Thin plate bending problem of partially bonded bi-material strips

Summary A general solution to the thin plate bending problem of partially bonded bi-material strips is obtained. The two strips are symmetrically bonded along a finite straight interface with debondings at both sides. Complex stress function approach together with the rational mapping function technique are utilized to obtain the general solution. A concentrated bending moment applied at eachtip of the strip is considered. Distributions of bending and torsional moments along the boundaries of the two strips as well as the Stress Intensity of Debonding (SID) at the debonding tips are demonstrated for different states of debonding lengths, material constants and rigidity ratios.

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Das Biegeverhalten dünner Platten bei teilweise verbundenen Bi-Materialstreifen

Übersicht Eine allgemein praktikable Lösung für das Problem der Biegung dünner Platten bei teilweise verbundenen Bi-Materialstreifen konnte gefunden werden. Die beiden Streifen werden dabei auf einer gegebenen Länge einer geraden Berührungsfläche verbunden, wobei symmetrisch zueinander am Ende einer jeden Seite zwei Stellen unverbunden bleiben. Zum Erhalt einer allgemein gültigen Lösung wird hierzu der Weg über komplexe Belastungsfunktionen gemeinsam mit geeigneten Aufzeichnungsfunktionstechniken beschritten. Dabei wird ein konzentriertes Biegemoment, das an beiden Streifenenden ansetzt, angenommen. Die Verteilung der Verbiegungs- und Verdrehungsmomente entlang der Begrenzungslinien beider Streifen, sowie auch die Größe der Anspannung an den unverbundenen Stellen (SID) für die beiden nicht verbundenen Enden, wird für verschiedene Fälle von unverbundenen Längen, Materialkonstanten und Steifigkeitsverhältnissen gezeigt.

     

FRP加固梁的FRP-混凝土界面脱胶分析

为了研究纤维增强聚合物(fiber reinforced polymer, FRP) 加固梁的FRP-混凝土界面脱胶破坏过程,本文将混凝土梁和FRP 板均视为线弹性的欧拉-伯努利梁(Euler-Bernoulli beams), 且两者通过粘结层胶结在一起. 对于FRP-混凝土结构,有两种形式的脱胶破坏：板端脱胶破坏和跨中裂缝导致的脱胶破坏.对于FRP-混凝土梁,利用合理的粘结模型按第2 种脱胶失效形式,详细讨论了FRP-混凝土界面的脱胶过程,得到了不同阶段的胶结滑移、界面剪应力和FRP 轴向力的解析解. 实验研究验证了理论分析的结果,参数研究进一步探讨了胶结长度和粘结层厚度对于FRP-混凝土界面脱胶行为的影响.     

Green's function of a point dislocation for the bending of a composite infinite plate with an elliptical hole at interface

Summary  The problem of a hole at bimaterial interface is of practical importance in providing a good understanding of the debonding phenomenon and for determining factors that affect the mechanical properties of composite elements of structures. The problem of a point dislocation in bending bonded dissimilar semi-infinite plates with an elliptical hole at interface is tackled in this paper. Based on the method of analytic continuation and the rational mapping function technique, the problem of obtaining the stress functions in the upper and lower plates is decoupled, and reduced to two Riemann–Hilbert problems. The closed-form solution is obtained. The stress distributions at the bimaterial interface, as well as the debonding at both vertices of the elliptical hole are studied. The stress intensities of debonding are depicted for various parameters. Received 16 March 2000; accepted for publication 12 July 2000     

Dynamic self-similar debonding of interface at very high velocity: Anti-plane case

This paper analyzes the anti-plane problem of dynamic self-similar debonding of interface at very high velocity. The debonding is modeled as an interface crack propagating self-similarly from zero-length. The extending speed is assumed to be transonic or supersonic. We first consider the dynamic debonding under moving concentrated loads. The moving dislocation model of self-similar propagation of an interface crack is used to formulate the problem to a singular integral equation which is solved analytically. The singularity of stresses near the crack tip is discussed and the dynamic stress intensity factors are presented. Finally the solution of dynamic debonding underx ²-type loads is obtained by using the superposition method.     

含空心球涂层粒子复合材料界面的脱粘应力分析

在球对称拉伸载荷作用下针对空心球涂层复合材料分析了空心球涂层粒子增强复合材料的局部应力场，得到了界面临界脱粘应力的解析表达式．讨论了各相几何参数对非均匀涂层空心球粒子临界脱粘应力的影响，比较了均匀涂层和非均匀涂层的脱粘应力．结果表明：在球对称拉伸下界面脱粘更容易发生在涂层相与基体相界面间，空心球的壁厚和涂层厚度是影响界面临界脱粘应力的重要因素，因而选择适当的空心球、涂层厚度和提高界面粘结能将有利于提高界面的临界脱粘应力．     

Theoretical analysis on the local critical stress and size effect for interfacial debonding in particle reinforced rheological materials

The mechanisms of interfacial debonding of particle reinforced rheological materials are studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived and expressed in terms of the interfacial energy. The particle size effect on interface debonding can then be analyzed easily owing to the fact that critical stress is inversely proportional to the square root of particle radius. By taking PP/CaCO₃ system as an example, the present energy criterion is compared with the mechanical debonding criterion, and it is found that under the condition that bond strength is equal to matrix strength and particle radius not over 0.2μm, the mechanical debonding criterion can be automatically satisfied if the energy criterion is satisfied. A relation between critical time and interface energy is calculated by using the energy criterion. The influences of the particle volume fraction and the parlicle size, the loading rate and the relaxation time of the matrix on the critical time of interfacial debonding are also discussed. Supported by the National Natural Science Foundation of China (19632030 and 19872007) and Natural Science Foundation of Jiangsu Province.     

Debonding of particles in thin films

Thin composite films consisting of a matrix with embedded particles are currently being developed both as hard, wear resistant coatings and as functional surfaces. The effect of stiff particles in the film are studied for systems where the film is under residual tensile stresses. The particles, when they are fully bonded to the matrix, increase the stiffness of the composite film. In cases where the particles debond from the matrix material, the stiffness of the composite film decreases. The conditions under which the debonding process is stable are studied. For systems properly designed, a controlled debonding process of the particles can thus be used to reduce the stress levels in composite film lowering the risk for delamination of the composite film from the substrate as well as the risk of through cracks in the film. The work includes finite element based unit cell calculations of interface debonding between spherical particles and the film, and the release of residual stresses following this. The three dimensional unit cell calculations assume a periodic distribution of particles in the plane parallel to the substrate interface with equi-biaxial tension and periodicity with zero overall stress perpendicular to the substrate interface.     

Process of debonding in RC beams shear-strengthened with FRP U-strips or side strips

Reinforced concrete (RC) beams may be strengthened for shear using externally bonded fiber reinforced polymer (FRP) composites in the form of side bonding, U-jacketing or complete wrapping. The shear failure of almost all RC beams shear-strengthened with side bonded FRP and the majority of those strengthened with FRP U-jackets, is due to debonding of the FRP. The bond behavior between the externally-bonded FRP reinforcement (referred to as FRP strips for simplicity) and the concrete substrate therefore plays a crucial role in the failure process of these beams. Despite extensive research in the past decade, there is still a lack of understanding of how debonding of FRP strips in such a beam propagates and how the debonding process affects its shear behavior. This paper presents an analytical study on the progressive debonding of FRP strips in such strengthened beams. The complete debonding process is modeled and the contribution of the FRP strips to the shear capacity of the beam is quantified. The validity of the analytical solution is verified by comparing its predictions with numerical results from a finite element analysis. This analytical treatment represents a significant step forward in understanding how interaction between FRP strips, steel stirrups and concrete affects the shear resistance of RC beams shear-strengthened with FRP strips.     

微粒填充流变材料界面开裂的局部临界应力及尺寸效应的理论分析

研究了以等轴粒子填充流变材料的边界开裂机理，采用能量准则导出了以界面能表示的界面开裂局部临界应力的简洁表达式。由于临界应力正比于１√α，从而可以非常方便地研究粒子开裂的尺寸效应，以碳酸钙微粒填充的聚丙烯复合材料为例进行了理论分析，通过比较界面开裂的能量准则和张应力准则得出结论：即使按照保守的方法估算，即在界面强度等于基体强度的条件下，只要粒径不超过０．２微米，若能量准则得到满足，则张应力准则也会得     

Analysis of a partially debonded elliptic inhomogeneity in piezoelectric materials

A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroeiastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity , totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.     

Solution of problem of two dissimilar materials bonded at one interface subjected to temperature

A solution of problem of two dissimilar materials bonded at one interface subjected to temperature is derived. To obtain a closed-form solution, a rational mapping function and a complex variable method are used. The coefficients of the homogeneous part of the stress function are expressed by Dunders’ parameters, but loading term of temperature is not expressed by them. As a demonstration, semi-strips bonded at one part at the ends are considered. The each strip is subjected to uniform temperature. Examples of stress distributions are shown. The relations of stress and temperature on the interface are described. Debondings on both sides of the interface are considered. Stress intensity of debonding (SID) is defined, and the values are investigated for various debonding lengths. And the debonding extension or the crack initiation into the material is investigated. The effects of material constants (Dundurs’ parameter) on SID are also investigated. By changing mapping function, other geometries can be analyzed.     

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.     

界面超高速自相似动态分层分析：反平面情况

对材料界面超高速自相似动态分层的反平面问题进行了解析分析。分层模拟为界面裂纹由零长度自相似扩展，扩展速度为蹭音速或超音速。首先考虑运动集中载荷作用下界面动态分层的情况，利用界面裂纹自相似扩展的运动位错模型将问题归结为奇异积分方程，并求得解析解，分析了裂纹尖端的应力奇性，获得了动应力强度因子。最后，利用叠加原理给出了ｘ＾ｎ型载荷作用下界面动态分层的解。     

Dynamic stress analysis of the interface in a particle-reinforced composite

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FRP-to-concrete interfaces between two adjacent cracks: Theoretical model for debonding failure

External bonding of fibre reinforced polymer (FRP) composites has become a popular technique for strengthening concrete structures all over the world. The performance of the interface between FRP and concrete is one of the key factors affecting the behaviour of the strengthened structure. Existing laboratory research has shown that the majority of reinforced concrete (RC) beams strengthened with a bonded FRP soffit plate fail due to debonding of the plate from the concrete. Two types of debonding failures have been commonly observed: plate end debonding and intermediate crack induced debonding. In order to understand and develop methods to predict such debonding failures, the bond behaviour between concrete and FRP has been widely studied using simple shear tests on FRP plate/sheet-to-concrete bonded joints and a great deal of research is now available on the behaviour of these bonded joints. However, for intermediate crack induced debonding failures, the debonding behaviour can be significantly different from that observed in a simple shear test. Among other factors, the most significant difference may be that the FRP plate between two adjacent cracks is subject to tension at both cracks. This paper presents an analytical solution for the debonding process in an FRP-to-concrete bonded joint model where the FRP plate is subject to tension at both ends. A realistic bi-linear local bond-slip law is employed. Expressions for the interfacial shear stress distribution and the load–displacement response are derived for different loading stages. The debonding process is discussed in detail. Finally, results from the analytical solution are presented to illustrate how the bond length affects the behaviour of such bonded joints. While the emphasis of the paper is on FRP-to-concrete joints, the analytical solution is equally applicable to similar joints between thin plates of other materials (e.g. steel and aluminium) and concrete.     

Micromechanics-based model for cement-treated clays

Cementation is produced by mixing a certain amount of cement with the saturated clay. The purpose of this paper is to model the cementation effect on the mechanical behavior of cement-treated clay. A micromechanical stress-strain model is developed considering explicitly the cementation at inter-cluster contacts. The inter-cluster bonding and debonding during mechanical loading are introduced in two ways: an additional cohesion in the shear sliding and a higher yield stress in normal compression. The model is used to simulate isotropic compression and undrained triaxial tests under various confining stresses on cement-treated Singapore clay with various cement contents. The applicability of the present model is evaluated through comparisons between numerical and experimental results. The evolution of local stresses and local strains in inter-cluster planes is discussed in order to explain the induced anisotropy due to debonding at contact level under the applied loads.     

Local buckling and debonding problem of a bonded two-layer plate

The problem of local buckling, debonding initiation and growth process of the debonding of a bonded two-layer plate is treated. In the weaker layer of the plate, compression appears due to the external compressive axial force and bending moment. The conditions for local buckling of the weaker layer have been studied where the possibility that the stress state in the layers could be in elasto-plastic domain has been considered.A mathematical model is developed to determine the bending displacements of laminate layers after the weaker layer buckles locally, and in the state after the plate has been unloaded. The third-order theory introduced by Chwalla has been implemented. Mechanical properties of the layers and adhesive used in the numerical model were measured with experiments. Experimental work comprised the determination of mechanical properties of the chosen materials and experimental verification of the presented mathematical model. Numerically obtained results are compared with those obtained by an experimental approach, and are found to be in good agreement.     

Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams

A cohesive interface modeling approach to debonding analysis of adhesively bonded interface between two balanced adjacent flexural cracks in conventional material (e.g., concrete or wood) beams strengthened with externally bonded FRP plates is presented. Both the strengthened beam and strengthening FRP are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin adhesive layer. A bi-linear cohesive model, which is commonly used in the literature, is adopted to characterize the stress-deformation relationship of the FRP–concrete interface. Completely different from the single-lap or double-shear pull models in which only the axial pull force is considered, the present model takes the couple moment and transverse shear forces in both the substrates into account to study the second type of intermediate crack-induced debonding (IC debonding) along the interface. The whole debonding process of the FRP–concrete interface is discussed in detail, and closed-form solutions of bond slip, interface shear stress, and axial force of FRP in different stages are obtained. A rotational spring model is introduced at locations of the two adjacent flexural cracks to model the local flexibility of the cracked concrete beam, with which the relationship between the local bond slip and externally applied load is established and the real bond failure process of the FRP-plated concrete beam with the increasing of the externally applied load is revealed. Parametric studies are further conducted to investigate the effect of the thickness of adhesive layer on the bond behavior of FRP–concrete interface. The present closed-form solution and analysis on the local bond slip versus applied load relationship for the second type of IC debonding along the interface shed light on the bond failure process of structures externally strengthened with FRP composite plates and can be used effectively and efficiently to predict ductility and ultimate load of FRP-strengthened structures.     

碳纤维布与钢板复合加固梁剥离破坏研究

通过12根碳纤维布与钢板复合加固钢筋混凝土梁的抗弯性能研究,结果表明复合加固方式能有效地改善被加固构件的受力性能,但常由于复合加固层的剥离可能导致加固效果的降低。复合加固层与被加固构件之间的剥离是由于薄弱截面在剪应力及正应力的集中作用下而产生的,文中对复合加固层与混凝土之间的粘结剪应力及剥离正应力的计算公式分别进行推导,并进一步对碳纤维布与钢板复合加固的剥离机理进行分析,为工程应用提供依据。     

Experimental determination of residual stresses in paperboard

A method for the experimental determination of the through-thickness residual stress distribution in paperboard is presented. The successive removal of thin layers from strips of board through surface grinding changes the stress-state and the bending stiffness resulting in a changed curvature, which is measurable. From tests of strips in both in-plane directions, stress distributions can then be evaluated using the Treuting-Read method. Geometrically nonlinear effects at the large deformations taking place are avoided through a proper choice of strip dimensions. Typical results are presented and factors influencing the accuracy of the determination are thoroughly discussed.