An analytical solution for the analysis of symmetric composite adhesively bonded joints

Analytical solutions for adhesively bonded balanced composite and metallic joints are presented in this paper. The classical laminate plate theory and adhesive interface constitutive model are employed for this deduction. Both theoretical and numerical (finite element analysis) studies of the balanced joints are conducted to reveal the adhesive peel and shear stresses. The methodology can be extended to the application of various joint configurations, such as single-lap and single-strap joints to name a few. The methodology was used to evaluate stresses in several balanced adhesively bonded metallic and composite joints subjected to the tensile, moment and transverse shear loadings. The results showed good agreements with those obtained through FEM.     

复合材料夹芯管胶接连接结构力学特性分析

针对在航空结构中广泛应用的复合材料蜂窝夹芯圆管中的接头这一最脆弱的部分,发展了一种分析复合材料蜂窝夹芯圆管胶粘接头力学特性的解析模型.该模型根据Gibson修正公式得到了蜂窝芯子的等效弹性参数,再运用经典的复合材料壳理论和线弹性理论得到管接头的控制方程,并通过状态空间法进行求解.运用本文模型,计算了管接头在扭矩和弯矩作用下胶层内的剪应力和剥离应力;同时采用有限元法对模型进行了数值模拟,并将模拟结果与模型计算结果进行了对比,最后分析了搭接长度对胶层内应力的影响.     

Investigation of elastic stresses in an adhesively bonded single lap joint with functionally graded adherends in tension

In this study three-dimensional elastic stress state of an adhesively bonded single lap joint with functionally graded adherends in tension was investigated. The adherends compose of a functionally gradient layer between a pure ceramic (Al₂O₃) layer and a pure metal (Ni) layer. Stress concentrations are observed along the free edges of the adhesive layer and through the corresponding zones in the upper and lower adherends. The adhesive layer experiences stress concentrations along the left and right free edges in the horizontal plane, and the normal stresses and the shear stress σ_xy are critical. Whereas the middle overlap region has a uniform low stress distribution the zones in the upper adherend corresponding to the left free edge of the adhesive layer and the zones in the lower adherend corresponding to the right free edge of the adhesive layer are subjected to higher stresses. The normal stress σ_xx among the normal stresses and the shear stress σ_xy among the shear stresses are dominant in both upper and lower adherends. The normal stress σ_xx changes uniformly from compression in the ceramic layer to tension in the metal layer through the upper plate-thickness and from tension in the ceramic layer to compression in the metal layer through the lower plate-thickness. In the adhesive layer, the normal stress σ_yy becomes peak at the left free edge of the upper adherend–adhesive interface and at the right free edge of the lower adherend–adhesive interface and then decreases uniformly across the adhesive layer towards the other adherend–adhesive interface. The functionally gradient region across the adherend thickness was modelled using the layers with the mechanical properties calculated based on the power law. However, a layer number larger than 20 has a minor effect on the through-thickness profiles and magnitudes of von Mises and normal stresses in both the adherends and the adhesive. In addition, increasing the ceramic phase in the material composition (compositional gradient exponent n) of the functionally gradient region does not affect the through-thickness profiles of von Mises and normal stresses in the adherends and adhesive whereas their magnitudes in the ceramic rich layer of both adherends and along the adherend–adhesive interfaces increase considerably. On the contrary, the layer number and compositional gradient exponent have an evident effect on the through-thickness profiles and magnitudes of the critical stress components in the adherends and adhesive layer of the functionally graded adhesively bonded joints.     

Time-resolved strain and deformation measurement on the vibrating saxophone reed

Single-reed musical instruments, such as the saxophone, generate sound through a complex interplay between the mechanics of the reed and the hydrodynamic and acoustic pressure in the instrument mouthpiece. To understand this complex mechanism, experimental data are lacking. This paper presents full-field, time-resolved measurements of strain and displacement of a vibrating saxophone reed, measured under mimicked realistic playing conditions. It is found that strain along the length axis of the reed is mainly expansive, except in a small zone near the tip where it becomes compressive when the reed touches the front edge of the mouthpiece. At the instant in the vibration phase where the reed touches the mouthpiece, significant bending and compressive strain appear along the direction perpendicular to the reed axis. Strain magnitudes in both directions are similar, with absolute values of 0.1%. Full-field strain maps reveal subtle characteristics which are not revealed by displacement measurements. Bi-axial bending and strain may be an essential component in reed mechanics, which up till now has been fully neglected in modelling.     

Damage monitoring and analysis of composite laminates with an open hole and adhesively bonded repairs using digital image correlation

High performance composite materials, such as Carbon–Fibre Reinforced Plastic (CFRP) composites, are being increasingly used in aerospace industry, such as fuselage primary structures in Boeing 787 or Airbus 350, where high strength and stiffness are required at minimum weight [1]. The design of composite structures frequently includes discontinuities such as cut-outs for access and fastener holes for joining and they become critical regions under thermo-mechanical loading. Understanding of notched specimen behaviour is necessary for the design of complex structures where parts are mostly connected with bolts and rivets [2]. The effect of these discontinuities on the behaviour of composite materials is an important topic because it causes a relatively large reduction in strength compared to the unnotched laminate [3]. In the first part of the current work, the assessment of the damage process taking place in notched (open-hole) specimens under uniaxial tensile loading was studied. Two-dimensional (2D) and three-dimensional (3D) Digital Image Correlation (DIC) techniques were employed to obtain full-field surface strain measurements in carbon–fibre/epoxy M21/T700 composite plates with different stacking sequences in the presence of an open circular hole. Penetrant enhanced X-ray radiographs were taken to identify damage location and extent after loading around the hole. DIC strain fields were compared to numerical predictions. In the second part of the study, DIC techniques were used to characterise damage and performance of adhesively bonded patch repairs in composite panels under tensile loading. This part of work relates to strength/stiffness restoration of damaged composite aircraft that becomes more important as composites are used more extensively in the construction of modern jet airliners. In the current work, external bonded patches have been studied. Adhesively bonded repairs are the most common type of repair carried out with composite materials [1], [4]. The behaviour of bonded patches under loading was monitored using DIC full-field strain measurements. Location and extent of damage identified by X-ray radiography correlates well with DIC strain results giving confidence to the technique for structural health monitoring of bonded patches.     

Environmental degradation of the interfacial fracture energy in an adhesively bonded joint

The mixed mode flexure and notched coating adhesion tests have been carried out in order to characterise interfacial fracture for a range of environmental exposure conditions and to find a meaningful interfacial strength parameter using a fracture mechanics approach. The moisture uptake of the adhesive was accelerated using an open-faced configuration. The critical loading to cause interfacial fracture was measured and was used in conjunction with finite element analysis (FEA) to determine the fracture energy under various exposure conditions. Moisture dependent material properties were incorporated in the FEA. Scanning electron microscopy was used to characterise the nature of the failure surface. Significant degradation of the fracture energy of the interface was found and this was matched by observed changes to the failure surface. The fracture energies were found to be largely independent of test method, exposure environment and time and was primarily related only to the moisture concentration.     

Basic principle of digital image correlation for in-plane displacement and strain measurement

The basic principle and the algorithm of a digital image correlation method, and the procedure for obtaining displacements and strains are described. In order to describe the basic principle precisely, only in-plane displacement and strain measurement of a planar object are explained. Gray levels between integer pixels of a digital image after deformation are interpolated to obtain displacements with subpixel resolution. Displacements are then determined by solving nonlinear simultaneous equations taking the deformation of a subset into consideration. Strains are obtainable by differentiating the measured displacements. In addition to the basic principle of digital image correlation, the example of the measurement and its results are shown.     

An Evaluation of Digital Image Correlation Criteria for Strain Mapping Applications

Abstract:  The performance of four digital image correlation criteria widely used in strain mapping applications has been critically examined using three sets of digital images with various whole-field deformation characteristics. The deformed images in these image sets are digitally modified to simulate the less-than-ideal image acquisition conditions in an actual experiment, such as variable brightness, contrast, uneven local lighting and blurring. The relative robustness, computational cost and reliability of each criterion are assessed for precision strain mapping applications. Recommendations are given for selecting a proper image correlation criterion to efficiently extract reliable deformation data from a given set of digital images.     

Whole-field strain analysis and damage assessment of adhesively bonded patch repair of CFRP laminates using 3D-DIC and FEA

The problem of damage evolution in composite structures, the way it propagates, performance and behavior is of paramount importance in utilizing them for structural applications. In the present work, an experimental study is carried out using digital image correlation (DIC) technique to analyze the behavior of adhesively bonded patch repair of carbon/epoxy unidirectional composite laminates under tensile loading. The damaged panel is repaired with both double and single sided circular patch made of same parent material. Damage initiation and propagation in notched and repaired panel as well as patch debonding is studied using 3D-DIC. Also a 3-D finite element analysis is carried out and obtained strain values are compared with the experimental prediction. They are found to be in good agreement.     

Tensile deformation behaviour of a dissimilar metal weldment of P91 and 347H steels

Deformation of a weldment is governed by the mechanical properties of its base metals and fusion zone. In a weldment, the base metals and fusion zone exhibit changing microstructural features with various phases present along the weldment. Specifically, the heat affected zone of a base metal exhibits a heterogeneous microstructure generated during weld thermal cycles and by post-weld heat treatment. As a result, the mechanical properties in a weldment are often non-uniformly distributed. In this study, tensile tests combined with digital image correlation were performed to obtain the non-uniform distributions of the mechanical properties of a weldment composed of P91 and 347H steels. From the experimental tensile tests, it was found that the 347H base metal had significantly distinct mechanical properties compared to the other zones of the weldment. Furthermore, the 347H base metal had the lowest yield stress but the highest strain hardening exponent. Because of its lowest yield stress, the 347H base metal had the highest plastic strain accumulation at any stage of global deformation. However, the strain hardening rate of the P91 base metal enabled it to accumulate the necessary plastic strain to activate its necking first. Therefore, the failure location of the P91-347H weldment was expected to occur at the P91 base metal. A 3D finite element simulation of the tensile deformation of P91-347H weldment also suggested the same. However, from the present experimental observations, one weldment out of three was found to fail unexpectedly at the heat affected zone of the P91 base metal. The reason for this unexpected failure was determined by microscopic analysis to be the presence of a large defect.     

非接触数字图像相关应变测量的仿真与实验研究

数字图像相关法测量全场位移和应变是一种新的实验力学方法.该测量算法中相关函数和子区大小的选择是影响最终应变测量精度的重要因素.本文采用已知应变变形的仿真散斑图,研究了测量算法中主要相关函数和子区大小在正常光照与高斯不均匀光照条件下,对应变测量精度的影响.得出了不同测量要求下,可选择的相关函数和最佳计算窗口.通过实验验证与分析了此算法的测量精度.研究结果表明,数字图像处理技术测量应变的测试精度满足基本要求.     

The effect of the spew fillet on an adhesively bonded single-lap joint subjected to bending moment

The mechanical behaviors of an adhesively bonded single lap joint with a spew fillet under bending moment, where the widths of the upper-adherend and lower-adherend are not the same, were studied experimentally and numerically. Using AA2024-T3 aluminum alloy as adherend and DP460 as paste adhesive, four different types of single-lap joint samples (without spew fillet, with spew fillet at joint edges, with spew fillet at joint ends and with spew fillet at all edges) were produced for experimental studies. Stress analyses in the single-lap joint were performed with a three dimensional non-linear finite element method by considering the geometrical non-linearity and non-linear material behaviors of both adhesives (DP460) and adherend (AA2024-T3). The single lap joint with the spew fillet with different widths had a significant effect on the stress distribution. Additionally, the spew fillet increased the load carrying capacity of the joint and decreased the stress concentration of the joint.     

Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymer-matrix composite

As a direct extension of previous mode-I work on the adhesion of composite joints, this paper uses a cohesive-zone approach to model the mixed-mode fracture of adhesive joints made from a polymer-matrix composite. Mode-II cohesive-zone parameters were obtained using sandwich end-notch flexure specimens. These parameters were used directly with the previously determined mode-I parameters to predict the fracture and deformation of mixed-mode geometries. It was shown that numerical simulations provided quantitative predictions for these geometries, including predictions for both the strengths of the joints and for the failure mechanisms. In conjunction with the earlier work, these results demonstrate the use of cohesive-zone approaches for the design of adhesively bonded composite joints, and indicate approaches for determining the relevant material properties to describe mixed-mode fracture.     

Performance Assessment of a Numerical Simulation Tool for Wooden Boards with Knots by Means of Full‐Field Deformation Measurements

In wooden boards, knots and the resulting fibre deviations in their vicinities are mainly responsible for qualitative downgrading of timber elements. Thus, the development of reliable numerical simulation tools for the determination of effective strength and stiffness properties of timber elements and, in a next step, for the development and evaluation of grading criteria is highly desirable. Due to the complexity of such tools, a comprehensive validation is required. Within this work, the suitability of full‐field deformation measurements for four‐point bending tests on wooden boards with knots is evaluated first. Next, the test series is used to validate a previously developed three‐dimensional numerical simulation tool, which combines a geometrical model for the grain course and a micromechanical model for a density and moisture dependent characterisation of the clear‐wood material. The digital image correlation technique proved to be capable to reproduce the strain fields in the vicinity of knots under bending load. Moreover, a very good correlation between numerical and experimental results was obtained.     

Free vibration analysis of adhesively bonded single lap joints with wide and narrow functionally graded plates

This study investigates the three-dimensional free vibration behaviour of an adhesively bonded functionally graded single lap joint. The functionally graded plates of the adhesive joint are composed of ceramic (Al₂O₃) and metal (Ni) phases varying through the plate thickness. The effects of geometrical parameters, such as plate width, plate thickness and overlap length, especially the effect of the similar and dissimilar material composition variations through-the-thicknesses of both upper and lower plates on the natural frequencies and corresponding mode shapes of the adhesive joint were also investigated using both the finite element method and the back-propagation artificial neural network (ANN) method. A series of the free vibration analyses were carried out for various random values of the geometrical parameters and the through-the-thickness material composition so that a suitable ANN model could be trained successfully. The proposed ANN models indicated that increasing plate thickness and compositional gradient exponent resulted in increases in the first 10 frequencies whereas the overlap length has negligible effect. In contrast, the natural frequencies decrease suddenly with increasing the plate width. For the plate width >50 mm, the natural frequencies become very low and the effect of the other design parameters on the natural frequencies becomes minor. In case the upper and lower plates have similar or dissimilar material composition variations the mode shapes were affected considerably, but the natural frequencies.     

Thermal deformation measurement of flip-chip substrate using digital image correlation method

With the accelerated development of electronic products, flip-chip packaging has become one of the most prominently used and efficient designs in the integrated circuit (IC) industry. In daily application, the IC chip will be subjected to a temperature increase when it is in operation. With the rise in temperature, the chip is liable to a series of deformations which lead to possible malfunction of the IC unit. Therefore, the investigation of thermal deformation of flip-chip substrates is important. In this study, the thermal deformation of flip-chip substrates is measured with dual-camera digital image correlation technology, and with the measured data, a basis is established to predict the warpage conditions and strain tendencies of substrates due to thermal effect. Experiments were carried out with the substrates heated from room temperature to 200°C in a specialized vacuum-sealed oven. The topographic surface profile at higher temperatures can be obtained by adding the measured deformation to the surface profile of the substrates at room temperature. Experimental results show that the center area of the specimen had been warped up around 90?µm from the initial condition and the warpage effect of the substrate is obvious when the temperature increases to 200°C. The related maximum normal and shear strains are also discussed.     

Experimental Investigations of Fracture Process Using DIC in Plain and Reinforced Concrete Beams under Bending

The fracture behaviour of concrete and reinforced concrete beams under quasi‐static three‐point bending was comprehensively investigated with experiments at laboratory scale. The eight various concrete mixes were tested. The influence of the shape, volume and size of aggregate particles and reinforcement on concrete fracture under bending was studied. Displacements on the surface of concrete beams were measured by means of the digital image correlation (DIC) technique. Attention was paid to the formation of a localized zone and its characteristics. In order to avoid the effect of the search patch size and the cut‐off value at displacement and strain profiles, a consistent method was proposed to determine uniformly and accurately the width of a localized zone. Measured surface displacements from DIC were fitted by the error function ERF, whereas surface strains calculated from displacements were fitted by the usual normal distribution (Gauss) function. The width of a localized zone preceding a macro‐crack grew strongly with increasing maximum aggregate size and slightly with diminishing aggregate volume. It did not depend on the aggregate roughness and reinforcement presence.     

Experimental analysis of surgically corrected knee joint

Holographic interferometry, speckle photography and photoelasticity have been employed in the experimental investigations of the knee joint in four conditions - anatomically normal joint, varus joint, joint after Coventry popliteal osteotomy and joint after correction made using a new variety of the Coventry procedure¹. The studies included the investigations of the displacements of the bone in the sagittal plane, the displacements of points on the bone's surface in the frontal plane and the three dimensional state of stress. The obtained results show to what degree changes in the lower limb geometry affect the knee joint and in particular, its stability, functionality and the way in which it carries loads.     

Evaluation of Methodologies for Compensation of Out of Plane Motions in a 2D Digital Image Correlation Setup

In 2D digital image correlation, out of plane motions are an important experimental factor to consider. Because a 2D setup does not provide any depth information, movements towards the camera (out of plane motions) are disadvantageous for the surface measurement. The effects of out of plane motions in a 2D digital image correlation (DIC) setup have been investigated profoundly in previous works. The compensation of these motions however is less investigated. Therefore, this paper will handle on solutions for correcting or minimising out of plane motions in 2D DIC measurements. Three compensation methods are implemented and validated. Firstly, a mechanical camera positioning tool is developed to avoid misalignments of the camera and therefore avoid most of the out of plane motions. Secondly, the camera is aligned numerically using the camera pinhole model and numerically deforming the images. Finally, a method proposed in literature using a region of compensation is used in this validation. All three methods have shown to be able to minimise out of plane motions. Validated in an experimental setup, a great improvement of the identified Poisson ratio is observed during multiple tensile tests.     

Fatigue damage analysis in a duplex stainless steel by digital image correlation technique

Strain field measurements by digital image correlation today offer new possibilities for analysing the mechanical behaviour of materials in situ during mechanical tests. The originality of the present study is to use this technique on the micro-structural scale, in order to understand and to obtain quantitative values of the fatigue surface damage in a two-phased alloy. In this paper, low-cycle fatigue damage micromechanisms in an austenitic-ferritic stainless steel are studied. Surface damage is observed in real time, with an in situ microscopic device, during a low-cycle fatigue test performed at room temperature. Surface displacement and strain fields are calculated using digital image correlation from images taken during cycling. A detailed analysis of optical images and strain fields measured enables us to follow precisely the evolution of surface strain fields and the damage micromechanisms. Firstly, strain heterogeneities are observed in austenitic grains. Initially, the austenitic phase accommodates the cyclic plastic strain and is then followed by the ferritic phase. Microcrack initiation takes place at the ferrite/ferrite grain boundaries. Microcracks propagate to the neighbouring austenitic grains following the slip markings. Displacement and strain gradients indicate probable microcrack initiation sites.