made of the identical adherends, and then general solutions of the governing equations are studied. The analytical solutions are applied to a cantilever beam with a partially bonded PZT patch to the fixed end. For the given boundary conditions, exact solutions of the steady state motions are obtained. Based on the exact solutions, frequency spectra, natural frequencies, normal mode shapes, harmonic responses of the shear and peel stresses are discussed for the PZT actuator. The details of the numerical results and sensing electric charges will be presented in Part II of this work. The exact dynamic solutions can be directly applied to a PZT bimorph bender. To compare with the classic shear lag model whose numerical demonstrations will be given in Part II, the related equations are also derived for the shear lag rod model and shear lag beam model.     

Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading

Composite pipes are becoming popular in the offshore oil and gas industry. These pipes are connected to one-another by various configurations of joints. The joints are usually the weakest link in the system. In this investigation we examine the response of various joint configurations subjected to torsion, one of the most common loading conditions in piping systems. Specifically, the theoretical analysis used to evaluate the stress field in the adhesive layers of tubular and socket type bonded sandwich lap joints is presented here. The two adherends of the joints may have different thickness and materials, and the adhesive layer may be flexible or brittle. The analysis is based on the general composite shell theory. The stress concentrations at and near the end of the joints as functions of various parameters, such as the overlap length, and thickness of the adhesive layer are studied. The effects of different adherend thickness ratios, adhesive thickness and overlap length are also studied. Results obtained from the proposed analytical solutions agree well with the results obtained from finite element analysis and those obtained by other workers.     

Thermal effects on adhesively bonded composite repair of cracked aluminum panels

This study introduces the two-dimensional finite element analysis involving three layer technique to investigate the adhesively bonded composite repair of cracked metallic structure under thermo-mechanical loading. The thermal loading involves, in this study, the temperature drop such as seen during the bonding process. Three patch materials having different stiffnesses and coefficients of thermal expansion are investigated to analyze the thermal effects on the damage tolerance of the crack in the repaired structure and of the debond in the adhesive bondline. For the single sided repair, the patch material having the maximum mismatch in the coefficient of thermal expansion with that of the cracked aluminum plate provides the better damage tolerance capability for both the crack in the panel and the debond in the adhesive. On the other hand, for double sided repair, the patch material having the minimal mismatch in the coefficient of thermal expansion with that of the cracked plate provides the better damage tolerance capability.